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_coefficient(
1513 __isl_take isl_constraint *constraint,
1514 enum isl_dim_type type, int pos, isl_int v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, int v);
1518 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1519 __isl_take isl_basic_map *bmap,
1520 __isl_take isl_constraint *constraint);
1521 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1522 __isl_take isl_basic_set *bset,
1523 __isl_take isl_constraint *constraint);
1524 __isl_give isl_map *isl_map_add_constraint(
1525 __isl_take isl_map *map,
1526 __isl_take isl_constraint *constraint);
1527 __isl_give isl_set *isl_set_add_constraint(
1528 __isl_take isl_set *set,
1529 __isl_take isl_constraint *constraint);
1530 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1531 __isl_take isl_basic_set *bset,
1532 __isl_take isl_constraint *constraint);
1534 For example, to create a set containing the even integers
1535 between 10 and 42, you would use the following code.
1538 isl_local_space *ls;
1540 isl_basic_set *bset;
1542 space = isl_space_set_alloc(ctx, 0, 2);
1543 bset = isl_basic_set_universe(isl_space_copy(space));
1544 ls = isl_local_space_from_space(space);
1546 c = isl_equality_alloc(isl_local_space_copy(ls));
1547 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1548 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1549 bset = isl_basic_set_add_constraint(bset, c);
1551 c = isl_inequality_alloc(isl_local_space_copy(ls));
1552 c = isl_constraint_set_constant_si(c, -10);
1553 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1554 bset = isl_basic_set_add_constraint(bset, c);
1556 c = isl_inequality_alloc(ls);
1557 c = isl_constraint_set_constant_si(c, 42);
1558 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1559 bset = isl_basic_set_add_constraint(bset, c);
1561 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1565 isl_basic_set *bset;
1566 bset = isl_basic_set_read_from_str(ctx,
1567 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1569 A basic set or relation can also be constructed from two matrices
1570 describing the equalities and the inequalities.
1572 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1573 __isl_take isl_space *space,
1574 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1575 enum isl_dim_type c1,
1576 enum isl_dim_type c2, enum isl_dim_type c3,
1577 enum isl_dim_type c4);
1578 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1579 __isl_take isl_space *space,
1580 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1581 enum isl_dim_type c1,
1582 enum isl_dim_type c2, enum isl_dim_type c3,
1583 enum isl_dim_type c4, enum isl_dim_type c5);
1585 The C<isl_dim_type> arguments indicate the order in which
1586 different kinds of variables appear in the input matrices
1587 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1588 C<isl_dim_set> and C<isl_dim_div> for sets and
1589 of C<isl_dim_cst>, C<isl_dim_param>,
1590 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1592 A (basic or union) set or relation can also be constructed from a
1593 (union) (piecewise) (multiple) affine expression
1594 or a list of affine expressions
1595 (See L<"Piecewise Quasi Affine Expressions"> and
1596 L<"Piecewise Multiple Quasi Affine Expressions">).
1598 __isl_give isl_basic_map *isl_basic_map_from_aff(
1599 __isl_take isl_aff *aff);
1600 __isl_give isl_map *isl_map_from_aff(
1601 __isl_take isl_aff *aff);
1602 __isl_give isl_set *isl_set_from_pw_aff(
1603 __isl_take isl_pw_aff *pwaff);
1604 __isl_give isl_map *isl_map_from_pw_aff(
1605 __isl_take isl_pw_aff *pwaff);
1606 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1607 __isl_take isl_space *domain_space,
1608 __isl_take isl_aff_list *list);
1609 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1610 __isl_take isl_multi_aff *maff)
1611 __isl_give isl_map *isl_map_from_multi_aff(
1612 __isl_take isl_multi_aff *maff)
1613 __isl_give isl_set *isl_set_from_pw_multi_aff(
1614 __isl_take isl_pw_multi_aff *pma);
1615 __isl_give isl_map *isl_map_from_pw_multi_aff(
1616 __isl_take isl_pw_multi_aff *pma);
1617 __isl_give isl_union_map *
1618 isl_union_map_from_union_pw_multi_aff(
1619 __isl_take isl_union_pw_multi_aff *upma);
1621 The C<domain_dim> argument describes the domain of the resulting
1622 basic relation. It is required because the C<list> may consist
1623 of zero affine expressions.
1625 =head2 Inspecting Sets and Relations
1627 Usually, the user should not have to care about the actual constraints
1628 of the sets and maps, but should instead apply the abstract operations
1629 explained in the following sections.
1630 Occasionally, however, it may be required to inspect the individual
1631 coefficients of the constraints. This section explains how to do so.
1632 In these cases, it may also be useful to have C<isl> compute
1633 an explicit representation of the existentially quantified variables.
1635 __isl_give isl_set *isl_set_compute_divs(
1636 __isl_take isl_set *set);
1637 __isl_give isl_map *isl_map_compute_divs(
1638 __isl_take isl_map *map);
1639 __isl_give isl_union_set *isl_union_set_compute_divs(
1640 __isl_take isl_union_set *uset);
1641 __isl_give isl_union_map *isl_union_map_compute_divs(
1642 __isl_take isl_union_map *umap);
1644 This explicit representation defines the existentially quantified
1645 variables as integer divisions of the other variables, possibly
1646 including earlier existentially quantified variables.
1647 An explicitly represented existentially quantified variable therefore
1648 has a unique value when the values of the other variables are known.
1649 If, furthermore, the same existentials, i.e., existentials
1650 with the same explicit representations, should appear in the
1651 same order in each of the disjuncts of a set or map, then the user should call
1652 either of the following functions.
1654 __isl_give isl_set *isl_set_align_divs(
1655 __isl_take isl_set *set);
1656 __isl_give isl_map *isl_map_align_divs(
1657 __isl_take isl_map *map);
1659 Alternatively, the existentially quantified variables can be removed
1660 using the following functions, which compute an overapproximation.
1662 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1663 __isl_take isl_basic_set *bset);
1664 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1665 __isl_take isl_basic_map *bmap);
1666 __isl_give isl_set *isl_set_remove_divs(
1667 __isl_take isl_set *set);
1668 __isl_give isl_map *isl_map_remove_divs(
1669 __isl_take isl_map *map);
1671 It is also possible to only remove those divs that are defined
1672 in terms of a given range of dimensions or only those for which
1673 no explicit representation is known.
1675 __isl_give isl_basic_set *
1676 isl_basic_set_remove_divs_involving_dims(
1677 __isl_take isl_basic_set *bset,
1678 enum isl_dim_type type,
1679 unsigned first, unsigned n);
1680 __isl_give isl_basic_map *
1681 isl_basic_map_remove_divs_involving_dims(
1682 __isl_take isl_basic_map *bmap,
1683 enum isl_dim_type type,
1684 unsigned first, unsigned n);
1685 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1686 __isl_take isl_set *set, enum isl_dim_type type,
1687 unsigned first, unsigned n);
1688 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1689 __isl_take isl_map *map, enum isl_dim_type type,
1690 unsigned first, unsigned n);
1692 __isl_give isl_basic_set *
1693 isl_basic_set_remove_unknown_divs(
1694 __isl_take isl_basic_set *bset);
1695 __isl_give isl_set *isl_set_remove_unknown_divs(
1696 __isl_take isl_set *set);
1697 __isl_give isl_map *isl_map_remove_unknown_divs(
1698 __isl_take isl_map *map);
1700 To iterate over all the sets or maps in a union set or map, use
1702 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1703 int (*fn)(__isl_take isl_set *set, void *user),
1705 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1706 int (*fn)(__isl_take isl_map *map, void *user),
1709 The number of sets or maps in a union set or map can be obtained
1712 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1713 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1715 To extract the set or map in a given space from a union, use
1717 __isl_give isl_set *isl_union_set_extract_set(
1718 __isl_keep isl_union_set *uset,
1719 __isl_take isl_space *space);
1720 __isl_give isl_map *isl_union_map_extract_map(
1721 __isl_keep isl_union_map *umap,
1722 __isl_take isl_space *space);
1724 To iterate over all the basic sets or maps in a set or map, use
1726 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1727 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1729 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1730 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1733 The callback function C<fn> should return 0 if successful and
1734 -1 if an error occurs. In the latter case, or if any other error
1735 occurs, the above functions will return -1.
1737 It should be noted that C<isl> does not guarantee that
1738 the basic sets or maps passed to C<fn> are disjoint.
1739 If this is required, then the user should call one of
1740 the following functions first.
1742 __isl_give isl_set *isl_set_make_disjoint(
1743 __isl_take isl_set *set);
1744 __isl_give isl_map *isl_map_make_disjoint(
1745 __isl_take isl_map *map);
1747 The number of basic sets in a set can be obtained
1750 int isl_set_n_basic_set(__isl_keep isl_set *set);
1752 To iterate over the constraints of a basic set or map, use
1754 #include <isl/constraint.h>
1756 int isl_basic_set_n_constraint(
1757 __isl_keep isl_basic_set *bset);
1758 int isl_basic_set_foreach_constraint(
1759 __isl_keep isl_basic_set *bset,
1760 int (*fn)(__isl_take isl_constraint *c, void *user),
1762 int isl_basic_map_foreach_constraint(
1763 __isl_keep isl_basic_map *bmap,
1764 int (*fn)(__isl_take isl_constraint *c, void *user),
1766 void *isl_constraint_free(__isl_take isl_constraint *c);
1768 Again, the callback function C<fn> should return 0 if successful and
1769 -1 if an error occurs. In the latter case, or if any other error
1770 occurs, the above functions will return -1.
1771 The constraint C<c> represents either an equality or an inequality.
1772 Use the following function to find out whether a constraint
1773 represents an equality. If not, it represents an inequality.
1775 int isl_constraint_is_equality(
1776 __isl_keep isl_constraint *constraint);
1778 The coefficients of the constraints can be inspected using
1779 the following functions.
1781 int isl_constraint_is_lower_bound(
1782 __isl_keep isl_constraint *constraint,
1783 enum isl_dim_type type, unsigned pos);
1784 int isl_constraint_is_upper_bound(
1785 __isl_keep isl_constraint *constraint,
1786 enum isl_dim_type type, unsigned pos);
1787 void isl_constraint_get_constant(
1788 __isl_keep isl_constraint *constraint, isl_int *v);
1789 void isl_constraint_get_coefficient(
1790 __isl_keep isl_constraint *constraint,
1791 enum isl_dim_type type, int pos, isl_int *v);
1792 int isl_constraint_involves_dims(
1793 __isl_keep isl_constraint *constraint,
1794 enum isl_dim_type type, unsigned first, unsigned n);
1796 The explicit representations of the existentially quantified
1797 variables can be inspected using the following function.
1798 Note that the user is only allowed to use this function
1799 if the inspected set or map is the result of a call
1800 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1801 The existentially quantified variable is equal to the floor
1802 of the returned affine expression. The affine expression
1803 itself can be inspected using the functions in
1804 L<"Piecewise Quasi Affine Expressions">.
1806 __isl_give isl_aff *isl_constraint_get_div(
1807 __isl_keep isl_constraint *constraint, int pos);
1809 To obtain the constraints of a basic set or map in matrix
1810 form, use the following functions.
1812 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1813 __isl_keep isl_basic_set *bset,
1814 enum isl_dim_type c1, enum isl_dim_type c2,
1815 enum isl_dim_type c3, enum isl_dim_type c4);
1816 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1817 __isl_keep isl_basic_set *bset,
1818 enum isl_dim_type c1, enum isl_dim_type c2,
1819 enum isl_dim_type c3, enum isl_dim_type c4);
1820 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1821 __isl_keep isl_basic_map *bmap,
1822 enum isl_dim_type c1,
1823 enum isl_dim_type c2, enum isl_dim_type c3,
1824 enum isl_dim_type c4, enum isl_dim_type c5);
1825 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1826 __isl_keep isl_basic_map *bmap,
1827 enum isl_dim_type c1,
1828 enum isl_dim_type c2, enum isl_dim_type c3,
1829 enum isl_dim_type c4, enum isl_dim_type c5);
1831 The C<isl_dim_type> arguments dictate the order in which
1832 different kinds of variables appear in the resulting matrix
1833 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1834 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1836 The number of parameters, input, output or set dimensions can
1837 be obtained using the following functions.
1839 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1840 enum isl_dim_type type);
1841 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1842 enum isl_dim_type type);
1843 unsigned isl_set_dim(__isl_keep isl_set *set,
1844 enum isl_dim_type type);
1845 unsigned isl_map_dim(__isl_keep isl_map *map,
1846 enum isl_dim_type type);
1848 To check whether the description of a set or relation depends
1849 on one or more given dimensions, it is not necessary to iterate over all
1850 constraints. Instead the following functions can be used.
1852 int isl_basic_set_involves_dims(
1853 __isl_keep isl_basic_set *bset,
1854 enum isl_dim_type type, unsigned first, unsigned n);
1855 int isl_set_involves_dims(__isl_keep isl_set *set,
1856 enum isl_dim_type type, unsigned first, unsigned n);
1857 int isl_basic_map_involves_dims(
1858 __isl_keep isl_basic_map *bmap,
1859 enum isl_dim_type type, unsigned first, unsigned n);
1860 int isl_map_involves_dims(__isl_keep isl_map *map,
1861 enum isl_dim_type type, unsigned first, unsigned n);
1863 Similarly, the following functions can be used to check whether
1864 a given dimension is involved in any lower or upper bound.
1866 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1867 enum isl_dim_type type, unsigned pos);
1868 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1869 enum isl_dim_type type, unsigned pos);
1871 Note that these functions return true even if there is a bound on
1872 the dimension on only some of the basic sets of C<set>.
1873 To check if they have a bound for all of the basic sets in C<set>,
1874 use the following functions instead.
1876 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1877 enum isl_dim_type type, unsigned pos);
1878 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1881 The identifiers or names of the domain and range spaces of a set
1882 or relation can be read off or set using the following functions.
1884 __isl_give isl_set *isl_set_set_tuple_id(
1885 __isl_take isl_set *set, __isl_take isl_id *id);
1886 __isl_give isl_set *isl_set_reset_tuple_id(
1887 __isl_take isl_set *set);
1888 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1889 __isl_give isl_id *isl_set_get_tuple_id(
1890 __isl_keep isl_set *set);
1891 __isl_give isl_map *isl_map_set_tuple_id(
1892 __isl_take isl_map *map, enum isl_dim_type type,
1893 __isl_take isl_id *id);
1894 __isl_give isl_map *isl_map_reset_tuple_id(
1895 __isl_take isl_map *map, enum isl_dim_type type);
1896 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1897 enum isl_dim_type type);
1898 __isl_give isl_id *isl_map_get_tuple_id(
1899 __isl_keep isl_map *map, enum isl_dim_type type);
1901 const char *isl_basic_set_get_tuple_name(
1902 __isl_keep isl_basic_set *bset);
1903 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1904 __isl_take isl_basic_set *set, const char *s);
1905 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1906 const char *isl_set_get_tuple_name(
1907 __isl_keep isl_set *set);
1908 const char *isl_basic_map_get_tuple_name(
1909 __isl_keep isl_basic_map *bmap,
1910 enum isl_dim_type type);
1911 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1912 __isl_take isl_basic_map *bmap,
1913 enum isl_dim_type type, const char *s);
1914 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1915 enum isl_dim_type type);
1916 const char *isl_map_get_tuple_name(
1917 __isl_keep isl_map *map,
1918 enum isl_dim_type type);
1920 As with C<isl_space_get_tuple_name>, the value returned points to
1921 an internal data structure.
1922 The identifiers, positions or names of individual dimensions can be
1923 read off using the following functions.
1925 __isl_give isl_id *isl_basic_set_get_dim_id(
1926 __isl_keep isl_basic_set *bset,
1927 enum isl_dim_type type, unsigned pos);
1928 __isl_give isl_set *isl_set_set_dim_id(
1929 __isl_take isl_set *set, enum isl_dim_type type,
1930 unsigned pos, __isl_take isl_id *id);
1931 int isl_set_has_dim_id(__isl_keep isl_set *set,
1932 enum isl_dim_type type, unsigned pos);
1933 __isl_give isl_id *isl_set_get_dim_id(
1934 __isl_keep isl_set *set, enum isl_dim_type type,
1936 int isl_basic_map_has_dim_id(
1937 __isl_keep isl_basic_map *bmap,
1938 enum isl_dim_type type, unsigned pos);
1939 __isl_give isl_map *isl_map_set_dim_id(
1940 __isl_take isl_map *map, enum isl_dim_type type,
1941 unsigned pos, __isl_take isl_id *id);
1942 int isl_map_has_dim_id(__isl_keep isl_map *map,
1943 enum isl_dim_type type, unsigned pos);
1944 __isl_give isl_id *isl_map_get_dim_id(
1945 __isl_keep isl_map *map, enum isl_dim_type type,
1948 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1949 enum isl_dim_type type, __isl_keep isl_id *id);
1950 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1951 enum isl_dim_type type, __isl_keep isl_id *id);
1952 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1953 enum isl_dim_type type, const char *name);
1954 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1955 enum isl_dim_type type, const char *name);
1957 const char *isl_constraint_get_dim_name(
1958 __isl_keep isl_constraint *constraint,
1959 enum isl_dim_type type, unsigned pos);
1960 const char *isl_basic_set_get_dim_name(
1961 __isl_keep isl_basic_set *bset,
1962 enum isl_dim_type type, unsigned pos);
1963 int isl_set_has_dim_name(__isl_keep isl_set *set,
1964 enum isl_dim_type type, unsigned pos);
1965 const char *isl_set_get_dim_name(
1966 __isl_keep isl_set *set,
1967 enum isl_dim_type type, unsigned pos);
1968 const char *isl_basic_map_get_dim_name(
1969 __isl_keep isl_basic_map *bmap,
1970 enum isl_dim_type type, unsigned pos);
1971 int isl_map_has_dim_name(__isl_keep isl_map *map,
1972 enum isl_dim_type type, unsigned pos);
1973 const char *isl_map_get_dim_name(
1974 __isl_keep isl_map *map,
1975 enum isl_dim_type type, unsigned pos);
1977 These functions are mostly useful to obtain the identifiers, positions
1978 or names of the parameters. Identifiers of individual dimensions are
1979 essentially only useful for printing. They are ignored by all other
1980 operations and may not be preserved across those operations.
1984 =head3 Unary Properties
1990 The following functions test whether the given set or relation
1991 contains any integer points. The ``plain'' variants do not perform
1992 any computations, but simply check if the given set or relation
1993 is already known to be empty.
1995 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1996 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1997 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1998 int isl_set_is_empty(__isl_keep isl_set *set);
1999 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2000 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2001 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2002 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2003 int isl_map_is_empty(__isl_keep isl_map *map);
2004 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2006 =item * Universality
2008 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2009 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2010 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2012 =item * Single-valuedness
2014 int isl_basic_map_is_single_valued(
2015 __isl_keep isl_basic_map *bmap);
2016 int isl_map_plain_is_single_valued(
2017 __isl_keep isl_map *map);
2018 int isl_map_is_single_valued(__isl_keep isl_map *map);
2019 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2023 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2024 int isl_map_is_injective(__isl_keep isl_map *map);
2025 int isl_union_map_plain_is_injective(
2026 __isl_keep isl_union_map *umap);
2027 int isl_union_map_is_injective(
2028 __isl_keep isl_union_map *umap);
2032 int isl_map_is_bijective(__isl_keep isl_map *map);
2033 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2037 int isl_basic_map_plain_is_fixed(
2038 __isl_keep isl_basic_map *bmap,
2039 enum isl_dim_type type, unsigned pos,
2041 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2042 enum isl_dim_type type, unsigned pos,
2044 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2045 enum isl_dim_type type, unsigned pos,
2048 Check if the relation obviously lies on a hyperplane where the given dimension
2049 has a fixed value and if so, return that value in C<*val>.
2053 To check whether a set is a parameter domain, use this function:
2055 int isl_set_is_params(__isl_keep isl_set *set);
2056 int isl_union_set_is_params(
2057 __isl_keep isl_union_set *uset);
2061 The following functions check whether the domain of the given
2062 (basic) set is a wrapped relation.
2064 int isl_basic_set_is_wrapping(
2065 __isl_keep isl_basic_set *bset);
2066 int isl_set_is_wrapping(__isl_keep isl_set *set);
2068 =item * Internal Product
2070 int isl_basic_map_can_zip(
2071 __isl_keep isl_basic_map *bmap);
2072 int isl_map_can_zip(__isl_keep isl_map *map);
2074 Check whether the product of domain and range of the given relation
2076 i.e., whether both domain and range are nested relations.
2080 int isl_basic_map_can_curry(
2081 __isl_keep isl_basic_map *bmap);
2082 int isl_map_can_curry(__isl_keep isl_map *map);
2084 Check whether the domain of the (basic) relation is a wrapped relation.
2086 int isl_basic_map_can_uncurry(
2087 __isl_keep isl_basic_map *bmap);
2088 int isl_map_can_uncurry(__isl_keep isl_map *map);
2090 Check whether the range of the (basic) relation is a wrapped relation.
2094 =head3 Binary Properties
2100 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2101 __isl_keep isl_set *set2);
2102 int isl_set_is_equal(__isl_keep isl_set *set1,
2103 __isl_keep isl_set *set2);
2104 int isl_union_set_is_equal(
2105 __isl_keep isl_union_set *uset1,
2106 __isl_keep isl_union_set *uset2);
2107 int isl_basic_map_is_equal(
2108 __isl_keep isl_basic_map *bmap1,
2109 __isl_keep isl_basic_map *bmap2);
2110 int isl_map_is_equal(__isl_keep isl_map *map1,
2111 __isl_keep isl_map *map2);
2112 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2113 __isl_keep isl_map *map2);
2114 int isl_union_map_is_equal(
2115 __isl_keep isl_union_map *umap1,
2116 __isl_keep isl_union_map *umap2);
2118 =item * Disjointness
2120 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2121 __isl_keep isl_set *set2);
2122 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2123 __isl_keep isl_set *set2);
2124 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2125 __isl_keep isl_map *map2);
2129 int isl_basic_set_is_subset(
2130 __isl_keep isl_basic_set *bset1,
2131 __isl_keep isl_basic_set *bset2);
2132 int isl_set_is_subset(__isl_keep isl_set *set1,
2133 __isl_keep isl_set *set2);
2134 int isl_set_is_strict_subset(
2135 __isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_union_set_is_subset(
2138 __isl_keep isl_union_set *uset1,
2139 __isl_keep isl_union_set *uset2);
2140 int isl_union_set_is_strict_subset(
2141 __isl_keep isl_union_set *uset1,
2142 __isl_keep isl_union_set *uset2);
2143 int isl_basic_map_is_subset(
2144 __isl_keep isl_basic_map *bmap1,
2145 __isl_keep isl_basic_map *bmap2);
2146 int isl_basic_map_is_strict_subset(
2147 __isl_keep isl_basic_map *bmap1,
2148 __isl_keep isl_basic_map *bmap2);
2149 int isl_map_is_subset(
2150 __isl_keep isl_map *map1,
2151 __isl_keep isl_map *map2);
2152 int isl_map_is_strict_subset(
2153 __isl_keep isl_map *map1,
2154 __isl_keep isl_map *map2);
2155 int isl_union_map_is_subset(
2156 __isl_keep isl_union_map *umap1,
2157 __isl_keep isl_union_map *umap2);
2158 int isl_union_map_is_strict_subset(
2159 __isl_keep isl_union_map *umap1,
2160 __isl_keep isl_union_map *umap2);
2162 Check whether the first argument is a (strict) subset of the
2167 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2168 __isl_keep isl_set *set2);
2170 This function is useful for sorting C<isl_set>s.
2171 The order depends on the internal representation of the inputs.
2172 The order is fixed over different calls to the function (assuming
2173 the internal representation of the inputs has not changed), but may
2174 change over different versions of C<isl>.
2178 =head2 Unary Operations
2184 __isl_give isl_set *isl_set_complement(
2185 __isl_take isl_set *set);
2186 __isl_give isl_map *isl_map_complement(
2187 __isl_take isl_map *map);
2191 __isl_give isl_basic_map *isl_basic_map_reverse(
2192 __isl_take isl_basic_map *bmap);
2193 __isl_give isl_map *isl_map_reverse(
2194 __isl_take isl_map *map);
2195 __isl_give isl_union_map *isl_union_map_reverse(
2196 __isl_take isl_union_map *umap);
2200 __isl_give isl_basic_set *isl_basic_set_project_out(
2201 __isl_take isl_basic_set *bset,
2202 enum isl_dim_type type, unsigned first, unsigned n);
2203 __isl_give isl_basic_map *isl_basic_map_project_out(
2204 __isl_take isl_basic_map *bmap,
2205 enum isl_dim_type type, unsigned first, unsigned n);
2206 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2207 enum isl_dim_type type, unsigned first, unsigned n);
2208 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2209 enum isl_dim_type type, unsigned first, unsigned n);
2210 __isl_give isl_basic_set *isl_basic_set_params(
2211 __isl_take isl_basic_set *bset);
2212 __isl_give isl_basic_set *isl_basic_map_domain(
2213 __isl_take isl_basic_map *bmap);
2214 __isl_give isl_basic_set *isl_basic_map_range(
2215 __isl_take isl_basic_map *bmap);
2216 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2217 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2218 __isl_give isl_set *isl_map_domain(
2219 __isl_take isl_map *bmap);
2220 __isl_give isl_set *isl_map_range(
2221 __isl_take isl_map *map);
2222 __isl_give isl_set *isl_union_set_params(
2223 __isl_take isl_union_set *uset);
2224 __isl_give isl_set *isl_union_map_params(
2225 __isl_take isl_union_map *umap);
2226 __isl_give isl_union_set *isl_union_map_domain(
2227 __isl_take isl_union_map *umap);
2228 __isl_give isl_union_set *isl_union_map_range(
2229 __isl_take isl_union_map *umap);
2231 __isl_give isl_basic_map *isl_basic_map_domain_map(
2232 __isl_take isl_basic_map *bmap);
2233 __isl_give isl_basic_map *isl_basic_map_range_map(
2234 __isl_take isl_basic_map *bmap);
2235 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2236 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2237 __isl_give isl_union_map *isl_union_map_domain_map(
2238 __isl_take isl_union_map *umap);
2239 __isl_give isl_union_map *isl_union_map_range_map(
2240 __isl_take isl_union_map *umap);
2242 The functions above construct a (basic, regular or union) relation
2243 that maps (a wrapped version of) the input relation to its domain or range.
2247 __isl_give isl_basic_set *isl_basic_set_eliminate(
2248 __isl_take isl_basic_set *bset,
2249 enum isl_dim_type type,
2250 unsigned first, unsigned n);
2251 __isl_give isl_set *isl_set_eliminate(
2252 __isl_take isl_set *set, enum isl_dim_type type,
2253 unsigned first, unsigned n);
2254 __isl_give isl_basic_map *isl_basic_map_eliminate(
2255 __isl_take isl_basic_map *bmap,
2256 enum isl_dim_type type,
2257 unsigned first, unsigned n);
2258 __isl_give isl_map *isl_map_eliminate(
2259 __isl_take isl_map *map, enum isl_dim_type type,
2260 unsigned first, unsigned n);
2262 Eliminate the coefficients for the given dimensions from the constraints,
2263 without removing the dimensions.
2267 __isl_give isl_basic_set *isl_basic_set_fix(
2268 __isl_take isl_basic_set *bset,
2269 enum isl_dim_type type, unsigned pos,
2271 __isl_give isl_basic_set *isl_basic_set_fix_si(
2272 __isl_take isl_basic_set *bset,
2273 enum isl_dim_type type, unsigned pos, int value);
2274 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2275 enum isl_dim_type type, unsigned pos,
2277 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos, int value);
2279 __isl_give isl_basic_map *isl_basic_map_fix_si(
2280 __isl_take isl_basic_map *bmap,
2281 enum isl_dim_type type, unsigned pos, int value);
2282 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2283 enum isl_dim_type type, unsigned pos,
2285 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2286 enum isl_dim_type type, unsigned pos, int value);
2288 Intersect the set or relation with the hyperplane where the given
2289 dimension has the fixed given value.
2291 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2295 __isl_take isl_basic_map *bmap,
2296 enum isl_dim_type type, unsigned pos, int value);
2297 __isl_give isl_set *isl_set_lower_bound(
2298 __isl_take isl_set *set,
2299 enum isl_dim_type type, unsigned pos,
2301 __isl_give isl_set *isl_set_lower_bound_si(
2302 __isl_take isl_set *set,
2303 enum isl_dim_type type, unsigned pos, int value);
2304 __isl_give isl_map *isl_map_lower_bound_si(
2305 __isl_take isl_map *map,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_set *isl_set_upper_bound(
2308 __isl_take isl_set *set,
2309 enum isl_dim_type type, unsigned pos,
2311 __isl_give isl_set *isl_set_upper_bound_si(
2312 __isl_take isl_set *set,
2313 enum isl_dim_type type, unsigned pos, int value);
2314 __isl_give isl_map *isl_map_upper_bound_si(
2315 __isl_take isl_map *map,
2316 enum isl_dim_type type, unsigned pos, int value);
2318 Intersect the set or relation with the half-space where the given
2319 dimension has a value bounded by the fixed given value.
2321 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2322 enum isl_dim_type type1, int pos1,
2323 enum isl_dim_type type2, int pos2);
2324 __isl_give isl_basic_map *isl_basic_map_equate(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2328 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2329 enum isl_dim_type type1, int pos1,
2330 enum isl_dim_type type2, int pos2);
2332 Intersect the set or relation with the hyperplane where the given
2333 dimensions are equal to each other.
2335 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2336 enum isl_dim_type type1, int pos1,
2337 enum isl_dim_type type2, int pos2);
2339 Intersect the relation with the hyperplane where the given
2340 dimensions have opposite values.
2342 __isl_give isl_basic_map *isl_basic_map_order_ge(
2343 __isl_take isl_basic_map *bmap,
2344 enum isl_dim_type type1, int pos1,
2345 enum isl_dim_type type2, int pos2);
2346 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2347 enum isl_dim_type type1, int pos1,
2348 enum isl_dim_type type2, int pos2);
2349 __isl_give isl_basic_map *isl_basic_map_order_gt(
2350 __isl_take isl_basic_map *bmap,
2351 enum isl_dim_type type1, int pos1,
2352 enum isl_dim_type type2, int pos2);
2353 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2354 enum isl_dim_type type1, int pos1,
2355 enum isl_dim_type type2, int pos2);
2357 Intersect the relation with the half-space where the given
2358 dimensions satisfy the given ordering.
2362 __isl_give isl_map *isl_set_identity(
2363 __isl_take isl_set *set);
2364 __isl_give isl_union_map *isl_union_set_identity(
2365 __isl_take isl_union_set *uset);
2367 Construct an identity relation on the given (union) set.
2371 __isl_give isl_basic_set *isl_basic_map_deltas(
2372 __isl_take isl_basic_map *bmap);
2373 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2374 __isl_give isl_union_set *isl_union_map_deltas(
2375 __isl_take isl_union_map *umap);
2377 These functions return a (basic) set containing the differences
2378 between image elements and corresponding domain elements in the input.
2380 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2381 __isl_take isl_basic_map *bmap);
2382 __isl_give isl_map *isl_map_deltas_map(
2383 __isl_take isl_map *map);
2384 __isl_give isl_union_map *isl_union_map_deltas_map(
2385 __isl_take isl_union_map *umap);
2387 The functions above construct a (basic, regular or union) relation
2388 that maps (a wrapped version of) the input relation to its delta set.
2392 Simplify the representation of a set or relation by trying
2393 to combine pairs of basic sets or relations into a single
2394 basic set or relation.
2396 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2397 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2398 __isl_give isl_union_set *isl_union_set_coalesce(
2399 __isl_take isl_union_set *uset);
2400 __isl_give isl_union_map *isl_union_map_coalesce(
2401 __isl_take isl_union_map *umap);
2403 One of the methods for combining pairs of basic sets or relations
2404 can result in coefficients that are much larger than those that appear
2405 in the constraints of the input. By default, the coefficients are
2406 not allowed to grow larger, but this can be changed by unsetting
2407 the following option.
2409 int isl_options_set_coalesce_bounded_wrapping(
2410 isl_ctx *ctx, int val);
2411 int isl_options_get_coalesce_bounded_wrapping(
2414 =item * Detecting equalities
2416 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2417 __isl_take isl_basic_set *bset);
2418 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2419 __isl_take isl_basic_map *bmap);
2420 __isl_give isl_set *isl_set_detect_equalities(
2421 __isl_take isl_set *set);
2422 __isl_give isl_map *isl_map_detect_equalities(
2423 __isl_take isl_map *map);
2424 __isl_give isl_union_set *isl_union_set_detect_equalities(
2425 __isl_take isl_union_set *uset);
2426 __isl_give isl_union_map *isl_union_map_detect_equalities(
2427 __isl_take isl_union_map *umap);
2429 Simplify the representation of a set or relation by detecting implicit
2432 =item * Removing redundant constraints
2434 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2435 __isl_take isl_basic_set *bset);
2436 __isl_give isl_set *isl_set_remove_redundancies(
2437 __isl_take isl_set *set);
2438 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2439 __isl_take isl_basic_map *bmap);
2440 __isl_give isl_map *isl_map_remove_redundancies(
2441 __isl_take isl_map *map);
2445 __isl_give isl_basic_set *isl_set_convex_hull(
2446 __isl_take isl_set *set);
2447 __isl_give isl_basic_map *isl_map_convex_hull(
2448 __isl_take isl_map *map);
2450 If the input set or relation has any existentially quantified
2451 variables, then the result of these operations is currently undefined.
2455 __isl_give isl_basic_set *
2456 isl_set_unshifted_simple_hull(
2457 __isl_take isl_set *set);
2458 __isl_give isl_basic_map *
2459 isl_map_unshifted_simple_hull(
2460 __isl_take isl_map *map);
2461 __isl_give isl_basic_set *isl_set_simple_hull(
2462 __isl_take isl_set *set);
2463 __isl_give isl_basic_map *isl_map_simple_hull(
2464 __isl_take isl_map *map);
2465 __isl_give isl_union_map *isl_union_map_simple_hull(
2466 __isl_take isl_union_map *umap);
2468 These functions compute a single basic set or relation
2469 that contains the whole input set or relation.
2470 In particular, the output is described by translates
2471 of the constraints describing the basic sets or relations in the input.
2472 In case of C<isl_set_unshifted_simple_hull>, only the original
2473 constraints are used, without any translation.
2477 (See \autoref{s:simple hull}.)
2483 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2484 __isl_take isl_basic_set *bset);
2485 __isl_give isl_basic_set *isl_set_affine_hull(
2486 __isl_take isl_set *set);
2487 __isl_give isl_union_set *isl_union_set_affine_hull(
2488 __isl_take isl_union_set *uset);
2489 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2490 __isl_take isl_basic_map *bmap);
2491 __isl_give isl_basic_map *isl_map_affine_hull(
2492 __isl_take isl_map *map);
2493 __isl_give isl_union_map *isl_union_map_affine_hull(
2494 __isl_take isl_union_map *umap);
2496 In case of union sets and relations, the affine hull is computed
2499 =item * Polyhedral hull
2501 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2502 __isl_take isl_set *set);
2503 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2504 __isl_take isl_map *map);
2505 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2506 __isl_take isl_union_set *uset);
2507 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2508 __isl_take isl_union_map *umap);
2510 These functions compute a single basic set or relation
2511 not involving any existentially quantified variables
2512 that contains the whole input set or relation.
2513 In case of union sets and relations, the polyhedral hull is computed
2516 =item * Other approximations
2518 __isl_give isl_basic_set *
2519 isl_basic_set_drop_constraints_involving_dims(
2520 __isl_take isl_basic_set *bset,
2521 enum isl_dim_type type,
2522 unsigned first, unsigned n);
2523 __isl_give isl_basic_map *
2524 isl_basic_map_drop_constraints_involving_dims(
2525 __isl_take isl_basic_map *bmap,
2526 enum isl_dim_type type,
2527 unsigned first, unsigned n);
2528 __isl_give isl_basic_set *
2529 isl_basic_set_drop_constraints_not_involving_dims(
2530 __isl_take isl_basic_set *bset,
2531 enum isl_dim_type type,
2532 unsigned first, unsigned n);
2533 __isl_give isl_set *
2534 isl_set_drop_constraints_involving_dims(
2535 __isl_take isl_set *set,
2536 enum isl_dim_type type,
2537 unsigned first, unsigned n);
2538 __isl_give isl_map *
2539 isl_map_drop_constraints_involving_dims(
2540 __isl_take isl_map *map,
2541 enum isl_dim_type type,
2542 unsigned first, unsigned n);
2544 These functions drop any constraints (not) involving the specified dimensions.
2545 Note that the result depends on the representation of the input.
2549 __isl_give isl_basic_set *isl_basic_set_sample(
2550 __isl_take isl_basic_set *bset);
2551 __isl_give isl_basic_set *isl_set_sample(
2552 __isl_take isl_set *set);
2553 __isl_give isl_basic_map *isl_basic_map_sample(
2554 __isl_take isl_basic_map *bmap);
2555 __isl_give isl_basic_map *isl_map_sample(
2556 __isl_take isl_map *map);
2558 If the input (basic) set or relation is non-empty, then return
2559 a singleton subset of the input. Otherwise, return an empty set.
2561 =item * Optimization
2563 #include <isl/ilp.h>
2564 enum isl_lp_result isl_basic_set_max(
2565 __isl_keep isl_basic_set *bset,
2566 __isl_keep isl_aff *obj, isl_int *opt)
2567 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2568 __isl_keep isl_aff *obj, isl_int *opt);
2569 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2570 __isl_keep isl_aff *obj, isl_int *opt);
2572 Compute the minimum or maximum of the integer affine expression C<obj>
2573 over the points in C<set>, returning the result in C<opt>.
2574 The return value may be one of C<isl_lp_error>,
2575 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2577 =item * Parametric optimization
2579 __isl_give isl_pw_aff *isl_set_dim_min(
2580 __isl_take isl_set *set, int pos);
2581 __isl_give isl_pw_aff *isl_set_dim_max(
2582 __isl_take isl_set *set, int pos);
2583 __isl_give isl_pw_aff *isl_map_dim_max(
2584 __isl_take isl_map *map, int pos);
2586 Compute the minimum or maximum of the given set or output dimension
2587 as a function of the parameters (and input dimensions), but independently
2588 of the other set or output dimensions.
2589 For lexicographic optimization, see L<"Lexicographic Optimization">.
2593 The following functions compute either the set of (rational) coefficient
2594 values of valid constraints for the given set or the set of (rational)
2595 values satisfying the constraints with coefficients from the given set.
2596 Internally, these two sets of functions perform essentially the
2597 same operations, except that the set of coefficients is assumed to
2598 be a cone, while the set of values may be any polyhedron.
2599 The current implementation is based on the Farkas lemma and
2600 Fourier-Motzkin elimination, but this may change or be made optional
2601 in future. In particular, future implementations may use different
2602 dualization algorithms or skip the elimination step.
2604 __isl_give isl_basic_set *isl_basic_set_coefficients(
2605 __isl_take isl_basic_set *bset);
2606 __isl_give isl_basic_set *isl_set_coefficients(
2607 __isl_take isl_set *set);
2608 __isl_give isl_union_set *isl_union_set_coefficients(
2609 __isl_take isl_union_set *bset);
2610 __isl_give isl_basic_set *isl_basic_set_solutions(
2611 __isl_take isl_basic_set *bset);
2612 __isl_give isl_basic_set *isl_set_solutions(
2613 __isl_take isl_set *set);
2614 __isl_give isl_union_set *isl_union_set_solutions(
2615 __isl_take isl_union_set *bset);
2619 __isl_give isl_map *isl_map_fixed_power(
2620 __isl_take isl_map *map, isl_int exp);
2621 __isl_give isl_union_map *isl_union_map_fixed_power(
2622 __isl_take isl_union_map *umap, isl_int exp);
2624 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2625 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2626 of C<map> is computed.
2628 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2630 __isl_give isl_union_map *isl_union_map_power(
2631 __isl_take isl_union_map *umap, int *exact);
2633 Compute a parametric representation for all positive powers I<k> of C<map>.
2634 The result maps I<k> to a nested relation corresponding to the
2635 I<k>th power of C<map>.
2636 The result may be an overapproximation. If the result is known to be exact,
2637 then C<*exact> is set to C<1>.
2639 =item * Transitive closure
2641 __isl_give isl_map *isl_map_transitive_closure(
2642 __isl_take isl_map *map, int *exact);
2643 __isl_give isl_union_map *isl_union_map_transitive_closure(
2644 __isl_take isl_union_map *umap, int *exact);
2646 Compute the transitive closure of C<map>.
2647 The result may be an overapproximation. If the result is known to be exact,
2648 then C<*exact> is set to C<1>.
2650 =item * Reaching path lengths
2652 __isl_give isl_map *isl_map_reaching_path_lengths(
2653 __isl_take isl_map *map, int *exact);
2655 Compute a relation that maps each element in the range of C<map>
2656 to the lengths of all paths composed of edges in C<map> that
2657 end up in the given element.
2658 The result may be an overapproximation. If the result is known to be exact,
2659 then C<*exact> is set to C<1>.
2660 To compute the I<maximal> path length, the resulting relation
2661 should be postprocessed by C<isl_map_lexmax>.
2662 In particular, if the input relation is a dependence relation
2663 (mapping sources to sinks), then the maximal path length corresponds
2664 to the free schedule.
2665 Note, however, that C<isl_map_lexmax> expects the maximum to be
2666 finite, so if the path lengths are unbounded (possibly due to
2667 the overapproximation), then you will get an error message.
2671 __isl_give isl_basic_set *isl_basic_map_wrap(
2672 __isl_take isl_basic_map *bmap);
2673 __isl_give isl_set *isl_map_wrap(
2674 __isl_take isl_map *map);
2675 __isl_give isl_union_set *isl_union_map_wrap(
2676 __isl_take isl_union_map *umap);
2677 __isl_give isl_basic_map *isl_basic_set_unwrap(
2678 __isl_take isl_basic_set *bset);
2679 __isl_give isl_map *isl_set_unwrap(
2680 __isl_take isl_set *set);
2681 __isl_give isl_union_map *isl_union_set_unwrap(
2682 __isl_take isl_union_set *uset);
2686 Remove any internal structure of domain (and range) of the given
2687 set or relation. If there is any such internal structure in the input,
2688 then the name of the space is also removed.
2690 __isl_give isl_basic_set *isl_basic_set_flatten(
2691 __isl_take isl_basic_set *bset);
2692 __isl_give isl_set *isl_set_flatten(
2693 __isl_take isl_set *set);
2694 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2695 __isl_take isl_basic_map *bmap);
2696 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2697 __isl_take isl_basic_map *bmap);
2698 __isl_give isl_map *isl_map_flatten_range(
2699 __isl_take isl_map *map);
2700 __isl_give isl_map *isl_map_flatten_domain(
2701 __isl_take isl_map *map);
2702 __isl_give isl_basic_map *isl_basic_map_flatten(
2703 __isl_take isl_basic_map *bmap);
2704 __isl_give isl_map *isl_map_flatten(
2705 __isl_take isl_map *map);
2707 __isl_give isl_map *isl_set_flatten_map(
2708 __isl_take isl_set *set);
2710 The function above constructs a relation
2711 that maps the input set to a flattened version of the set.
2715 Lift the input set to a space with extra dimensions corresponding
2716 to the existentially quantified variables in the input.
2717 In particular, the result lives in a wrapped map where the domain
2718 is the original space and the range corresponds to the original
2719 existentially quantified variables.
2721 __isl_give isl_basic_set *isl_basic_set_lift(
2722 __isl_take isl_basic_set *bset);
2723 __isl_give isl_set *isl_set_lift(
2724 __isl_take isl_set *set);
2725 __isl_give isl_union_set *isl_union_set_lift(
2726 __isl_take isl_union_set *uset);
2728 Given a local space that contains the existentially quantified
2729 variables of a set, a basic relation that, when applied to
2730 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2731 can be constructed using the following function.
2733 #include <isl/local_space.h>
2734 __isl_give isl_basic_map *isl_local_space_lifting(
2735 __isl_take isl_local_space *ls);
2737 =item * Internal Product
2739 __isl_give isl_basic_map *isl_basic_map_zip(
2740 __isl_take isl_basic_map *bmap);
2741 __isl_give isl_map *isl_map_zip(
2742 __isl_take isl_map *map);
2743 __isl_give isl_union_map *isl_union_map_zip(
2744 __isl_take isl_union_map *umap);
2746 Given a relation with nested relations for domain and range,
2747 interchange the range of the domain with the domain of the range.
2751 __isl_give isl_basic_map *isl_basic_map_curry(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_basic_map *isl_basic_map_uncurry(
2754 __isl_take isl_basic_map *bmap);
2755 __isl_give isl_map *isl_map_curry(
2756 __isl_take isl_map *map);
2757 __isl_give isl_map *isl_map_uncurry(
2758 __isl_take isl_map *map);
2759 __isl_give isl_union_map *isl_union_map_curry(
2760 __isl_take isl_union_map *umap);
2761 __isl_give isl_union_map *isl_union_map_uncurry(
2762 __isl_take isl_union_map *umap);
2764 Given a relation with a nested relation for domain,
2765 the C<curry> functions
2766 move the range of the nested relation out of the domain
2767 and use it as the domain of a nested relation in the range,
2768 with the original range as range of this nested relation.
2769 The C<uncurry> functions perform the inverse operation.
2771 =item * Aligning parameters
2773 __isl_give isl_basic_set *isl_basic_set_align_params(
2774 __isl_take isl_basic_set *bset,
2775 __isl_take isl_space *model);
2776 __isl_give isl_set *isl_set_align_params(
2777 __isl_take isl_set *set,
2778 __isl_take isl_space *model);
2779 __isl_give isl_basic_map *isl_basic_map_align_params(
2780 __isl_take isl_basic_map *bmap,
2781 __isl_take isl_space *model);
2782 __isl_give isl_map *isl_map_align_params(
2783 __isl_take isl_map *map,
2784 __isl_take isl_space *model);
2786 Change the order of the parameters of the given set or relation
2787 such that the first parameters match those of C<model>.
2788 This may involve the introduction of extra parameters.
2789 All parameters need to be named.
2791 =item * Dimension manipulation
2793 __isl_give isl_basic_set *isl_basic_set_add_dims(
2794 __isl_take isl_basic_set *bset,
2795 enum isl_dim_type type, unsigned n);
2796 __isl_give isl_set *isl_set_add_dims(
2797 __isl_take isl_set *set,
2798 enum isl_dim_type type, unsigned n);
2799 __isl_give isl_map *isl_map_add_dims(
2800 __isl_take isl_map *map,
2801 enum isl_dim_type type, unsigned n);
2802 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2803 __isl_take isl_basic_set *bset,
2804 enum isl_dim_type type, unsigned pos,
2806 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2807 __isl_take isl_basic_map *bmap,
2808 enum isl_dim_type type, unsigned pos,
2810 __isl_give isl_set *isl_set_insert_dims(
2811 __isl_take isl_set *set,
2812 enum isl_dim_type type, unsigned pos, unsigned n);
2813 __isl_give isl_map *isl_map_insert_dims(
2814 __isl_take isl_map *map,
2815 enum isl_dim_type type, unsigned pos, unsigned n);
2816 __isl_give isl_basic_set *isl_basic_set_move_dims(
2817 __isl_take isl_basic_set *bset,
2818 enum isl_dim_type dst_type, unsigned dst_pos,
2819 enum isl_dim_type src_type, unsigned src_pos,
2821 __isl_give isl_basic_map *isl_basic_map_move_dims(
2822 __isl_take isl_basic_map *bmap,
2823 enum isl_dim_type dst_type, unsigned dst_pos,
2824 enum isl_dim_type src_type, unsigned src_pos,
2826 __isl_give isl_set *isl_set_move_dims(
2827 __isl_take isl_set *set,
2828 enum isl_dim_type dst_type, unsigned dst_pos,
2829 enum isl_dim_type src_type, unsigned src_pos,
2831 __isl_give isl_map *isl_map_move_dims(
2832 __isl_take isl_map *map,
2833 enum isl_dim_type dst_type, unsigned dst_pos,
2834 enum isl_dim_type src_type, unsigned src_pos,
2837 It is usually not advisable to directly change the (input or output)
2838 space of a set or a relation as this removes the name and the internal
2839 structure of the space. However, the above functions can be useful
2840 to add new parameters, assuming
2841 C<isl_set_align_params> and C<isl_map_align_params>
2846 =head2 Binary Operations
2848 The two arguments of a binary operation not only need to live
2849 in the same C<isl_ctx>, they currently also need to have
2850 the same (number of) parameters.
2852 =head3 Basic Operations
2856 =item * Intersection
2858 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2859 __isl_take isl_basic_set *bset1,
2860 __isl_take isl_basic_set *bset2);
2861 __isl_give isl_basic_set *isl_basic_set_intersect(
2862 __isl_take isl_basic_set *bset1,
2863 __isl_take isl_basic_set *bset2);
2864 __isl_give isl_set *isl_set_intersect_params(
2865 __isl_take isl_set *set,
2866 __isl_take isl_set *params);
2867 __isl_give isl_set *isl_set_intersect(
2868 __isl_take isl_set *set1,
2869 __isl_take isl_set *set2);
2870 __isl_give isl_union_set *isl_union_set_intersect_params(
2871 __isl_take isl_union_set *uset,
2872 __isl_take isl_set *set);
2873 __isl_give isl_union_map *isl_union_map_intersect_params(
2874 __isl_take isl_union_map *umap,
2875 __isl_take isl_set *set);
2876 __isl_give isl_union_set *isl_union_set_intersect(
2877 __isl_take isl_union_set *uset1,
2878 __isl_take isl_union_set *uset2);
2879 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2880 __isl_take isl_basic_map *bmap,
2881 __isl_take isl_basic_set *bset);
2882 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2883 __isl_take isl_basic_map *bmap,
2884 __isl_take isl_basic_set *bset);
2885 __isl_give isl_basic_map *isl_basic_map_intersect(
2886 __isl_take isl_basic_map *bmap1,
2887 __isl_take isl_basic_map *bmap2);
2888 __isl_give isl_map *isl_map_intersect_params(
2889 __isl_take isl_map *map,
2890 __isl_take isl_set *params);
2891 __isl_give isl_map *isl_map_intersect_domain(
2892 __isl_take isl_map *map,
2893 __isl_take isl_set *set);
2894 __isl_give isl_map *isl_map_intersect_range(
2895 __isl_take isl_map *map,
2896 __isl_take isl_set *set);
2897 __isl_give isl_map *isl_map_intersect(
2898 __isl_take isl_map *map1,
2899 __isl_take isl_map *map2);
2900 __isl_give isl_union_map *isl_union_map_intersect_domain(
2901 __isl_take isl_union_map *umap,
2902 __isl_take isl_union_set *uset);
2903 __isl_give isl_union_map *isl_union_map_intersect_range(
2904 __isl_take isl_union_map *umap,
2905 __isl_take isl_union_set *uset);
2906 __isl_give isl_union_map *isl_union_map_intersect(
2907 __isl_take isl_union_map *umap1,
2908 __isl_take isl_union_map *umap2);
2910 The second argument to the C<_params> functions needs to be
2911 a parametric (basic) set. For the other functions, a parametric set
2912 for either argument is only allowed if the other argument is
2913 a parametric set as well.
2917 __isl_give isl_set *isl_basic_set_union(
2918 __isl_take isl_basic_set *bset1,
2919 __isl_take isl_basic_set *bset2);
2920 __isl_give isl_map *isl_basic_map_union(
2921 __isl_take isl_basic_map *bmap1,
2922 __isl_take isl_basic_map *bmap2);
2923 __isl_give isl_set *isl_set_union(
2924 __isl_take isl_set *set1,
2925 __isl_take isl_set *set2);
2926 __isl_give isl_map *isl_map_union(
2927 __isl_take isl_map *map1,
2928 __isl_take isl_map *map2);
2929 __isl_give isl_union_set *isl_union_set_union(
2930 __isl_take isl_union_set *uset1,
2931 __isl_take isl_union_set *uset2);
2932 __isl_give isl_union_map *isl_union_map_union(
2933 __isl_take isl_union_map *umap1,
2934 __isl_take isl_union_map *umap2);
2936 =item * Set difference
2938 __isl_give isl_set *isl_set_subtract(
2939 __isl_take isl_set *set1,
2940 __isl_take isl_set *set2);
2941 __isl_give isl_map *isl_map_subtract(
2942 __isl_take isl_map *map1,
2943 __isl_take isl_map *map2);
2944 __isl_give isl_map *isl_map_subtract_domain(
2945 __isl_take isl_map *map,
2946 __isl_take isl_set *dom);
2947 __isl_give isl_map *isl_map_subtract_range(
2948 __isl_take isl_map *map,
2949 __isl_take isl_set *dom);
2950 __isl_give isl_union_set *isl_union_set_subtract(
2951 __isl_take isl_union_set *uset1,
2952 __isl_take isl_union_set *uset2);
2953 __isl_give isl_union_map *isl_union_map_subtract(
2954 __isl_take isl_union_map *umap1,
2955 __isl_take isl_union_map *umap2);
2956 __isl_give isl_union_map *isl_union_map_subtract_domain(
2957 __isl_take isl_union_map *umap,
2958 __isl_take isl_union_set *dom);
2959 __isl_give isl_union_map *isl_union_map_subtract_range(
2960 __isl_take isl_union_map *umap,
2961 __isl_take isl_union_set *dom);
2965 __isl_give isl_basic_set *isl_basic_set_apply(
2966 __isl_take isl_basic_set *bset,
2967 __isl_take isl_basic_map *bmap);
2968 __isl_give isl_set *isl_set_apply(
2969 __isl_take isl_set *set,
2970 __isl_take isl_map *map);
2971 __isl_give isl_union_set *isl_union_set_apply(
2972 __isl_take isl_union_set *uset,
2973 __isl_take isl_union_map *umap);
2974 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2975 __isl_take isl_basic_map *bmap1,
2976 __isl_take isl_basic_map *bmap2);
2977 __isl_give isl_basic_map *isl_basic_map_apply_range(
2978 __isl_take isl_basic_map *bmap1,
2979 __isl_take isl_basic_map *bmap2);
2980 __isl_give isl_map *isl_map_apply_domain(
2981 __isl_take isl_map *map1,
2982 __isl_take isl_map *map2);
2983 __isl_give isl_union_map *isl_union_map_apply_domain(
2984 __isl_take isl_union_map *umap1,
2985 __isl_take isl_union_map *umap2);
2986 __isl_give isl_map *isl_map_apply_range(
2987 __isl_take isl_map *map1,
2988 __isl_take isl_map *map2);
2989 __isl_give isl_union_map *isl_union_map_apply_range(
2990 __isl_take isl_union_map *umap1,
2991 __isl_take isl_union_map *umap2);
2995 __isl_give isl_basic_set *
2996 isl_basic_set_preimage_multi_aff(
2997 __isl_take isl_basic_set *bset,
2998 __isl_take isl_multi_aff *ma);
2999 __isl_give isl_set *isl_set_preimage_multi_aff(
3000 __isl_take isl_set *set,
3001 __isl_take isl_multi_aff *ma);
3002 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3003 __isl_take isl_set *set,
3004 __isl_take isl_pw_multi_aff *pma);
3005 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3006 __isl_take isl_map *map,
3007 __isl_take isl_multi_aff *ma);
3008 __isl_give isl_union_map *
3009 isl_union_map_preimage_domain_multi_aff(
3010 __isl_take isl_union_map *umap,
3011 __isl_take isl_multi_aff *ma);
3013 These functions compute the preimage of the given set or map domain under
3014 the given function. In other words, the expression is plugged
3015 into the set description or into the domain of the map.
3016 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3017 L</"Piecewise Multiple Quasi Affine Expressions">.
3019 =item * Cartesian Product
3021 __isl_give isl_set *isl_set_product(
3022 __isl_take isl_set *set1,
3023 __isl_take isl_set *set2);
3024 __isl_give isl_union_set *isl_union_set_product(
3025 __isl_take isl_union_set *uset1,
3026 __isl_take isl_union_set *uset2);
3027 __isl_give isl_basic_map *isl_basic_map_domain_product(
3028 __isl_take isl_basic_map *bmap1,
3029 __isl_take isl_basic_map *bmap2);
3030 __isl_give isl_basic_map *isl_basic_map_range_product(
3031 __isl_take isl_basic_map *bmap1,
3032 __isl_take isl_basic_map *bmap2);
3033 __isl_give isl_basic_map *isl_basic_map_product(
3034 __isl_take isl_basic_map *bmap1,
3035 __isl_take isl_basic_map *bmap2);
3036 __isl_give isl_map *isl_map_domain_product(
3037 __isl_take isl_map *map1,
3038 __isl_take isl_map *map2);
3039 __isl_give isl_map *isl_map_range_product(
3040 __isl_take isl_map *map1,
3041 __isl_take isl_map *map2);
3042 __isl_give isl_union_map *isl_union_map_domain_product(
3043 __isl_take isl_union_map *umap1,
3044 __isl_take isl_union_map *umap2);
3045 __isl_give isl_union_map *isl_union_map_range_product(
3046 __isl_take isl_union_map *umap1,
3047 __isl_take isl_union_map *umap2);
3048 __isl_give isl_map *isl_map_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_union_map *isl_union_map_product(
3052 __isl_take isl_union_map *umap1,
3053 __isl_take isl_union_map *umap2);
3055 The above functions compute the cross product of the given
3056 sets or relations. The domains and ranges of the results
3057 are wrapped maps between domains and ranges of the inputs.
3058 To obtain a ``flat'' product, use the following functions
3061 __isl_give isl_basic_set *isl_basic_set_flat_product(
3062 __isl_take isl_basic_set *bset1,
3063 __isl_take isl_basic_set *bset2);
3064 __isl_give isl_set *isl_set_flat_product(
3065 __isl_take isl_set *set1,
3066 __isl_take isl_set *set2);
3067 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3068 __isl_take isl_basic_map *bmap1,
3069 __isl_take isl_basic_map *bmap2);
3070 __isl_give isl_map *isl_map_flat_domain_product(
3071 __isl_take isl_map *map1,
3072 __isl_take isl_map *map2);
3073 __isl_give isl_map *isl_map_flat_range_product(
3074 __isl_take isl_map *map1,
3075 __isl_take isl_map *map2);
3076 __isl_give isl_union_map *isl_union_map_flat_range_product(
3077 __isl_take isl_union_map *umap1,
3078 __isl_take isl_union_map *umap2);
3079 __isl_give isl_basic_map *isl_basic_map_flat_product(
3080 __isl_take isl_basic_map *bmap1,
3081 __isl_take isl_basic_map *bmap2);
3082 __isl_give isl_map *isl_map_flat_product(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3086 =item * Simplification
3088 __isl_give isl_basic_set *isl_basic_set_gist(
3089 __isl_take isl_basic_set *bset,
3090 __isl_take isl_basic_set *context);
3091 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3092 __isl_take isl_set *context);
3093 __isl_give isl_set *isl_set_gist_params(
3094 __isl_take isl_set *set,
3095 __isl_take isl_set *context);
3096 __isl_give isl_union_set *isl_union_set_gist(
3097 __isl_take isl_union_set *uset,
3098 __isl_take isl_union_set *context);
3099 __isl_give isl_union_set *isl_union_set_gist_params(
3100 __isl_take isl_union_set *uset,
3101 __isl_take isl_set *set);
3102 __isl_give isl_basic_map *isl_basic_map_gist(
3103 __isl_take isl_basic_map *bmap,
3104 __isl_take isl_basic_map *context);
3105 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3106 __isl_take isl_map *context);
3107 __isl_give isl_map *isl_map_gist_params(
3108 __isl_take isl_map *map,
3109 __isl_take isl_set *context);
3110 __isl_give isl_map *isl_map_gist_domain(
3111 __isl_take isl_map *map,
3112 __isl_take isl_set *context);
3113 __isl_give isl_map *isl_map_gist_range(
3114 __isl_take isl_map *map,
3115 __isl_take isl_set *context);
3116 __isl_give isl_union_map *isl_union_map_gist(
3117 __isl_take isl_union_map *umap,
3118 __isl_take isl_union_map *context);
3119 __isl_give isl_union_map *isl_union_map_gist_params(
3120 __isl_take isl_union_map *umap,
3121 __isl_take isl_set *set);
3122 __isl_give isl_union_map *isl_union_map_gist_domain(
3123 __isl_take isl_union_map *umap,
3124 __isl_take isl_union_set *uset);
3125 __isl_give isl_union_map *isl_union_map_gist_range(
3126 __isl_take isl_union_map *umap,
3127 __isl_take isl_union_set *uset);
3129 The gist operation returns a set or relation that has the
3130 same intersection with the context as the input set or relation.
3131 Any implicit equality in the intersection is made explicit in the result,
3132 while all inequalities that are redundant with respect to the intersection
3134 In case of union sets and relations, the gist operation is performed
3139 =head3 Lexicographic Optimization
3141 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3142 the following functions
3143 compute a set that contains the lexicographic minimum or maximum
3144 of the elements in C<set> (or C<bset>) for those values of the parameters
3145 that satisfy C<dom>.
3146 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3147 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3149 In other words, the union of the parameter values
3150 for which the result is non-empty and of C<*empty>
3153 __isl_give isl_set *isl_basic_set_partial_lexmin(
3154 __isl_take isl_basic_set *bset,
3155 __isl_take isl_basic_set *dom,
3156 __isl_give isl_set **empty);
3157 __isl_give isl_set *isl_basic_set_partial_lexmax(
3158 __isl_take isl_basic_set *bset,
3159 __isl_take isl_basic_set *dom,
3160 __isl_give isl_set **empty);
3161 __isl_give isl_set *isl_set_partial_lexmin(
3162 __isl_take isl_set *set, __isl_take isl_set *dom,
3163 __isl_give isl_set **empty);
3164 __isl_give isl_set *isl_set_partial_lexmax(
3165 __isl_take isl_set *set, __isl_take isl_set *dom,
3166 __isl_give isl_set **empty);
3168 Given a (basic) set C<set> (or C<bset>), the following functions simply
3169 return a set containing the lexicographic minimum or maximum
3170 of the elements in C<set> (or C<bset>).
3171 In case of union sets, the optimum is computed per space.
3173 __isl_give isl_set *isl_basic_set_lexmin(
3174 __isl_take isl_basic_set *bset);
3175 __isl_give isl_set *isl_basic_set_lexmax(
3176 __isl_take isl_basic_set *bset);
3177 __isl_give isl_set *isl_set_lexmin(
3178 __isl_take isl_set *set);
3179 __isl_give isl_set *isl_set_lexmax(
3180 __isl_take isl_set *set);
3181 __isl_give isl_union_set *isl_union_set_lexmin(
3182 __isl_take isl_union_set *uset);
3183 __isl_give isl_union_set *isl_union_set_lexmax(
3184 __isl_take isl_union_set *uset);
3186 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3187 the following functions
3188 compute a relation that maps each element of C<dom>
3189 to the single lexicographic minimum or maximum
3190 of the elements that are associated to that same
3191 element in C<map> (or C<bmap>).
3192 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3193 that contains the elements in C<dom> that do not map
3194 to any elements in C<map> (or C<bmap>).
3195 In other words, the union of the domain of the result and of C<*empty>
3198 __isl_give isl_map *isl_basic_map_partial_lexmax(
3199 __isl_take isl_basic_map *bmap,
3200 __isl_take isl_basic_set *dom,
3201 __isl_give isl_set **empty);
3202 __isl_give isl_map *isl_basic_map_partial_lexmin(
3203 __isl_take isl_basic_map *bmap,
3204 __isl_take isl_basic_set *dom,
3205 __isl_give isl_set **empty);
3206 __isl_give isl_map *isl_map_partial_lexmax(
3207 __isl_take isl_map *map, __isl_take isl_set *dom,
3208 __isl_give isl_set **empty);
3209 __isl_give isl_map *isl_map_partial_lexmin(
3210 __isl_take isl_map *map, __isl_take isl_set *dom,
3211 __isl_give isl_set **empty);
3213 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3214 return a map mapping each element in the domain of
3215 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3216 of all elements associated to that element.
3217 In case of union relations, the optimum is computed per space.
3219 __isl_give isl_map *isl_basic_map_lexmin(
3220 __isl_take isl_basic_map *bmap);
3221 __isl_give isl_map *isl_basic_map_lexmax(
3222 __isl_take isl_basic_map *bmap);
3223 __isl_give isl_map *isl_map_lexmin(
3224 __isl_take isl_map *map);
3225 __isl_give isl_map *isl_map_lexmax(
3226 __isl_take isl_map *map);
3227 __isl_give isl_union_map *isl_union_map_lexmin(
3228 __isl_take isl_union_map *umap);
3229 __isl_give isl_union_map *isl_union_map_lexmax(
3230 __isl_take isl_union_map *umap);
3232 The following functions return their result in the form of
3233 a piecewise multi-affine expression
3234 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3235 but are otherwise equivalent to the corresponding functions
3236 returning a basic set or relation.
3238 __isl_give isl_pw_multi_aff *
3239 isl_basic_map_lexmin_pw_multi_aff(
3240 __isl_take isl_basic_map *bmap);
3241 __isl_give isl_pw_multi_aff *
3242 isl_basic_set_partial_lexmin_pw_multi_aff(
3243 __isl_take isl_basic_set *bset,
3244 __isl_take isl_basic_set *dom,
3245 __isl_give isl_set **empty);
3246 __isl_give isl_pw_multi_aff *
3247 isl_basic_set_partial_lexmax_pw_multi_aff(
3248 __isl_take isl_basic_set *bset,
3249 __isl_take isl_basic_set *dom,
3250 __isl_give isl_set **empty);
3251 __isl_give isl_pw_multi_aff *
3252 isl_basic_map_partial_lexmin_pw_multi_aff(
3253 __isl_take isl_basic_map *bmap,
3254 __isl_take isl_basic_set *dom,
3255 __isl_give isl_set **empty);
3256 __isl_give isl_pw_multi_aff *
3257 isl_basic_map_partial_lexmax_pw_multi_aff(
3258 __isl_take isl_basic_map *bmap,
3259 __isl_take isl_basic_set *dom,
3260 __isl_give isl_set **empty);
3261 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3262 __isl_take isl_set *set);
3263 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3264 __isl_take isl_set *set);
3265 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3266 __isl_take isl_map *map);
3267 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3268 __isl_take isl_map *map);
3272 Lists are defined over several element types, including
3273 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3274 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3275 Here we take lists of C<isl_set>s as an example.
3276 Lists can be created, copied, modified and freed using the following functions.
3278 #include <isl/list.h>
3279 __isl_give isl_set_list *isl_set_list_from_set(
3280 __isl_take isl_set *el);
3281 __isl_give isl_set_list *isl_set_list_alloc(
3282 isl_ctx *ctx, int n);
3283 __isl_give isl_set_list *isl_set_list_copy(
3284 __isl_keep isl_set_list *list);
3285 __isl_give isl_set_list *isl_set_list_insert(
3286 __isl_take isl_set_list *list, unsigned pos,
3287 __isl_take isl_set *el);
3288 __isl_give isl_set_list *isl_set_list_add(
3289 __isl_take isl_set_list *list,
3290 __isl_take isl_set *el);
3291 __isl_give isl_set_list *isl_set_list_drop(
3292 __isl_take isl_set_list *list,
3293 unsigned first, unsigned n);
3294 __isl_give isl_set_list *isl_set_list_set_set(
3295 __isl_take isl_set_list *list, int index,
3296 __isl_take isl_set *set);
3297 __isl_give isl_set_list *isl_set_list_concat(
3298 __isl_take isl_set_list *list1,
3299 __isl_take isl_set_list *list2);
3300 __isl_give isl_set_list *isl_set_list_sort(
3301 __isl_take isl_set_list *list,
3302 int (*cmp)(__isl_keep isl_set *a,
3303 __isl_keep isl_set *b, void *user),
3305 void *isl_set_list_free(__isl_take isl_set_list *list);
3307 C<isl_set_list_alloc> creates an empty list with a capacity for
3308 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3311 Lists can be inspected using the following functions.
3313 #include <isl/list.h>
3314 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3315 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3316 __isl_give isl_set *isl_set_list_get_set(
3317 __isl_keep isl_set_list *list, int index);
3318 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3319 int (*fn)(__isl_take isl_set *el, void *user),
3321 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3322 int (*follows)(__isl_keep isl_set *a,
3323 __isl_keep isl_set *b, void *user),
3325 int (*fn)(__isl_take isl_set *el, void *user),
3328 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3329 strongly connected components of the graph with as vertices the elements
3330 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3331 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3332 should return C<-1> on error.
3334 Lists can be printed using
3336 #include <isl/list.h>
3337 __isl_give isl_printer *isl_printer_print_set_list(
3338 __isl_take isl_printer *p,
3339 __isl_keep isl_set_list *list);
3341 =head2 Multiple Values
3343 An C<isl_multi_val> object represents a sequence of zero or more values,
3344 living in a set space.
3346 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3347 using the following function
3349 #include <isl/val.h>
3350 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3351 __isl_take isl_space *space,
3352 __isl_take isl_val_list *list);
3354 The zero multiple value (with value zero for each set dimension)
3355 can be created using the following function.
3357 #include <isl/val.h>
3358 __isl_give isl_multi_val *isl_multi_val_zero(
3359 __isl_take isl_space *space);
3361 Multiple values can be copied and freed using
3363 #include <isl/val.h>
3364 __isl_give isl_multi_val *isl_multi_val_copy(
3365 __isl_keep isl_multi_val *mv);
3366 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3368 They can be inspected using
3370 #include <isl/val.h>
3371 isl_ctx *isl_multi_val_get_ctx(
3372 __isl_keep isl_multi_val *mv);
3373 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3374 enum isl_dim_type type);
3375 __isl_give isl_val *isl_multi_val_get_val(
3376 __isl_keep isl_multi_val *mv, int pos);
3377 const char *isl_multi_val_get_tuple_name(
3378 __isl_keep isl_multi_val *mv,
3379 enum isl_dim_type type);
3381 They can be modified using
3383 #include <isl/val.h>
3384 __isl_give isl_multi_val *isl_multi_val_set_val(
3385 __isl_take isl_multi_val *mv, int pos,
3386 __isl_take isl_val *val);
3387 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3388 __isl_take isl_multi_val *mv,
3389 enum isl_dim_type type, unsigned pos, const char *s);
3390 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3391 __isl_take isl_multi_val *mv,
3392 enum isl_dim_type type, const char *s);
3393 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3394 __isl_take isl_multi_val *mv,
3395 enum isl_dim_type type, __isl_take isl_id *id);
3397 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3398 __isl_take isl_multi_val *mv,
3399 enum isl_dim_type type, unsigned first, unsigned n);
3400 __isl_give isl_multi_val *isl_multi_val_add_dims(
3401 __isl_take isl_multi_val *mv,
3402 enum isl_dim_type type, unsigned n);
3403 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3404 __isl_take isl_multi_val *mv,
3405 enum isl_dim_type type, unsigned first, unsigned n);
3409 #include <isl/val.h>
3410 __isl_give isl_multi_val *isl_multi_val_align_params(
3411 __isl_take isl_multi_val *mv,
3412 __isl_take isl_space *model);
3413 __isl_give isl_multi_val *isl_multi_val_range_splice(
3414 __isl_take isl_multi_val *mv1, unsigned pos,
3415 __isl_take isl_multi_val *mv2);
3416 __isl_give isl_multi_val *isl_multi_val_range_product(
3417 __isl_take isl_multi_val *mv1,
3418 __isl_take isl_multi_val *mv2);
3419 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3420 __isl_take isl_multi_val *mv1,
3421 __isl_take isl_multi_aff *mv2);
3422 __isl_give isl_multi_val *isl_multi_val_add_val(
3423 __isl_take isl_multi_val *mv,
3424 __isl_take isl_val *v);
3425 __isl_give isl_multi_val *isl_multi_val_mod_val(
3426 __isl_take isl_multi_val *mv,
3427 __isl_take isl_val *v);
3431 Vectors can be created, copied and freed using the following functions.
3433 #include <isl/vec.h>
3434 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3436 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3437 void *isl_vec_free(__isl_take isl_vec *vec);
3439 Note that the elements of a newly created vector may have arbitrary values.
3440 The elements can be changed and inspected using the following functions.
3442 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3443 int isl_vec_size(__isl_keep isl_vec *vec);
3444 int isl_vec_get_element(__isl_keep isl_vec *vec,
3445 int pos, isl_int *v);
3446 __isl_give isl_val *isl_vec_get_element_val(
3447 __isl_keep isl_vec *vec, int pos);
3448 __isl_give isl_vec *isl_vec_set_element(
3449 __isl_take isl_vec *vec, int pos, isl_int v);
3450 __isl_give isl_vec *isl_vec_set_element_si(
3451 __isl_take isl_vec *vec, int pos, int v);
3452 __isl_give isl_vec *isl_vec_set_element_val(
3453 __isl_take isl_vec *vec, int pos,
3454 __isl_take isl_val *v);
3455 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3457 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3459 __isl_give isl_vec *isl_vec_set_val(
3460 __isl_take isl_vec *vec, __isl_take isl_val *v);
3461 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3464 C<isl_vec_get_element> will return a negative value if anything went wrong.
3465 In that case, the value of C<*v> is undefined.
3467 The following function can be used to concatenate two vectors.
3469 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3470 __isl_take isl_vec *vec2);
3474 Matrices can be created, copied and freed using the following functions.
3476 #include <isl/mat.h>
3477 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3478 unsigned n_row, unsigned n_col);
3479 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3480 void *isl_mat_free(__isl_take isl_mat *mat);
3482 Note that the elements of a newly created matrix may have arbitrary values.
3483 The elements can be changed and inspected using the following functions.
3485 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3486 int isl_mat_rows(__isl_keep isl_mat *mat);
3487 int isl_mat_cols(__isl_keep isl_mat *mat);
3488 int isl_mat_get_element(__isl_keep isl_mat *mat,
3489 int row, int col, isl_int *v);
3490 __isl_give isl_val *isl_mat_get_element_val(
3491 __isl_keep isl_mat *mat, int row, int col);
3492 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3493 int row, int col, isl_int v);
3494 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3495 int row, int col, int v);
3496 __isl_give isl_mat *isl_mat_set_element_val(
3497 __isl_take isl_mat *mat, int row, int col,
3498 __isl_take isl_val *v);
3500 C<isl_mat_get_element> will return a negative value if anything went wrong.
3501 In that case, the value of C<*v> is undefined.
3503 The following function can be used to compute the (right) inverse
3504 of a matrix, i.e., a matrix such that the product of the original
3505 and the inverse (in that order) is a multiple of the identity matrix.
3506 The input matrix is assumed to be of full row-rank.
3508 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3510 The following function can be used to compute the (right) kernel
3511 (or null space) of a matrix, i.e., a matrix such that the product of
3512 the original and the kernel (in that order) is the zero matrix.
3514 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3516 =head2 Piecewise Quasi Affine Expressions
3518 The zero quasi affine expression or the quasi affine expression
3519 that is equal to a specified dimension on a given domain can be created using
3521 __isl_give isl_aff *isl_aff_zero_on_domain(
3522 __isl_take isl_local_space *ls);
3523 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3524 __isl_take isl_local_space *ls);
3525 __isl_give isl_aff *isl_aff_var_on_domain(
3526 __isl_take isl_local_space *ls,
3527 enum isl_dim_type type, unsigned pos);
3528 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3529 __isl_take isl_local_space *ls,
3530 enum isl_dim_type type, unsigned pos);
3532 Note that the space in which the resulting objects live is a map space
3533 with the given space as domain and a one-dimensional range.
3535 An empty piecewise quasi affine expression (one with no cells)
3536 or a piecewise quasi affine expression with a single cell can
3537 be created using the following functions.
3539 #include <isl/aff.h>
3540 __isl_give isl_pw_aff *isl_pw_aff_empty(
3541 __isl_take isl_space *space);
3542 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3543 __isl_take isl_set *set, __isl_take isl_aff *aff);
3544 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3545 __isl_take isl_aff *aff);
3547 A piecewise quasi affine expression that is equal to 1 on a set
3548 and 0 outside the set can be created using the following function.
3550 #include <isl/aff.h>
3551 __isl_give isl_pw_aff *isl_set_indicator_function(
3552 __isl_take isl_set *set);
3554 Quasi affine expressions can be copied and freed using
3556 #include <isl/aff.h>
3557 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3558 void *isl_aff_free(__isl_take isl_aff *aff);
3560 __isl_give isl_pw_aff *isl_pw_aff_copy(
3561 __isl_keep isl_pw_aff *pwaff);
3562 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3564 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3565 using the following function. The constraint is required to have
3566 a non-zero coefficient for the specified dimension.
3568 #include <isl/constraint.h>
3569 __isl_give isl_aff *isl_constraint_get_bound(
3570 __isl_keep isl_constraint *constraint,
3571 enum isl_dim_type type, int pos);
3573 The entire affine expression of the constraint can also be extracted
3574 using the following function.
3576 #include <isl/constraint.h>
3577 __isl_give isl_aff *isl_constraint_get_aff(
3578 __isl_keep isl_constraint *constraint);
3580 Conversely, an equality constraint equating
3581 the affine expression to zero or an inequality constraint enforcing
3582 the affine expression to be non-negative, can be constructed using
3584 __isl_give isl_constraint *isl_equality_from_aff(
3585 __isl_take isl_aff *aff);
3586 __isl_give isl_constraint *isl_inequality_from_aff(
3587 __isl_take isl_aff *aff);
3589 The expression can be inspected using
3591 #include <isl/aff.h>
3592 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3593 int isl_aff_dim(__isl_keep isl_aff *aff,
3594 enum isl_dim_type type);
3595 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3596 __isl_keep isl_aff *aff);
3597 __isl_give isl_local_space *isl_aff_get_local_space(
3598 __isl_keep isl_aff *aff);
3599 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3600 enum isl_dim_type type, unsigned pos);
3601 const char *isl_pw_aff_get_dim_name(
3602 __isl_keep isl_pw_aff *pa,
3603 enum isl_dim_type type, unsigned pos);
3604 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3605 enum isl_dim_type type, unsigned pos);
3606 __isl_give isl_id *isl_pw_aff_get_dim_id(
3607 __isl_keep isl_pw_aff *pa,
3608 enum isl_dim_type type, unsigned pos);
3609 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3610 __isl_keep isl_pw_aff *pa,
3611 enum isl_dim_type type);
3612 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3614 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3615 enum isl_dim_type type, int pos, isl_int *v);
3616 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3618 __isl_give isl_aff *isl_aff_get_div(
3619 __isl_keep isl_aff *aff, int pos);
3621 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3622 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3623 int (*fn)(__isl_take isl_set *set,
3624 __isl_take isl_aff *aff,
3625 void *user), void *user);
3627 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3628 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3630 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3631 enum isl_dim_type type, unsigned first, unsigned n);
3632 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3633 enum isl_dim_type type, unsigned first, unsigned n);
3635 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3636 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3637 enum isl_dim_type type);
3638 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3640 It can be modified using
3642 #include <isl/aff.h>
3643 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3644 __isl_take isl_pw_aff *pwaff,
3645 enum isl_dim_type type, __isl_take isl_id *id);
3646 __isl_give isl_aff *isl_aff_set_dim_name(
3647 __isl_take isl_aff *aff, enum isl_dim_type type,
3648 unsigned pos, const char *s);
3649 __isl_give isl_aff *isl_aff_set_dim_id(
3650 __isl_take isl_aff *aff, enum isl_dim_type type,
3651 unsigned pos, __isl_take isl_id *id);
3652 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3653 __isl_take isl_pw_aff *pma,
3654 enum isl_dim_type type, unsigned pos,
3655 __isl_take isl_id *id);
3656 __isl_give isl_aff *isl_aff_set_constant(
3657 __isl_take isl_aff *aff, isl_int v);
3658 __isl_give isl_aff *isl_aff_set_constant_si(
3659 __isl_take isl_aff *aff, int v);
3660 __isl_give isl_aff *isl_aff_set_coefficient(
3661 __isl_take isl_aff *aff,
3662 enum isl_dim_type type, int pos, isl_int v);
3663 __isl_give isl_aff *isl_aff_set_coefficient_si(
3664 __isl_take isl_aff *aff,
3665 enum isl_dim_type type, int pos, int v);
3666 __isl_give isl_aff *isl_aff_set_denominator(
3667 __isl_take isl_aff *aff, isl_int v);
3669 __isl_give isl_aff *isl_aff_add_constant(
3670 __isl_take isl_aff *aff, isl_int v);
3671 __isl_give isl_aff *isl_aff_add_constant_si(
3672 __isl_take isl_aff *aff, int v);
3673 __isl_give isl_aff *isl_aff_add_constant_num(
3674 __isl_take isl_aff *aff, isl_int v);
3675 __isl_give isl_aff *isl_aff_add_constant_num_si(
3676 __isl_take isl_aff *aff, int v);
3677 __isl_give isl_aff *isl_aff_add_coefficient(
3678 __isl_take isl_aff *aff,
3679 enum isl_dim_type type, int pos, isl_int v);
3680 __isl_give isl_aff *isl_aff_add_coefficient_si(
3681 __isl_take isl_aff *aff,
3682 enum isl_dim_type type, int pos, int v);
3684 __isl_give isl_aff *isl_aff_insert_dims(
3685 __isl_take isl_aff *aff,
3686 enum isl_dim_type type, unsigned first, unsigned n);
3687 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3688 __isl_take isl_pw_aff *pwaff,
3689 enum isl_dim_type type, unsigned first, unsigned n);
3690 __isl_give isl_aff *isl_aff_add_dims(
3691 __isl_take isl_aff *aff,
3692 enum isl_dim_type type, unsigned n);
3693 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3694 __isl_take isl_pw_aff *pwaff,
3695 enum isl_dim_type type, unsigned n);
3696 __isl_give isl_aff *isl_aff_drop_dims(
3697 __isl_take isl_aff *aff,
3698 enum isl_dim_type type, unsigned first, unsigned n);
3699 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3700 __isl_take isl_pw_aff *pwaff,
3701 enum isl_dim_type type, unsigned first, unsigned n);
3703 Note that the C<set_constant> and C<set_coefficient> functions
3704 set the I<numerator> of the constant or coefficient, while
3705 C<add_constant> and C<add_coefficient> add an integer value to
3706 the possibly rational constant or coefficient.
3707 The C<add_constant_num> functions add an integer value to
3710 To check whether an affine expressions is obviously zero
3711 or obviously equal to some other affine expression, use
3713 #include <isl/aff.h>
3714 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3715 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3716 __isl_keep isl_aff *aff2);
3717 int isl_pw_aff_plain_is_equal(
3718 __isl_keep isl_pw_aff *pwaff1,
3719 __isl_keep isl_pw_aff *pwaff2);
3723 #include <isl/aff.h>
3724 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3725 __isl_take isl_aff *aff2);
3726 __isl_give isl_pw_aff *isl_pw_aff_add(
3727 __isl_take isl_pw_aff *pwaff1,
3728 __isl_take isl_pw_aff *pwaff2);
3729 __isl_give isl_pw_aff *isl_pw_aff_min(
3730 __isl_take isl_pw_aff *pwaff1,
3731 __isl_take isl_pw_aff *pwaff2);
3732 __isl_give isl_pw_aff *isl_pw_aff_max(
3733 __isl_take isl_pw_aff *pwaff1,
3734 __isl_take isl_pw_aff *pwaff2);
3735 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3736 __isl_take isl_aff *aff2);
3737 __isl_give isl_pw_aff *isl_pw_aff_sub(
3738 __isl_take isl_pw_aff *pwaff1,
3739 __isl_take isl_pw_aff *pwaff2);
3740 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3741 __isl_give isl_pw_aff *isl_pw_aff_neg(
3742 __isl_take isl_pw_aff *pwaff);
3743 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3744 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3745 __isl_take isl_pw_aff *pwaff);
3746 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3747 __isl_give isl_pw_aff *isl_pw_aff_floor(
3748 __isl_take isl_pw_aff *pwaff);
3749 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3751 __isl_give isl_pw_aff *isl_pw_aff_mod(
3752 __isl_take isl_pw_aff *pwaff, isl_int mod);
3753 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3755 __isl_give isl_pw_aff *isl_pw_aff_scale(
3756 __isl_take isl_pw_aff *pwaff, isl_int f);
3757 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3759 __isl_give isl_aff *isl_aff_scale_down_ui(
3760 __isl_take isl_aff *aff, unsigned f);
3761 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3762 __isl_take isl_pw_aff *pwaff, isl_int f);
3764 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3765 __isl_take isl_pw_aff_list *list);
3766 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3767 __isl_take isl_pw_aff_list *list);
3769 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3770 __isl_take isl_pw_aff *pwqp);
3772 __isl_give isl_aff *isl_aff_align_params(
3773 __isl_take isl_aff *aff,
3774 __isl_take isl_space *model);
3775 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3776 __isl_take isl_pw_aff *pwaff,
3777 __isl_take isl_space *model);
3779 __isl_give isl_aff *isl_aff_project_domain_on_params(
3780 __isl_take isl_aff *aff);
3782 __isl_give isl_aff *isl_aff_gist_params(
3783 __isl_take isl_aff *aff,
3784 __isl_take isl_set *context);
3785 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3786 __isl_take isl_set *context);
3787 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3788 __isl_take isl_pw_aff *pwaff,
3789 __isl_take isl_set *context);
3790 __isl_give isl_pw_aff *isl_pw_aff_gist(
3791 __isl_take isl_pw_aff *pwaff,
3792 __isl_take isl_set *context);
3794 __isl_give isl_set *isl_pw_aff_domain(
3795 __isl_take isl_pw_aff *pwaff);
3796 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3797 __isl_take isl_pw_aff *pa,
3798 __isl_take isl_set *set);
3799 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3800 __isl_take isl_pw_aff *pa,
3801 __isl_take isl_set *set);
3803 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3804 __isl_take isl_aff *aff2);
3805 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3806 __isl_take isl_aff *aff2);
3807 __isl_give isl_pw_aff *isl_pw_aff_mul(
3808 __isl_take isl_pw_aff *pwaff1,
3809 __isl_take isl_pw_aff *pwaff2);
3810 __isl_give isl_pw_aff *isl_pw_aff_div(
3811 __isl_take isl_pw_aff *pa1,
3812 __isl_take isl_pw_aff *pa2);
3813 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3814 __isl_take isl_pw_aff *pa1,
3815 __isl_take isl_pw_aff *pa2);
3816 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3817 __isl_take isl_pw_aff *pa1,
3818 __isl_take isl_pw_aff *pa2);
3820 When multiplying two affine expressions, at least one of the two needs
3821 to be a constant. Similarly, when dividing an affine expression by another,
3822 the second expression needs to be a constant.
3823 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3824 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3827 #include <isl/aff.h>
3828 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3829 __isl_take isl_aff *aff,
3830 __isl_take isl_multi_aff *ma);
3831 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3832 __isl_take isl_pw_aff *pa,
3833 __isl_take isl_multi_aff *ma);
3834 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3835 __isl_take isl_pw_aff *pa,
3836 __isl_take isl_pw_multi_aff *pma);
3838 These functions precompose the input expression by the given
3839 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3840 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3841 into the (piecewise) affine expression.
3842 Objects of type C<isl_multi_aff> are described in
3843 L</"Piecewise Multiple Quasi Affine Expressions">.
3845 #include <isl/aff.h>
3846 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3847 __isl_take isl_aff *aff);
3848 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3849 __isl_take isl_aff *aff);
3850 __isl_give isl_basic_set *isl_aff_le_basic_set(
3851 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3852 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3853 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3854 __isl_give isl_set *isl_pw_aff_eq_set(
3855 __isl_take isl_pw_aff *pwaff1,
3856 __isl_take isl_pw_aff *pwaff2);
3857 __isl_give isl_set *isl_pw_aff_ne_set(
3858 __isl_take isl_pw_aff *pwaff1,
3859 __isl_take isl_pw_aff *pwaff2);
3860 __isl_give isl_set *isl_pw_aff_le_set(
3861 __isl_take isl_pw_aff *pwaff1,
3862 __isl_take isl_pw_aff *pwaff2);
3863 __isl_give isl_set *isl_pw_aff_lt_set(
3864 __isl_take isl_pw_aff *pwaff1,
3865 __isl_take isl_pw_aff *pwaff2);
3866 __isl_give isl_set *isl_pw_aff_ge_set(
3867 __isl_take isl_pw_aff *pwaff1,
3868 __isl_take isl_pw_aff *pwaff2);
3869 __isl_give isl_set *isl_pw_aff_gt_set(
3870 __isl_take isl_pw_aff *pwaff1,
3871 __isl_take isl_pw_aff *pwaff2);
3873 __isl_give isl_set *isl_pw_aff_list_eq_set(
3874 __isl_take isl_pw_aff_list *list1,
3875 __isl_take isl_pw_aff_list *list2);
3876 __isl_give isl_set *isl_pw_aff_list_ne_set(
3877 __isl_take isl_pw_aff_list *list1,
3878 __isl_take isl_pw_aff_list *list2);
3879 __isl_give isl_set *isl_pw_aff_list_le_set(
3880 __isl_take isl_pw_aff_list *list1,
3881 __isl_take isl_pw_aff_list *list2);
3882 __isl_give isl_set *isl_pw_aff_list_lt_set(
3883 __isl_take isl_pw_aff_list *list1,
3884 __isl_take isl_pw_aff_list *list2);
3885 __isl_give isl_set *isl_pw_aff_list_ge_set(
3886 __isl_take isl_pw_aff_list *list1,
3887 __isl_take isl_pw_aff_list *list2);
3888 __isl_give isl_set *isl_pw_aff_list_gt_set(
3889 __isl_take isl_pw_aff_list *list1,
3890 __isl_take isl_pw_aff_list *list2);
3892 The function C<isl_aff_neg_basic_set> returns a basic set
3893 containing those elements in the domain space
3894 of C<aff> where C<aff> is negative.
3895 The function C<isl_aff_ge_basic_set> returns a basic set
3896 containing those elements in the shared space
3897 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3898 The function C<isl_pw_aff_ge_set> returns a set
3899 containing those elements in the shared domain
3900 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3901 The functions operating on C<isl_pw_aff_list> apply the corresponding
3902 C<isl_pw_aff> function to each pair of elements in the two lists.
3904 #include <isl/aff.h>
3905 __isl_give isl_set *isl_pw_aff_nonneg_set(
3906 __isl_take isl_pw_aff *pwaff);
3907 __isl_give isl_set *isl_pw_aff_zero_set(
3908 __isl_take isl_pw_aff *pwaff);
3909 __isl_give isl_set *isl_pw_aff_non_zero_set(
3910 __isl_take isl_pw_aff *pwaff);
3912 The function C<isl_pw_aff_nonneg_set> returns a set
3913 containing those elements in the domain
3914 of C<pwaff> where C<pwaff> is non-negative.
3916 #include <isl/aff.h>
3917 __isl_give isl_pw_aff *isl_pw_aff_cond(
3918 __isl_take isl_pw_aff *cond,
3919 __isl_take isl_pw_aff *pwaff_true,
3920 __isl_take isl_pw_aff *pwaff_false);
3922 The function C<isl_pw_aff_cond> performs a conditional operator
3923 and returns an expression that is equal to C<pwaff_true>
3924 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3925 where C<cond> is zero.
3927 #include <isl/aff.h>
3928 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3929 __isl_take isl_pw_aff *pwaff1,
3930 __isl_take isl_pw_aff *pwaff2);
3931 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3932 __isl_take isl_pw_aff *pwaff1,
3933 __isl_take isl_pw_aff *pwaff2);
3934 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3935 __isl_take isl_pw_aff *pwaff1,
3936 __isl_take isl_pw_aff *pwaff2);
3938 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3939 expression with a domain that is the union of those of C<pwaff1> and
3940 C<pwaff2> and such that on each cell, the quasi-affine expression is
3941 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3942 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3943 associated expression is the defined one.
3945 An expression can be read from input using
3947 #include <isl/aff.h>
3948 __isl_give isl_aff *isl_aff_read_from_str(
3949 isl_ctx *ctx, const char *str);
3950 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3951 isl_ctx *ctx, const char *str);
3953 An expression can be printed using
3955 #include <isl/aff.h>
3956 __isl_give isl_printer *isl_printer_print_aff(
3957 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3959 __isl_give isl_printer *isl_printer_print_pw_aff(
3960 __isl_take isl_printer *p,
3961 __isl_keep isl_pw_aff *pwaff);
3963 =head2 Piecewise Multiple Quasi Affine Expressions
3965 An C<isl_multi_aff> object represents a sequence of
3966 zero or more affine expressions, all defined on the same domain space.
3967 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3968 zero or more piecewise affine expressions.
3970 An C<isl_multi_aff> can be constructed from a single
3971 C<isl_aff> or an C<isl_aff_list> using the
3972 following functions. Similarly for C<isl_multi_pw_aff>.
3974 #include <isl/aff.h>
3975 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3976 __isl_take isl_aff *aff);
3977 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3978 __isl_take isl_pw_aff *pa);
3979 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3980 __isl_take isl_space *space,
3981 __isl_take isl_aff_list *list);
3983 An empty piecewise multiple quasi affine expression (one with no cells),
3984 the zero piecewise multiple quasi affine expression (with value zero
3985 for each output dimension),
3986 a piecewise multiple quasi affine expression with a single cell (with
3987 either a universe or a specified domain) or
3988 a zero-dimensional piecewise multiple quasi affine expression
3990 can be created using the following functions.
3992 #include <isl/aff.h>
3993 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3994 __isl_take isl_space *space);
3995 __isl_give isl_multi_aff *isl_multi_aff_zero(
3996 __isl_take isl_space *space);
3997 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3998 __isl_take isl_space *space);
3999 __isl_give isl_multi_aff *isl_multi_aff_identity(
4000 __isl_take isl_space *space);
4001 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4002 __isl_take isl_space *space);
4003 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4004 __isl_take isl_space *space);
4005 __isl_give isl_pw_multi_aff *
4006 isl_pw_multi_aff_from_multi_aff(
4007 __isl_take isl_multi_aff *ma);
4008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4009 __isl_take isl_set *set,
4010 __isl_take isl_multi_aff *maff);
4011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4012 __isl_take isl_set *set);
4014 __isl_give isl_union_pw_multi_aff *
4015 isl_union_pw_multi_aff_empty(
4016 __isl_take isl_space *space);
4017 __isl_give isl_union_pw_multi_aff *
4018 isl_union_pw_multi_aff_add_pw_multi_aff(
4019 __isl_take isl_union_pw_multi_aff *upma,
4020 __isl_take isl_pw_multi_aff *pma);
4021 __isl_give isl_union_pw_multi_aff *
4022 isl_union_pw_multi_aff_from_domain(
4023 __isl_take isl_union_set *uset);
4025 A piecewise multiple quasi affine expression can also be initialized
4026 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4027 and the C<isl_map> is single-valued.
4028 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4029 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4031 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4032 __isl_take isl_set *set);
4033 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4034 __isl_take isl_map *map);
4036 __isl_give isl_union_pw_multi_aff *
4037 isl_union_pw_multi_aff_from_union_set(
4038 __isl_take isl_union_set *uset);
4039 __isl_give isl_union_pw_multi_aff *
4040 isl_union_pw_multi_aff_from_union_map(
4041 __isl_take isl_union_map *umap);
4043 Multiple quasi affine expressions can be copied and freed using
4045 #include <isl/aff.h>
4046 __isl_give isl_multi_aff *isl_multi_aff_copy(
4047 __isl_keep isl_multi_aff *maff);
4048 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4051 __isl_keep isl_pw_multi_aff *pma);
4052 void *isl_pw_multi_aff_free(
4053 __isl_take isl_pw_multi_aff *pma);
4055 __isl_give isl_union_pw_multi_aff *
4056 isl_union_pw_multi_aff_copy(
4057 __isl_keep isl_union_pw_multi_aff *upma);
4058 void *isl_union_pw_multi_aff_free(
4059 __isl_take isl_union_pw_multi_aff *upma);
4061 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4062 __isl_keep isl_multi_pw_aff *mpa);
4063 void *isl_multi_pw_aff_free(
4064 __isl_take isl_multi_pw_aff *mpa);
4066 The expression can be inspected using
4068 #include <isl/aff.h>
4069 isl_ctx *isl_multi_aff_get_ctx(
4070 __isl_keep isl_multi_aff *maff);
4071 isl_ctx *isl_pw_multi_aff_get_ctx(
4072 __isl_keep isl_pw_multi_aff *pma);
4073 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4074 __isl_keep isl_union_pw_multi_aff *upma);
4075 isl_ctx *isl_multi_pw_aff_get_ctx(
4076 __isl_keep isl_multi_pw_aff *mpa);
4077 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4078 enum isl_dim_type type);
4079 unsigned isl_pw_multi_aff_dim(
4080 __isl_keep isl_pw_multi_aff *pma,
4081 enum isl_dim_type type);
4082 unsigned isl_multi_pw_aff_dim(
4083 __isl_keep isl_multi_pw_aff *mpa,
4084 enum isl_dim_type type);
4085 __isl_give isl_aff *isl_multi_aff_get_aff(
4086 __isl_keep isl_multi_aff *multi, int pos);
4087 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4088 __isl_keep isl_pw_multi_aff *pma, int pos);
4089 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4090 __isl_keep isl_multi_pw_aff *mpa, int pos);
4091 const char *isl_pw_multi_aff_get_dim_name(
4092 __isl_keep isl_pw_multi_aff *pma,
4093 enum isl_dim_type type, unsigned pos);
4094 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4095 __isl_keep isl_pw_multi_aff *pma,
4096 enum isl_dim_type type, unsigned pos);
4097 const char *isl_multi_aff_get_tuple_name(
4098 __isl_keep isl_multi_aff *multi,
4099 enum isl_dim_type type);
4100 int isl_pw_multi_aff_has_tuple_name(
4101 __isl_keep isl_pw_multi_aff *pma,
4102 enum isl_dim_type type);
4103 const char *isl_pw_multi_aff_get_tuple_name(
4104 __isl_keep isl_pw_multi_aff *pma,
4105 enum isl_dim_type type);
4106 int isl_pw_multi_aff_has_tuple_id(
4107 __isl_keep isl_pw_multi_aff *pma,
4108 enum isl_dim_type type);
4109 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4110 __isl_keep isl_pw_multi_aff *pma,
4111 enum isl_dim_type type);
4113 int isl_pw_multi_aff_foreach_piece(
4114 __isl_keep isl_pw_multi_aff *pma,
4115 int (*fn)(__isl_take isl_set *set,
4116 __isl_take isl_multi_aff *maff,
4117 void *user), void *user);
4119 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4120 __isl_keep isl_union_pw_multi_aff *upma,
4121 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4122 void *user), void *user);
4124 It can be modified using
4126 #include <isl/aff.h>
4127 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4128 __isl_take isl_multi_aff *multi, int pos,
4129 __isl_take isl_aff *aff);
4130 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4131 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4132 __isl_take isl_pw_aff *pa);
4133 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4134 __isl_take isl_multi_aff *maff,
4135 enum isl_dim_type type, unsigned pos, const char *s);
4136 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4137 __isl_take isl_multi_aff *maff,
4138 enum isl_dim_type type, const char *s);
4139 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4140 __isl_take isl_multi_aff *maff,
4141 enum isl_dim_type type, __isl_take isl_id *id);
4142 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4143 __isl_take isl_pw_multi_aff *pma,
4144 enum isl_dim_type type, __isl_take isl_id *id);
4146 __isl_give isl_multi_pw_aff *
4147 isl_multi_pw_aff_set_dim_name(
4148 __isl_take isl_multi_pw_aff *mpa,
4149 enum isl_dim_type type, unsigned pos, const char *s);
4150 __isl_give isl_multi_pw_aff *
4151 isl_multi_pw_aff_set_tuple_name(
4152 __isl_take isl_multi_pw_aff *mpa,
4153 enum isl_dim_type type, const char *s);
4155 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4156 __isl_take isl_multi_aff *ma,
4157 enum isl_dim_type type, unsigned first, unsigned n);
4158 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4159 __isl_take isl_multi_aff *ma,
4160 enum isl_dim_type type, unsigned n);
4161 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4162 __isl_take isl_multi_aff *maff,
4163 enum isl_dim_type type, unsigned first, unsigned n);
4164 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4165 __isl_take isl_pw_multi_aff *pma,
4166 enum isl_dim_type type, unsigned first, unsigned n);
4168 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4169 __isl_take isl_multi_pw_aff *mpa,
4170 enum isl_dim_type type, unsigned first, unsigned n);
4171 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4172 __isl_take isl_multi_pw_aff *mpa,
4173 enum isl_dim_type type, unsigned n);
4175 To check whether two multiple affine expressions are
4176 obviously equal to each other, use
4178 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4179 __isl_keep isl_multi_aff *maff2);
4180 int isl_pw_multi_aff_plain_is_equal(
4181 __isl_keep isl_pw_multi_aff *pma1,
4182 __isl_keep isl_pw_multi_aff *pma2);
4186 #include <isl/aff.h>
4187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4188 __isl_take isl_pw_multi_aff *pma1,
4189 __isl_take isl_pw_multi_aff *pma2);
4190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4191 __isl_take isl_pw_multi_aff *pma1,
4192 __isl_take isl_pw_multi_aff *pma2);
4193 __isl_give isl_multi_aff *isl_multi_aff_add(
4194 __isl_take isl_multi_aff *maff1,
4195 __isl_take isl_multi_aff *maff2);
4196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4197 __isl_take isl_pw_multi_aff *pma1,
4198 __isl_take isl_pw_multi_aff *pma2);
4199 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4200 __isl_take isl_union_pw_multi_aff *upma1,
4201 __isl_take isl_union_pw_multi_aff *upma2);
4202 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4203 __isl_take isl_pw_multi_aff *pma1,
4204 __isl_take isl_pw_multi_aff *pma2);
4205 __isl_give isl_multi_aff *isl_multi_aff_sub(
4206 __isl_take isl_multi_aff *ma1,
4207 __isl_take isl_multi_aff *ma2);
4208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4209 __isl_take isl_pw_multi_aff *pma1,
4210 __isl_take isl_pw_multi_aff *pma2);
4211 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4212 __isl_take isl_union_pw_multi_aff *upma1,
4213 __isl_take isl_union_pw_multi_aff *upma2);
4215 C<isl_multi_aff_sub> subtracts the second argument from the first.
4217 __isl_give isl_multi_aff *isl_multi_aff_scale(
4218 __isl_take isl_multi_aff *maff,
4220 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4221 __isl_take isl_multi_aff *ma,
4222 __isl_take isl_vec *v);
4223 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4224 __isl_take isl_pw_multi_aff *pma,
4225 __isl_take isl_vec *v);
4226 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4227 __isl_take isl_union_pw_multi_aff *upma,
4228 __isl_take isl_vec *v);
4230 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4231 by the corresponding elements of C<v>.
4233 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4234 __isl_take isl_pw_multi_aff *pma,
4235 __isl_take isl_set *set);
4236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4237 __isl_take isl_pw_multi_aff *pma,
4238 __isl_take isl_set *set);
4239 __isl_give isl_union_pw_multi_aff *
4240 isl_union_pw_multi_aff_intersect_domain(
4241 __isl_take isl_union_pw_multi_aff *upma,
4242 __isl_take isl_union_set *uset);
4243 __isl_give isl_multi_aff *isl_multi_aff_lift(
4244 __isl_take isl_multi_aff *maff,
4245 __isl_give isl_local_space **ls);
4246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4247 __isl_take isl_pw_multi_aff *pma);
4248 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4249 __isl_take isl_multi_aff *multi,
4250 __isl_take isl_space *model);
4251 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4252 __isl_take isl_pw_multi_aff *pma,
4253 __isl_take isl_space *model);
4254 __isl_give isl_pw_multi_aff *
4255 isl_pw_multi_aff_project_domain_on_params(
4256 __isl_take isl_pw_multi_aff *pma);
4257 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4258 __isl_take isl_multi_aff *maff,
4259 __isl_take isl_set *context);
4260 __isl_give isl_multi_aff *isl_multi_aff_gist(
4261 __isl_take isl_multi_aff *maff,
4262 __isl_take isl_set *context);
4263 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4264 __isl_take isl_pw_multi_aff *pma,
4265 __isl_take isl_set *set);
4266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4267 __isl_take isl_pw_multi_aff *pma,
4268 __isl_take isl_set *set);
4269 __isl_give isl_set *isl_pw_multi_aff_domain(
4270 __isl_take isl_pw_multi_aff *pma);
4271 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4272 __isl_take isl_union_pw_multi_aff *upma);
4273 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4274 __isl_take isl_multi_aff *ma1, unsigned pos,
4275 __isl_take isl_multi_aff *ma2);
4276 __isl_give isl_multi_aff *isl_multi_aff_splice(
4277 __isl_take isl_multi_aff *ma1,
4278 unsigned in_pos, unsigned out_pos,
4279 __isl_take isl_multi_aff *ma2);
4280 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4281 __isl_take isl_multi_aff *ma1,
4282 __isl_take isl_multi_aff *ma2);
4283 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4284 __isl_take isl_multi_aff *ma1,
4285 __isl_take isl_multi_aff *ma2);
4286 __isl_give isl_multi_aff *isl_multi_aff_product(
4287 __isl_take isl_multi_aff *ma1,
4288 __isl_take isl_multi_aff *ma2);
4289 __isl_give isl_pw_multi_aff *
4290 isl_pw_multi_aff_range_product(
4291 __isl_take isl_pw_multi_aff *pma1,
4292 __isl_take isl_pw_multi_aff *pma2);
4293 __isl_give isl_pw_multi_aff *
4294 isl_pw_multi_aff_flat_range_product(
4295 __isl_take isl_pw_multi_aff *pma1,
4296 __isl_take isl_pw_multi_aff *pma2);
4297 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4298 __isl_take isl_pw_multi_aff *pma1,
4299 __isl_take isl_pw_multi_aff *pma2);
4300 __isl_give isl_union_pw_multi_aff *
4301 isl_union_pw_multi_aff_flat_range_product(
4302 __isl_take isl_union_pw_multi_aff *upma1,
4303 __isl_take isl_union_pw_multi_aff *upma2);
4304 __isl_give isl_multi_pw_aff *
4305 isl_multi_pw_aff_range_splice(
4306 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4307 __isl_take isl_multi_pw_aff *mpa2);
4308 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4309 __isl_take isl_multi_pw_aff *mpa1,
4310 unsigned in_pos, unsigned out_pos,
4311 __isl_take isl_multi_pw_aff *mpa2);
4312 __isl_give isl_multi_pw_aff *
4313 isl_multi_pw_aff_range_product(
4314 __isl_take isl_multi_pw_aff *mpa1,
4315 __isl_take isl_multi_pw_aff *mpa2);
4316 __isl_give isl_multi_pw_aff *
4317 isl_multi_pw_aff_flat_range_product(
4318 __isl_take isl_multi_pw_aff *mpa1,
4319 __isl_take isl_multi_pw_aff *mpa2);
4321 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4322 then it is assigned the local space that lies at the basis of
4323 the lifting applied.
4325 #include <isl/aff.h>
4326 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4327 __isl_take isl_multi_aff *ma1,
4328 __isl_take isl_multi_aff *ma2);
4329 __isl_give isl_pw_multi_aff *
4330 isl_pw_multi_aff_pullback_multi_aff(
4331 __isl_take isl_pw_multi_aff *pma,
4332 __isl_take isl_multi_aff *ma);
4333 __isl_give isl_pw_multi_aff *
4334 isl_pw_multi_aff_pullback_pw_multi_aff(
4335 __isl_take isl_pw_multi_aff *pma1,
4336 __isl_take isl_pw_multi_aff *pma2);
4338 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4339 In other words, C<ma2> is plugged
4342 __isl_give isl_set *isl_multi_aff_lex_le_set(
4343 __isl_take isl_multi_aff *ma1,
4344 __isl_take isl_multi_aff *ma2);
4345 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4346 __isl_take isl_multi_aff *ma1,
4347 __isl_take isl_multi_aff *ma2);
4349 The function C<isl_multi_aff_lex_le_set> returns a set
4350 containing those elements in the shared domain space
4351 where C<ma1> is lexicographically smaller than or
4354 An expression can be read from input using
4356 #include <isl/aff.h>
4357 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4358 isl_ctx *ctx, const char *str);
4359 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4360 isl_ctx *ctx, const char *str);
4361 __isl_give isl_union_pw_multi_aff *
4362 isl_union_pw_multi_aff_read_from_str(
4363 isl_ctx *ctx, const char *str);
4365 An expression can be printed using
4367 #include <isl/aff.h>
4368 __isl_give isl_printer *isl_printer_print_multi_aff(
4369 __isl_take isl_printer *p,
4370 __isl_keep isl_multi_aff *maff);
4371 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4372 __isl_take isl_printer *p,
4373 __isl_keep isl_pw_multi_aff *pma);
4374 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4375 __isl_take isl_printer *p,
4376 __isl_keep isl_union_pw_multi_aff *upma);
4377 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4378 __isl_take isl_printer *p,
4379 __isl_keep isl_multi_pw_aff *mpa);
4383 Points are elements of a set. They can be used to construct
4384 simple sets (boxes) or they can be used to represent the
4385 individual elements of a set.
4386 The zero point (the origin) can be created using
4388 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4390 The coordinates of a point can be inspected, set and changed
4393 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4394 enum isl_dim_type type, int pos, isl_int *v);
4395 __isl_give isl_point *isl_point_set_coordinate(
4396 __isl_take isl_point *pnt,
4397 enum isl_dim_type type, int pos, isl_int v);
4398 __isl_give isl_point *isl_point_set_coordinate_val(
4399 __isl_take isl_point *pnt,
4400 enum isl_dim_type type, int pos,
4401 __isl_take isl_val *v);
4403 __isl_give isl_point *isl_point_add_ui(
4404 __isl_take isl_point *pnt,
4405 enum isl_dim_type type, int pos, unsigned val);
4406 __isl_give isl_point *isl_point_sub_ui(
4407 __isl_take isl_point *pnt,
4408 enum isl_dim_type type, int pos, unsigned val);
4410 Other properties can be obtained using
4412 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4414 Points can be copied or freed using
4416 __isl_give isl_point *isl_point_copy(
4417 __isl_keep isl_point *pnt);
4418 void isl_point_free(__isl_take isl_point *pnt);
4420 A singleton set can be created from a point using
4422 __isl_give isl_basic_set *isl_basic_set_from_point(
4423 __isl_take isl_point *pnt);
4424 __isl_give isl_set *isl_set_from_point(
4425 __isl_take isl_point *pnt);
4427 and a box can be created from two opposite extremal points using
4429 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4430 __isl_take isl_point *pnt1,
4431 __isl_take isl_point *pnt2);
4432 __isl_give isl_set *isl_set_box_from_points(
4433 __isl_take isl_point *pnt1,
4434 __isl_take isl_point *pnt2);
4436 All elements of a B<bounded> (union) set can be enumerated using
4437 the following functions.
4439 int isl_set_foreach_point(__isl_keep isl_set *set,
4440 int (*fn)(__isl_take isl_point *pnt, void *user),
4442 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4443 int (*fn)(__isl_take isl_point *pnt, void *user),
4446 The function C<fn> is called for each integer point in
4447 C<set> with as second argument the last argument of
4448 the C<isl_set_foreach_point> call. The function C<fn>
4449 should return C<0> on success and C<-1> on failure.
4450 In the latter case, C<isl_set_foreach_point> will stop
4451 enumerating and return C<-1> as well.
4452 If the enumeration is performed successfully and to completion,
4453 then C<isl_set_foreach_point> returns C<0>.
4455 To obtain a single point of a (basic) set, use
4457 __isl_give isl_point *isl_basic_set_sample_point(
4458 __isl_take isl_basic_set *bset);
4459 __isl_give isl_point *isl_set_sample_point(
4460 __isl_take isl_set *set);
4462 If C<set> does not contain any (integer) points, then the
4463 resulting point will be ``void'', a property that can be
4466 int isl_point_is_void(__isl_keep isl_point *pnt);
4468 =head2 Piecewise Quasipolynomials
4470 A piecewise quasipolynomial is a particular kind of function that maps
4471 a parametric point to a rational value.
4472 More specifically, a quasipolynomial is a polynomial expression in greatest
4473 integer parts of affine expressions of parameters and variables.
4474 A piecewise quasipolynomial is a subdivision of a given parametric
4475 domain into disjoint cells with a quasipolynomial associated to
4476 each cell. The value of the piecewise quasipolynomial at a given
4477 point is the value of the quasipolynomial associated to the cell
4478 that contains the point. Outside of the union of cells,
4479 the value is assumed to be zero.
4480 For example, the piecewise quasipolynomial
4482 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4484 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4485 A given piecewise quasipolynomial has a fixed domain dimension.
4486 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4487 defined over different domains.
4488 Piecewise quasipolynomials are mainly used by the C<barvinok>
4489 library for representing the number of elements in a parametric set or map.
4490 For example, the piecewise quasipolynomial above represents
4491 the number of points in the map
4493 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4495 =head3 Input and Output
4497 Piecewise quasipolynomials can be read from input using
4499 __isl_give isl_union_pw_qpolynomial *
4500 isl_union_pw_qpolynomial_read_from_str(
4501 isl_ctx *ctx, const char *str);
4503 Quasipolynomials and piecewise quasipolynomials can be printed
4504 using the following functions.
4506 __isl_give isl_printer *isl_printer_print_qpolynomial(
4507 __isl_take isl_printer *p,
4508 __isl_keep isl_qpolynomial *qp);
4510 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4511 __isl_take isl_printer *p,
4512 __isl_keep isl_pw_qpolynomial *pwqp);
4514 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4515 __isl_take isl_printer *p,
4516 __isl_keep isl_union_pw_qpolynomial *upwqp);
4518 The output format of the printer
4519 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4520 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4522 In case of printing in C<ISL_FORMAT_C>, the user may want
4523 to set the names of all dimensions
4525 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4526 __isl_take isl_qpolynomial *qp,
4527 enum isl_dim_type type, unsigned pos,
4529 __isl_give isl_pw_qpolynomial *
4530 isl_pw_qpolynomial_set_dim_name(
4531 __isl_take isl_pw_qpolynomial *pwqp,
4532 enum isl_dim_type type, unsigned pos,
4535 =head3 Creating New (Piecewise) Quasipolynomials
4537 Some simple quasipolynomials can be created using the following functions.
4538 More complicated quasipolynomials can be created by applying
4539 operations such as addition and multiplication
4540 on the resulting quasipolynomials
4542 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4543 __isl_take isl_space *domain);
4544 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4545 __isl_take isl_space *domain);
4546 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4547 __isl_take isl_space *domain);
4548 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4549 __isl_take isl_space *domain);
4550 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4551 __isl_take isl_space *domain);
4552 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4553 __isl_take isl_space *domain,
4554 const isl_int n, const isl_int d);
4555 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4556 __isl_take isl_space *domain,
4557 enum isl_dim_type type, unsigned pos);
4558 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4559 __isl_take isl_aff *aff);
4561 Note that the space in which a quasipolynomial lives is a map space
4562 with a one-dimensional range. The C<domain> argument in some of
4563 the functions above corresponds to the domain of this map space.
4565 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4566 with a single cell can be created using the following functions.
4567 Multiple of these single cell piecewise quasipolynomials can
4568 be combined to create more complicated piecewise quasipolynomials.
4570 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4571 __isl_take isl_space *space);
4572 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4573 __isl_take isl_set *set,
4574 __isl_take isl_qpolynomial *qp);
4575 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4576 __isl_take isl_qpolynomial *qp);
4577 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4578 __isl_take isl_pw_aff *pwaff);
4580 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4581 __isl_take isl_space *space);
4582 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4583 __isl_take isl_pw_qpolynomial *pwqp);
4584 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4585 __isl_take isl_union_pw_qpolynomial *upwqp,
4586 __isl_take isl_pw_qpolynomial *pwqp);
4588 Quasipolynomials can be copied and freed again using the following
4591 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4592 __isl_keep isl_qpolynomial *qp);
4593 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4595 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4596 __isl_keep isl_pw_qpolynomial *pwqp);
4597 void *isl_pw_qpolynomial_free(
4598 __isl_take isl_pw_qpolynomial *pwqp);
4600 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4601 __isl_keep isl_union_pw_qpolynomial *upwqp);
4602 void *isl_union_pw_qpolynomial_free(
4603 __isl_take isl_union_pw_qpolynomial *upwqp);
4605 =head3 Inspecting (Piecewise) Quasipolynomials
4607 To iterate over all piecewise quasipolynomials in a union
4608 piecewise quasipolynomial, use the following function
4610 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4611 __isl_keep isl_union_pw_qpolynomial *upwqp,
4612 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4615 To extract the piecewise quasipolynomial in a given space from a union, use
4617 __isl_give isl_pw_qpolynomial *
4618 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4619 __isl_keep isl_union_pw_qpolynomial *upwqp,
4620 __isl_take isl_space *space);
4622 To iterate over the cells in a piecewise quasipolynomial,
4623 use either of the following two functions
4625 int isl_pw_qpolynomial_foreach_piece(
4626 __isl_keep isl_pw_qpolynomial *pwqp,
4627 int (*fn)(__isl_take isl_set *set,
4628 __isl_take isl_qpolynomial *qp,
4629 void *user), void *user);
4630 int isl_pw_qpolynomial_foreach_lifted_piece(
4631 __isl_keep isl_pw_qpolynomial *pwqp,
4632 int (*fn)(__isl_take isl_set *set,
4633 __isl_take isl_qpolynomial *qp,
4634 void *user), void *user);
4636 As usual, the function C<fn> should return C<0> on success
4637 and C<-1> on failure. The difference between
4638 C<isl_pw_qpolynomial_foreach_piece> and
4639 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4640 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4641 compute unique representations for all existentially quantified
4642 variables and then turn these existentially quantified variables
4643 into extra set variables, adapting the associated quasipolynomial
4644 accordingly. This means that the C<set> passed to C<fn>
4645 will not have any existentially quantified variables, but that
4646 the dimensions of the sets may be different for different
4647 invocations of C<fn>.
4649 To iterate over all terms in a quasipolynomial,
4652 int isl_qpolynomial_foreach_term(
4653 __isl_keep isl_qpolynomial *qp,
4654 int (*fn)(__isl_take isl_term *term,
4655 void *user), void *user);
4657 The terms themselves can be inspected and freed using
4660 unsigned isl_term_dim(__isl_keep isl_term *term,
4661 enum isl_dim_type type);
4662 void isl_term_get_num(__isl_keep isl_term *term,
4664 void isl_term_get_den(__isl_keep isl_term *term,
4666 int isl_term_get_exp(__isl_keep isl_term *term,
4667 enum isl_dim_type type, unsigned pos);
4668 __isl_give isl_aff *isl_term_get_div(
4669 __isl_keep isl_term *term, unsigned pos);
4670 void isl_term_free(__isl_take isl_term *term);
4672 Each term is a product of parameters, set variables and
4673 integer divisions. The function C<isl_term_get_exp>
4674 returns the exponent of a given dimensions in the given term.
4675 The C<isl_int>s in the arguments of C<isl_term_get_num>
4676 and C<isl_term_get_den> need to have been initialized
4677 using C<isl_int_init> before calling these functions.
4679 =head3 Properties of (Piecewise) Quasipolynomials
4681 To check whether a quasipolynomial is actually a constant,
4682 use the following function.
4684 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4685 isl_int *n, isl_int *d);
4687 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4688 then the numerator and denominator of the constant
4689 are returned in C<*n> and C<*d>, respectively.
4691 To check whether two union piecewise quasipolynomials are
4692 obviously equal, use
4694 int isl_union_pw_qpolynomial_plain_is_equal(
4695 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4696 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4698 =head3 Operations on (Piecewise) Quasipolynomials
4700 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4701 __isl_take isl_qpolynomial *qp, isl_int v);
4702 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4703 __isl_take isl_qpolynomial *qp);
4704 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4705 __isl_take isl_qpolynomial *qp1,
4706 __isl_take isl_qpolynomial *qp2);
4707 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4708 __isl_take isl_qpolynomial *qp1,
4709 __isl_take isl_qpolynomial *qp2);
4710 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4711 __isl_take isl_qpolynomial *qp1,
4712 __isl_take isl_qpolynomial *qp2);
4713 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4714 __isl_take isl_qpolynomial *qp, unsigned exponent);
4716 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4717 __isl_take isl_pw_qpolynomial *pwqp1,
4718 __isl_take isl_pw_qpolynomial *pwqp2);
4719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4720 __isl_take isl_pw_qpolynomial *pwqp1,
4721 __isl_take isl_pw_qpolynomial *pwqp2);
4722 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4723 __isl_take isl_pw_qpolynomial *pwqp1,
4724 __isl_take isl_pw_qpolynomial *pwqp2);
4725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4726 __isl_take isl_pw_qpolynomial *pwqp);
4727 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4728 __isl_take isl_pw_qpolynomial *pwqp1,
4729 __isl_take isl_pw_qpolynomial *pwqp2);
4730 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4731 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4733 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4734 __isl_take isl_union_pw_qpolynomial *upwqp1,
4735 __isl_take isl_union_pw_qpolynomial *upwqp2);
4736 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4737 __isl_take isl_union_pw_qpolynomial *upwqp1,
4738 __isl_take isl_union_pw_qpolynomial *upwqp2);
4739 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4740 __isl_take isl_union_pw_qpolynomial *upwqp1,
4741 __isl_take isl_union_pw_qpolynomial *upwqp2);
4743 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4744 __isl_take isl_pw_qpolynomial *pwqp,
4745 __isl_take isl_point *pnt);
4747 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4748 __isl_take isl_union_pw_qpolynomial *upwqp,
4749 __isl_take isl_point *pnt);
4751 __isl_give isl_set *isl_pw_qpolynomial_domain(
4752 __isl_take isl_pw_qpolynomial *pwqp);
4753 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4754 __isl_take isl_pw_qpolynomial *pwpq,
4755 __isl_take isl_set *set);
4756 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4757 __isl_take isl_pw_qpolynomial *pwpq,
4758 __isl_take isl_set *set);
4760 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4761 __isl_take isl_union_pw_qpolynomial *upwqp);
4762 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4763 __isl_take isl_union_pw_qpolynomial *upwpq,
4764 __isl_take isl_union_set *uset);
4765 __isl_give isl_union_pw_qpolynomial *
4766 isl_union_pw_qpolynomial_intersect_params(
4767 __isl_take isl_union_pw_qpolynomial *upwpq,
4768 __isl_take isl_set *set);
4770 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4771 __isl_take isl_qpolynomial *qp,
4772 __isl_take isl_space *model);
4774 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4775 __isl_take isl_qpolynomial *qp);
4776 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4777 __isl_take isl_pw_qpolynomial *pwqp);
4779 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4780 __isl_take isl_union_pw_qpolynomial *upwqp);
4782 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4783 __isl_take isl_qpolynomial *qp,
4784 __isl_take isl_set *context);
4785 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4786 __isl_take isl_qpolynomial *qp,
4787 __isl_take isl_set *context);
4789 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4790 __isl_take isl_pw_qpolynomial *pwqp,
4791 __isl_take isl_set *context);
4792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4793 __isl_take isl_pw_qpolynomial *pwqp,
4794 __isl_take isl_set *context);
4796 __isl_give isl_union_pw_qpolynomial *
4797 isl_union_pw_qpolynomial_gist_params(
4798 __isl_take isl_union_pw_qpolynomial *upwqp,
4799 __isl_take isl_set *context);
4800 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4801 __isl_take isl_union_pw_qpolynomial *upwqp,
4802 __isl_take isl_union_set *context);
4804 The gist operation applies the gist operation to each of
4805 the cells in the domain of the input piecewise quasipolynomial.
4806 The context is also exploited
4807 to simplify the quasipolynomials associated to each cell.
4809 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4810 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4811 __isl_give isl_union_pw_qpolynomial *
4812 isl_union_pw_qpolynomial_to_polynomial(
4813 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4815 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4816 the polynomial will be an overapproximation. If C<sign> is negative,
4817 it will be an underapproximation. If C<sign> is zero, the approximation
4818 will lie somewhere in between.
4820 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4822 A piecewise quasipolynomial reduction is a piecewise
4823 reduction (or fold) of quasipolynomials.
4824 In particular, the reduction can be maximum or a minimum.
4825 The objects are mainly used to represent the result of
4826 an upper or lower bound on a quasipolynomial over its domain,
4827 i.e., as the result of the following function.
4829 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4830 __isl_take isl_pw_qpolynomial *pwqp,
4831 enum isl_fold type, int *tight);
4833 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4834 __isl_take isl_union_pw_qpolynomial *upwqp,
4835 enum isl_fold type, int *tight);
4837 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4838 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4839 is the returned bound is known be tight, i.e., for each value
4840 of the parameters there is at least
4841 one element in the domain that reaches the bound.
4842 If the domain of C<pwqp> is not wrapping, then the bound is computed
4843 over all elements in that domain and the result has a purely parametric
4844 domain. If the domain of C<pwqp> is wrapping, then the bound is
4845 computed over the range of the wrapped relation. The domain of the
4846 wrapped relation becomes the domain of the result.
4848 A (piecewise) quasipolynomial reduction can be copied or freed using the
4849 following functions.
4851 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4852 __isl_keep isl_qpolynomial_fold *fold);
4853 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4854 __isl_keep isl_pw_qpolynomial_fold *pwf);
4855 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4856 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4857 void isl_qpolynomial_fold_free(
4858 __isl_take isl_qpolynomial_fold *fold);
4859 void *isl_pw_qpolynomial_fold_free(
4860 __isl_take isl_pw_qpolynomial_fold *pwf);
4861 void *isl_union_pw_qpolynomial_fold_free(
4862 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4864 =head3 Printing Piecewise Quasipolynomial Reductions
4866 Piecewise quasipolynomial reductions can be printed
4867 using the following function.
4869 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4870 __isl_take isl_printer *p,
4871 __isl_keep isl_pw_qpolynomial_fold *pwf);
4872 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4873 __isl_take isl_printer *p,
4874 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4876 For C<isl_printer_print_pw_qpolynomial_fold>,
4877 output format of the printer
4878 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4879 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4880 output format of the printer
4881 needs to be set to C<ISL_FORMAT_ISL>.
4882 In case of printing in C<ISL_FORMAT_C>, the user may want
4883 to set the names of all dimensions
4885 __isl_give isl_pw_qpolynomial_fold *
4886 isl_pw_qpolynomial_fold_set_dim_name(
4887 __isl_take isl_pw_qpolynomial_fold *pwf,
4888 enum isl_dim_type type, unsigned pos,
4891 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4893 To iterate over all piecewise quasipolynomial reductions in a union
4894 piecewise quasipolynomial reduction, use the following function
4896 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4897 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4898 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4899 void *user), void *user);
4901 To iterate over the cells in a piecewise quasipolynomial reduction,
4902 use either of the following two functions
4904 int isl_pw_qpolynomial_fold_foreach_piece(
4905 __isl_keep isl_pw_qpolynomial_fold *pwf,
4906 int (*fn)(__isl_take isl_set *set,
4907 __isl_take isl_qpolynomial_fold *fold,
4908 void *user), void *user);
4909 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4910 __isl_keep isl_pw_qpolynomial_fold *pwf,
4911 int (*fn)(__isl_take isl_set *set,
4912 __isl_take isl_qpolynomial_fold *fold,
4913 void *user), void *user);
4915 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4916 of the difference between these two functions.
4918 To iterate over all quasipolynomials in a reduction, use
4920 int isl_qpolynomial_fold_foreach_qpolynomial(
4921 __isl_keep isl_qpolynomial_fold *fold,
4922 int (*fn)(__isl_take isl_qpolynomial *qp,
4923 void *user), void *user);
4925 =head3 Properties of Piecewise Quasipolynomial Reductions
4927 To check whether two union piecewise quasipolynomial reductions are
4928 obviously equal, use
4930 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4931 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4932 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4934 =head3 Operations on Piecewise Quasipolynomial Reductions
4936 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4937 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4939 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4940 __isl_take isl_pw_qpolynomial_fold *pwf1,
4941 __isl_take isl_pw_qpolynomial_fold *pwf2);
4943 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4944 __isl_take isl_pw_qpolynomial_fold *pwf1,
4945 __isl_take isl_pw_qpolynomial_fold *pwf2);
4947 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4948 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4949 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4951 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4952 __isl_take isl_pw_qpolynomial_fold *pwf,
4953 __isl_take isl_point *pnt);
4955 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4956 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4957 __isl_take isl_point *pnt);
4959 __isl_give isl_pw_qpolynomial_fold *
4960 isl_pw_qpolynomial_fold_intersect_params(
4961 __isl_take isl_pw_qpolynomial_fold *pwf,
4962 __isl_take isl_set *set);
4964 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4965 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4966 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4967 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4968 __isl_take isl_union_set *uset);
4969 __isl_give isl_union_pw_qpolynomial_fold *
4970 isl_union_pw_qpolynomial_fold_intersect_params(
4971 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4972 __isl_take isl_set *set);
4974 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4975 __isl_take isl_pw_qpolynomial_fold *pwf);
4977 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4978 __isl_take isl_pw_qpolynomial_fold *pwf);
4980 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4981 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4983 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4984 __isl_take isl_qpolynomial_fold *fold,
4985 __isl_take isl_set *context);
4986 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4987 __isl_take isl_qpolynomial_fold *fold,
4988 __isl_take isl_set *context);
4990 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4991 __isl_take isl_pw_qpolynomial_fold *pwf,
4992 __isl_take isl_set *context);
4993 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4994 __isl_take isl_pw_qpolynomial_fold *pwf,
4995 __isl_take isl_set *context);
4997 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4998 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4999 __isl_take isl_union_set *context);
5000 __isl_give isl_union_pw_qpolynomial_fold *
5001 isl_union_pw_qpolynomial_fold_gist_params(
5002 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5003 __isl_take isl_set *context);
5005 The gist operation applies the gist operation to each of
5006 the cells in the domain of the input piecewise quasipolynomial reduction.
5007 In future, the operation will also exploit the context
5008 to simplify the quasipolynomial reductions associated to each cell.
5010 __isl_give isl_pw_qpolynomial_fold *
5011 isl_set_apply_pw_qpolynomial_fold(
5012 __isl_take isl_set *set,
5013 __isl_take isl_pw_qpolynomial_fold *pwf,
5015 __isl_give isl_pw_qpolynomial_fold *
5016 isl_map_apply_pw_qpolynomial_fold(
5017 __isl_take isl_map *map,
5018 __isl_take isl_pw_qpolynomial_fold *pwf,
5020 __isl_give isl_union_pw_qpolynomial_fold *
5021 isl_union_set_apply_union_pw_qpolynomial_fold(
5022 __isl_take isl_union_set *uset,
5023 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5025 __isl_give isl_union_pw_qpolynomial_fold *
5026 isl_union_map_apply_union_pw_qpolynomial_fold(
5027 __isl_take isl_union_map *umap,
5028 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5031 The functions taking a map
5032 compose the given map with the given piecewise quasipolynomial reduction.
5033 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5034 over all elements in the intersection of the range of the map
5035 and the domain of the piecewise quasipolynomial reduction
5036 as a function of an element in the domain of the map.
5037 The functions taking a set compute a bound over all elements in the
5038 intersection of the set and the domain of the
5039 piecewise quasipolynomial reduction.
5041 =head2 Parametric Vertex Enumeration
5043 The parametric vertex enumeration described in this section
5044 is mainly intended to be used internally and by the C<barvinok>
5047 #include <isl/vertices.h>
5048 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5049 __isl_keep isl_basic_set *bset);
5051 The function C<isl_basic_set_compute_vertices> performs the
5052 actual computation of the parametric vertices and the chamber
5053 decomposition and store the result in an C<isl_vertices> object.
5054 This information can be queried by either iterating over all
5055 the vertices or iterating over all the chambers or cells
5056 and then iterating over all vertices that are active on the chamber.
5058 int isl_vertices_foreach_vertex(
5059 __isl_keep isl_vertices *vertices,
5060 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5063 int isl_vertices_foreach_cell(
5064 __isl_keep isl_vertices *vertices,
5065 int (*fn)(__isl_take isl_cell *cell, void *user),
5067 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5068 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5071 Other operations that can be performed on an C<isl_vertices> object are
5074 isl_ctx *isl_vertices_get_ctx(
5075 __isl_keep isl_vertices *vertices);
5076 int isl_vertices_get_n_vertices(
5077 __isl_keep isl_vertices *vertices);
5078 void isl_vertices_free(__isl_take isl_vertices *vertices);
5080 Vertices can be inspected and destroyed using the following functions.
5082 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5083 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5084 __isl_give isl_basic_set *isl_vertex_get_domain(
5085 __isl_keep isl_vertex *vertex);
5086 __isl_give isl_basic_set *isl_vertex_get_expr(
5087 __isl_keep isl_vertex *vertex);
5088 void isl_vertex_free(__isl_take isl_vertex *vertex);
5090 C<isl_vertex_get_expr> returns a singleton parametric set describing
5091 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5093 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5094 B<rational> basic sets, so they should mainly be used for inspection
5095 and should not be mixed with integer sets.
5097 Chambers can be inspected and destroyed using the following functions.
5099 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5100 __isl_give isl_basic_set *isl_cell_get_domain(
5101 __isl_keep isl_cell *cell);
5102 void isl_cell_free(__isl_take isl_cell *cell);
5104 =head1 Polyhedral Compilation Library
5106 This section collects functionality in C<isl> that has been specifically
5107 designed for use during polyhedral compilation.
5109 =head2 Dependence Analysis
5111 C<isl> contains specialized functionality for performing
5112 array dataflow analysis. That is, given a I<sink> access relation
5113 and a collection of possible I<source> access relations,
5114 C<isl> can compute relations that describe
5115 for each iteration of the sink access, which iteration
5116 of which of the source access relations was the last
5117 to access the same data element before the given iteration
5119 The resulting dependence relations map source iterations
5120 to the corresponding sink iterations.
5121 To compute standard flow dependences, the sink should be
5122 a read, while the sources should be writes.
5123 If any of the source accesses are marked as being I<may>
5124 accesses, then there will be a dependence from the last
5125 I<must> access B<and> from any I<may> access that follows
5126 this last I<must> access.
5127 In particular, if I<all> sources are I<may> accesses,
5128 then memory based dependence analysis is performed.
5129 If, on the other hand, all sources are I<must> accesses,
5130 then value based dependence analysis is performed.
5132 #include <isl/flow.h>
5134 typedef int (*isl_access_level_before)(void *first, void *second);
5136 __isl_give isl_access_info *isl_access_info_alloc(
5137 __isl_take isl_map *sink,
5138 void *sink_user, isl_access_level_before fn,
5140 __isl_give isl_access_info *isl_access_info_add_source(
5141 __isl_take isl_access_info *acc,
5142 __isl_take isl_map *source, int must,
5144 void *isl_access_info_free(__isl_take isl_access_info *acc);
5146 __isl_give isl_flow *isl_access_info_compute_flow(
5147 __isl_take isl_access_info *acc);
5149 int isl_flow_foreach(__isl_keep isl_flow *deps,
5150 int (*fn)(__isl_take isl_map *dep, int must,
5151 void *dep_user, void *user),
5153 __isl_give isl_map *isl_flow_get_no_source(
5154 __isl_keep isl_flow *deps, int must);
5155 void isl_flow_free(__isl_take isl_flow *deps);
5157 The function C<isl_access_info_compute_flow> performs the actual
5158 dependence analysis. The other functions are used to construct
5159 the input for this function or to read off the output.
5161 The input is collected in an C<isl_access_info>, which can
5162 be created through a call to C<isl_access_info_alloc>.
5163 The arguments to this functions are the sink access relation
5164 C<sink>, a token C<sink_user> used to identify the sink
5165 access to the user, a callback function for specifying the
5166 relative order of source and sink accesses, and the number
5167 of source access relations that will be added.
5168 The callback function has type C<int (*)(void *first, void *second)>.
5169 The function is called with two user supplied tokens identifying
5170 either a source or the sink and it should return the shared nesting
5171 level and the relative order of the two accesses.
5172 In particular, let I<n> be the number of loops shared by
5173 the two accesses. If C<first> precedes C<second> textually,
5174 then the function should return I<2 * n + 1>; otherwise,
5175 it should return I<2 * n>.
5176 The sources can be added to the C<isl_access_info> by performing
5177 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5178 C<must> indicates whether the source is a I<must> access
5179 or a I<may> access. Note that a multi-valued access relation
5180 should only be marked I<must> if every iteration in the domain
5181 of the relation accesses I<all> elements in its image.
5182 The C<source_user> token is again used to identify
5183 the source access. The range of the source access relation
5184 C<source> should have the same dimension as the range
5185 of the sink access relation.
5186 The C<isl_access_info_free> function should usually not be
5187 called explicitly, because it is called implicitly by
5188 C<isl_access_info_compute_flow>.
5190 The result of the dependence analysis is collected in an
5191 C<isl_flow>. There may be elements of
5192 the sink access for which no preceding source access could be
5193 found or for which all preceding sources are I<may> accesses.
5194 The relations containing these elements can be obtained through
5195 calls to C<isl_flow_get_no_source>, the first with C<must> set
5196 and the second with C<must> unset.
5197 In the case of standard flow dependence analysis,
5198 with the sink a read and the sources I<must> writes,
5199 the first relation corresponds to the reads from uninitialized
5200 array elements and the second relation is empty.
5201 The actual flow dependences can be extracted using
5202 C<isl_flow_foreach>. This function will call the user-specified
5203 callback function C<fn> for each B<non-empty> dependence between
5204 a source and the sink. The callback function is called
5205 with four arguments, the actual flow dependence relation
5206 mapping source iterations to sink iterations, a boolean that
5207 indicates whether it is a I<must> or I<may> dependence, a token
5208 identifying the source and an additional C<void *> with value
5209 equal to the third argument of the C<isl_flow_foreach> call.
5210 A dependence is marked I<must> if it originates from a I<must>
5211 source and if it is not followed by any I<may> sources.
5213 After finishing with an C<isl_flow>, the user should call
5214 C<isl_flow_free> to free all associated memory.
5216 A higher-level interface to dependence analysis is provided
5217 by the following function.
5219 #include <isl/flow.h>
5221 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5222 __isl_take isl_union_map *must_source,
5223 __isl_take isl_union_map *may_source,
5224 __isl_take isl_union_map *schedule,
5225 __isl_give isl_union_map **must_dep,
5226 __isl_give isl_union_map **may_dep,
5227 __isl_give isl_union_map **must_no_source,
5228 __isl_give isl_union_map **may_no_source);
5230 The arrays are identified by the tuple names of the ranges
5231 of the accesses. The iteration domains by the tuple names
5232 of the domains of the accesses and of the schedule.
5233 The relative order of the iteration domains is given by the
5234 schedule. The relations returned through C<must_no_source>
5235 and C<may_no_source> are subsets of C<sink>.
5236 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5237 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5238 any of the other arguments is treated as an error.
5240 =head3 Interaction with Dependence Analysis
5242 During the dependence analysis, we frequently need to perform
5243 the following operation. Given a relation between sink iterations
5244 and potential source iterations from a particular source domain,
5245 what is the last potential source iteration corresponding to each
5246 sink iteration. It can sometimes be convenient to adjust
5247 the set of potential source iterations before or after each such operation.
5248 The prototypical example is fuzzy array dataflow analysis,
5249 where we need to analyze if, based on data-dependent constraints,
5250 the sink iteration can ever be executed without one or more of
5251 the corresponding potential source iterations being executed.
5252 If so, we can introduce extra parameters and select an unknown
5253 but fixed source iteration from the potential source iterations.
5254 To be able to perform such manipulations, C<isl> provides the following
5257 #include <isl/flow.h>
5259 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5260 __isl_keep isl_map *source_map,
5261 __isl_keep isl_set *sink, void *source_user,
5263 __isl_give isl_access_info *isl_access_info_set_restrict(
5264 __isl_take isl_access_info *acc,
5265 isl_access_restrict fn, void *user);
5267 The function C<isl_access_info_set_restrict> should be called
5268 before calling C<isl_access_info_compute_flow> and registers a callback function
5269 that will be called any time C<isl> is about to compute the last
5270 potential source. The first argument is the (reverse) proto-dependence,
5271 mapping sink iterations to potential source iterations.
5272 The second argument represents the sink iterations for which
5273 we want to compute the last source iteration.
5274 The third argument is the token corresponding to the source
5275 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5276 The callback is expected to return a restriction on either the input or
5277 the output of the operation computing the last potential source.
5278 If the input needs to be restricted then restrictions are needed
5279 for both the source and the sink iterations. The sink iterations
5280 and the potential source iterations will be intersected with these sets.
5281 If the output needs to be restricted then only a restriction on the source
5282 iterations is required.
5283 If any error occurs, the callback should return C<NULL>.
5284 An C<isl_restriction> object can be created, freed and inspected
5285 using the following functions.
5287 #include <isl/flow.h>
5289 __isl_give isl_restriction *isl_restriction_input(
5290 __isl_take isl_set *source_restr,
5291 __isl_take isl_set *sink_restr);
5292 __isl_give isl_restriction *isl_restriction_output(
5293 __isl_take isl_set *source_restr);
5294 __isl_give isl_restriction *isl_restriction_none(
5295 __isl_take isl_map *source_map);
5296 __isl_give isl_restriction *isl_restriction_empty(
5297 __isl_take isl_map *source_map);
5298 void *isl_restriction_free(
5299 __isl_take isl_restriction *restr);
5300 isl_ctx *isl_restriction_get_ctx(
5301 __isl_keep isl_restriction *restr);
5303 C<isl_restriction_none> and C<isl_restriction_empty> are special
5304 cases of C<isl_restriction_input>. C<isl_restriction_none>
5305 is essentially equivalent to
5307 isl_restriction_input(isl_set_universe(
5308 isl_space_range(isl_map_get_space(source_map))),
5310 isl_space_domain(isl_map_get_space(source_map))));
5312 whereas C<isl_restriction_empty> is essentially equivalent to
5314 isl_restriction_input(isl_set_empty(
5315 isl_space_range(isl_map_get_space(source_map))),
5317 isl_space_domain(isl_map_get_space(source_map))));
5321 B<The functionality described in this section is fairly new
5322 and may be subject to change.>
5324 The following function can be used to compute a schedule
5325 for a union of domains.
5326 By default, the algorithm used to construct the schedule is similar
5327 to that of C<Pluto>.
5328 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5330 The generated schedule respects all C<validity> dependences.
5331 That is, all dependence distances over these dependences in the
5332 scheduled space are lexicographically positive.
5333 The default algorithm tries to minimize the dependence distances over
5334 C<proximity> dependences.
5335 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5336 for groups of domains where the dependence distances have only
5337 non-negative values.
5338 When using Feautrier's algorithm, the C<proximity> dependence
5339 distances are only minimized during the extension to a
5340 full-dimensional schedule.
5342 #include <isl/schedule.h>
5343 __isl_give isl_schedule *isl_union_set_compute_schedule(
5344 __isl_take isl_union_set *domain,
5345 __isl_take isl_union_map *validity,
5346 __isl_take isl_union_map *proximity);
5347 void *isl_schedule_free(__isl_take isl_schedule *sched);
5349 A mapping from the domains to the scheduled space can be obtained
5350 from an C<isl_schedule> using the following function.
5352 __isl_give isl_union_map *isl_schedule_get_map(
5353 __isl_keep isl_schedule *sched);
5355 A representation of the schedule can be printed using
5357 __isl_give isl_printer *isl_printer_print_schedule(
5358 __isl_take isl_printer *p,
5359 __isl_keep isl_schedule *schedule);
5361 A representation of the schedule as a forest of bands can be obtained
5362 using the following function.
5364 __isl_give isl_band_list *isl_schedule_get_band_forest(
5365 __isl_keep isl_schedule *schedule);
5367 The individual bands can be visited in depth-first post-order
5368 using the following function.
5370 #include <isl/schedule.h>
5371 int isl_schedule_foreach_band(
5372 __isl_keep isl_schedule *sched,
5373 int (*fn)(__isl_keep isl_band *band, void *user),
5376 The list can be manipulated as explained in L<"Lists">.
5377 The bands inside the list can be copied and freed using the following
5380 #include <isl/band.h>
5381 __isl_give isl_band *isl_band_copy(
5382 __isl_keep isl_band *band);
5383 void *isl_band_free(__isl_take isl_band *band);
5385 Each band contains zero or more scheduling dimensions.
5386 These are referred to as the members of the band.
5387 The section of the schedule that corresponds to the band is
5388 referred to as the partial schedule of the band.
5389 For those nodes that participate in a band, the outer scheduling
5390 dimensions form the prefix schedule, while the inner scheduling
5391 dimensions form the suffix schedule.
5392 That is, if we take a cut of the band forest, then the union of
5393 the concatenations of the prefix, partial and suffix schedules of
5394 each band in the cut is equal to the entire schedule (modulo
5395 some possible padding at the end with zero scheduling dimensions).
5396 The properties of a band can be inspected using the following functions.
5398 #include <isl/band.h>
5399 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5401 int isl_band_has_children(__isl_keep isl_band *band);
5402 __isl_give isl_band_list *isl_band_get_children(
5403 __isl_keep isl_band *band);
5405 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5406 __isl_keep isl_band *band);
5407 __isl_give isl_union_map *isl_band_get_partial_schedule(
5408 __isl_keep isl_band *band);
5409 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5410 __isl_keep isl_band *band);
5412 int isl_band_n_member(__isl_keep isl_band *band);
5413 int isl_band_member_is_zero_distance(
5414 __isl_keep isl_band *band, int pos);
5416 int isl_band_list_foreach_band(
5417 __isl_keep isl_band_list *list,
5418 int (*fn)(__isl_keep isl_band *band, void *user),
5421 Note that a scheduling dimension is considered to be ``zero
5422 distance'' if it does not carry any proximity dependences
5424 That is, if the dependence distances of the proximity
5425 dependences are all zero in that direction (for fixed
5426 iterations of outer bands).
5427 Like C<isl_schedule_foreach_band>,
5428 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5429 in depth-first post-order.
5431 A band can be tiled using the following function.
5433 #include <isl/band.h>
5434 int isl_band_tile(__isl_keep isl_band *band,
5435 __isl_take isl_vec *sizes);
5437 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5439 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5440 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5442 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5444 The C<isl_band_tile> function tiles the band using the given tile sizes
5445 inside its schedule.
5446 A new child band is created to represent the point loops and it is
5447 inserted between the modified band and its children.
5448 The C<tile_scale_tile_loops> option specifies whether the tile
5449 loops iterators should be scaled by the tile sizes.
5450 If the C<tile_shift_point_loops> option is set, then the point loops
5451 are shifted to start at zero.
5453 A band can be split into two nested bands using the following function.
5455 int isl_band_split(__isl_keep isl_band *band, int pos);
5457 The resulting outer band contains the first C<pos> dimensions of C<band>
5458 while the inner band contains the remaining dimensions.
5460 A representation of the band can be printed using
5462 #include <isl/band.h>
5463 __isl_give isl_printer *isl_printer_print_band(
5464 __isl_take isl_printer *p,
5465 __isl_keep isl_band *band);
5469 #include <isl/schedule.h>
5470 int isl_options_set_schedule_max_coefficient(
5471 isl_ctx *ctx, int val);
5472 int isl_options_get_schedule_max_coefficient(
5474 int isl_options_set_schedule_max_constant_term(
5475 isl_ctx *ctx, int val);
5476 int isl_options_get_schedule_max_constant_term(
5478 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5479 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5480 int isl_options_set_schedule_maximize_band_depth(
5481 isl_ctx *ctx, int val);
5482 int isl_options_get_schedule_maximize_band_depth(
5484 int isl_options_set_schedule_outer_zero_distance(
5485 isl_ctx *ctx, int val);
5486 int isl_options_get_schedule_outer_zero_distance(
5488 int isl_options_set_schedule_split_scaled(
5489 isl_ctx *ctx, int val);
5490 int isl_options_get_schedule_split_scaled(
5492 int isl_options_set_schedule_algorithm(
5493 isl_ctx *ctx, int val);
5494 int isl_options_get_schedule_algorithm(
5496 int isl_options_set_schedule_separate_components(
5497 isl_ctx *ctx, int val);
5498 int isl_options_get_schedule_separate_components(
5503 =item * schedule_max_coefficient
5505 This option enforces that the coefficients for variable and parameter
5506 dimensions in the calculated schedule are not larger than the specified value.
5507 This option can significantly increase the speed of the scheduling calculation
5508 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5509 this option does not introduce bounds on the variable or parameter
5512 =item * schedule_max_constant_term
5514 This option enforces that the constant coefficients in the calculated schedule
5515 are not larger than the maximal constant term. This option can significantly
5516 increase the speed of the scheduling calculation and may also prevent fusing of
5517 unrelated dimensions. A value of -1 means that this option does not introduce
5518 bounds on the constant coefficients.
5520 =item * schedule_fuse
5522 This option controls the level of fusion.
5523 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5524 resulting schedule will be distributed as much as possible.
5525 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5526 try to fuse loops in the resulting schedule.
5528 =item * schedule_maximize_band_depth
5530 If this option is set, we do not split bands at the point
5531 where we detect splitting is necessary. Instead, we
5532 backtrack and split bands as early as possible. This
5533 reduces the number of splits and maximizes the width of
5534 the bands. Wider bands give more possibilities for tiling.
5535 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5536 then bands will be split as early as possible, even if there is no need.
5537 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5539 =item * schedule_outer_zero_distance
5541 If this option is set, then we try to construct schedules
5542 where the outermost scheduling dimension in each band
5543 results in a zero dependence distance over the proximity
5546 =item * schedule_split_scaled
5548 If this option is set, then we try to construct schedules in which the
5549 constant term is split off from the linear part if the linear parts of
5550 the scheduling rows for all nodes in the graphs have a common non-trivial
5552 The constant term is then placed in a separate band and the linear
5555 =item * schedule_algorithm
5557 Selects the scheduling algorithm to be used.
5558 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5559 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5561 =item * schedule_separate_components
5563 If at any point the dependence graph contains any (weakly connected) components,
5564 then these components are scheduled separately.
5565 If this option is not set, then some iterations of the domains
5566 in these components may be scheduled together.
5567 If this option is set, then the components are given consecutive
5572 =head2 AST Generation
5574 This section describes the C<isl> functionality for generating
5575 ASTs that visit all the elements
5576 in a domain in an order specified by a schedule.
5577 In particular, given a C<isl_union_map>, an AST is generated
5578 that visits all the elements in the domain of the C<isl_union_map>
5579 according to the lexicographic order of the corresponding image
5580 element(s). If the range of the C<isl_union_map> consists of
5581 elements in more than one space, then each of these spaces is handled
5582 separately in an arbitrary order.
5583 It should be noted that the image elements only specify the I<order>
5584 in which the corresponding domain elements should be visited.
5585 No direct relation between the image elements and the loop iterators
5586 in the generated AST should be assumed.
5588 Each AST is generated within a build. The initial build
5589 simply specifies the constraints on the parameters (if any)
5590 and can be created, inspected, copied and freed using the following functions.
5592 #include <isl/ast_build.h>
5593 __isl_give isl_ast_build *isl_ast_build_from_context(
5594 __isl_take isl_set *set);
5595 isl_ctx *isl_ast_build_get_ctx(
5596 __isl_keep isl_ast_build *build);
5597 __isl_give isl_ast_build *isl_ast_build_copy(
5598 __isl_keep isl_ast_build *build);
5599 void *isl_ast_build_free(
5600 __isl_take isl_ast_build *build);
5602 The C<set> argument is usually a parameter set with zero or more parameters.
5603 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5604 and L</"Fine-grained Control over AST Generation">.
5605 Finally, the AST itself can be constructed using the following
5608 #include <isl/ast_build.h>
5609 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5610 __isl_keep isl_ast_build *build,
5611 __isl_take isl_union_map *schedule);
5613 =head3 Inspecting the AST
5615 The basic properties of an AST node can be obtained as follows.
5617 #include <isl/ast.h>
5618 isl_ctx *isl_ast_node_get_ctx(
5619 __isl_keep isl_ast_node *node);
5620 enum isl_ast_node_type isl_ast_node_get_type(
5621 __isl_keep isl_ast_node *node);
5623 The type of an AST node is one of
5624 C<isl_ast_node_for>,
5626 C<isl_ast_node_block> or
5627 C<isl_ast_node_user>.
5628 An C<isl_ast_node_for> represents a for node.
5629 An C<isl_ast_node_if> represents an if node.
5630 An C<isl_ast_node_block> represents a compound node.
5631 An C<isl_ast_node_user> represents an expression statement.
5632 An expression statement typically corresponds to a domain element, i.e.,
5633 one of the elements that is visited by the AST.
5635 Each type of node has its own additional properties.
5637 #include <isl/ast.h>
5638 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5639 __isl_keep isl_ast_node *node);
5640 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5641 __isl_keep isl_ast_node *node);
5642 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5643 __isl_keep isl_ast_node *node);
5644 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5645 __isl_keep isl_ast_node *node);
5646 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5647 __isl_keep isl_ast_node *node);
5648 int isl_ast_node_for_is_degenerate(
5649 __isl_keep isl_ast_node *node);
5651 An C<isl_ast_for> is considered degenerate if it is known to execute
5654 #include <isl/ast.h>
5655 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5656 __isl_keep isl_ast_node *node);
5657 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5658 __isl_keep isl_ast_node *node);
5659 int isl_ast_node_if_has_else(
5660 __isl_keep isl_ast_node *node);
5661 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5662 __isl_keep isl_ast_node *node);
5664 __isl_give isl_ast_node_list *
5665 isl_ast_node_block_get_children(
5666 __isl_keep isl_ast_node *node);
5668 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5669 __isl_keep isl_ast_node *node);
5671 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5672 the following functions.
5674 #include <isl/ast.h>
5675 isl_ctx *isl_ast_expr_get_ctx(
5676 __isl_keep isl_ast_expr *expr);
5677 enum isl_ast_expr_type isl_ast_expr_get_type(
5678 __isl_keep isl_ast_expr *expr);
5680 The type of an AST expression is one of
5682 C<isl_ast_expr_id> or
5683 C<isl_ast_expr_int>.
5684 An C<isl_ast_expr_op> represents the result of an operation.
5685 An C<isl_ast_expr_id> represents an identifier.
5686 An C<isl_ast_expr_int> represents an integer value.
5688 Each type of expression has its own additional properties.
5690 #include <isl/ast.h>
5691 enum isl_ast_op_type isl_ast_expr_get_op_type(
5692 __isl_keep isl_ast_expr *expr);
5693 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5694 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5695 __isl_keep isl_ast_expr *expr, int pos);
5696 int isl_ast_node_foreach_ast_op_type(
5697 __isl_keep isl_ast_node *node,
5698 int (*fn)(enum isl_ast_op_type type, void *user),
5701 C<isl_ast_expr_get_op_type> returns the type of the operation
5702 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5703 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5705 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5706 C<isl_ast_op_type> that appears in C<node>.
5707 The operation type is one of the following.
5711 =item C<isl_ast_op_and>
5713 Logical I<and> of two arguments.
5714 Both arguments can be evaluated.
5716 =item C<isl_ast_op_and_then>
5718 Logical I<and> of two arguments.
5719 The second argument can only be evaluated if the first evaluates to true.
5721 =item C<isl_ast_op_or>
5723 Logical I<or> of two arguments.
5724 Both arguments can be evaluated.
5726 =item C<isl_ast_op_or_else>
5728 Logical I<or> of two arguments.
5729 The second argument can only be evaluated if the first evaluates to false.
5731 =item C<isl_ast_op_max>
5733 Maximum of two or more arguments.
5735 =item C<isl_ast_op_min>
5737 Minimum of two or more arguments.
5739 =item C<isl_ast_op_minus>
5743 =item C<isl_ast_op_add>
5745 Sum of two arguments.
5747 =item C<isl_ast_op_sub>
5749 Difference of two arguments.
5751 =item C<isl_ast_op_mul>
5753 Product of two arguments.
5755 =item C<isl_ast_op_div>
5757 Exact division. That is, the result is known to be an integer.
5759 =item C<isl_ast_op_fdiv_q>
5761 Result of integer division, rounded towards negative
5764 =item C<isl_ast_op_pdiv_q>
5766 Result of integer division, where dividend is known to be non-negative.
5768 =item C<isl_ast_op_pdiv_r>
5770 Remainder of integer division, where dividend is known to be non-negative.
5772 =item C<isl_ast_op_cond>
5774 Conditional operator defined on three arguments.
5775 If the first argument evaluates to true, then the result
5776 is equal to the second argument. Otherwise, the result
5777 is equal to the third argument.
5778 The second and third argument may only be evaluated if
5779 the first argument evaluates to true and false, respectively.
5780 Corresponds to C<a ? b : c> in C.
5782 =item C<isl_ast_op_select>
5784 Conditional operator defined on three arguments.
5785 If the first argument evaluates to true, then the result
5786 is equal to the second argument. Otherwise, the result
5787 is equal to the third argument.
5788 The second and third argument may be evaluated independently
5789 of the value of the first argument.
5790 Corresponds to C<a * b + (1 - a) * c> in C.
5792 =item C<isl_ast_op_eq>
5796 =item C<isl_ast_op_le>
5798 Less than or equal relation.
5800 =item C<isl_ast_op_lt>
5804 =item C<isl_ast_op_ge>
5806 Greater than or equal relation.
5808 =item C<isl_ast_op_gt>
5810 Greater than relation.
5812 =item C<isl_ast_op_call>
5815 The number of arguments of the C<isl_ast_expr> is one more than
5816 the number of arguments in the function call, the first argument
5817 representing the function being called.
5821 #include <isl/ast.h>
5822 __isl_give isl_id *isl_ast_expr_get_id(
5823 __isl_keep isl_ast_expr *expr);
5825 Return the identifier represented by the AST expression.
5827 #include <isl/ast.h>
5828 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5831 Return the integer represented by the AST expression.
5832 Note that the integer is returned through the C<v> argument.
5833 The return value of the function itself indicates whether the
5834 operation was performed successfully.
5836 =head3 Manipulating and printing the AST
5838 AST nodes can be copied and freed using the following functions.
5840 #include <isl/ast.h>
5841 __isl_give isl_ast_node *isl_ast_node_copy(
5842 __isl_keep isl_ast_node *node);
5843 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5845 AST expressions can be copied and freed using the following functions.
5847 #include <isl/ast.h>
5848 __isl_give isl_ast_expr *isl_ast_expr_copy(
5849 __isl_keep isl_ast_expr *expr);
5850 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5852 New AST expressions can be created either directly or within
5853 the context of an C<isl_ast_build>.
5855 #include <isl/ast.h>
5856 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5857 __isl_take isl_id *id);
5858 __isl_give isl_ast_expr *isl_ast_expr_neg(
5859 __isl_take isl_ast_expr *expr);
5860 __isl_give isl_ast_expr *isl_ast_expr_add(
5861 __isl_take isl_ast_expr *expr1,
5862 __isl_take isl_ast_expr *expr2);
5863 __isl_give isl_ast_expr *isl_ast_expr_sub(
5864 __isl_take isl_ast_expr *expr1,
5865 __isl_take isl_ast_expr *expr2);
5866 __isl_give isl_ast_expr *isl_ast_expr_mul(
5867 __isl_take isl_ast_expr *expr1,
5868 __isl_take isl_ast_expr *expr2);
5869 __isl_give isl_ast_expr *isl_ast_expr_div(
5870 __isl_take isl_ast_expr *expr1,
5871 __isl_take isl_ast_expr *expr2);
5872 __isl_give isl_ast_expr *isl_ast_expr_and(
5873 __isl_take isl_ast_expr *expr1,
5874 __isl_take isl_ast_expr *expr2)
5875 __isl_give isl_ast_expr *isl_ast_expr_or(
5876 __isl_take isl_ast_expr *expr1,
5877 __isl_take isl_ast_expr *expr2)
5879 #include <isl/ast_build.h>
5880 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5881 __isl_keep isl_ast_build *build,
5882 __isl_take isl_pw_aff *pa);
5883 __isl_give isl_ast_expr *
5884 isl_ast_build_call_from_pw_multi_aff(
5885 __isl_keep isl_ast_build *build,
5886 __isl_take isl_pw_multi_aff *pma);
5888 The domains of C<pa> and C<pma> should correspond
5889 to the schedule space of C<build>.
5890 The tuple id of C<pma> is used as the function being called.
5892 User specified data can be attached to an C<isl_ast_node> and obtained
5893 from the same C<isl_ast_node> using the following functions.
5895 #include <isl/ast.h>
5896 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5897 __isl_take isl_ast_node *node,
5898 __isl_take isl_id *annotation);
5899 __isl_give isl_id *isl_ast_node_get_annotation(
5900 __isl_keep isl_ast_node *node);
5902 Basic printing can be performed using the following functions.
5904 #include <isl/ast.h>
5905 __isl_give isl_printer *isl_printer_print_ast_expr(
5906 __isl_take isl_printer *p,
5907 __isl_keep isl_ast_expr *expr);
5908 __isl_give isl_printer *isl_printer_print_ast_node(
5909 __isl_take isl_printer *p,
5910 __isl_keep isl_ast_node *node);
5912 More advanced printing can be performed using the following functions.
5914 #include <isl/ast.h>
5915 __isl_give isl_printer *isl_ast_op_type_print_macro(
5916 enum isl_ast_op_type type,
5917 __isl_take isl_printer *p);
5918 __isl_give isl_printer *isl_ast_node_print_macros(
5919 __isl_keep isl_ast_node *node,
5920 __isl_take isl_printer *p);
5921 __isl_give isl_printer *isl_ast_node_print(
5922 __isl_keep isl_ast_node *node,
5923 __isl_take isl_printer *p,
5924 __isl_take isl_ast_print_options *options);
5925 __isl_give isl_printer *isl_ast_node_for_print(
5926 __isl_keep isl_ast_node *node,
5927 __isl_take isl_printer *p,
5928 __isl_take isl_ast_print_options *options);
5929 __isl_give isl_printer *isl_ast_node_if_print(
5930 __isl_keep isl_ast_node *node,
5931 __isl_take isl_printer *p,
5932 __isl_take isl_ast_print_options *options);
5934 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5935 C<isl> may print out an AST that makes use of macros such
5936 as C<floord>, C<min> and C<max>.
5937 C<isl_ast_op_type_print_macro> prints out the macro
5938 corresponding to a specific C<isl_ast_op_type>.
5939 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5940 for expressions where these macros would be used and prints
5941 out the required macro definitions.
5942 Essentially, C<isl_ast_node_print_macros> calls
5943 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5944 as function argument.
5945 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5946 C<isl_ast_node_if_print> print an C<isl_ast_node>
5947 in C<ISL_FORMAT_C>, but allow for some extra control
5948 through an C<isl_ast_print_options> object.
5949 This object can be created using the following functions.
5951 #include <isl/ast.h>
5952 __isl_give isl_ast_print_options *
5953 isl_ast_print_options_alloc(isl_ctx *ctx);
5954 __isl_give isl_ast_print_options *
5955 isl_ast_print_options_copy(
5956 __isl_keep isl_ast_print_options *options);
5957 void *isl_ast_print_options_free(
5958 __isl_take isl_ast_print_options *options);
5960 __isl_give isl_ast_print_options *
5961 isl_ast_print_options_set_print_user(
5962 __isl_take isl_ast_print_options *options,
5963 __isl_give isl_printer *(*print_user)(
5964 __isl_take isl_printer *p,
5965 __isl_take isl_ast_print_options *options,
5966 __isl_keep isl_ast_node *node, void *user),
5968 __isl_give isl_ast_print_options *
5969 isl_ast_print_options_set_print_for(
5970 __isl_take isl_ast_print_options *options,
5971 __isl_give isl_printer *(*print_for)(
5972 __isl_take isl_printer *p,
5973 __isl_take isl_ast_print_options *options,
5974 __isl_keep isl_ast_node *node, void *user),
5977 The callback set by C<isl_ast_print_options_set_print_user>
5978 is called whenever a node of type C<isl_ast_node_user> needs to
5980 The callback set by C<isl_ast_print_options_set_print_for>
5981 is called whenever a node of type C<isl_ast_node_for> needs to
5983 Note that C<isl_ast_node_for_print> will I<not> call the
5984 callback set by C<isl_ast_print_options_set_print_for> on the node
5985 on which C<isl_ast_node_for_print> is called, but only on nested
5986 nodes of type C<isl_ast_node_for>. It is therefore safe to
5987 call C<isl_ast_node_for_print> from within the callback set by
5988 C<isl_ast_print_options_set_print_for>.
5990 The following option determines the type to be used for iterators
5991 while printing the AST.
5993 int isl_options_set_ast_iterator_type(
5994 isl_ctx *ctx, const char *val);
5995 const char *isl_options_get_ast_iterator_type(
6000 #include <isl/ast_build.h>
6001 int isl_options_set_ast_build_atomic_upper_bound(
6002 isl_ctx *ctx, int val);
6003 int isl_options_get_ast_build_atomic_upper_bound(
6005 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6007 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6008 int isl_options_set_ast_build_exploit_nested_bounds(
6009 isl_ctx *ctx, int val);
6010 int isl_options_get_ast_build_exploit_nested_bounds(
6012 int isl_options_set_ast_build_group_coscheduled(
6013 isl_ctx *ctx, int val);
6014 int isl_options_get_ast_build_group_coscheduled(
6016 int isl_options_set_ast_build_scale_strides(
6017 isl_ctx *ctx, int val);
6018 int isl_options_get_ast_build_scale_strides(
6020 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6022 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6023 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6025 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6029 =item * ast_build_atomic_upper_bound
6031 Generate loop upper bounds that consist of the current loop iterator,
6032 an operator and an expression not involving the iterator.
6033 If this option is not set, then the current loop iterator may appear
6034 several times in the upper bound.
6035 For example, when this option is turned off, AST generation
6038 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6042 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6045 When the option is turned on, the following AST is generated
6047 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6050 =item * ast_build_prefer_pdiv
6052 If this option is turned off, then the AST generation will
6053 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6054 operators, but no C<isl_ast_op_pdiv_q> or
6055 C<isl_ast_op_pdiv_r> operators.
6056 If this options is turned on, then C<isl> will try to convert
6057 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6058 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6060 =item * ast_build_exploit_nested_bounds
6062 Simplify conditions based on bounds of nested for loops.
6063 In particular, remove conditions that are implied by the fact
6064 that one or more nested loops have at least one iteration,
6065 meaning that the upper bound is at least as large as the lower bound.
6066 For example, when this option is turned off, AST generation
6069 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6075 for (int c0 = 0; c0 <= N; c0 += 1)
6076 for (int c1 = 0; c1 <= M; c1 += 1)
6079 When the option is turned on, the following AST is generated
6081 for (int c0 = 0; c0 <= N; c0 += 1)
6082 for (int c1 = 0; c1 <= M; c1 += 1)
6085 =item * ast_build_group_coscheduled
6087 If two domain elements are assigned the same schedule point, then
6088 they may be executed in any order and they may even appear in different
6089 loops. If this options is set, then the AST generator will make
6090 sure that coscheduled domain elements do not appear in separate parts
6091 of the AST. This is useful in case of nested AST generation
6092 if the outer AST generation is given only part of a schedule
6093 and the inner AST generation should handle the domains that are
6094 coscheduled by this initial part of the schedule together.
6095 For example if an AST is generated for a schedule
6097 { A[i] -> [0]; B[i] -> [0] }
6099 then the C<isl_ast_build_set_create_leaf> callback described
6100 below may get called twice, once for each domain.
6101 Setting this option ensures that the callback is only called once
6102 on both domains together.
6104 =item * ast_build_separation_bounds
6106 This option specifies which bounds to use during separation.
6107 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6108 then all (possibly implicit) bounds on the current dimension will
6109 be used during separation.
6110 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6111 then only those bounds that are explicitly available will
6112 be used during separation.
6114 =item * ast_build_scale_strides
6116 This option specifies whether the AST generator is allowed
6117 to scale down iterators of strided loops.
6119 =item * ast_build_allow_else
6121 This option specifies whether the AST generator is allowed
6122 to construct if statements with else branches.
6124 =item * ast_build_allow_or
6126 This option specifies whether the AST generator is allowed
6127 to construct if conditions with disjunctions.
6131 =head3 Fine-grained Control over AST Generation
6133 Besides specifying the constraints on the parameters,
6134 an C<isl_ast_build> object can be used to control
6135 various aspects of the AST generation process.
6136 The most prominent way of control is through ``options'',
6137 which can be set using the following function.
6139 #include <isl/ast_build.h>
6140 __isl_give isl_ast_build *
6141 isl_ast_build_set_options(
6142 __isl_take isl_ast_build *control,
6143 __isl_take isl_union_map *options);
6145 The options are encoded in an <isl_union_map>.
6146 The domain of this union relation refers to the schedule domain,
6147 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6148 In the case of nested AST generation (see L</"Nested AST Generation">),
6149 the domain of C<options> should refer to the extra piece of the schedule.
6150 That is, it should be equal to the range of the wrapped relation in the
6151 range of the schedule.
6152 The range of the options can consist of elements in one or more spaces,
6153 the names of which determine the effect of the option.
6154 The values of the range typically also refer to the schedule dimension
6155 to which the option applies. In case of nested AST generation
6156 (see L</"Nested AST Generation">), these values refer to the position
6157 of the schedule dimension within the innermost AST generation.
6158 The constraints on the domain elements of
6159 the option should only refer to this dimension and earlier dimensions.
6160 We consider the following spaces.
6164 =item C<separation_class>
6166 This space is a wrapped relation between two one dimensional spaces.
6167 The input space represents the schedule dimension to which the option
6168 applies and the output space represents the separation class.
6169 While constructing a loop corresponding to the specified schedule
6170 dimension(s), the AST generator will try to generate separate loops
6171 for domain elements that are assigned different classes.
6172 If only some of the elements are assigned a class, then those elements
6173 that are not assigned any class will be treated as belonging to a class
6174 that is separate from the explicitly assigned classes.
6175 The typical use case for this option is to separate full tiles from
6177 The other options, described below, are applied after the separation
6180 As an example, consider the separation into full and partial tiles
6181 of a tiling of a triangular domain.
6182 Take, for example, the domain
6184 { A[i,j] : 0 <= i,j and i + j <= 100 }
6186 and a tiling into tiles of 10 by 10. The input to the AST generator
6187 is then the schedule
6189 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6192 Without any options, the following AST is generated
6194 for (int c0 = 0; c0 <= 10; c0 += 1)
6195 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6196 for (int c2 = 10 * c0;
6197 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6199 for (int c3 = 10 * c1;
6200 c3 <= min(10 * c1 + 9, -c2 + 100);
6204 Separation into full and partial tiles can be obtained by assigning
6205 a class, say C<0>, to the full tiles. The full tiles are represented by those
6206 values of the first and second schedule dimensions for which there are
6207 values of the third and fourth dimensions to cover an entire tile.
6208 That is, we need to specify the following option
6210 { [a,b,c,d] -> separation_class[[0]->[0]] :
6211 exists b': 0 <= 10a,10b' and
6212 10a+9+10b'+9 <= 100;
6213 [a,b,c,d] -> separation_class[[1]->[0]] :
6214 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6218 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6219 a >= 0 and b >= 0 and b <= 8 - a;
6220 [a, b, c, d] -> separation_class[[0] -> [0]] :
6223 With this option, the generated AST is as follows
6226 for (int c0 = 0; c0 <= 8; c0 += 1) {
6227 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6228 for (int c2 = 10 * c0;
6229 c2 <= 10 * c0 + 9; c2 += 1)
6230 for (int c3 = 10 * c1;
6231 c3 <= 10 * c1 + 9; c3 += 1)
6233 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6234 for (int c2 = 10 * c0;
6235 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6237 for (int c3 = 10 * c1;
6238 c3 <= min(-c2 + 100, 10 * c1 + 9);
6242 for (int c0 = 9; c0 <= 10; c0 += 1)
6243 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6244 for (int c2 = 10 * c0;
6245 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6247 for (int c3 = 10 * c1;
6248 c3 <= min(10 * c1 + 9, -c2 + 100);
6255 This is a single-dimensional space representing the schedule dimension(s)
6256 to which ``separation'' should be applied. Separation tries to split
6257 a loop into several pieces if this can avoid the generation of guards
6259 See also the C<atomic> option.
6263 This is a single-dimensional space representing the schedule dimension(s)
6264 for which the domains should be considered ``atomic''. That is, the
6265 AST generator will make sure that any given domain space will only appear
6266 in a single loop at the specified level.
6268 Consider the following schedule
6270 { a[i] -> [i] : 0 <= i < 10;
6271 b[i] -> [i+1] : 0 <= i < 10 }
6273 If the following option is specified
6275 { [i] -> separate[x] }
6277 then the following AST will be generated
6281 for (int c0 = 1; c0 <= 9; c0 += 1) {
6288 If, on the other hand, the following option is specified
6290 { [i] -> atomic[x] }
6292 then the following AST will be generated
6294 for (int c0 = 0; c0 <= 10; c0 += 1) {
6301 If neither C<atomic> nor C<separate> is specified, then the AST generator
6302 may produce either of these two results or some intermediate form.
6306 This is a single-dimensional space representing the schedule dimension(s)
6307 that should be I<completely> unrolled.
6308 To obtain a partial unrolling, the user should apply an additional
6309 strip-mining to the schedule and fully unroll the inner loop.
6313 Additional control is available through the following functions.
6315 #include <isl/ast_build.h>
6316 __isl_give isl_ast_build *
6317 isl_ast_build_set_iterators(
6318 __isl_take isl_ast_build *control,
6319 __isl_take isl_id_list *iterators);
6321 The function C<isl_ast_build_set_iterators> allows the user to
6322 specify a list of iterator C<isl_id>s to be used as iterators.
6323 If the input schedule is injective, then
6324 the number of elements in this list should be as large as the dimension
6325 of the schedule space, but no direct correspondence should be assumed
6326 between dimensions and elements.
6327 If the input schedule is not injective, then an additional number
6328 of C<isl_id>s equal to the largest dimension of the input domains
6330 If the number of provided C<isl_id>s is insufficient, then additional
6331 names are automatically generated.
6333 #include <isl/ast_build.h>
6334 __isl_give isl_ast_build *
6335 isl_ast_build_set_create_leaf(
6336 __isl_take isl_ast_build *control,
6337 __isl_give isl_ast_node *(*fn)(
6338 __isl_take isl_ast_build *build,
6339 void *user), void *user);
6342 C<isl_ast_build_set_create_leaf> function allows for the
6343 specification of a callback that should be called whenever the AST
6344 generator arrives at an element of the schedule domain.
6345 The callback should return an AST node that should be inserted
6346 at the corresponding position of the AST. The default action (when
6347 the callback is not set) is to continue generating parts of the AST to scan
6348 all the domain elements associated to the schedule domain element
6349 and to insert user nodes, ``calling'' the domain element, for each of them.
6350 The C<build> argument contains the current state of the C<isl_ast_build>.
6351 To ease nested AST generation (see L</"Nested AST Generation">),
6352 all control information that is
6353 specific to the current AST generation such as the options and
6354 the callbacks has been removed from this C<isl_ast_build>.
6355 The callback would typically return the result of a nested
6357 user defined node created using the following function.
6359 #include <isl/ast.h>
6360 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6361 __isl_take isl_ast_expr *expr);
6363 #include <isl/ast_build.h>
6364 __isl_give isl_ast_build *
6365 isl_ast_build_set_at_each_domain(
6366 __isl_take isl_ast_build *build,
6367 __isl_give isl_ast_node *(*fn)(
6368 __isl_take isl_ast_node *node,
6369 __isl_keep isl_ast_build *build,
6370 void *user), void *user);
6371 __isl_give isl_ast_build *
6372 isl_ast_build_set_before_each_for(
6373 __isl_take isl_ast_build *build,
6374 __isl_give isl_id *(*fn)(
6375 __isl_keep isl_ast_build *build,
6376 void *user), void *user);
6377 __isl_give isl_ast_build *
6378 isl_ast_build_set_after_each_for(
6379 __isl_take isl_ast_build *build,
6380 __isl_give isl_ast_node *(*fn)(
6381 __isl_take isl_ast_node *node,
6382 __isl_keep isl_ast_build *build,
6383 void *user), void *user);
6385 The callback set by C<isl_ast_build_set_at_each_domain> will
6386 be called for each domain AST node.
6387 The callbacks set by C<isl_ast_build_set_before_each_for>
6388 and C<isl_ast_build_set_after_each_for> will be called
6389 for each for AST node. The first will be called in depth-first
6390 pre-order, while the second will be called in depth-first post-order.
6391 Since C<isl_ast_build_set_before_each_for> is called before the for
6392 node is actually constructed, it is only passed an C<isl_ast_build>.
6393 The returned C<isl_id> will be added as an annotation (using
6394 C<isl_ast_node_set_annotation>) to the constructed for node.
6395 In particular, if the user has also specified an C<after_each_for>
6396 callback, then the annotation can be retrieved from the node passed to
6397 that callback using C<isl_ast_node_get_annotation>.
6398 All callbacks should C<NULL> on failure.
6399 The given C<isl_ast_build> can be used to create new
6400 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6401 or C<isl_ast_build_call_from_pw_multi_aff>.
6403 =head3 Nested AST Generation
6405 C<isl> allows the user to create an AST within the context
6406 of another AST. These nested ASTs are created using the
6407 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6408 outer AST. The C<build> argument should be an C<isl_ast_build>
6409 passed to a callback set by
6410 C<isl_ast_build_set_create_leaf>.
6411 The space of the range of the C<schedule> argument should refer
6412 to this build. In particular, the space should be a wrapped
6413 relation and the domain of this wrapped relation should be the
6414 same as that of the range of the schedule returned by
6415 C<isl_ast_build_get_schedule> below.
6416 In practice, the new schedule is typically
6417 created by calling C<isl_union_map_range_product> on the old schedule
6418 and some extra piece of the schedule.
6419 The space of the schedule domain is also available from
6420 the C<isl_ast_build>.
6422 #include <isl/ast_build.h>
6423 __isl_give isl_union_map *isl_ast_build_get_schedule(
6424 __isl_keep isl_ast_build *build);
6425 __isl_give isl_space *isl_ast_build_get_schedule_space(
6426 __isl_keep isl_ast_build *build);
6427 __isl_give isl_ast_build *isl_ast_build_restrict(
6428 __isl_take isl_ast_build *build,
6429 __isl_take isl_set *set);
6431 The C<isl_ast_build_get_schedule> function returns a (partial)
6432 schedule for the domains elements for which part of the AST still needs to
6433 be generated in the current build.
6434 In particular, the domain elements are mapped to those iterations of the loops
6435 enclosing the current point of the AST generation inside which
6436 the domain elements are executed.
6437 No direct correspondence between
6438 the input schedule and this schedule should be assumed.
6439 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6440 to create a set for C<isl_ast_build_restrict> to intersect
6441 with the current build. In particular, the set passed to
6442 C<isl_ast_build_restrict> can have additional parameters.
6443 The ids of the set dimensions in the space returned by
6444 C<isl_ast_build_get_schedule_space> correspond to the
6445 iterators of the already generated loops.
6446 The user should not rely on the ids of the output dimensions
6447 of the relations in the union relation returned by
6448 C<isl_ast_build_get_schedule> having any particular value.
6452 Although C<isl> is mainly meant to be used as a library,
6453 it also contains some basic applications that use some
6454 of the functionality of C<isl>.
6455 The input may be specified in either the L<isl format>
6456 or the L<PolyLib format>.
6458 =head2 C<isl_polyhedron_sample>
6460 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6461 an integer element of the polyhedron, if there is any.
6462 The first column in the output is the denominator and is always
6463 equal to 1. If the polyhedron contains no integer points,
6464 then a vector of length zero is printed.
6468 C<isl_pip> takes the same input as the C<example> program
6469 from the C<piplib> distribution, i.e., a set of constraints
6470 on the parameters, a line containing only -1 and finally a set
6471 of constraints on a parametric polyhedron.
6472 The coefficients of the parameters appear in the last columns
6473 (but before the final constant column).
6474 The output is the lexicographic minimum of the parametric polyhedron.
6475 As C<isl> currently does not have its own output format, the output
6476 is just a dump of the internal state.
6478 =head2 C<isl_polyhedron_minimize>
6480 C<isl_polyhedron_minimize> computes the minimum of some linear
6481 or affine objective function over the integer points in a polyhedron.
6482 If an affine objective function
6483 is given, then the constant should appear in the last column.
6485 =head2 C<isl_polytope_scan>
6487 Given a polytope, C<isl_polytope_scan> prints
6488 all integer points in the polytope.
6490 =head2 C<isl_codegen>
6492 Given a schedule, a context set and an options relation,
6493 C<isl_codegen> prints out an AST that scans the domain elements
6494 of the schedule in the order of their image(s) taking into account
6495 the constraints in the context set.