3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1522 __isl_take isl_basic_map *bmap,
1523 __isl_take isl_constraint *constraint);
1524 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1525 __isl_take isl_basic_set *bset,
1526 __isl_take isl_constraint *constraint);
1527 __isl_give isl_map *isl_map_add_constraint(
1528 __isl_take isl_map *map,
1529 __isl_take isl_constraint *constraint);
1530 __isl_give isl_set *isl_set_add_constraint(
1531 __isl_take isl_set *set,
1532 __isl_take isl_constraint *constraint);
1533 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1534 __isl_take isl_basic_set *bset,
1535 __isl_take isl_constraint *constraint);
1537 For example, to create a set containing the even integers
1538 between 10 and 42, you would use the following code.
1541 isl_local_space *ls;
1543 isl_basic_set *bset;
1545 space = isl_space_set_alloc(ctx, 0, 2);
1546 bset = isl_basic_set_universe(isl_space_copy(space));
1547 ls = isl_local_space_from_space(space);
1549 c = isl_equality_alloc(isl_local_space_copy(ls));
1550 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1551 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1552 bset = isl_basic_set_add_constraint(bset, c);
1554 c = isl_inequality_alloc(isl_local_space_copy(ls));
1555 c = isl_constraint_set_constant_si(c, -10);
1556 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1557 bset = isl_basic_set_add_constraint(bset, c);
1559 c = isl_inequality_alloc(ls);
1560 c = isl_constraint_set_constant_si(c, 42);
1561 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1562 bset = isl_basic_set_add_constraint(bset, c);
1564 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1568 isl_basic_set *bset;
1569 bset = isl_basic_set_read_from_str(ctx,
1570 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1572 A basic set or relation can also be constructed from two matrices
1573 describing the equalities and the inequalities.
1575 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1576 __isl_take isl_space *space,
1577 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1578 enum isl_dim_type c1,
1579 enum isl_dim_type c2, enum isl_dim_type c3,
1580 enum isl_dim_type c4);
1581 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1582 __isl_take isl_space *space,
1583 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1584 enum isl_dim_type c1,
1585 enum isl_dim_type c2, enum isl_dim_type c3,
1586 enum isl_dim_type c4, enum isl_dim_type c5);
1588 The C<isl_dim_type> arguments indicate the order in which
1589 different kinds of variables appear in the input matrices
1590 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1591 C<isl_dim_set> and C<isl_dim_div> for sets and
1592 of C<isl_dim_cst>, C<isl_dim_param>,
1593 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1595 A (basic or union) set or relation can also be constructed from a
1596 (union) (piecewise) (multiple) affine expression
1597 or a list of affine expressions
1598 (See L<"Piecewise Quasi Affine Expressions"> and
1599 L<"Piecewise Multiple Quasi Affine Expressions">).
1601 __isl_give isl_basic_map *isl_basic_map_from_aff(
1602 __isl_take isl_aff *aff);
1603 __isl_give isl_map *isl_map_from_aff(
1604 __isl_take isl_aff *aff);
1605 __isl_give isl_set *isl_set_from_pw_aff(
1606 __isl_take isl_pw_aff *pwaff);
1607 __isl_give isl_map *isl_map_from_pw_aff(
1608 __isl_take isl_pw_aff *pwaff);
1609 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1610 __isl_take isl_space *domain_space,
1611 __isl_take isl_aff_list *list);
1612 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1613 __isl_take isl_multi_aff *maff)
1614 __isl_give isl_map *isl_map_from_multi_aff(
1615 __isl_take isl_multi_aff *maff)
1616 __isl_give isl_set *isl_set_from_pw_multi_aff(
1617 __isl_take isl_pw_multi_aff *pma);
1618 __isl_give isl_map *isl_map_from_pw_multi_aff(
1619 __isl_take isl_pw_multi_aff *pma);
1620 __isl_give isl_union_map *
1621 isl_union_map_from_union_pw_multi_aff(
1622 __isl_take isl_union_pw_multi_aff *upma);
1624 The C<domain_dim> argument describes the domain of the resulting
1625 basic relation. It is required because the C<list> may consist
1626 of zero affine expressions.
1628 =head2 Inspecting Sets and Relations
1630 Usually, the user should not have to care about the actual constraints
1631 of the sets and maps, but should instead apply the abstract operations
1632 explained in the following sections.
1633 Occasionally, however, it may be required to inspect the individual
1634 coefficients of the constraints. This section explains how to do so.
1635 In these cases, it may also be useful to have C<isl> compute
1636 an explicit representation of the existentially quantified variables.
1638 __isl_give isl_set *isl_set_compute_divs(
1639 __isl_take isl_set *set);
1640 __isl_give isl_map *isl_map_compute_divs(
1641 __isl_take isl_map *map);
1642 __isl_give isl_union_set *isl_union_set_compute_divs(
1643 __isl_take isl_union_set *uset);
1644 __isl_give isl_union_map *isl_union_map_compute_divs(
1645 __isl_take isl_union_map *umap);
1647 This explicit representation defines the existentially quantified
1648 variables as integer divisions of the other variables, possibly
1649 including earlier existentially quantified variables.
1650 An explicitly represented existentially quantified variable therefore
1651 has a unique value when the values of the other variables are known.
1652 If, furthermore, the same existentials, i.e., existentials
1653 with the same explicit representations, should appear in the
1654 same order in each of the disjuncts of a set or map, then the user should call
1655 either of the following functions.
1657 __isl_give isl_set *isl_set_align_divs(
1658 __isl_take isl_set *set);
1659 __isl_give isl_map *isl_map_align_divs(
1660 __isl_take isl_map *map);
1662 Alternatively, the existentially quantified variables can be removed
1663 using the following functions, which compute an overapproximation.
1665 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1666 __isl_take isl_basic_set *bset);
1667 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1668 __isl_take isl_basic_map *bmap);
1669 __isl_give isl_set *isl_set_remove_divs(
1670 __isl_take isl_set *set);
1671 __isl_give isl_map *isl_map_remove_divs(
1672 __isl_take isl_map *map);
1674 It is also possible to only remove those divs that are defined
1675 in terms of a given range of dimensions or only those for which
1676 no explicit representation is known.
1678 __isl_give isl_basic_set *
1679 isl_basic_set_remove_divs_involving_dims(
1680 __isl_take isl_basic_set *bset,
1681 enum isl_dim_type type,
1682 unsigned first, unsigned n);
1683 __isl_give isl_basic_map *
1684 isl_basic_map_remove_divs_involving_dims(
1685 __isl_take isl_basic_map *bmap,
1686 enum isl_dim_type type,
1687 unsigned first, unsigned n);
1688 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1689 __isl_take isl_set *set, enum isl_dim_type type,
1690 unsigned first, unsigned n);
1691 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1692 __isl_take isl_map *map, enum isl_dim_type type,
1693 unsigned first, unsigned n);
1695 __isl_give isl_basic_set *
1696 isl_basic_set_remove_unknown_divs(
1697 __isl_take isl_basic_set *bset);
1698 __isl_give isl_set *isl_set_remove_unknown_divs(
1699 __isl_take isl_set *set);
1700 __isl_give isl_map *isl_map_remove_unknown_divs(
1701 __isl_take isl_map *map);
1703 To iterate over all the sets or maps in a union set or map, use
1705 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1706 int (*fn)(__isl_take isl_set *set, void *user),
1708 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1709 int (*fn)(__isl_take isl_map *map, void *user),
1712 The number of sets or maps in a union set or map can be obtained
1715 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1716 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1718 To extract the set or map in a given space from a union, use
1720 __isl_give isl_set *isl_union_set_extract_set(
1721 __isl_keep isl_union_set *uset,
1722 __isl_take isl_space *space);
1723 __isl_give isl_map *isl_union_map_extract_map(
1724 __isl_keep isl_union_map *umap,
1725 __isl_take isl_space *space);
1727 To iterate over all the basic sets or maps in a set or map, use
1729 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1730 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1732 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1733 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1736 The callback function C<fn> should return 0 if successful and
1737 -1 if an error occurs. In the latter case, or if any other error
1738 occurs, the above functions will return -1.
1740 It should be noted that C<isl> does not guarantee that
1741 the basic sets or maps passed to C<fn> are disjoint.
1742 If this is required, then the user should call one of
1743 the following functions first.
1745 __isl_give isl_set *isl_set_make_disjoint(
1746 __isl_take isl_set *set);
1747 __isl_give isl_map *isl_map_make_disjoint(
1748 __isl_take isl_map *map);
1750 The number of basic sets in a set can be obtained
1753 int isl_set_n_basic_set(__isl_keep isl_set *set);
1755 To iterate over the constraints of a basic set or map, use
1757 #include <isl/constraint.h>
1759 int isl_basic_set_n_constraint(
1760 __isl_keep isl_basic_set *bset);
1761 int isl_basic_set_foreach_constraint(
1762 __isl_keep isl_basic_set *bset,
1763 int (*fn)(__isl_take isl_constraint *c, void *user),
1765 int isl_basic_map_foreach_constraint(
1766 __isl_keep isl_basic_map *bmap,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 void *isl_constraint_free(__isl_take isl_constraint *c);
1771 Again, the callback function C<fn> should return 0 if successful and
1772 -1 if an error occurs. In the latter case, or if any other error
1773 occurs, the above functions will return -1.
1774 The constraint C<c> represents either an equality or an inequality.
1775 Use the following function to find out whether a constraint
1776 represents an equality. If not, it represents an inequality.
1778 int isl_constraint_is_equality(
1779 __isl_keep isl_constraint *constraint);
1781 The coefficients of the constraints can be inspected using
1782 the following functions.
1784 int isl_constraint_is_lower_bound(
1785 __isl_keep isl_constraint *constraint,
1786 enum isl_dim_type type, unsigned pos);
1787 int isl_constraint_is_upper_bound(
1788 __isl_keep isl_constraint *constraint,
1789 enum isl_dim_type type, unsigned pos);
1790 void isl_constraint_get_constant(
1791 __isl_keep isl_constraint *constraint, isl_int *v);
1792 void isl_constraint_get_coefficient(
1793 __isl_keep isl_constraint *constraint,
1794 enum isl_dim_type type, int pos, isl_int *v);
1795 int isl_constraint_involves_dims(
1796 __isl_keep isl_constraint *constraint,
1797 enum isl_dim_type type, unsigned first, unsigned n);
1799 The explicit representations of the existentially quantified
1800 variables can be inspected using the following function.
1801 Note that the user is only allowed to use this function
1802 if the inspected set or map is the result of a call
1803 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1804 The existentially quantified variable is equal to the floor
1805 of the returned affine expression. The affine expression
1806 itself can be inspected using the functions in
1807 L<"Piecewise Quasi Affine Expressions">.
1809 __isl_give isl_aff *isl_constraint_get_div(
1810 __isl_keep isl_constraint *constraint, int pos);
1812 To obtain the constraints of a basic set or map in matrix
1813 form, use the following functions.
1815 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1816 __isl_keep isl_basic_set *bset,
1817 enum isl_dim_type c1, enum isl_dim_type c2,
1818 enum isl_dim_type c3, enum isl_dim_type c4);
1819 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1820 __isl_keep isl_basic_set *bset,
1821 enum isl_dim_type c1, enum isl_dim_type c2,
1822 enum isl_dim_type c3, enum isl_dim_type c4);
1823 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1824 __isl_keep isl_basic_map *bmap,
1825 enum isl_dim_type c1,
1826 enum isl_dim_type c2, enum isl_dim_type c3,
1827 enum isl_dim_type c4, enum isl_dim_type c5);
1828 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1829 __isl_keep isl_basic_map *bmap,
1830 enum isl_dim_type c1,
1831 enum isl_dim_type c2, enum isl_dim_type c3,
1832 enum isl_dim_type c4, enum isl_dim_type c5);
1834 The C<isl_dim_type> arguments dictate the order in which
1835 different kinds of variables appear in the resulting matrix
1836 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1837 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1839 The number of parameters, input, output or set dimensions can
1840 be obtained using the following functions.
1842 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1843 enum isl_dim_type type);
1844 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1845 enum isl_dim_type type);
1846 unsigned isl_set_dim(__isl_keep isl_set *set,
1847 enum isl_dim_type type);
1848 unsigned isl_map_dim(__isl_keep isl_map *map,
1849 enum isl_dim_type type);
1851 To check whether the description of a set or relation depends
1852 on one or more given dimensions, it is not necessary to iterate over all
1853 constraints. Instead the following functions can be used.
1855 int isl_basic_set_involves_dims(
1856 __isl_keep isl_basic_set *bset,
1857 enum isl_dim_type type, unsigned first, unsigned n);
1858 int isl_set_involves_dims(__isl_keep isl_set *set,
1859 enum isl_dim_type type, unsigned first, unsigned n);
1860 int isl_basic_map_involves_dims(
1861 __isl_keep isl_basic_map *bmap,
1862 enum isl_dim_type type, unsigned first, unsigned n);
1863 int isl_map_involves_dims(__isl_keep isl_map *map,
1864 enum isl_dim_type type, unsigned first, unsigned n);
1866 Similarly, the following functions can be used to check whether
1867 a given dimension is involved in any lower or upper bound.
1869 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1870 enum isl_dim_type type, unsigned pos);
1871 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1872 enum isl_dim_type type, unsigned pos);
1874 Note that these functions return true even if there is a bound on
1875 the dimension on only some of the basic sets of C<set>.
1876 To check if they have a bound for all of the basic sets in C<set>,
1877 use the following functions instead.
1879 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1880 enum isl_dim_type type, unsigned pos);
1881 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1882 enum isl_dim_type type, unsigned pos);
1884 The identifiers or names of the domain and range spaces of a set
1885 or relation can be read off or set using the following functions.
1887 __isl_give isl_set *isl_set_set_tuple_id(
1888 __isl_take isl_set *set, __isl_take isl_id *id);
1889 __isl_give isl_set *isl_set_reset_tuple_id(
1890 __isl_take isl_set *set);
1891 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1892 __isl_give isl_id *isl_set_get_tuple_id(
1893 __isl_keep isl_set *set);
1894 __isl_give isl_map *isl_map_set_tuple_id(
1895 __isl_take isl_map *map, enum isl_dim_type type,
1896 __isl_take isl_id *id);
1897 __isl_give isl_map *isl_map_reset_tuple_id(
1898 __isl_take isl_map *map, enum isl_dim_type type);
1899 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1900 enum isl_dim_type type);
1901 __isl_give isl_id *isl_map_get_tuple_id(
1902 __isl_keep isl_map *map, enum isl_dim_type type);
1904 const char *isl_basic_set_get_tuple_name(
1905 __isl_keep isl_basic_set *bset);
1906 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1907 __isl_take isl_basic_set *set, const char *s);
1908 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1909 const char *isl_set_get_tuple_name(
1910 __isl_keep isl_set *set);
1911 const char *isl_basic_map_get_tuple_name(
1912 __isl_keep isl_basic_map *bmap,
1913 enum isl_dim_type type);
1914 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1915 __isl_take isl_basic_map *bmap,
1916 enum isl_dim_type type, const char *s);
1917 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1918 enum isl_dim_type type);
1919 const char *isl_map_get_tuple_name(
1920 __isl_keep isl_map *map,
1921 enum isl_dim_type type);
1923 As with C<isl_space_get_tuple_name>, the value returned points to
1924 an internal data structure.
1925 The identifiers, positions or names of individual dimensions can be
1926 read off using the following functions.
1928 __isl_give isl_id *isl_basic_set_get_dim_id(
1929 __isl_keep isl_basic_set *bset,
1930 enum isl_dim_type type, unsigned pos);
1931 __isl_give isl_set *isl_set_set_dim_id(
1932 __isl_take isl_set *set, enum isl_dim_type type,
1933 unsigned pos, __isl_take isl_id *id);
1934 int isl_set_has_dim_id(__isl_keep isl_set *set,
1935 enum isl_dim_type type, unsigned pos);
1936 __isl_give isl_id *isl_set_get_dim_id(
1937 __isl_keep isl_set *set, enum isl_dim_type type,
1939 int isl_basic_map_has_dim_id(
1940 __isl_keep isl_basic_map *bmap,
1941 enum isl_dim_type type, unsigned pos);
1942 __isl_give isl_map *isl_map_set_dim_id(
1943 __isl_take isl_map *map, enum isl_dim_type type,
1944 unsigned pos, __isl_take isl_id *id);
1945 int isl_map_has_dim_id(__isl_keep isl_map *map,
1946 enum isl_dim_type type, unsigned pos);
1947 __isl_give isl_id *isl_map_get_dim_id(
1948 __isl_keep isl_map *map, enum isl_dim_type type,
1951 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1952 enum isl_dim_type type, __isl_keep isl_id *id);
1953 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1954 enum isl_dim_type type, __isl_keep isl_id *id);
1955 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1956 enum isl_dim_type type, const char *name);
1957 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1958 enum isl_dim_type type, const char *name);
1960 const char *isl_constraint_get_dim_name(
1961 __isl_keep isl_constraint *constraint,
1962 enum isl_dim_type type, unsigned pos);
1963 const char *isl_basic_set_get_dim_name(
1964 __isl_keep isl_basic_set *bset,
1965 enum isl_dim_type type, unsigned pos);
1966 int isl_set_has_dim_name(__isl_keep isl_set *set,
1967 enum isl_dim_type type, unsigned pos);
1968 const char *isl_set_get_dim_name(
1969 __isl_keep isl_set *set,
1970 enum isl_dim_type type, unsigned pos);
1971 const char *isl_basic_map_get_dim_name(
1972 __isl_keep isl_basic_map *bmap,
1973 enum isl_dim_type type, unsigned pos);
1974 int isl_map_has_dim_name(__isl_keep isl_map *map,
1975 enum isl_dim_type type, unsigned pos);
1976 const char *isl_map_get_dim_name(
1977 __isl_keep isl_map *map,
1978 enum isl_dim_type type, unsigned pos);
1980 These functions are mostly useful to obtain the identifiers, positions
1981 or names of the parameters. Identifiers of individual dimensions are
1982 essentially only useful for printing. They are ignored by all other
1983 operations and may not be preserved across those operations.
1987 =head3 Unary Properties
1993 The following functions test whether the given set or relation
1994 contains any integer points. The ``plain'' variants do not perform
1995 any computations, but simply check if the given set or relation
1996 is already known to be empty.
1998 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1999 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2000 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2001 int isl_set_is_empty(__isl_keep isl_set *set);
2002 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2003 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2004 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2005 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2006 int isl_map_is_empty(__isl_keep isl_map *map);
2007 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2009 =item * Universality
2011 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2012 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2013 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2015 =item * Single-valuedness
2017 int isl_basic_map_is_single_valued(
2018 __isl_keep isl_basic_map *bmap);
2019 int isl_map_plain_is_single_valued(
2020 __isl_keep isl_map *map);
2021 int isl_map_is_single_valued(__isl_keep isl_map *map);
2022 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2026 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2027 int isl_map_is_injective(__isl_keep isl_map *map);
2028 int isl_union_map_plain_is_injective(
2029 __isl_keep isl_union_map *umap);
2030 int isl_union_map_is_injective(
2031 __isl_keep isl_union_map *umap);
2035 int isl_map_is_bijective(__isl_keep isl_map *map);
2036 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2040 int isl_basic_map_plain_is_fixed(
2041 __isl_keep isl_basic_map *bmap,
2042 enum isl_dim_type type, unsigned pos,
2044 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2045 enum isl_dim_type type, unsigned pos,
2047 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2048 enum isl_dim_type type, unsigned pos,
2051 Check if the relation obviously lies on a hyperplane where the given dimension
2052 has a fixed value and if so, return that value in C<*val>.
2056 To check whether a set is a parameter domain, use this function:
2058 int isl_set_is_params(__isl_keep isl_set *set);
2059 int isl_union_set_is_params(
2060 __isl_keep isl_union_set *uset);
2064 The following functions check whether the domain of the given
2065 (basic) set is a wrapped relation.
2067 int isl_basic_set_is_wrapping(
2068 __isl_keep isl_basic_set *bset);
2069 int isl_set_is_wrapping(__isl_keep isl_set *set);
2071 =item * Internal Product
2073 int isl_basic_map_can_zip(
2074 __isl_keep isl_basic_map *bmap);
2075 int isl_map_can_zip(__isl_keep isl_map *map);
2077 Check whether the product of domain and range of the given relation
2079 i.e., whether both domain and range are nested relations.
2083 int isl_basic_map_can_curry(
2084 __isl_keep isl_basic_map *bmap);
2085 int isl_map_can_curry(__isl_keep isl_map *map);
2087 Check whether the domain of the (basic) relation is a wrapped relation.
2089 int isl_basic_map_can_uncurry(
2090 __isl_keep isl_basic_map *bmap);
2091 int isl_map_can_uncurry(__isl_keep isl_map *map);
2093 Check whether the range of the (basic) relation is a wrapped relation.
2097 =head3 Binary Properties
2103 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2104 __isl_keep isl_set *set2);
2105 int isl_set_is_equal(__isl_keep isl_set *set1,
2106 __isl_keep isl_set *set2);
2107 int isl_union_set_is_equal(
2108 __isl_keep isl_union_set *uset1,
2109 __isl_keep isl_union_set *uset2);
2110 int isl_basic_map_is_equal(
2111 __isl_keep isl_basic_map *bmap1,
2112 __isl_keep isl_basic_map *bmap2);
2113 int isl_map_is_equal(__isl_keep isl_map *map1,
2114 __isl_keep isl_map *map2);
2115 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2116 __isl_keep isl_map *map2);
2117 int isl_union_map_is_equal(
2118 __isl_keep isl_union_map *umap1,
2119 __isl_keep isl_union_map *umap2);
2121 =item * Disjointness
2123 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2124 __isl_keep isl_set *set2);
2125 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2126 __isl_keep isl_set *set2);
2127 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2128 __isl_keep isl_map *map2);
2132 int isl_basic_set_is_subset(
2133 __isl_keep isl_basic_set *bset1,
2134 __isl_keep isl_basic_set *bset2);
2135 int isl_set_is_subset(__isl_keep isl_set *set1,
2136 __isl_keep isl_set *set2);
2137 int isl_set_is_strict_subset(
2138 __isl_keep isl_set *set1,
2139 __isl_keep isl_set *set2);
2140 int isl_union_set_is_subset(
2141 __isl_keep isl_union_set *uset1,
2142 __isl_keep isl_union_set *uset2);
2143 int isl_union_set_is_strict_subset(
2144 __isl_keep isl_union_set *uset1,
2145 __isl_keep isl_union_set *uset2);
2146 int isl_basic_map_is_subset(
2147 __isl_keep isl_basic_map *bmap1,
2148 __isl_keep isl_basic_map *bmap2);
2149 int isl_basic_map_is_strict_subset(
2150 __isl_keep isl_basic_map *bmap1,
2151 __isl_keep isl_basic_map *bmap2);
2152 int isl_map_is_subset(
2153 __isl_keep isl_map *map1,
2154 __isl_keep isl_map *map2);
2155 int isl_map_is_strict_subset(
2156 __isl_keep isl_map *map1,
2157 __isl_keep isl_map *map2);
2158 int isl_union_map_is_subset(
2159 __isl_keep isl_union_map *umap1,
2160 __isl_keep isl_union_map *umap2);
2161 int isl_union_map_is_strict_subset(
2162 __isl_keep isl_union_map *umap1,
2163 __isl_keep isl_union_map *umap2);
2165 Check whether the first argument is a (strict) subset of the
2170 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2171 __isl_keep isl_set *set2);
2173 This function is useful for sorting C<isl_set>s.
2174 The order depends on the internal representation of the inputs.
2175 The order is fixed over different calls to the function (assuming
2176 the internal representation of the inputs has not changed), but may
2177 change over different versions of C<isl>.
2181 =head2 Unary Operations
2187 __isl_give isl_set *isl_set_complement(
2188 __isl_take isl_set *set);
2189 __isl_give isl_map *isl_map_complement(
2190 __isl_take isl_map *map);
2194 __isl_give isl_basic_map *isl_basic_map_reverse(
2195 __isl_take isl_basic_map *bmap);
2196 __isl_give isl_map *isl_map_reverse(
2197 __isl_take isl_map *map);
2198 __isl_give isl_union_map *isl_union_map_reverse(
2199 __isl_take isl_union_map *umap);
2203 __isl_give isl_basic_set *isl_basic_set_project_out(
2204 __isl_take isl_basic_set *bset,
2205 enum isl_dim_type type, unsigned first, unsigned n);
2206 __isl_give isl_basic_map *isl_basic_map_project_out(
2207 __isl_take isl_basic_map *bmap,
2208 enum isl_dim_type type, unsigned first, unsigned n);
2209 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2210 enum isl_dim_type type, unsigned first, unsigned n);
2211 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2212 enum isl_dim_type type, unsigned first, unsigned n);
2213 __isl_give isl_basic_set *isl_basic_set_params(
2214 __isl_take isl_basic_set *bset);
2215 __isl_give isl_basic_set *isl_basic_map_domain(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_basic_set *isl_basic_map_range(
2218 __isl_take isl_basic_map *bmap);
2219 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2220 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2221 __isl_give isl_set *isl_map_domain(
2222 __isl_take isl_map *bmap);
2223 __isl_give isl_set *isl_map_range(
2224 __isl_take isl_map *map);
2225 __isl_give isl_set *isl_union_set_params(
2226 __isl_take isl_union_set *uset);
2227 __isl_give isl_set *isl_union_map_params(
2228 __isl_take isl_union_map *umap);
2229 __isl_give isl_union_set *isl_union_map_domain(
2230 __isl_take isl_union_map *umap);
2231 __isl_give isl_union_set *isl_union_map_range(
2232 __isl_take isl_union_map *umap);
2234 __isl_give isl_basic_map *isl_basic_map_domain_map(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_give isl_basic_map *isl_basic_map_range_map(
2237 __isl_take isl_basic_map *bmap);
2238 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2239 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2240 __isl_give isl_union_map *isl_union_map_domain_map(
2241 __isl_take isl_union_map *umap);
2242 __isl_give isl_union_map *isl_union_map_range_map(
2243 __isl_take isl_union_map *umap);
2245 The functions above construct a (basic, regular or union) relation
2246 that maps (a wrapped version of) the input relation to its domain or range.
2250 __isl_give isl_basic_set *isl_basic_set_eliminate(
2251 __isl_take isl_basic_set *bset,
2252 enum isl_dim_type type,
2253 unsigned first, unsigned n);
2254 __isl_give isl_set *isl_set_eliminate(
2255 __isl_take isl_set *set, enum isl_dim_type type,
2256 unsigned first, unsigned n);
2257 __isl_give isl_basic_map *isl_basic_map_eliminate(
2258 __isl_take isl_basic_map *bmap,
2259 enum isl_dim_type type,
2260 unsigned first, unsigned n);
2261 __isl_give isl_map *isl_map_eliminate(
2262 __isl_take isl_map *map, enum isl_dim_type type,
2263 unsigned first, unsigned n);
2265 Eliminate the coefficients for the given dimensions from the constraints,
2266 without removing the dimensions.
2270 __isl_give isl_basic_set *isl_basic_set_fix(
2271 __isl_take isl_basic_set *bset,
2272 enum isl_dim_type type, unsigned pos,
2274 __isl_give isl_basic_set *isl_basic_set_fix_si(
2275 __isl_take isl_basic_set *bset,
2276 enum isl_dim_type type, unsigned pos, int value);
2277 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos,
2280 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2281 enum isl_dim_type type, unsigned pos, int value);
2282 __isl_give isl_basic_map *isl_basic_map_fix_si(
2283 __isl_take isl_basic_map *bmap,
2284 enum isl_dim_type type, unsigned pos, int value);
2285 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2286 enum isl_dim_type type, unsigned pos,
2288 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2289 enum isl_dim_type type, unsigned pos, int value);
2291 Intersect the set or relation with the hyperplane where the given
2292 dimension has the fixed given value.
2294 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2295 __isl_take isl_basic_map *bmap,
2296 enum isl_dim_type type, unsigned pos, int value);
2297 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2298 __isl_take isl_basic_map *bmap,
2299 enum isl_dim_type type, unsigned pos, int value);
2300 __isl_give isl_set *isl_set_lower_bound(
2301 __isl_take isl_set *set,
2302 enum isl_dim_type type, unsigned pos,
2304 __isl_give isl_set *isl_set_lower_bound_si(
2305 __isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_map *isl_map_lower_bound_si(
2308 __isl_take isl_map *map,
2309 enum isl_dim_type type, unsigned pos, int value);
2310 __isl_give isl_set *isl_set_upper_bound(
2311 __isl_take isl_set *set,
2312 enum isl_dim_type type, unsigned pos,
2314 __isl_give isl_set *isl_set_upper_bound_si(
2315 __isl_take isl_set *set,
2316 enum isl_dim_type type, unsigned pos, int value);
2317 __isl_give isl_map *isl_map_upper_bound_si(
2318 __isl_take isl_map *map,
2319 enum isl_dim_type type, unsigned pos, int value);
2321 Intersect the set or relation with the half-space where the given
2322 dimension has a value bounded by the fixed given value.
2324 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2325 enum isl_dim_type type1, int pos1,
2326 enum isl_dim_type type2, int pos2);
2327 __isl_give isl_basic_map *isl_basic_map_equate(
2328 __isl_take isl_basic_map *bmap,
2329 enum isl_dim_type type1, int pos1,
2330 enum isl_dim_type type2, int pos2);
2331 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2332 enum isl_dim_type type1, int pos1,
2333 enum isl_dim_type type2, int pos2);
2335 Intersect the set or relation with the hyperplane where the given
2336 dimensions are equal to each other.
2338 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2339 enum isl_dim_type type1, int pos1,
2340 enum isl_dim_type type2, int pos2);
2342 Intersect the relation with the hyperplane where the given
2343 dimensions have opposite values.
2345 __isl_give isl_basic_map *isl_basic_map_order_ge(
2346 __isl_take isl_basic_map *bmap,
2347 enum isl_dim_type type1, int pos1,
2348 enum isl_dim_type type2, int pos2);
2349 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2350 enum isl_dim_type type1, int pos1,
2351 enum isl_dim_type type2, int pos2);
2352 __isl_give isl_basic_map *isl_basic_map_order_gt(
2353 __isl_take isl_basic_map *bmap,
2354 enum isl_dim_type type1, int pos1,
2355 enum isl_dim_type type2, int pos2);
2356 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2357 enum isl_dim_type type1, int pos1,
2358 enum isl_dim_type type2, int pos2);
2360 Intersect the relation with the half-space where the given
2361 dimensions satisfy the given ordering.
2365 __isl_give isl_map *isl_set_identity(
2366 __isl_take isl_set *set);
2367 __isl_give isl_union_map *isl_union_set_identity(
2368 __isl_take isl_union_set *uset);
2370 Construct an identity relation on the given (union) set.
2374 __isl_give isl_basic_set *isl_basic_map_deltas(
2375 __isl_take isl_basic_map *bmap);
2376 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2377 __isl_give isl_union_set *isl_union_map_deltas(
2378 __isl_take isl_union_map *umap);
2380 These functions return a (basic) set containing the differences
2381 between image elements and corresponding domain elements in the input.
2383 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_map *isl_map_deltas_map(
2386 __isl_take isl_map *map);
2387 __isl_give isl_union_map *isl_union_map_deltas_map(
2388 __isl_take isl_union_map *umap);
2390 The functions above construct a (basic, regular or union) relation
2391 that maps (a wrapped version of) the input relation to its delta set.
2395 Simplify the representation of a set or relation by trying
2396 to combine pairs of basic sets or relations into a single
2397 basic set or relation.
2399 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2400 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2401 __isl_give isl_union_set *isl_union_set_coalesce(
2402 __isl_take isl_union_set *uset);
2403 __isl_give isl_union_map *isl_union_map_coalesce(
2404 __isl_take isl_union_map *umap);
2406 One of the methods for combining pairs of basic sets or relations
2407 can result in coefficients that are much larger than those that appear
2408 in the constraints of the input. By default, the coefficients are
2409 not allowed to grow larger, but this can be changed by unsetting
2410 the following option.
2412 int isl_options_set_coalesce_bounded_wrapping(
2413 isl_ctx *ctx, int val);
2414 int isl_options_get_coalesce_bounded_wrapping(
2417 =item * Detecting equalities
2419 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2420 __isl_take isl_basic_set *bset);
2421 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2422 __isl_take isl_basic_map *bmap);
2423 __isl_give isl_set *isl_set_detect_equalities(
2424 __isl_take isl_set *set);
2425 __isl_give isl_map *isl_map_detect_equalities(
2426 __isl_take isl_map *map);
2427 __isl_give isl_union_set *isl_union_set_detect_equalities(
2428 __isl_take isl_union_set *uset);
2429 __isl_give isl_union_map *isl_union_map_detect_equalities(
2430 __isl_take isl_union_map *umap);
2432 Simplify the representation of a set or relation by detecting implicit
2435 =item * Removing redundant constraints
2437 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2438 __isl_take isl_basic_set *bset);
2439 __isl_give isl_set *isl_set_remove_redundancies(
2440 __isl_take isl_set *set);
2441 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2442 __isl_take isl_basic_map *bmap);
2443 __isl_give isl_map *isl_map_remove_redundancies(
2444 __isl_take isl_map *map);
2448 __isl_give isl_basic_set *isl_set_convex_hull(
2449 __isl_take isl_set *set);
2450 __isl_give isl_basic_map *isl_map_convex_hull(
2451 __isl_take isl_map *map);
2453 If the input set or relation has any existentially quantified
2454 variables, then the result of these operations is currently undefined.
2458 __isl_give isl_basic_set *
2459 isl_set_unshifted_simple_hull(
2460 __isl_take isl_set *set);
2461 __isl_give isl_basic_map *
2462 isl_map_unshifted_simple_hull(
2463 __isl_take isl_map *map);
2464 __isl_give isl_basic_set *isl_set_simple_hull(
2465 __isl_take isl_set *set);
2466 __isl_give isl_basic_map *isl_map_simple_hull(
2467 __isl_take isl_map *map);
2468 __isl_give isl_union_map *isl_union_map_simple_hull(
2469 __isl_take isl_union_map *umap);
2471 These functions compute a single basic set or relation
2472 that contains the whole input set or relation.
2473 In particular, the output is described by translates
2474 of the constraints describing the basic sets or relations in the input.
2475 In case of C<isl_set_unshifted_simple_hull>, only the original
2476 constraints are used, without any translation.
2480 (See \autoref{s:simple hull}.)
2486 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2487 __isl_take isl_basic_set *bset);
2488 __isl_give isl_basic_set *isl_set_affine_hull(
2489 __isl_take isl_set *set);
2490 __isl_give isl_union_set *isl_union_set_affine_hull(
2491 __isl_take isl_union_set *uset);
2492 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2493 __isl_take isl_basic_map *bmap);
2494 __isl_give isl_basic_map *isl_map_affine_hull(
2495 __isl_take isl_map *map);
2496 __isl_give isl_union_map *isl_union_map_affine_hull(
2497 __isl_take isl_union_map *umap);
2499 In case of union sets and relations, the affine hull is computed
2502 =item * Polyhedral hull
2504 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2505 __isl_take isl_set *set);
2506 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2507 __isl_take isl_map *map);
2508 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2509 __isl_take isl_union_set *uset);
2510 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2511 __isl_take isl_union_map *umap);
2513 These functions compute a single basic set or relation
2514 not involving any existentially quantified variables
2515 that contains the whole input set or relation.
2516 In case of union sets and relations, the polyhedral hull is computed
2519 =item * Other approximations
2521 __isl_give isl_basic_set *
2522 isl_basic_set_drop_constraints_involving_dims(
2523 __isl_take isl_basic_set *bset,
2524 enum isl_dim_type type,
2525 unsigned first, unsigned n);
2526 __isl_give isl_basic_map *
2527 isl_basic_map_drop_constraints_involving_dims(
2528 __isl_take isl_basic_map *bmap,
2529 enum isl_dim_type type,
2530 unsigned first, unsigned n);
2531 __isl_give isl_basic_set *
2532 isl_basic_set_drop_constraints_not_involving_dims(
2533 __isl_take isl_basic_set *bset,
2534 enum isl_dim_type type,
2535 unsigned first, unsigned n);
2536 __isl_give isl_set *
2537 isl_set_drop_constraints_involving_dims(
2538 __isl_take isl_set *set,
2539 enum isl_dim_type type,
2540 unsigned first, unsigned n);
2541 __isl_give isl_map *
2542 isl_map_drop_constraints_involving_dims(
2543 __isl_take isl_map *map,
2544 enum isl_dim_type type,
2545 unsigned first, unsigned n);
2547 These functions drop any constraints (not) involving the specified dimensions.
2548 Note that the result depends on the representation of the input.
2552 __isl_give isl_basic_set *isl_basic_set_sample(
2553 __isl_take isl_basic_set *bset);
2554 __isl_give isl_basic_set *isl_set_sample(
2555 __isl_take isl_set *set);
2556 __isl_give isl_basic_map *isl_basic_map_sample(
2557 __isl_take isl_basic_map *bmap);
2558 __isl_give isl_basic_map *isl_map_sample(
2559 __isl_take isl_map *map);
2561 If the input (basic) set or relation is non-empty, then return
2562 a singleton subset of the input. Otherwise, return an empty set.
2564 =item * Optimization
2566 #include <isl/ilp.h>
2567 enum isl_lp_result isl_basic_set_max(
2568 __isl_keep isl_basic_set *bset,
2569 __isl_keep isl_aff *obj, isl_int *opt)
2570 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2571 __isl_keep isl_aff *obj, isl_int *opt);
2572 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2573 __isl_keep isl_aff *obj, isl_int *opt);
2575 Compute the minimum or maximum of the integer affine expression C<obj>
2576 over the points in C<set>, returning the result in C<opt>.
2577 The return value may be one of C<isl_lp_error>,
2578 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2580 =item * Parametric optimization
2582 __isl_give isl_pw_aff *isl_set_dim_min(
2583 __isl_take isl_set *set, int pos);
2584 __isl_give isl_pw_aff *isl_set_dim_max(
2585 __isl_take isl_set *set, int pos);
2586 __isl_give isl_pw_aff *isl_map_dim_max(
2587 __isl_take isl_map *map, int pos);
2589 Compute the minimum or maximum of the given set or output dimension
2590 as a function of the parameters (and input dimensions), but independently
2591 of the other set or output dimensions.
2592 For lexicographic optimization, see L<"Lexicographic Optimization">.
2596 The following functions compute either the set of (rational) coefficient
2597 values of valid constraints for the given set or the set of (rational)
2598 values satisfying the constraints with coefficients from the given set.
2599 Internally, these two sets of functions perform essentially the
2600 same operations, except that the set of coefficients is assumed to
2601 be a cone, while the set of values may be any polyhedron.
2602 The current implementation is based on the Farkas lemma and
2603 Fourier-Motzkin elimination, but this may change or be made optional
2604 in future. In particular, future implementations may use different
2605 dualization algorithms or skip the elimination step.
2607 __isl_give isl_basic_set *isl_basic_set_coefficients(
2608 __isl_take isl_basic_set *bset);
2609 __isl_give isl_basic_set *isl_set_coefficients(
2610 __isl_take isl_set *set);
2611 __isl_give isl_union_set *isl_union_set_coefficients(
2612 __isl_take isl_union_set *bset);
2613 __isl_give isl_basic_set *isl_basic_set_solutions(
2614 __isl_take isl_basic_set *bset);
2615 __isl_give isl_basic_set *isl_set_solutions(
2616 __isl_take isl_set *set);
2617 __isl_give isl_union_set *isl_union_set_solutions(
2618 __isl_take isl_union_set *bset);
2622 __isl_give isl_map *isl_map_fixed_power(
2623 __isl_take isl_map *map, isl_int exp);
2624 __isl_give isl_union_map *isl_union_map_fixed_power(
2625 __isl_take isl_union_map *umap, isl_int exp);
2627 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2628 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2629 of C<map> is computed.
2631 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2633 __isl_give isl_union_map *isl_union_map_power(
2634 __isl_take isl_union_map *umap, int *exact);
2636 Compute a parametric representation for all positive powers I<k> of C<map>.
2637 The result maps I<k> to a nested relation corresponding to the
2638 I<k>th power of C<map>.
2639 The result may be an overapproximation. If the result is known to be exact,
2640 then C<*exact> is set to C<1>.
2642 =item * Transitive closure
2644 __isl_give isl_map *isl_map_transitive_closure(
2645 __isl_take isl_map *map, int *exact);
2646 __isl_give isl_union_map *isl_union_map_transitive_closure(
2647 __isl_take isl_union_map *umap, int *exact);
2649 Compute the transitive closure of C<map>.
2650 The result may be an overapproximation. If the result is known to be exact,
2651 then C<*exact> is set to C<1>.
2653 =item * Reaching path lengths
2655 __isl_give isl_map *isl_map_reaching_path_lengths(
2656 __isl_take isl_map *map, int *exact);
2658 Compute a relation that maps each element in the range of C<map>
2659 to the lengths of all paths composed of edges in C<map> that
2660 end up in the given element.
2661 The result may be an overapproximation. If the result is known to be exact,
2662 then C<*exact> is set to C<1>.
2663 To compute the I<maximal> path length, the resulting relation
2664 should be postprocessed by C<isl_map_lexmax>.
2665 In particular, if the input relation is a dependence relation
2666 (mapping sources to sinks), then the maximal path length corresponds
2667 to the free schedule.
2668 Note, however, that C<isl_map_lexmax> expects the maximum to be
2669 finite, so if the path lengths are unbounded (possibly due to
2670 the overapproximation), then you will get an error message.
2674 __isl_give isl_basic_set *isl_basic_map_wrap(
2675 __isl_take isl_basic_map *bmap);
2676 __isl_give isl_set *isl_map_wrap(
2677 __isl_take isl_map *map);
2678 __isl_give isl_union_set *isl_union_map_wrap(
2679 __isl_take isl_union_map *umap);
2680 __isl_give isl_basic_map *isl_basic_set_unwrap(
2681 __isl_take isl_basic_set *bset);
2682 __isl_give isl_map *isl_set_unwrap(
2683 __isl_take isl_set *set);
2684 __isl_give isl_union_map *isl_union_set_unwrap(
2685 __isl_take isl_union_set *uset);
2689 Remove any internal structure of domain (and range) of the given
2690 set or relation. If there is any such internal structure in the input,
2691 then the name of the space is also removed.
2693 __isl_give isl_basic_set *isl_basic_set_flatten(
2694 __isl_take isl_basic_set *bset);
2695 __isl_give isl_set *isl_set_flatten(
2696 __isl_take isl_set *set);
2697 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2698 __isl_take isl_basic_map *bmap);
2699 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2700 __isl_take isl_basic_map *bmap);
2701 __isl_give isl_map *isl_map_flatten_range(
2702 __isl_take isl_map *map);
2703 __isl_give isl_map *isl_map_flatten_domain(
2704 __isl_take isl_map *map);
2705 __isl_give isl_basic_map *isl_basic_map_flatten(
2706 __isl_take isl_basic_map *bmap);
2707 __isl_give isl_map *isl_map_flatten(
2708 __isl_take isl_map *map);
2710 __isl_give isl_map *isl_set_flatten_map(
2711 __isl_take isl_set *set);
2713 The function above constructs a relation
2714 that maps the input set to a flattened version of the set.
2718 Lift the input set to a space with extra dimensions corresponding
2719 to the existentially quantified variables in the input.
2720 In particular, the result lives in a wrapped map where the domain
2721 is the original space and the range corresponds to the original
2722 existentially quantified variables.
2724 __isl_give isl_basic_set *isl_basic_set_lift(
2725 __isl_take isl_basic_set *bset);
2726 __isl_give isl_set *isl_set_lift(
2727 __isl_take isl_set *set);
2728 __isl_give isl_union_set *isl_union_set_lift(
2729 __isl_take isl_union_set *uset);
2731 Given a local space that contains the existentially quantified
2732 variables of a set, a basic relation that, when applied to
2733 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2734 can be constructed using the following function.
2736 #include <isl/local_space.h>
2737 __isl_give isl_basic_map *isl_local_space_lifting(
2738 __isl_take isl_local_space *ls);
2740 =item * Internal Product
2742 __isl_give isl_basic_map *isl_basic_map_zip(
2743 __isl_take isl_basic_map *bmap);
2744 __isl_give isl_map *isl_map_zip(
2745 __isl_take isl_map *map);
2746 __isl_give isl_union_map *isl_union_map_zip(
2747 __isl_take isl_union_map *umap);
2749 Given a relation with nested relations for domain and range,
2750 interchange the range of the domain with the domain of the range.
2754 __isl_give isl_basic_map *isl_basic_map_curry(
2755 __isl_take isl_basic_map *bmap);
2756 __isl_give isl_basic_map *isl_basic_map_uncurry(
2757 __isl_take isl_basic_map *bmap);
2758 __isl_give isl_map *isl_map_curry(
2759 __isl_take isl_map *map);
2760 __isl_give isl_map *isl_map_uncurry(
2761 __isl_take isl_map *map);
2762 __isl_give isl_union_map *isl_union_map_curry(
2763 __isl_take isl_union_map *umap);
2764 __isl_give isl_union_map *isl_union_map_uncurry(
2765 __isl_take isl_union_map *umap);
2767 Given a relation with a nested relation for domain,
2768 the C<curry> functions
2769 move the range of the nested relation out of the domain
2770 and use it as the domain of a nested relation in the range,
2771 with the original range as range of this nested relation.
2772 The C<uncurry> functions perform the inverse operation.
2774 =item * Aligning parameters
2776 __isl_give isl_basic_set *isl_basic_set_align_params(
2777 __isl_take isl_basic_set *bset,
2778 __isl_take isl_space *model);
2779 __isl_give isl_set *isl_set_align_params(
2780 __isl_take isl_set *set,
2781 __isl_take isl_space *model);
2782 __isl_give isl_basic_map *isl_basic_map_align_params(
2783 __isl_take isl_basic_map *bmap,
2784 __isl_take isl_space *model);
2785 __isl_give isl_map *isl_map_align_params(
2786 __isl_take isl_map *map,
2787 __isl_take isl_space *model);
2789 Change the order of the parameters of the given set or relation
2790 such that the first parameters match those of C<model>.
2791 This may involve the introduction of extra parameters.
2792 All parameters need to be named.
2794 =item * Dimension manipulation
2796 __isl_give isl_basic_set *isl_basic_set_add_dims(
2797 __isl_take isl_basic_set *bset,
2798 enum isl_dim_type type, unsigned n);
2799 __isl_give isl_set *isl_set_add_dims(
2800 __isl_take isl_set *set,
2801 enum isl_dim_type type, unsigned n);
2802 __isl_give isl_map *isl_map_add_dims(
2803 __isl_take isl_map *map,
2804 enum isl_dim_type type, unsigned n);
2805 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2806 __isl_take isl_basic_set *bset,
2807 enum isl_dim_type type, unsigned pos,
2809 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2810 __isl_take isl_basic_map *bmap,
2811 enum isl_dim_type type, unsigned pos,
2813 __isl_give isl_set *isl_set_insert_dims(
2814 __isl_take isl_set *set,
2815 enum isl_dim_type type, unsigned pos, unsigned n);
2816 __isl_give isl_map *isl_map_insert_dims(
2817 __isl_take isl_map *map,
2818 enum isl_dim_type type, unsigned pos, unsigned n);
2819 __isl_give isl_basic_set *isl_basic_set_move_dims(
2820 __isl_take isl_basic_set *bset,
2821 enum isl_dim_type dst_type, unsigned dst_pos,
2822 enum isl_dim_type src_type, unsigned src_pos,
2824 __isl_give isl_basic_map *isl_basic_map_move_dims(
2825 __isl_take isl_basic_map *bmap,
2826 enum isl_dim_type dst_type, unsigned dst_pos,
2827 enum isl_dim_type src_type, unsigned src_pos,
2829 __isl_give isl_set *isl_set_move_dims(
2830 __isl_take isl_set *set,
2831 enum isl_dim_type dst_type, unsigned dst_pos,
2832 enum isl_dim_type src_type, unsigned src_pos,
2834 __isl_give isl_map *isl_map_move_dims(
2835 __isl_take isl_map *map,
2836 enum isl_dim_type dst_type, unsigned dst_pos,
2837 enum isl_dim_type src_type, unsigned src_pos,
2840 It is usually not advisable to directly change the (input or output)
2841 space of a set or a relation as this removes the name and the internal
2842 structure of the space. However, the above functions can be useful
2843 to add new parameters, assuming
2844 C<isl_set_align_params> and C<isl_map_align_params>
2849 =head2 Binary Operations
2851 The two arguments of a binary operation not only need to live
2852 in the same C<isl_ctx>, they currently also need to have
2853 the same (number of) parameters.
2855 =head3 Basic Operations
2859 =item * Intersection
2861 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2862 __isl_take isl_basic_set *bset1,
2863 __isl_take isl_basic_set *bset2);
2864 __isl_give isl_basic_set *isl_basic_set_intersect(
2865 __isl_take isl_basic_set *bset1,
2866 __isl_take isl_basic_set *bset2);
2867 __isl_give isl_set *isl_set_intersect_params(
2868 __isl_take isl_set *set,
2869 __isl_take isl_set *params);
2870 __isl_give isl_set *isl_set_intersect(
2871 __isl_take isl_set *set1,
2872 __isl_take isl_set *set2);
2873 __isl_give isl_union_set *isl_union_set_intersect_params(
2874 __isl_take isl_union_set *uset,
2875 __isl_take isl_set *set);
2876 __isl_give isl_union_map *isl_union_map_intersect_params(
2877 __isl_take isl_union_map *umap,
2878 __isl_take isl_set *set);
2879 __isl_give isl_union_set *isl_union_set_intersect(
2880 __isl_take isl_union_set *uset1,
2881 __isl_take isl_union_set *uset2);
2882 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2883 __isl_take isl_basic_map *bmap,
2884 __isl_take isl_basic_set *bset);
2885 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2886 __isl_take isl_basic_map *bmap,
2887 __isl_take isl_basic_set *bset);
2888 __isl_give isl_basic_map *isl_basic_map_intersect(
2889 __isl_take isl_basic_map *bmap1,
2890 __isl_take isl_basic_map *bmap2);
2891 __isl_give isl_map *isl_map_intersect_params(
2892 __isl_take isl_map *map,
2893 __isl_take isl_set *params);
2894 __isl_give isl_map *isl_map_intersect_domain(
2895 __isl_take isl_map *map,
2896 __isl_take isl_set *set);
2897 __isl_give isl_map *isl_map_intersect_range(
2898 __isl_take isl_map *map,
2899 __isl_take isl_set *set);
2900 __isl_give isl_map *isl_map_intersect(
2901 __isl_take isl_map *map1,
2902 __isl_take isl_map *map2);
2903 __isl_give isl_union_map *isl_union_map_intersect_domain(
2904 __isl_take isl_union_map *umap,
2905 __isl_take isl_union_set *uset);
2906 __isl_give isl_union_map *isl_union_map_intersect_range(
2907 __isl_take isl_union_map *umap,
2908 __isl_take isl_union_set *uset);
2909 __isl_give isl_union_map *isl_union_map_intersect(
2910 __isl_take isl_union_map *umap1,
2911 __isl_take isl_union_map *umap2);
2913 The second argument to the C<_params> functions needs to be
2914 a parametric (basic) set. For the other functions, a parametric set
2915 for either argument is only allowed if the other argument is
2916 a parametric set as well.
2920 __isl_give isl_set *isl_basic_set_union(
2921 __isl_take isl_basic_set *bset1,
2922 __isl_take isl_basic_set *bset2);
2923 __isl_give isl_map *isl_basic_map_union(
2924 __isl_take isl_basic_map *bmap1,
2925 __isl_take isl_basic_map *bmap2);
2926 __isl_give isl_set *isl_set_union(
2927 __isl_take isl_set *set1,
2928 __isl_take isl_set *set2);
2929 __isl_give isl_map *isl_map_union(
2930 __isl_take isl_map *map1,
2931 __isl_take isl_map *map2);
2932 __isl_give isl_union_set *isl_union_set_union(
2933 __isl_take isl_union_set *uset1,
2934 __isl_take isl_union_set *uset2);
2935 __isl_give isl_union_map *isl_union_map_union(
2936 __isl_take isl_union_map *umap1,
2937 __isl_take isl_union_map *umap2);
2939 =item * Set difference
2941 __isl_give isl_set *isl_set_subtract(
2942 __isl_take isl_set *set1,
2943 __isl_take isl_set *set2);
2944 __isl_give isl_map *isl_map_subtract(
2945 __isl_take isl_map *map1,
2946 __isl_take isl_map *map2);
2947 __isl_give isl_map *isl_map_subtract_domain(
2948 __isl_take isl_map *map,
2949 __isl_take isl_set *dom);
2950 __isl_give isl_map *isl_map_subtract_range(
2951 __isl_take isl_map *map,
2952 __isl_take isl_set *dom);
2953 __isl_give isl_union_set *isl_union_set_subtract(
2954 __isl_take isl_union_set *uset1,
2955 __isl_take isl_union_set *uset2);
2956 __isl_give isl_union_map *isl_union_map_subtract(
2957 __isl_take isl_union_map *umap1,
2958 __isl_take isl_union_map *umap2);
2959 __isl_give isl_union_map *isl_union_map_subtract_domain(
2960 __isl_take isl_union_map *umap,
2961 __isl_take isl_union_set *dom);
2962 __isl_give isl_union_map *isl_union_map_subtract_range(
2963 __isl_take isl_union_map *umap,
2964 __isl_take isl_union_set *dom);
2968 __isl_give isl_basic_set *isl_basic_set_apply(
2969 __isl_take isl_basic_set *bset,
2970 __isl_take isl_basic_map *bmap);
2971 __isl_give isl_set *isl_set_apply(
2972 __isl_take isl_set *set,
2973 __isl_take isl_map *map);
2974 __isl_give isl_union_set *isl_union_set_apply(
2975 __isl_take isl_union_set *uset,
2976 __isl_take isl_union_map *umap);
2977 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2978 __isl_take isl_basic_map *bmap1,
2979 __isl_take isl_basic_map *bmap2);
2980 __isl_give isl_basic_map *isl_basic_map_apply_range(
2981 __isl_take isl_basic_map *bmap1,
2982 __isl_take isl_basic_map *bmap2);
2983 __isl_give isl_map *isl_map_apply_domain(
2984 __isl_take isl_map *map1,
2985 __isl_take isl_map *map2);
2986 __isl_give isl_union_map *isl_union_map_apply_domain(
2987 __isl_take isl_union_map *umap1,
2988 __isl_take isl_union_map *umap2);
2989 __isl_give isl_map *isl_map_apply_range(
2990 __isl_take isl_map *map1,
2991 __isl_take isl_map *map2);
2992 __isl_give isl_union_map *isl_union_map_apply_range(
2993 __isl_take isl_union_map *umap1,
2994 __isl_take isl_union_map *umap2);
2998 __isl_give isl_basic_set *
2999 isl_basic_set_preimage_multi_aff(
3000 __isl_take isl_basic_set *bset,
3001 __isl_take isl_multi_aff *ma);
3002 __isl_give isl_set *isl_set_preimage_multi_aff(
3003 __isl_take isl_set *set,
3004 __isl_take isl_multi_aff *ma);
3005 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3006 __isl_take isl_set *set,
3007 __isl_take isl_pw_multi_aff *pma);
3008 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3009 __isl_take isl_map *map,
3010 __isl_take isl_multi_aff *ma);
3011 __isl_give isl_union_map *
3012 isl_union_map_preimage_domain_multi_aff(
3013 __isl_take isl_union_map *umap,
3014 __isl_take isl_multi_aff *ma);
3016 These functions compute the preimage of the given set or map domain under
3017 the given function. In other words, the expression is plugged
3018 into the set description or into the domain of the map.
3019 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3020 L</"Piecewise Multiple Quasi Affine Expressions">.
3022 =item * Cartesian Product
3024 __isl_give isl_set *isl_set_product(
3025 __isl_take isl_set *set1,
3026 __isl_take isl_set *set2);
3027 __isl_give isl_union_set *isl_union_set_product(
3028 __isl_take isl_union_set *uset1,
3029 __isl_take isl_union_set *uset2);
3030 __isl_give isl_basic_map *isl_basic_map_domain_product(
3031 __isl_take isl_basic_map *bmap1,
3032 __isl_take isl_basic_map *bmap2);
3033 __isl_give isl_basic_map *isl_basic_map_range_product(
3034 __isl_take isl_basic_map *bmap1,
3035 __isl_take isl_basic_map *bmap2);
3036 __isl_give isl_basic_map *isl_basic_map_product(
3037 __isl_take isl_basic_map *bmap1,
3038 __isl_take isl_basic_map *bmap2);
3039 __isl_give isl_map *isl_map_domain_product(
3040 __isl_take isl_map *map1,
3041 __isl_take isl_map *map2);
3042 __isl_give isl_map *isl_map_range_product(
3043 __isl_take isl_map *map1,
3044 __isl_take isl_map *map2);
3045 __isl_give isl_union_map *isl_union_map_domain_product(
3046 __isl_take isl_union_map *umap1,
3047 __isl_take isl_union_map *umap2);
3048 __isl_give isl_union_map *isl_union_map_range_product(
3049 __isl_take isl_union_map *umap1,
3050 __isl_take isl_union_map *umap2);
3051 __isl_give isl_map *isl_map_product(
3052 __isl_take isl_map *map1,
3053 __isl_take isl_map *map2);
3054 __isl_give isl_union_map *isl_union_map_product(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3058 The above functions compute the cross product of the given
3059 sets or relations. The domains and ranges of the results
3060 are wrapped maps between domains and ranges of the inputs.
3061 To obtain a ``flat'' product, use the following functions
3064 __isl_give isl_basic_set *isl_basic_set_flat_product(
3065 __isl_take isl_basic_set *bset1,
3066 __isl_take isl_basic_set *bset2);
3067 __isl_give isl_set *isl_set_flat_product(
3068 __isl_take isl_set *set1,
3069 __isl_take isl_set *set2);
3070 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3071 __isl_take isl_basic_map *bmap1,
3072 __isl_take isl_basic_map *bmap2);
3073 __isl_give isl_map *isl_map_flat_domain_product(
3074 __isl_take isl_map *map1,
3075 __isl_take isl_map *map2);
3076 __isl_give isl_map *isl_map_flat_range_product(
3077 __isl_take isl_map *map1,
3078 __isl_take isl_map *map2);
3079 __isl_give isl_union_map *isl_union_map_flat_range_product(
3080 __isl_take isl_union_map *umap1,
3081 __isl_take isl_union_map *umap2);
3082 __isl_give isl_basic_map *isl_basic_map_flat_product(
3083 __isl_take isl_basic_map *bmap1,
3084 __isl_take isl_basic_map *bmap2);
3085 __isl_give isl_map *isl_map_flat_product(
3086 __isl_take isl_map *map1,
3087 __isl_take isl_map *map2);
3089 =item * Simplification
3091 __isl_give isl_basic_set *isl_basic_set_gist(
3092 __isl_take isl_basic_set *bset,
3093 __isl_take isl_basic_set *context);
3094 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3095 __isl_take isl_set *context);
3096 __isl_give isl_set *isl_set_gist_params(
3097 __isl_take isl_set *set,
3098 __isl_take isl_set *context);
3099 __isl_give isl_union_set *isl_union_set_gist(
3100 __isl_take isl_union_set *uset,
3101 __isl_take isl_union_set *context);
3102 __isl_give isl_union_set *isl_union_set_gist_params(
3103 __isl_take isl_union_set *uset,
3104 __isl_take isl_set *set);
3105 __isl_give isl_basic_map *isl_basic_map_gist(
3106 __isl_take isl_basic_map *bmap,
3107 __isl_take isl_basic_map *context);
3108 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3109 __isl_take isl_map *context);
3110 __isl_give isl_map *isl_map_gist_params(
3111 __isl_take isl_map *map,
3112 __isl_take isl_set *context);
3113 __isl_give isl_map *isl_map_gist_domain(
3114 __isl_take isl_map *map,
3115 __isl_take isl_set *context);
3116 __isl_give isl_map *isl_map_gist_range(
3117 __isl_take isl_map *map,
3118 __isl_take isl_set *context);
3119 __isl_give isl_union_map *isl_union_map_gist(
3120 __isl_take isl_union_map *umap,
3121 __isl_take isl_union_map *context);
3122 __isl_give isl_union_map *isl_union_map_gist_params(
3123 __isl_take isl_union_map *umap,
3124 __isl_take isl_set *set);
3125 __isl_give isl_union_map *isl_union_map_gist_domain(
3126 __isl_take isl_union_map *umap,
3127 __isl_take isl_union_set *uset);
3128 __isl_give isl_union_map *isl_union_map_gist_range(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_set *uset);
3132 The gist operation returns a set or relation that has the
3133 same intersection with the context as the input set or relation.
3134 Any implicit equality in the intersection is made explicit in the result,
3135 while all inequalities that are redundant with respect to the intersection
3137 In case of union sets and relations, the gist operation is performed
3142 =head3 Lexicographic Optimization
3144 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3145 the following functions
3146 compute a set that contains the lexicographic minimum or maximum
3147 of the elements in C<set> (or C<bset>) for those values of the parameters
3148 that satisfy C<dom>.
3149 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3150 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3152 In other words, the union of the parameter values
3153 for which the result is non-empty and of C<*empty>
3156 __isl_give isl_set *isl_basic_set_partial_lexmin(
3157 __isl_take isl_basic_set *bset,
3158 __isl_take isl_basic_set *dom,
3159 __isl_give isl_set **empty);
3160 __isl_give isl_set *isl_basic_set_partial_lexmax(
3161 __isl_take isl_basic_set *bset,
3162 __isl_take isl_basic_set *dom,
3163 __isl_give isl_set **empty);
3164 __isl_give isl_set *isl_set_partial_lexmin(
3165 __isl_take isl_set *set, __isl_take isl_set *dom,
3166 __isl_give isl_set **empty);
3167 __isl_give isl_set *isl_set_partial_lexmax(
3168 __isl_take isl_set *set, __isl_take isl_set *dom,
3169 __isl_give isl_set **empty);
3171 Given a (basic) set C<set> (or C<bset>), the following functions simply
3172 return a set containing the lexicographic minimum or maximum
3173 of the elements in C<set> (or C<bset>).
3174 In case of union sets, the optimum is computed per space.
3176 __isl_give isl_set *isl_basic_set_lexmin(
3177 __isl_take isl_basic_set *bset);
3178 __isl_give isl_set *isl_basic_set_lexmax(
3179 __isl_take isl_basic_set *bset);
3180 __isl_give isl_set *isl_set_lexmin(
3181 __isl_take isl_set *set);
3182 __isl_give isl_set *isl_set_lexmax(
3183 __isl_take isl_set *set);
3184 __isl_give isl_union_set *isl_union_set_lexmin(
3185 __isl_take isl_union_set *uset);
3186 __isl_give isl_union_set *isl_union_set_lexmax(
3187 __isl_take isl_union_set *uset);
3189 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3190 the following functions
3191 compute a relation that maps each element of C<dom>
3192 to the single lexicographic minimum or maximum
3193 of the elements that are associated to that same
3194 element in C<map> (or C<bmap>).
3195 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3196 that contains the elements in C<dom> that do not map
3197 to any elements in C<map> (or C<bmap>).
3198 In other words, the union of the domain of the result and of C<*empty>
3201 __isl_give isl_map *isl_basic_map_partial_lexmax(
3202 __isl_take isl_basic_map *bmap,
3203 __isl_take isl_basic_set *dom,
3204 __isl_give isl_set **empty);
3205 __isl_give isl_map *isl_basic_map_partial_lexmin(
3206 __isl_take isl_basic_map *bmap,
3207 __isl_take isl_basic_set *dom,
3208 __isl_give isl_set **empty);
3209 __isl_give isl_map *isl_map_partial_lexmax(
3210 __isl_take isl_map *map, __isl_take isl_set *dom,
3211 __isl_give isl_set **empty);
3212 __isl_give isl_map *isl_map_partial_lexmin(
3213 __isl_take isl_map *map, __isl_take isl_set *dom,
3214 __isl_give isl_set **empty);
3216 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3217 return a map mapping each element in the domain of
3218 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3219 of all elements associated to that element.
3220 In case of union relations, the optimum is computed per space.
3222 __isl_give isl_map *isl_basic_map_lexmin(
3223 __isl_take isl_basic_map *bmap);
3224 __isl_give isl_map *isl_basic_map_lexmax(
3225 __isl_take isl_basic_map *bmap);
3226 __isl_give isl_map *isl_map_lexmin(
3227 __isl_take isl_map *map);
3228 __isl_give isl_map *isl_map_lexmax(
3229 __isl_take isl_map *map);
3230 __isl_give isl_union_map *isl_union_map_lexmin(
3231 __isl_take isl_union_map *umap);
3232 __isl_give isl_union_map *isl_union_map_lexmax(
3233 __isl_take isl_union_map *umap);
3235 The following functions return their result in the form of
3236 a piecewise multi-affine expression
3237 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3238 but are otherwise equivalent to the corresponding functions
3239 returning a basic set or relation.
3241 __isl_give isl_pw_multi_aff *
3242 isl_basic_map_lexmin_pw_multi_aff(
3243 __isl_take isl_basic_map *bmap);
3244 __isl_give isl_pw_multi_aff *
3245 isl_basic_set_partial_lexmin_pw_multi_aff(
3246 __isl_take isl_basic_set *bset,
3247 __isl_take isl_basic_set *dom,
3248 __isl_give isl_set **empty);
3249 __isl_give isl_pw_multi_aff *
3250 isl_basic_set_partial_lexmax_pw_multi_aff(
3251 __isl_take isl_basic_set *bset,
3252 __isl_take isl_basic_set *dom,
3253 __isl_give isl_set **empty);
3254 __isl_give isl_pw_multi_aff *
3255 isl_basic_map_partial_lexmin_pw_multi_aff(
3256 __isl_take isl_basic_map *bmap,
3257 __isl_take isl_basic_set *dom,
3258 __isl_give isl_set **empty);
3259 __isl_give isl_pw_multi_aff *
3260 isl_basic_map_partial_lexmax_pw_multi_aff(
3261 __isl_take isl_basic_map *bmap,
3262 __isl_take isl_basic_set *dom,
3263 __isl_give isl_set **empty);
3264 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3265 __isl_take isl_set *set);
3266 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3267 __isl_take isl_set *set);
3268 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3269 __isl_take isl_map *map);
3270 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3271 __isl_take isl_map *map);
3275 Lists are defined over several element types, including
3276 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3277 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3278 Here we take lists of C<isl_set>s as an example.
3279 Lists can be created, copied, modified and freed using the following functions.
3281 #include <isl/list.h>
3282 __isl_give isl_set_list *isl_set_list_from_set(
3283 __isl_take isl_set *el);
3284 __isl_give isl_set_list *isl_set_list_alloc(
3285 isl_ctx *ctx, int n);
3286 __isl_give isl_set_list *isl_set_list_copy(
3287 __isl_keep isl_set_list *list);
3288 __isl_give isl_set_list *isl_set_list_insert(
3289 __isl_take isl_set_list *list, unsigned pos,
3290 __isl_take isl_set *el);
3291 __isl_give isl_set_list *isl_set_list_add(
3292 __isl_take isl_set_list *list,
3293 __isl_take isl_set *el);
3294 __isl_give isl_set_list *isl_set_list_drop(
3295 __isl_take isl_set_list *list,
3296 unsigned first, unsigned n);
3297 __isl_give isl_set_list *isl_set_list_set_set(
3298 __isl_take isl_set_list *list, int index,
3299 __isl_take isl_set *set);
3300 __isl_give isl_set_list *isl_set_list_concat(
3301 __isl_take isl_set_list *list1,
3302 __isl_take isl_set_list *list2);
3303 __isl_give isl_set_list *isl_set_list_sort(
3304 __isl_take isl_set_list *list,
3305 int (*cmp)(__isl_keep isl_set *a,
3306 __isl_keep isl_set *b, void *user),
3308 void *isl_set_list_free(__isl_take isl_set_list *list);
3310 C<isl_set_list_alloc> creates an empty list with a capacity for
3311 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3314 Lists can be inspected using the following functions.
3316 #include <isl/list.h>
3317 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3318 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3319 __isl_give isl_set *isl_set_list_get_set(
3320 __isl_keep isl_set_list *list, int index);
3321 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3322 int (*fn)(__isl_take isl_set *el, void *user),
3324 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3325 int (*follows)(__isl_keep isl_set *a,
3326 __isl_keep isl_set *b, void *user),
3328 int (*fn)(__isl_take isl_set *el, void *user),
3331 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3332 strongly connected components of the graph with as vertices the elements
3333 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3334 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3335 should return C<-1> on error.
3337 Lists can be printed using
3339 #include <isl/list.h>
3340 __isl_give isl_printer *isl_printer_print_set_list(
3341 __isl_take isl_printer *p,
3342 __isl_keep isl_set_list *list);
3344 =head2 Multiple Values
3346 An C<isl_multi_val> object represents a sequence of zero or more values,
3347 living in a set space.
3349 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3350 using the following function
3352 #include <isl/val.h>
3353 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3354 __isl_take isl_space *space,
3355 __isl_take isl_val_list *list);
3357 The zero multiple value (with value zero for each set dimension)
3358 can be created using the following function.
3360 #include <isl/val.h>
3361 __isl_give isl_multi_val *isl_multi_val_zero(
3362 __isl_take isl_space *space);
3364 Multiple values can be copied and freed using
3366 #include <isl/val.h>
3367 __isl_give isl_multi_val *isl_multi_val_copy(
3368 __isl_keep isl_multi_val *mv);
3369 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3371 They can be inspected using
3373 #include <isl/val.h>
3374 isl_ctx *isl_multi_val_get_ctx(
3375 __isl_keep isl_multi_val *mv);
3376 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3377 enum isl_dim_type type);
3378 __isl_give isl_val *isl_multi_val_get_val(
3379 __isl_keep isl_multi_val *mv, int pos);
3380 const char *isl_multi_val_get_tuple_name(
3381 __isl_keep isl_multi_val *mv,
3382 enum isl_dim_type type);
3384 They can be modified using
3386 #include <isl/val.h>
3387 __isl_give isl_multi_val *isl_multi_val_set_val(
3388 __isl_take isl_multi_val *mv, int pos,
3389 __isl_take isl_val *val);
3390 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3391 __isl_take isl_multi_val *mv,
3392 enum isl_dim_type type, unsigned pos, const char *s);
3393 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3394 __isl_take isl_multi_val *mv,
3395 enum isl_dim_type type, const char *s);
3396 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3397 __isl_take isl_multi_val *mv,
3398 enum isl_dim_type type, __isl_take isl_id *id);
3400 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3401 __isl_take isl_multi_val *mv,
3402 enum isl_dim_type type, unsigned first, unsigned n);
3403 __isl_give isl_multi_val *isl_multi_val_add_dims(
3404 __isl_take isl_multi_val *mv,
3405 enum isl_dim_type type, unsigned n);
3406 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3407 __isl_take isl_multi_val *mv,
3408 enum isl_dim_type type, unsigned first, unsigned n);
3412 #include <isl/val.h>
3413 __isl_give isl_multi_val *isl_multi_val_align_params(
3414 __isl_take isl_multi_val *mv,
3415 __isl_take isl_space *model);
3416 __isl_give isl_multi_val *isl_multi_val_range_splice(
3417 __isl_take isl_multi_val *mv1, unsigned pos,
3418 __isl_take isl_multi_val *mv2);
3419 __isl_give isl_multi_val *isl_multi_val_range_product(
3420 __isl_take isl_multi_val *mv1,
3421 __isl_take isl_multi_val *mv2);
3422 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3423 __isl_take isl_multi_val *mv1,
3424 __isl_take isl_multi_aff *mv2);
3425 __isl_give isl_multi_val *isl_multi_val_add_val(
3426 __isl_take isl_multi_val *mv,
3427 __isl_take isl_val *v);
3428 __isl_give isl_multi_val *isl_multi_val_mod_val(
3429 __isl_take isl_multi_val *mv,
3430 __isl_take isl_val *v);
3434 Vectors can be created, copied and freed using the following functions.
3436 #include <isl/vec.h>
3437 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3439 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3440 void *isl_vec_free(__isl_take isl_vec *vec);
3442 Note that the elements of a newly created vector may have arbitrary values.
3443 The elements can be changed and inspected using the following functions.
3445 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3446 int isl_vec_size(__isl_keep isl_vec *vec);
3447 int isl_vec_get_element(__isl_keep isl_vec *vec,
3448 int pos, isl_int *v);
3449 __isl_give isl_val *isl_vec_get_element_val(
3450 __isl_keep isl_vec *vec, int pos);
3451 __isl_give isl_vec *isl_vec_set_element(
3452 __isl_take isl_vec *vec, int pos, isl_int v);
3453 __isl_give isl_vec *isl_vec_set_element_si(
3454 __isl_take isl_vec *vec, int pos, int v);
3455 __isl_give isl_vec *isl_vec_set_element_val(
3456 __isl_take isl_vec *vec, int pos,
3457 __isl_take isl_val *v);
3458 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3460 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3462 __isl_give isl_vec *isl_vec_set_val(
3463 __isl_take isl_vec *vec, __isl_take isl_val *v);
3464 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3467 C<isl_vec_get_element> will return a negative value if anything went wrong.
3468 In that case, the value of C<*v> is undefined.
3470 The following function can be used to concatenate two vectors.
3472 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3473 __isl_take isl_vec *vec2);
3477 Matrices can be created, copied and freed using the following functions.
3479 #include <isl/mat.h>
3480 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3481 unsigned n_row, unsigned n_col);
3482 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3483 void *isl_mat_free(__isl_take isl_mat *mat);
3485 Note that the elements of a newly created matrix may have arbitrary values.
3486 The elements can be changed and inspected using the following functions.
3488 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3489 int isl_mat_rows(__isl_keep isl_mat *mat);
3490 int isl_mat_cols(__isl_keep isl_mat *mat);
3491 int isl_mat_get_element(__isl_keep isl_mat *mat,
3492 int row, int col, isl_int *v);
3493 __isl_give isl_val *isl_mat_get_element_val(
3494 __isl_keep isl_mat *mat, int row, int col);
3495 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3496 int row, int col, isl_int v);
3497 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3498 int row, int col, int v);
3499 __isl_give isl_mat *isl_mat_set_element_val(
3500 __isl_take isl_mat *mat, int row, int col,
3501 __isl_take isl_val *v);
3503 C<isl_mat_get_element> will return a negative value if anything went wrong.
3504 In that case, the value of C<*v> is undefined.
3506 The following function can be used to compute the (right) inverse
3507 of a matrix, i.e., a matrix such that the product of the original
3508 and the inverse (in that order) is a multiple of the identity matrix.
3509 The input matrix is assumed to be of full row-rank.
3511 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3513 The following function can be used to compute the (right) kernel
3514 (or null space) of a matrix, i.e., a matrix such that the product of
3515 the original and the kernel (in that order) is the zero matrix.
3517 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3519 =head2 Piecewise Quasi Affine Expressions
3521 The zero quasi affine expression or the quasi affine expression
3522 that is equal to a specified dimension on a given domain can be created using
3524 __isl_give isl_aff *isl_aff_zero_on_domain(
3525 __isl_take isl_local_space *ls);
3526 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3527 __isl_take isl_local_space *ls);
3528 __isl_give isl_aff *isl_aff_var_on_domain(
3529 __isl_take isl_local_space *ls,
3530 enum isl_dim_type type, unsigned pos);
3531 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3532 __isl_take isl_local_space *ls,
3533 enum isl_dim_type type, unsigned pos);
3535 Note that the space in which the resulting objects live is a map space
3536 with the given space as domain and a one-dimensional range.
3538 An empty piecewise quasi affine expression (one with no cells)
3539 or a piecewise quasi affine expression with a single cell can
3540 be created using the following functions.
3542 #include <isl/aff.h>
3543 __isl_give isl_pw_aff *isl_pw_aff_empty(
3544 __isl_take isl_space *space);
3545 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3546 __isl_take isl_set *set, __isl_take isl_aff *aff);
3547 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3548 __isl_take isl_aff *aff);
3550 A piecewise quasi affine expression that is equal to 1 on a set
3551 and 0 outside the set can be created using the following function.
3553 #include <isl/aff.h>
3554 __isl_give isl_pw_aff *isl_set_indicator_function(
3555 __isl_take isl_set *set);
3557 Quasi affine expressions can be copied and freed using
3559 #include <isl/aff.h>
3560 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3561 void *isl_aff_free(__isl_take isl_aff *aff);
3563 __isl_give isl_pw_aff *isl_pw_aff_copy(
3564 __isl_keep isl_pw_aff *pwaff);
3565 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3567 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3568 using the following function. The constraint is required to have
3569 a non-zero coefficient for the specified dimension.
3571 #include <isl/constraint.h>
3572 __isl_give isl_aff *isl_constraint_get_bound(
3573 __isl_keep isl_constraint *constraint,
3574 enum isl_dim_type type, int pos);
3576 The entire affine expression of the constraint can also be extracted
3577 using the following function.
3579 #include <isl/constraint.h>
3580 __isl_give isl_aff *isl_constraint_get_aff(
3581 __isl_keep isl_constraint *constraint);
3583 Conversely, an equality constraint equating
3584 the affine expression to zero or an inequality constraint enforcing
3585 the affine expression to be non-negative, can be constructed using
3587 __isl_give isl_constraint *isl_equality_from_aff(
3588 __isl_take isl_aff *aff);
3589 __isl_give isl_constraint *isl_inequality_from_aff(
3590 __isl_take isl_aff *aff);
3592 The expression can be inspected using
3594 #include <isl/aff.h>
3595 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3596 int isl_aff_dim(__isl_keep isl_aff *aff,
3597 enum isl_dim_type type);
3598 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3599 __isl_keep isl_aff *aff);
3600 __isl_give isl_local_space *isl_aff_get_local_space(
3601 __isl_keep isl_aff *aff);
3602 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3603 enum isl_dim_type type, unsigned pos);
3604 const char *isl_pw_aff_get_dim_name(
3605 __isl_keep isl_pw_aff *pa,
3606 enum isl_dim_type type, unsigned pos);
3607 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3608 enum isl_dim_type type, unsigned pos);
3609 __isl_give isl_id *isl_pw_aff_get_dim_id(
3610 __isl_keep isl_pw_aff *pa,
3611 enum isl_dim_type type, unsigned pos);
3612 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3613 __isl_keep isl_pw_aff *pa,
3614 enum isl_dim_type type);
3615 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3617 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3618 enum isl_dim_type type, int pos, isl_int *v);
3619 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3621 __isl_give isl_aff *isl_aff_get_div(
3622 __isl_keep isl_aff *aff, int pos);
3624 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3625 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3626 int (*fn)(__isl_take isl_set *set,
3627 __isl_take isl_aff *aff,
3628 void *user), void *user);
3630 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3631 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3633 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3634 enum isl_dim_type type, unsigned first, unsigned n);
3635 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3636 enum isl_dim_type type, unsigned first, unsigned n);
3638 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3639 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3640 enum isl_dim_type type);
3641 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3643 It can be modified using
3645 #include <isl/aff.h>
3646 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3647 __isl_take isl_pw_aff *pwaff,
3648 enum isl_dim_type type, __isl_take isl_id *id);
3649 __isl_give isl_aff *isl_aff_set_dim_name(
3650 __isl_take isl_aff *aff, enum isl_dim_type type,
3651 unsigned pos, const char *s);
3652 __isl_give isl_aff *isl_aff_set_dim_id(
3653 __isl_take isl_aff *aff, enum isl_dim_type type,
3654 unsigned pos, __isl_take isl_id *id);
3655 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3656 __isl_take isl_pw_aff *pma,
3657 enum isl_dim_type type, unsigned pos,
3658 __isl_take isl_id *id);
3659 __isl_give isl_aff *isl_aff_set_constant(
3660 __isl_take isl_aff *aff, isl_int v);
3661 __isl_give isl_aff *isl_aff_set_constant_si(
3662 __isl_take isl_aff *aff, int v);
3663 __isl_give isl_aff *isl_aff_set_coefficient(
3664 __isl_take isl_aff *aff,
3665 enum isl_dim_type type, int pos, isl_int v);
3666 __isl_give isl_aff *isl_aff_set_coefficient_si(
3667 __isl_take isl_aff *aff,
3668 enum isl_dim_type type, int pos, int v);
3669 __isl_give isl_aff *isl_aff_set_denominator(
3670 __isl_take isl_aff *aff, isl_int v);
3672 __isl_give isl_aff *isl_aff_add_constant(
3673 __isl_take isl_aff *aff, isl_int v);
3674 __isl_give isl_aff *isl_aff_add_constant_si(
3675 __isl_take isl_aff *aff, int v);
3676 __isl_give isl_aff *isl_aff_add_constant_num(
3677 __isl_take isl_aff *aff, isl_int v);
3678 __isl_give isl_aff *isl_aff_add_constant_num_si(
3679 __isl_take isl_aff *aff, int v);
3680 __isl_give isl_aff *isl_aff_add_coefficient(
3681 __isl_take isl_aff *aff,
3682 enum isl_dim_type type, int pos, isl_int v);
3683 __isl_give isl_aff *isl_aff_add_coefficient_si(
3684 __isl_take isl_aff *aff,
3685 enum isl_dim_type type, int pos, int v);
3687 __isl_give isl_aff *isl_aff_insert_dims(
3688 __isl_take isl_aff *aff,
3689 enum isl_dim_type type, unsigned first, unsigned n);
3690 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3691 __isl_take isl_pw_aff *pwaff,
3692 enum isl_dim_type type, unsigned first, unsigned n);
3693 __isl_give isl_aff *isl_aff_add_dims(
3694 __isl_take isl_aff *aff,
3695 enum isl_dim_type type, unsigned n);
3696 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3697 __isl_take isl_pw_aff *pwaff,
3698 enum isl_dim_type type, unsigned n);
3699 __isl_give isl_aff *isl_aff_drop_dims(
3700 __isl_take isl_aff *aff,
3701 enum isl_dim_type type, unsigned first, unsigned n);
3702 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3703 __isl_take isl_pw_aff *pwaff,
3704 enum isl_dim_type type, unsigned first, unsigned n);
3706 Note that the C<set_constant> and C<set_coefficient> functions
3707 set the I<numerator> of the constant or coefficient, while
3708 C<add_constant> and C<add_coefficient> add an integer value to
3709 the possibly rational constant or coefficient.
3710 The C<add_constant_num> functions add an integer value to
3713 To check whether an affine expressions is obviously zero
3714 or obviously equal to some other affine expression, use
3716 #include <isl/aff.h>
3717 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3718 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3719 __isl_keep isl_aff *aff2);
3720 int isl_pw_aff_plain_is_equal(
3721 __isl_keep isl_pw_aff *pwaff1,
3722 __isl_keep isl_pw_aff *pwaff2);
3726 #include <isl/aff.h>
3727 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3728 __isl_take isl_aff *aff2);
3729 __isl_give isl_pw_aff *isl_pw_aff_add(
3730 __isl_take isl_pw_aff *pwaff1,
3731 __isl_take isl_pw_aff *pwaff2);
3732 __isl_give isl_pw_aff *isl_pw_aff_min(
3733 __isl_take isl_pw_aff *pwaff1,
3734 __isl_take isl_pw_aff *pwaff2);
3735 __isl_give isl_pw_aff *isl_pw_aff_max(
3736 __isl_take isl_pw_aff *pwaff1,
3737 __isl_take isl_pw_aff *pwaff2);
3738 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3739 __isl_take isl_aff *aff2);
3740 __isl_give isl_pw_aff *isl_pw_aff_sub(
3741 __isl_take isl_pw_aff *pwaff1,
3742 __isl_take isl_pw_aff *pwaff2);
3743 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3744 __isl_give isl_pw_aff *isl_pw_aff_neg(
3745 __isl_take isl_pw_aff *pwaff);
3746 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3747 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3748 __isl_take isl_pw_aff *pwaff);
3749 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3750 __isl_give isl_pw_aff *isl_pw_aff_floor(
3751 __isl_take isl_pw_aff *pwaff);
3752 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3754 __isl_give isl_pw_aff *isl_pw_aff_mod(
3755 __isl_take isl_pw_aff *pwaff, isl_int mod);
3756 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3758 __isl_give isl_pw_aff *isl_pw_aff_scale(
3759 __isl_take isl_pw_aff *pwaff, isl_int f);
3760 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3762 __isl_give isl_aff *isl_aff_scale_down_ui(
3763 __isl_take isl_aff *aff, unsigned f);
3764 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3765 __isl_take isl_pw_aff *pwaff, isl_int f);
3767 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3768 __isl_take isl_pw_aff_list *list);
3769 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3770 __isl_take isl_pw_aff_list *list);
3772 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3773 __isl_take isl_pw_aff *pwqp);
3775 __isl_give isl_aff *isl_aff_align_params(
3776 __isl_take isl_aff *aff,
3777 __isl_take isl_space *model);
3778 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3779 __isl_take isl_pw_aff *pwaff,
3780 __isl_take isl_space *model);
3782 __isl_give isl_aff *isl_aff_project_domain_on_params(
3783 __isl_take isl_aff *aff);
3785 __isl_give isl_aff *isl_aff_gist_params(
3786 __isl_take isl_aff *aff,
3787 __isl_take isl_set *context);
3788 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3789 __isl_take isl_set *context);
3790 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3791 __isl_take isl_pw_aff *pwaff,
3792 __isl_take isl_set *context);
3793 __isl_give isl_pw_aff *isl_pw_aff_gist(
3794 __isl_take isl_pw_aff *pwaff,
3795 __isl_take isl_set *context);
3797 __isl_give isl_set *isl_pw_aff_domain(
3798 __isl_take isl_pw_aff *pwaff);
3799 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3800 __isl_take isl_pw_aff *pa,
3801 __isl_take isl_set *set);
3802 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3803 __isl_take isl_pw_aff *pa,
3804 __isl_take isl_set *set);
3806 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3807 __isl_take isl_aff *aff2);
3808 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3809 __isl_take isl_aff *aff2);
3810 __isl_give isl_pw_aff *isl_pw_aff_mul(
3811 __isl_take isl_pw_aff *pwaff1,
3812 __isl_take isl_pw_aff *pwaff2);
3813 __isl_give isl_pw_aff *isl_pw_aff_div(
3814 __isl_take isl_pw_aff *pa1,
3815 __isl_take isl_pw_aff *pa2);
3816 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3817 __isl_take isl_pw_aff *pa1,
3818 __isl_take isl_pw_aff *pa2);
3819 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3820 __isl_take isl_pw_aff *pa1,
3821 __isl_take isl_pw_aff *pa2);
3823 When multiplying two affine expressions, at least one of the two needs
3824 to be a constant. Similarly, when dividing an affine expression by another,
3825 the second expression needs to be a constant.
3826 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3827 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3830 #include <isl/aff.h>
3831 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3832 __isl_take isl_aff *aff,
3833 __isl_take isl_multi_aff *ma);
3834 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3835 __isl_take isl_pw_aff *pa,
3836 __isl_take isl_multi_aff *ma);
3837 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3838 __isl_take isl_pw_aff *pa,
3839 __isl_take isl_pw_multi_aff *pma);
3841 These functions precompose the input expression by the given
3842 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3843 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3844 into the (piecewise) affine expression.
3845 Objects of type C<isl_multi_aff> are described in
3846 L</"Piecewise Multiple Quasi Affine Expressions">.
3848 #include <isl/aff.h>
3849 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3850 __isl_take isl_aff *aff);
3851 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3852 __isl_take isl_aff *aff);
3853 __isl_give isl_basic_set *isl_aff_le_basic_set(
3854 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3855 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3856 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3857 __isl_give isl_set *isl_pw_aff_eq_set(
3858 __isl_take isl_pw_aff *pwaff1,
3859 __isl_take isl_pw_aff *pwaff2);
3860 __isl_give isl_set *isl_pw_aff_ne_set(
3861 __isl_take isl_pw_aff *pwaff1,
3862 __isl_take isl_pw_aff *pwaff2);
3863 __isl_give isl_set *isl_pw_aff_le_set(
3864 __isl_take isl_pw_aff *pwaff1,
3865 __isl_take isl_pw_aff *pwaff2);
3866 __isl_give isl_set *isl_pw_aff_lt_set(
3867 __isl_take isl_pw_aff *pwaff1,
3868 __isl_take isl_pw_aff *pwaff2);
3869 __isl_give isl_set *isl_pw_aff_ge_set(
3870 __isl_take isl_pw_aff *pwaff1,
3871 __isl_take isl_pw_aff *pwaff2);
3872 __isl_give isl_set *isl_pw_aff_gt_set(
3873 __isl_take isl_pw_aff *pwaff1,
3874 __isl_take isl_pw_aff *pwaff2);
3876 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_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_lt_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_ge_set(
3889 __isl_take isl_pw_aff_list *list1,
3890 __isl_take isl_pw_aff_list *list2);
3891 __isl_give isl_set *isl_pw_aff_list_gt_set(
3892 __isl_take isl_pw_aff_list *list1,
3893 __isl_take isl_pw_aff_list *list2);
3895 The function C<isl_aff_neg_basic_set> returns a basic set
3896 containing those elements in the domain space
3897 of C<aff> where C<aff> is negative.
3898 The function C<isl_aff_ge_basic_set> returns a basic set
3899 containing those elements in the shared space
3900 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3901 The function C<isl_pw_aff_ge_set> returns a set
3902 containing those elements in the shared domain
3903 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3904 The functions operating on C<isl_pw_aff_list> apply the corresponding
3905 C<isl_pw_aff> function to each pair of elements in the two lists.
3907 #include <isl/aff.h>
3908 __isl_give isl_set *isl_pw_aff_nonneg_set(
3909 __isl_take isl_pw_aff *pwaff);
3910 __isl_give isl_set *isl_pw_aff_zero_set(
3911 __isl_take isl_pw_aff *pwaff);
3912 __isl_give isl_set *isl_pw_aff_non_zero_set(
3913 __isl_take isl_pw_aff *pwaff);
3915 The function C<isl_pw_aff_nonneg_set> returns a set
3916 containing those elements in the domain
3917 of C<pwaff> where C<pwaff> is non-negative.
3919 #include <isl/aff.h>
3920 __isl_give isl_pw_aff *isl_pw_aff_cond(
3921 __isl_take isl_pw_aff *cond,
3922 __isl_take isl_pw_aff *pwaff_true,
3923 __isl_take isl_pw_aff *pwaff_false);
3925 The function C<isl_pw_aff_cond> performs a conditional operator
3926 and returns an expression that is equal to C<pwaff_true>
3927 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3928 where C<cond> is zero.
3930 #include <isl/aff.h>
3931 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3932 __isl_take isl_pw_aff *pwaff1,
3933 __isl_take isl_pw_aff *pwaff2);
3934 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3935 __isl_take isl_pw_aff *pwaff1,
3936 __isl_take isl_pw_aff *pwaff2);
3937 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3938 __isl_take isl_pw_aff *pwaff1,
3939 __isl_take isl_pw_aff *pwaff2);
3941 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3942 expression with a domain that is the union of those of C<pwaff1> and
3943 C<pwaff2> and such that on each cell, the quasi-affine expression is
3944 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3945 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3946 associated expression is the defined one.
3948 An expression can be read from input using
3950 #include <isl/aff.h>
3951 __isl_give isl_aff *isl_aff_read_from_str(
3952 isl_ctx *ctx, const char *str);
3953 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3954 isl_ctx *ctx, const char *str);
3956 An expression can be printed using
3958 #include <isl/aff.h>
3959 __isl_give isl_printer *isl_printer_print_aff(
3960 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3962 __isl_give isl_printer *isl_printer_print_pw_aff(
3963 __isl_take isl_printer *p,
3964 __isl_keep isl_pw_aff *pwaff);
3966 =head2 Piecewise Multiple Quasi Affine Expressions
3968 An C<isl_multi_aff> object represents a sequence of
3969 zero or more affine expressions, all defined on the same domain space.
3970 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3971 zero or more piecewise affine expressions.
3973 An C<isl_multi_aff> can be constructed from a single
3974 C<isl_aff> or an C<isl_aff_list> using the
3975 following functions. Similarly for C<isl_multi_pw_aff>.
3977 #include <isl/aff.h>
3978 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3979 __isl_take isl_aff *aff);
3980 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3981 __isl_take isl_pw_aff *pa);
3982 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3983 __isl_take isl_space *space,
3984 __isl_take isl_aff_list *list);
3986 An empty piecewise multiple quasi affine expression (one with no cells),
3987 the zero piecewise multiple quasi affine expression (with value zero
3988 for each output dimension),
3989 a piecewise multiple quasi affine expression with a single cell (with
3990 either a universe or a specified domain) or
3991 a zero-dimensional piecewise multiple quasi affine expression
3993 can be created using the following functions.
3995 #include <isl/aff.h>
3996 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3997 __isl_take isl_space *space);
3998 __isl_give isl_multi_aff *isl_multi_aff_zero(
3999 __isl_take isl_space *space);
4000 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4001 __isl_take isl_space *space);
4002 __isl_give isl_multi_aff *isl_multi_aff_identity(
4003 __isl_take isl_space *space);
4004 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4005 __isl_take isl_space *space);
4006 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4007 __isl_take isl_space *space);
4008 __isl_give isl_pw_multi_aff *
4009 isl_pw_multi_aff_from_multi_aff(
4010 __isl_take isl_multi_aff *ma);
4011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4012 __isl_take isl_set *set,
4013 __isl_take isl_multi_aff *maff);
4014 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4015 __isl_take isl_set *set);
4017 __isl_give isl_union_pw_multi_aff *
4018 isl_union_pw_multi_aff_empty(
4019 __isl_take isl_space *space);
4020 __isl_give isl_union_pw_multi_aff *
4021 isl_union_pw_multi_aff_add_pw_multi_aff(
4022 __isl_take isl_union_pw_multi_aff *upma,
4023 __isl_take isl_pw_multi_aff *pma);
4024 __isl_give isl_union_pw_multi_aff *
4025 isl_union_pw_multi_aff_from_domain(
4026 __isl_take isl_union_set *uset);
4028 A piecewise multiple quasi affine expression can also be initialized
4029 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4030 and the C<isl_map> is single-valued.
4031 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4032 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4034 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4035 __isl_take isl_set *set);
4036 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4037 __isl_take isl_map *map);
4039 __isl_give isl_union_pw_multi_aff *
4040 isl_union_pw_multi_aff_from_union_set(
4041 __isl_take isl_union_set *uset);
4042 __isl_give isl_union_pw_multi_aff *
4043 isl_union_pw_multi_aff_from_union_map(
4044 __isl_take isl_union_map *umap);
4046 Multiple quasi affine expressions can be copied and freed using
4048 #include <isl/aff.h>
4049 __isl_give isl_multi_aff *isl_multi_aff_copy(
4050 __isl_keep isl_multi_aff *maff);
4051 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4054 __isl_keep isl_pw_multi_aff *pma);
4055 void *isl_pw_multi_aff_free(
4056 __isl_take isl_pw_multi_aff *pma);
4058 __isl_give isl_union_pw_multi_aff *
4059 isl_union_pw_multi_aff_copy(
4060 __isl_keep isl_union_pw_multi_aff *upma);
4061 void *isl_union_pw_multi_aff_free(
4062 __isl_take isl_union_pw_multi_aff *upma);
4064 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4065 __isl_keep isl_multi_pw_aff *mpa);
4066 void *isl_multi_pw_aff_free(
4067 __isl_take isl_multi_pw_aff *mpa);
4069 The expression can be inspected using
4071 #include <isl/aff.h>
4072 isl_ctx *isl_multi_aff_get_ctx(
4073 __isl_keep isl_multi_aff *maff);
4074 isl_ctx *isl_pw_multi_aff_get_ctx(
4075 __isl_keep isl_pw_multi_aff *pma);
4076 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4077 __isl_keep isl_union_pw_multi_aff *upma);
4078 isl_ctx *isl_multi_pw_aff_get_ctx(
4079 __isl_keep isl_multi_pw_aff *mpa);
4080 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4081 enum isl_dim_type type);
4082 unsigned isl_pw_multi_aff_dim(
4083 __isl_keep isl_pw_multi_aff *pma,
4084 enum isl_dim_type type);
4085 unsigned isl_multi_pw_aff_dim(
4086 __isl_keep isl_multi_pw_aff *mpa,
4087 enum isl_dim_type type);
4088 __isl_give isl_aff *isl_multi_aff_get_aff(
4089 __isl_keep isl_multi_aff *multi, int pos);
4090 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4091 __isl_keep isl_pw_multi_aff *pma, int pos);
4092 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4093 __isl_keep isl_multi_pw_aff *mpa, int pos);
4094 const char *isl_pw_multi_aff_get_dim_name(
4095 __isl_keep isl_pw_multi_aff *pma,
4096 enum isl_dim_type type, unsigned pos);
4097 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4098 __isl_keep isl_pw_multi_aff *pma,
4099 enum isl_dim_type type, unsigned pos);
4100 const char *isl_multi_aff_get_tuple_name(
4101 __isl_keep isl_multi_aff *multi,
4102 enum isl_dim_type type);
4103 int isl_pw_multi_aff_has_tuple_name(
4104 __isl_keep isl_pw_multi_aff *pma,
4105 enum isl_dim_type type);
4106 const char *isl_pw_multi_aff_get_tuple_name(
4107 __isl_keep isl_pw_multi_aff *pma,
4108 enum isl_dim_type type);
4109 int isl_pw_multi_aff_has_tuple_id(
4110 __isl_keep isl_pw_multi_aff *pma,
4111 enum isl_dim_type type);
4112 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4113 __isl_keep isl_pw_multi_aff *pma,
4114 enum isl_dim_type type);
4116 int isl_pw_multi_aff_foreach_piece(
4117 __isl_keep isl_pw_multi_aff *pma,
4118 int (*fn)(__isl_take isl_set *set,
4119 __isl_take isl_multi_aff *maff,
4120 void *user), void *user);
4122 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4123 __isl_keep isl_union_pw_multi_aff *upma,
4124 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4125 void *user), void *user);
4127 It can be modified using
4129 #include <isl/aff.h>
4130 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4131 __isl_take isl_multi_aff *multi, int pos,
4132 __isl_take isl_aff *aff);
4133 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4134 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4135 __isl_take isl_pw_aff *pa);
4136 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4137 __isl_take isl_multi_aff *maff,
4138 enum isl_dim_type type, unsigned pos, const char *s);
4139 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4140 __isl_take isl_multi_aff *maff,
4141 enum isl_dim_type type, const char *s);
4142 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4143 __isl_take isl_multi_aff *maff,
4144 enum isl_dim_type type, __isl_take isl_id *id);
4145 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4146 __isl_take isl_pw_multi_aff *pma,
4147 enum isl_dim_type type, __isl_take isl_id *id);
4149 __isl_give isl_multi_pw_aff *
4150 isl_multi_pw_aff_set_dim_name(
4151 __isl_take isl_multi_pw_aff *mpa,
4152 enum isl_dim_type type, unsigned pos, const char *s);
4153 __isl_give isl_multi_pw_aff *
4154 isl_multi_pw_aff_set_tuple_name(
4155 __isl_take isl_multi_pw_aff *mpa,
4156 enum isl_dim_type type, const char *s);
4158 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4159 __isl_take isl_multi_aff *ma,
4160 enum isl_dim_type type, unsigned first, unsigned n);
4161 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4162 __isl_take isl_multi_aff *ma,
4163 enum isl_dim_type type, unsigned n);
4164 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4165 __isl_take isl_multi_aff *maff,
4166 enum isl_dim_type type, unsigned first, unsigned n);
4167 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4168 __isl_take isl_pw_multi_aff *pma,
4169 enum isl_dim_type type, unsigned first, unsigned n);
4171 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4172 __isl_take isl_multi_pw_aff *mpa,
4173 enum isl_dim_type type, unsigned first, unsigned n);
4174 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4175 __isl_take isl_multi_pw_aff *mpa,
4176 enum isl_dim_type type, unsigned n);
4178 To check whether two multiple affine expressions are
4179 obviously equal to each other, use
4181 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4182 __isl_keep isl_multi_aff *maff2);
4183 int isl_pw_multi_aff_plain_is_equal(
4184 __isl_keep isl_pw_multi_aff *pma1,
4185 __isl_keep isl_pw_multi_aff *pma2);
4189 #include <isl/aff.h>
4190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4191 __isl_take isl_pw_multi_aff *pma1,
4192 __isl_take isl_pw_multi_aff *pma2);
4193 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4194 __isl_take isl_pw_multi_aff *pma1,
4195 __isl_take isl_pw_multi_aff *pma2);
4196 __isl_give isl_multi_aff *isl_multi_aff_add(
4197 __isl_take isl_multi_aff *maff1,
4198 __isl_take isl_multi_aff *maff2);
4199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4200 __isl_take isl_pw_multi_aff *pma1,
4201 __isl_take isl_pw_multi_aff *pma2);
4202 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4203 __isl_take isl_union_pw_multi_aff *upma1,
4204 __isl_take isl_union_pw_multi_aff *upma2);
4205 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4206 __isl_take isl_pw_multi_aff *pma1,
4207 __isl_take isl_pw_multi_aff *pma2);
4208 __isl_give isl_multi_aff *isl_multi_aff_sub(
4209 __isl_take isl_multi_aff *ma1,
4210 __isl_take isl_multi_aff *ma2);
4211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4212 __isl_take isl_pw_multi_aff *pma1,
4213 __isl_take isl_pw_multi_aff *pma2);
4214 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4215 __isl_take isl_union_pw_multi_aff *upma1,
4216 __isl_take isl_union_pw_multi_aff *upma2);
4218 C<isl_multi_aff_sub> subtracts the second argument from the first.
4220 __isl_give isl_multi_aff *isl_multi_aff_scale(
4221 __isl_take isl_multi_aff *maff,
4223 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4224 __isl_take isl_multi_aff *ma,
4225 __isl_take isl_vec *v);
4226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4227 __isl_take isl_pw_multi_aff *pma,
4228 __isl_take isl_vec *v);
4229 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4230 __isl_take isl_union_pw_multi_aff *upma,
4231 __isl_take isl_vec *v);
4233 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4234 by the corresponding elements of C<v>.
4236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4237 __isl_take isl_pw_multi_aff *pma,
4238 __isl_take isl_set *set);
4239 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4240 __isl_take isl_pw_multi_aff *pma,
4241 __isl_take isl_set *set);
4242 __isl_give isl_union_pw_multi_aff *
4243 isl_union_pw_multi_aff_intersect_domain(
4244 __isl_take isl_union_pw_multi_aff *upma,
4245 __isl_take isl_union_set *uset);
4246 __isl_give isl_multi_aff *isl_multi_aff_lift(
4247 __isl_take isl_multi_aff *maff,
4248 __isl_give isl_local_space **ls);
4249 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4250 __isl_take isl_pw_multi_aff *pma);
4251 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4252 __isl_take isl_multi_aff *multi,
4253 __isl_take isl_space *model);
4254 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4255 __isl_take isl_pw_multi_aff *pma,
4256 __isl_take isl_space *model);
4257 __isl_give isl_pw_multi_aff *
4258 isl_pw_multi_aff_project_domain_on_params(
4259 __isl_take isl_pw_multi_aff *pma);
4260 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4261 __isl_take isl_multi_aff *maff,
4262 __isl_take isl_set *context);
4263 __isl_give isl_multi_aff *isl_multi_aff_gist(
4264 __isl_take isl_multi_aff *maff,
4265 __isl_take isl_set *context);
4266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4267 __isl_take isl_pw_multi_aff *pma,
4268 __isl_take isl_set *set);
4269 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4270 __isl_take isl_pw_multi_aff *pma,
4271 __isl_take isl_set *set);
4272 __isl_give isl_set *isl_pw_multi_aff_domain(
4273 __isl_take isl_pw_multi_aff *pma);
4274 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4275 __isl_take isl_union_pw_multi_aff *upma);
4276 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4277 __isl_take isl_multi_aff *ma1, unsigned pos,
4278 __isl_take isl_multi_aff *ma2);
4279 __isl_give isl_multi_aff *isl_multi_aff_splice(
4280 __isl_take isl_multi_aff *ma1,
4281 unsigned in_pos, unsigned out_pos,
4282 __isl_take isl_multi_aff *ma2);
4283 __isl_give isl_multi_aff *isl_multi_aff_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_flat_range_product(
4287 __isl_take isl_multi_aff *ma1,
4288 __isl_take isl_multi_aff *ma2);
4289 __isl_give isl_multi_aff *isl_multi_aff_product(
4290 __isl_take isl_multi_aff *ma1,
4291 __isl_take isl_multi_aff *ma2);
4292 __isl_give isl_pw_multi_aff *
4293 isl_pw_multi_aff_range_product(
4294 __isl_take isl_pw_multi_aff *pma1,
4295 __isl_take isl_pw_multi_aff *pma2);
4296 __isl_give isl_pw_multi_aff *
4297 isl_pw_multi_aff_flat_range_product(
4298 __isl_take isl_pw_multi_aff *pma1,
4299 __isl_take isl_pw_multi_aff *pma2);
4300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4301 __isl_take isl_pw_multi_aff *pma1,
4302 __isl_take isl_pw_multi_aff *pma2);
4303 __isl_give isl_union_pw_multi_aff *
4304 isl_union_pw_multi_aff_flat_range_product(
4305 __isl_take isl_union_pw_multi_aff *upma1,
4306 __isl_take isl_union_pw_multi_aff *upma2);
4307 __isl_give isl_multi_pw_aff *
4308 isl_multi_pw_aff_range_splice(
4309 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4310 __isl_take isl_multi_pw_aff *mpa2);
4311 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4312 __isl_take isl_multi_pw_aff *mpa1,
4313 unsigned in_pos, unsigned out_pos,
4314 __isl_take isl_multi_pw_aff *mpa2);
4315 __isl_give isl_multi_pw_aff *
4316 isl_multi_pw_aff_range_product(
4317 __isl_take isl_multi_pw_aff *mpa1,
4318 __isl_take isl_multi_pw_aff *mpa2);
4319 __isl_give isl_multi_pw_aff *
4320 isl_multi_pw_aff_flat_range_product(
4321 __isl_take isl_multi_pw_aff *mpa1,
4322 __isl_take isl_multi_pw_aff *mpa2);
4324 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4325 then it is assigned the local space that lies at the basis of
4326 the lifting applied.
4328 #include <isl/aff.h>
4329 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4330 __isl_take isl_multi_aff *ma1,
4331 __isl_take isl_multi_aff *ma2);
4332 __isl_give isl_pw_multi_aff *
4333 isl_pw_multi_aff_pullback_multi_aff(
4334 __isl_take isl_pw_multi_aff *pma,
4335 __isl_take isl_multi_aff *ma);
4336 __isl_give isl_pw_multi_aff *
4337 isl_pw_multi_aff_pullback_pw_multi_aff(
4338 __isl_take isl_pw_multi_aff *pma1,
4339 __isl_take isl_pw_multi_aff *pma2);
4341 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4342 In other words, C<ma2> is plugged
4345 __isl_give isl_set *isl_multi_aff_lex_le_set(
4346 __isl_take isl_multi_aff *ma1,
4347 __isl_take isl_multi_aff *ma2);
4348 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4349 __isl_take isl_multi_aff *ma1,
4350 __isl_take isl_multi_aff *ma2);
4352 The function C<isl_multi_aff_lex_le_set> returns a set
4353 containing those elements in the shared domain space
4354 where C<ma1> is lexicographically smaller than or
4357 An expression can be read from input using
4359 #include <isl/aff.h>
4360 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4361 isl_ctx *ctx, const char *str);
4362 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4363 isl_ctx *ctx, const char *str);
4364 __isl_give isl_union_pw_multi_aff *
4365 isl_union_pw_multi_aff_read_from_str(
4366 isl_ctx *ctx, const char *str);
4368 An expression can be printed using
4370 #include <isl/aff.h>
4371 __isl_give isl_printer *isl_printer_print_multi_aff(
4372 __isl_take isl_printer *p,
4373 __isl_keep isl_multi_aff *maff);
4374 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4375 __isl_take isl_printer *p,
4376 __isl_keep isl_pw_multi_aff *pma);
4377 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4378 __isl_take isl_printer *p,
4379 __isl_keep isl_union_pw_multi_aff *upma);
4380 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4381 __isl_take isl_printer *p,
4382 __isl_keep isl_multi_pw_aff *mpa);
4386 Points are elements of a set. They can be used to construct
4387 simple sets (boxes) or they can be used to represent the
4388 individual elements of a set.
4389 The zero point (the origin) can be created using
4391 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4393 The coordinates of a point can be inspected, set and changed
4396 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4397 enum isl_dim_type type, int pos, isl_int *v);
4398 __isl_give isl_val *isl_point_get_coordinate_val(
4399 __isl_keep isl_point *pnt,
4400 enum isl_dim_type type, int pos);
4401 __isl_give isl_point *isl_point_set_coordinate(
4402 __isl_take isl_point *pnt,
4403 enum isl_dim_type type, int pos, isl_int v);
4404 __isl_give isl_point *isl_point_set_coordinate_val(
4405 __isl_take isl_point *pnt,
4406 enum isl_dim_type type, int pos,
4407 __isl_take isl_val *v);
4409 __isl_give isl_point *isl_point_add_ui(
4410 __isl_take isl_point *pnt,
4411 enum isl_dim_type type, int pos, unsigned val);
4412 __isl_give isl_point *isl_point_sub_ui(
4413 __isl_take isl_point *pnt,
4414 enum isl_dim_type type, int pos, unsigned val);
4416 Other properties can be obtained using
4418 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4420 Points can be copied or freed using
4422 __isl_give isl_point *isl_point_copy(
4423 __isl_keep isl_point *pnt);
4424 void isl_point_free(__isl_take isl_point *pnt);
4426 A singleton set can be created from a point using
4428 __isl_give isl_basic_set *isl_basic_set_from_point(
4429 __isl_take isl_point *pnt);
4430 __isl_give isl_set *isl_set_from_point(
4431 __isl_take isl_point *pnt);
4433 and a box can be created from two opposite extremal points using
4435 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4436 __isl_take isl_point *pnt1,
4437 __isl_take isl_point *pnt2);
4438 __isl_give isl_set *isl_set_box_from_points(
4439 __isl_take isl_point *pnt1,
4440 __isl_take isl_point *pnt2);
4442 All elements of a B<bounded> (union) set can be enumerated using
4443 the following functions.
4445 int isl_set_foreach_point(__isl_keep isl_set *set,
4446 int (*fn)(__isl_take isl_point *pnt, void *user),
4448 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4449 int (*fn)(__isl_take isl_point *pnt, void *user),
4452 The function C<fn> is called for each integer point in
4453 C<set> with as second argument the last argument of
4454 the C<isl_set_foreach_point> call. The function C<fn>
4455 should return C<0> on success and C<-1> on failure.
4456 In the latter case, C<isl_set_foreach_point> will stop
4457 enumerating and return C<-1> as well.
4458 If the enumeration is performed successfully and to completion,
4459 then C<isl_set_foreach_point> returns C<0>.
4461 To obtain a single point of a (basic) set, use
4463 __isl_give isl_point *isl_basic_set_sample_point(
4464 __isl_take isl_basic_set *bset);
4465 __isl_give isl_point *isl_set_sample_point(
4466 __isl_take isl_set *set);
4468 If C<set> does not contain any (integer) points, then the
4469 resulting point will be ``void'', a property that can be
4472 int isl_point_is_void(__isl_keep isl_point *pnt);
4474 =head2 Piecewise Quasipolynomials
4476 A piecewise quasipolynomial is a particular kind of function that maps
4477 a parametric point to a rational value.
4478 More specifically, a quasipolynomial is a polynomial expression in greatest
4479 integer parts of affine expressions of parameters and variables.
4480 A piecewise quasipolynomial is a subdivision of a given parametric
4481 domain into disjoint cells with a quasipolynomial associated to
4482 each cell. The value of the piecewise quasipolynomial at a given
4483 point is the value of the quasipolynomial associated to the cell
4484 that contains the point. Outside of the union of cells,
4485 the value is assumed to be zero.
4486 For example, the piecewise quasipolynomial
4488 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4490 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4491 A given piecewise quasipolynomial has a fixed domain dimension.
4492 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4493 defined over different domains.
4494 Piecewise quasipolynomials are mainly used by the C<barvinok>
4495 library for representing the number of elements in a parametric set or map.
4496 For example, the piecewise quasipolynomial above represents
4497 the number of points in the map
4499 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4501 =head3 Input and Output
4503 Piecewise quasipolynomials can be read from input using
4505 __isl_give isl_union_pw_qpolynomial *
4506 isl_union_pw_qpolynomial_read_from_str(
4507 isl_ctx *ctx, const char *str);
4509 Quasipolynomials and piecewise quasipolynomials can be printed
4510 using the following functions.
4512 __isl_give isl_printer *isl_printer_print_qpolynomial(
4513 __isl_take isl_printer *p,
4514 __isl_keep isl_qpolynomial *qp);
4516 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4517 __isl_take isl_printer *p,
4518 __isl_keep isl_pw_qpolynomial *pwqp);
4520 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4521 __isl_take isl_printer *p,
4522 __isl_keep isl_union_pw_qpolynomial *upwqp);
4524 The output format of the printer
4525 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4526 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4528 In case of printing in C<ISL_FORMAT_C>, the user may want
4529 to set the names of all dimensions
4531 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4532 __isl_take isl_qpolynomial *qp,
4533 enum isl_dim_type type, unsigned pos,
4535 __isl_give isl_pw_qpolynomial *
4536 isl_pw_qpolynomial_set_dim_name(
4537 __isl_take isl_pw_qpolynomial *pwqp,
4538 enum isl_dim_type type, unsigned pos,
4541 =head3 Creating New (Piecewise) Quasipolynomials
4543 Some simple quasipolynomials can be created using the following functions.
4544 More complicated quasipolynomials can be created by applying
4545 operations such as addition and multiplication
4546 on the resulting quasipolynomials
4548 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4549 __isl_take isl_space *domain);
4550 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4551 __isl_take isl_space *domain);
4552 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4553 __isl_take isl_space *domain);
4554 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4555 __isl_take isl_space *domain);
4556 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4557 __isl_take isl_space *domain);
4558 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4559 __isl_take isl_space *domain,
4560 const isl_int n, const isl_int d);
4561 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4562 __isl_take isl_space *domain,
4563 enum isl_dim_type type, unsigned pos);
4564 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4565 __isl_take isl_aff *aff);
4567 Note that the space in which a quasipolynomial lives is a map space
4568 with a one-dimensional range. The C<domain> argument in some of
4569 the functions above corresponds to the domain of this map space.
4571 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4572 with a single cell can be created using the following functions.
4573 Multiple of these single cell piecewise quasipolynomials can
4574 be combined to create more complicated piecewise quasipolynomials.
4576 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4577 __isl_take isl_space *space);
4578 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4579 __isl_take isl_set *set,
4580 __isl_take isl_qpolynomial *qp);
4581 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4582 __isl_take isl_qpolynomial *qp);
4583 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4584 __isl_take isl_pw_aff *pwaff);
4586 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4587 __isl_take isl_space *space);
4588 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4589 __isl_take isl_pw_qpolynomial *pwqp);
4590 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4591 __isl_take isl_union_pw_qpolynomial *upwqp,
4592 __isl_take isl_pw_qpolynomial *pwqp);
4594 Quasipolynomials can be copied and freed again using the following
4597 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4598 __isl_keep isl_qpolynomial *qp);
4599 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4601 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4602 __isl_keep isl_pw_qpolynomial *pwqp);
4603 void *isl_pw_qpolynomial_free(
4604 __isl_take isl_pw_qpolynomial *pwqp);
4606 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4607 __isl_keep isl_union_pw_qpolynomial *upwqp);
4608 void *isl_union_pw_qpolynomial_free(
4609 __isl_take isl_union_pw_qpolynomial *upwqp);
4611 =head3 Inspecting (Piecewise) Quasipolynomials
4613 To iterate over all piecewise quasipolynomials in a union
4614 piecewise quasipolynomial, use the following function
4616 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4617 __isl_keep isl_union_pw_qpolynomial *upwqp,
4618 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4621 To extract the piecewise quasipolynomial in a given space from a union, use
4623 __isl_give isl_pw_qpolynomial *
4624 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4625 __isl_keep isl_union_pw_qpolynomial *upwqp,
4626 __isl_take isl_space *space);
4628 To iterate over the cells in a piecewise quasipolynomial,
4629 use either of the following two functions
4631 int isl_pw_qpolynomial_foreach_piece(
4632 __isl_keep isl_pw_qpolynomial *pwqp,
4633 int (*fn)(__isl_take isl_set *set,
4634 __isl_take isl_qpolynomial *qp,
4635 void *user), void *user);
4636 int isl_pw_qpolynomial_foreach_lifted_piece(
4637 __isl_keep isl_pw_qpolynomial *pwqp,
4638 int (*fn)(__isl_take isl_set *set,
4639 __isl_take isl_qpolynomial *qp,
4640 void *user), void *user);
4642 As usual, the function C<fn> should return C<0> on success
4643 and C<-1> on failure. The difference between
4644 C<isl_pw_qpolynomial_foreach_piece> and
4645 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4646 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4647 compute unique representations for all existentially quantified
4648 variables and then turn these existentially quantified variables
4649 into extra set variables, adapting the associated quasipolynomial
4650 accordingly. This means that the C<set> passed to C<fn>
4651 will not have any existentially quantified variables, but that
4652 the dimensions of the sets may be different for different
4653 invocations of C<fn>.
4655 To iterate over all terms in a quasipolynomial,
4658 int isl_qpolynomial_foreach_term(
4659 __isl_keep isl_qpolynomial *qp,
4660 int (*fn)(__isl_take isl_term *term,
4661 void *user), void *user);
4663 The terms themselves can be inspected and freed using
4666 unsigned isl_term_dim(__isl_keep isl_term *term,
4667 enum isl_dim_type type);
4668 void isl_term_get_num(__isl_keep isl_term *term,
4670 void isl_term_get_den(__isl_keep isl_term *term,
4672 int isl_term_get_exp(__isl_keep isl_term *term,
4673 enum isl_dim_type type, unsigned pos);
4674 __isl_give isl_aff *isl_term_get_div(
4675 __isl_keep isl_term *term, unsigned pos);
4676 void isl_term_free(__isl_take isl_term *term);
4678 Each term is a product of parameters, set variables and
4679 integer divisions. The function C<isl_term_get_exp>
4680 returns the exponent of a given dimensions in the given term.
4681 The C<isl_int>s in the arguments of C<isl_term_get_num>
4682 and C<isl_term_get_den> need to have been initialized
4683 using C<isl_int_init> before calling these functions.
4685 =head3 Properties of (Piecewise) Quasipolynomials
4687 To check whether a quasipolynomial is actually a constant,
4688 use the following function.
4690 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4691 isl_int *n, isl_int *d);
4693 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4694 then the numerator and denominator of the constant
4695 are returned in C<*n> and C<*d>, respectively.
4697 To check whether two union piecewise quasipolynomials are
4698 obviously equal, use
4700 int isl_union_pw_qpolynomial_plain_is_equal(
4701 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4702 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4704 =head3 Operations on (Piecewise) Quasipolynomials
4706 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4707 __isl_take isl_qpolynomial *qp, isl_int v);
4708 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4709 __isl_take isl_qpolynomial *qp);
4710 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4711 __isl_take isl_qpolynomial *qp1,
4712 __isl_take isl_qpolynomial *qp2);
4713 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4714 __isl_take isl_qpolynomial *qp1,
4715 __isl_take isl_qpolynomial *qp2);
4716 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4717 __isl_take isl_qpolynomial *qp1,
4718 __isl_take isl_qpolynomial *qp2);
4719 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4720 __isl_take isl_qpolynomial *qp, unsigned exponent);
4722 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4723 __isl_take isl_pw_qpolynomial *pwqp1,
4724 __isl_take isl_pw_qpolynomial *pwqp2);
4725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4726 __isl_take isl_pw_qpolynomial *pwqp1,
4727 __isl_take isl_pw_qpolynomial *pwqp2);
4728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4729 __isl_take isl_pw_qpolynomial *pwqp1,
4730 __isl_take isl_pw_qpolynomial *pwqp2);
4731 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4732 __isl_take isl_pw_qpolynomial *pwqp);
4733 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4734 __isl_take isl_pw_qpolynomial *pwqp1,
4735 __isl_take isl_pw_qpolynomial *pwqp2);
4736 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4737 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4739 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4740 __isl_take isl_union_pw_qpolynomial *upwqp1,
4741 __isl_take isl_union_pw_qpolynomial *upwqp2);
4742 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4743 __isl_take isl_union_pw_qpolynomial *upwqp1,
4744 __isl_take isl_union_pw_qpolynomial *upwqp2);
4745 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4746 __isl_take isl_union_pw_qpolynomial *upwqp1,
4747 __isl_take isl_union_pw_qpolynomial *upwqp2);
4749 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4750 __isl_take isl_pw_qpolynomial *pwqp,
4751 __isl_take isl_point *pnt);
4753 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4754 __isl_take isl_union_pw_qpolynomial *upwqp,
4755 __isl_take isl_point *pnt);
4757 __isl_give isl_set *isl_pw_qpolynomial_domain(
4758 __isl_take isl_pw_qpolynomial *pwqp);
4759 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4760 __isl_take isl_pw_qpolynomial *pwpq,
4761 __isl_take isl_set *set);
4762 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4763 __isl_take isl_pw_qpolynomial *pwpq,
4764 __isl_take isl_set *set);
4766 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4767 __isl_take isl_union_pw_qpolynomial *upwqp);
4768 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4769 __isl_take isl_union_pw_qpolynomial *upwpq,
4770 __isl_take isl_union_set *uset);
4771 __isl_give isl_union_pw_qpolynomial *
4772 isl_union_pw_qpolynomial_intersect_params(
4773 __isl_take isl_union_pw_qpolynomial *upwpq,
4774 __isl_take isl_set *set);
4776 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4777 __isl_take isl_qpolynomial *qp,
4778 __isl_take isl_space *model);
4780 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4781 __isl_take isl_qpolynomial *qp);
4782 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4783 __isl_take isl_pw_qpolynomial *pwqp);
4785 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4786 __isl_take isl_union_pw_qpolynomial *upwqp);
4788 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4789 __isl_take isl_qpolynomial *qp,
4790 __isl_take isl_set *context);
4791 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4792 __isl_take isl_qpolynomial *qp,
4793 __isl_take isl_set *context);
4795 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4796 __isl_take isl_pw_qpolynomial *pwqp,
4797 __isl_take isl_set *context);
4798 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4799 __isl_take isl_pw_qpolynomial *pwqp,
4800 __isl_take isl_set *context);
4802 __isl_give isl_union_pw_qpolynomial *
4803 isl_union_pw_qpolynomial_gist_params(
4804 __isl_take isl_union_pw_qpolynomial *upwqp,
4805 __isl_take isl_set *context);
4806 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4807 __isl_take isl_union_pw_qpolynomial *upwqp,
4808 __isl_take isl_union_set *context);
4810 The gist operation applies the gist operation to each of
4811 the cells in the domain of the input piecewise quasipolynomial.
4812 The context is also exploited
4813 to simplify the quasipolynomials associated to each cell.
4815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4816 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4817 __isl_give isl_union_pw_qpolynomial *
4818 isl_union_pw_qpolynomial_to_polynomial(
4819 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4821 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4822 the polynomial will be an overapproximation. If C<sign> is negative,
4823 it will be an underapproximation. If C<sign> is zero, the approximation
4824 will lie somewhere in between.
4826 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4828 A piecewise quasipolynomial reduction is a piecewise
4829 reduction (or fold) of quasipolynomials.
4830 In particular, the reduction can be maximum or a minimum.
4831 The objects are mainly used to represent the result of
4832 an upper or lower bound on a quasipolynomial over its domain,
4833 i.e., as the result of the following function.
4835 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4836 __isl_take isl_pw_qpolynomial *pwqp,
4837 enum isl_fold type, int *tight);
4839 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4840 __isl_take isl_union_pw_qpolynomial *upwqp,
4841 enum isl_fold type, int *tight);
4843 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4844 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4845 is the returned bound is known be tight, i.e., for each value
4846 of the parameters there is at least
4847 one element in the domain that reaches the bound.
4848 If the domain of C<pwqp> is not wrapping, then the bound is computed
4849 over all elements in that domain and the result has a purely parametric
4850 domain. If the domain of C<pwqp> is wrapping, then the bound is
4851 computed over the range of the wrapped relation. The domain of the
4852 wrapped relation becomes the domain of the result.
4854 A (piecewise) quasipolynomial reduction can be copied or freed using the
4855 following functions.
4857 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4858 __isl_keep isl_qpolynomial_fold *fold);
4859 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4860 __isl_keep isl_pw_qpolynomial_fold *pwf);
4861 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4862 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4863 void isl_qpolynomial_fold_free(
4864 __isl_take isl_qpolynomial_fold *fold);
4865 void *isl_pw_qpolynomial_fold_free(
4866 __isl_take isl_pw_qpolynomial_fold *pwf);
4867 void *isl_union_pw_qpolynomial_fold_free(
4868 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4870 =head3 Printing Piecewise Quasipolynomial Reductions
4872 Piecewise quasipolynomial reductions can be printed
4873 using the following function.
4875 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4876 __isl_take isl_printer *p,
4877 __isl_keep isl_pw_qpolynomial_fold *pwf);
4878 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4879 __isl_take isl_printer *p,
4880 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4882 For C<isl_printer_print_pw_qpolynomial_fold>,
4883 output format of the printer
4884 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4885 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4886 output format of the printer
4887 needs to be set to C<ISL_FORMAT_ISL>.
4888 In case of printing in C<ISL_FORMAT_C>, the user may want
4889 to set the names of all dimensions
4891 __isl_give isl_pw_qpolynomial_fold *
4892 isl_pw_qpolynomial_fold_set_dim_name(
4893 __isl_take isl_pw_qpolynomial_fold *pwf,
4894 enum isl_dim_type type, unsigned pos,
4897 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4899 To iterate over all piecewise quasipolynomial reductions in a union
4900 piecewise quasipolynomial reduction, use the following function
4902 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4903 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4904 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4905 void *user), void *user);
4907 To iterate over the cells in a piecewise quasipolynomial reduction,
4908 use either of the following two functions
4910 int isl_pw_qpolynomial_fold_foreach_piece(
4911 __isl_keep isl_pw_qpolynomial_fold *pwf,
4912 int (*fn)(__isl_take isl_set *set,
4913 __isl_take isl_qpolynomial_fold *fold,
4914 void *user), void *user);
4915 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4916 __isl_keep isl_pw_qpolynomial_fold *pwf,
4917 int (*fn)(__isl_take isl_set *set,
4918 __isl_take isl_qpolynomial_fold *fold,
4919 void *user), void *user);
4921 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4922 of the difference between these two functions.
4924 To iterate over all quasipolynomials in a reduction, use
4926 int isl_qpolynomial_fold_foreach_qpolynomial(
4927 __isl_keep isl_qpolynomial_fold *fold,
4928 int (*fn)(__isl_take isl_qpolynomial *qp,
4929 void *user), void *user);
4931 =head3 Properties of Piecewise Quasipolynomial Reductions
4933 To check whether two union piecewise quasipolynomial reductions are
4934 obviously equal, use
4936 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4937 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4938 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4940 =head3 Operations on Piecewise Quasipolynomial Reductions
4942 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4943 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4945 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4946 __isl_take isl_pw_qpolynomial_fold *pwf1,
4947 __isl_take isl_pw_qpolynomial_fold *pwf2);
4949 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4950 __isl_take isl_pw_qpolynomial_fold *pwf1,
4951 __isl_take isl_pw_qpolynomial_fold *pwf2);
4953 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4954 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4955 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4957 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4958 __isl_take isl_pw_qpolynomial_fold *pwf,
4959 __isl_take isl_point *pnt);
4961 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4962 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4963 __isl_take isl_point *pnt);
4965 __isl_give isl_pw_qpolynomial_fold *
4966 isl_pw_qpolynomial_fold_intersect_params(
4967 __isl_take isl_pw_qpolynomial_fold *pwf,
4968 __isl_take isl_set *set);
4970 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4971 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4972 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4973 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4974 __isl_take isl_union_set *uset);
4975 __isl_give isl_union_pw_qpolynomial_fold *
4976 isl_union_pw_qpolynomial_fold_intersect_params(
4977 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4978 __isl_take isl_set *set);
4980 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4981 __isl_take isl_pw_qpolynomial_fold *pwf);
4983 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4984 __isl_take isl_pw_qpolynomial_fold *pwf);
4986 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4987 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4989 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4990 __isl_take isl_qpolynomial_fold *fold,
4991 __isl_take isl_set *context);
4992 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4993 __isl_take isl_qpolynomial_fold *fold,
4994 __isl_take isl_set *context);
4996 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4997 __isl_take isl_pw_qpolynomial_fold *pwf,
4998 __isl_take isl_set *context);
4999 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5000 __isl_take isl_pw_qpolynomial_fold *pwf,
5001 __isl_take isl_set *context);
5003 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5004 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5005 __isl_take isl_union_set *context);
5006 __isl_give isl_union_pw_qpolynomial_fold *
5007 isl_union_pw_qpolynomial_fold_gist_params(
5008 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5009 __isl_take isl_set *context);
5011 The gist operation applies the gist operation to each of
5012 the cells in the domain of the input piecewise quasipolynomial reduction.
5013 In future, the operation will also exploit the context
5014 to simplify the quasipolynomial reductions associated to each cell.
5016 __isl_give isl_pw_qpolynomial_fold *
5017 isl_set_apply_pw_qpolynomial_fold(
5018 __isl_take isl_set *set,
5019 __isl_take isl_pw_qpolynomial_fold *pwf,
5021 __isl_give isl_pw_qpolynomial_fold *
5022 isl_map_apply_pw_qpolynomial_fold(
5023 __isl_take isl_map *map,
5024 __isl_take isl_pw_qpolynomial_fold *pwf,
5026 __isl_give isl_union_pw_qpolynomial_fold *
5027 isl_union_set_apply_union_pw_qpolynomial_fold(
5028 __isl_take isl_union_set *uset,
5029 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5031 __isl_give isl_union_pw_qpolynomial_fold *
5032 isl_union_map_apply_union_pw_qpolynomial_fold(
5033 __isl_take isl_union_map *umap,
5034 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5037 The functions taking a map
5038 compose the given map with the given piecewise quasipolynomial reduction.
5039 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5040 over all elements in the intersection of the range of the map
5041 and the domain of the piecewise quasipolynomial reduction
5042 as a function of an element in the domain of the map.
5043 The functions taking a set compute a bound over all elements in the
5044 intersection of the set and the domain of the
5045 piecewise quasipolynomial reduction.
5047 =head2 Parametric Vertex Enumeration
5049 The parametric vertex enumeration described in this section
5050 is mainly intended to be used internally and by the C<barvinok>
5053 #include <isl/vertices.h>
5054 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5055 __isl_keep isl_basic_set *bset);
5057 The function C<isl_basic_set_compute_vertices> performs the
5058 actual computation of the parametric vertices and the chamber
5059 decomposition and store the result in an C<isl_vertices> object.
5060 This information can be queried by either iterating over all
5061 the vertices or iterating over all the chambers or cells
5062 and then iterating over all vertices that are active on the chamber.
5064 int isl_vertices_foreach_vertex(
5065 __isl_keep isl_vertices *vertices,
5066 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5069 int isl_vertices_foreach_cell(
5070 __isl_keep isl_vertices *vertices,
5071 int (*fn)(__isl_take isl_cell *cell, void *user),
5073 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5074 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5077 Other operations that can be performed on an C<isl_vertices> object are
5080 isl_ctx *isl_vertices_get_ctx(
5081 __isl_keep isl_vertices *vertices);
5082 int isl_vertices_get_n_vertices(
5083 __isl_keep isl_vertices *vertices);
5084 void isl_vertices_free(__isl_take isl_vertices *vertices);
5086 Vertices can be inspected and destroyed using the following functions.
5088 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5089 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5090 __isl_give isl_basic_set *isl_vertex_get_domain(
5091 __isl_keep isl_vertex *vertex);
5092 __isl_give isl_basic_set *isl_vertex_get_expr(
5093 __isl_keep isl_vertex *vertex);
5094 void isl_vertex_free(__isl_take isl_vertex *vertex);
5096 C<isl_vertex_get_expr> returns a singleton parametric set describing
5097 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5099 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5100 B<rational> basic sets, so they should mainly be used for inspection
5101 and should not be mixed with integer sets.
5103 Chambers can be inspected and destroyed using the following functions.
5105 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5106 __isl_give isl_basic_set *isl_cell_get_domain(
5107 __isl_keep isl_cell *cell);
5108 void isl_cell_free(__isl_take isl_cell *cell);
5110 =head1 Polyhedral Compilation Library
5112 This section collects functionality in C<isl> that has been specifically
5113 designed for use during polyhedral compilation.
5115 =head2 Dependence Analysis
5117 C<isl> contains specialized functionality for performing
5118 array dataflow analysis. That is, given a I<sink> access relation
5119 and a collection of possible I<source> access relations,
5120 C<isl> can compute relations that describe
5121 for each iteration of the sink access, which iteration
5122 of which of the source access relations was the last
5123 to access the same data element before the given iteration
5125 The resulting dependence relations map source iterations
5126 to the corresponding sink iterations.
5127 To compute standard flow dependences, the sink should be
5128 a read, while the sources should be writes.
5129 If any of the source accesses are marked as being I<may>
5130 accesses, then there will be a dependence from the last
5131 I<must> access B<and> from any I<may> access that follows
5132 this last I<must> access.
5133 In particular, if I<all> sources are I<may> accesses,
5134 then memory based dependence analysis is performed.
5135 If, on the other hand, all sources are I<must> accesses,
5136 then value based dependence analysis is performed.
5138 #include <isl/flow.h>
5140 typedef int (*isl_access_level_before)(void *first, void *second);
5142 __isl_give isl_access_info *isl_access_info_alloc(
5143 __isl_take isl_map *sink,
5144 void *sink_user, isl_access_level_before fn,
5146 __isl_give isl_access_info *isl_access_info_add_source(
5147 __isl_take isl_access_info *acc,
5148 __isl_take isl_map *source, int must,
5150 void *isl_access_info_free(__isl_take isl_access_info *acc);
5152 __isl_give isl_flow *isl_access_info_compute_flow(
5153 __isl_take isl_access_info *acc);
5155 int isl_flow_foreach(__isl_keep isl_flow *deps,
5156 int (*fn)(__isl_take isl_map *dep, int must,
5157 void *dep_user, void *user),
5159 __isl_give isl_map *isl_flow_get_no_source(
5160 __isl_keep isl_flow *deps, int must);
5161 void isl_flow_free(__isl_take isl_flow *deps);
5163 The function C<isl_access_info_compute_flow> performs the actual
5164 dependence analysis. The other functions are used to construct
5165 the input for this function or to read off the output.
5167 The input is collected in an C<isl_access_info>, which can
5168 be created through a call to C<isl_access_info_alloc>.
5169 The arguments to this functions are the sink access relation
5170 C<sink>, a token C<sink_user> used to identify the sink
5171 access to the user, a callback function for specifying the
5172 relative order of source and sink accesses, and the number
5173 of source access relations that will be added.
5174 The callback function has type C<int (*)(void *first, void *second)>.
5175 The function is called with two user supplied tokens identifying
5176 either a source or the sink and it should return the shared nesting
5177 level and the relative order of the two accesses.
5178 In particular, let I<n> be the number of loops shared by
5179 the two accesses. If C<first> precedes C<second> textually,
5180 then the function should return I<2 * n + 1>; otherwise,
5181 it should return I<2 * n>.
5182 The sources can be added to the C<isl_access_info> by performing
5183 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5184 C<must> indicates whether the source is a I<must> access
5185 or a I<may> access. Note that a multi-valued access relation
5186 should only be marked I<must> if every iteration in the domain
5187 of the relation accesses I<all> elements in its image.
5188 The C<source_user> token is again used to identify
5189 the source access. The range of the source access relation
5190 C<source> should have the same dimension as the range
5191 of the sink access relation.
5192 The C<isl_access_info_free> function should usually not be
5193 called explicitly, because it is called implicitly by
5194 C<isl_access_info_compute_flow>.
5196 The result of the dependence analysis is collected in an
5197 C<isl_flow>. There may be elements of
5198 the sink access for which no preceding source access could be
5199 found or for which all preceding sources are I<may> accesses.
5200 The relations containing these elements can be obtained through
5201 calls to C<isl_flow_get_no_source>, the first with C<must> set
5202 and the second with C<must> unset.
5203 In the case of standard flow dependence analysis,
5204 with the sink a read and the sources I<must> writes,
5205 the first relation corresponds to the reads from uninitialized
5206 array elements and the second relation is empty.
5207 The actual flow dependences can be extracted using
5208 C<isl_flow_foreach>. This function will call the user-specified
5209 callback function C<fn> for each B<non-empty> dependence between
5210 a source and the sink. The callback function is called
5211 with four arguments, the actual flow dependence relation
5212 mapping source iterations to sink iterations, a boolean that
5213 indicates whether it is a I<must> or I<may> dependence, a token
5214 identifying the source and an additional C<void *> with value
5215 equal to the third argument of the C<isl_flow_foreach> call.
5216 A dependence is marked I<must> if it originates from a I<must>
5217 source and if it is not followed by any I<may> sources.
5219 After finishing with an C<isl_flow>, the user should call
5220 C<isl_flow_free> to free all associated memory.
5222 A higher-level interface to dependence analysis is provided
5223 by the following function.
5225 #include <isl/flow.h>
5227 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5228 __isl_take isl_union_map *must_source,
5229 __isl_take isl_union_map *may_source,
5230 __isl_take isl_union_map *schedule,
5231 __isl_give isl_union_map **must_dep,
5232 __isl_give isl_union_map **may_dep,
5233 __isl_give isl_union_map **must_no_source,
5234 __isl_give isl_union_map **may_no_source);
5236 The arrays are identified by the tuple names of the ranges
5237 of the accesses. The iteration domains by the tuple names
5238 of the domains of the accesses and of the schedule.
5239 The relative order of the iteration domains is given by the
5240 schedule. The relations returned through C<must_no_source>
5241 and C<may_no_source> are subsets of C<sink>.
5242 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5243 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5244 any of the other arguments is treated as an error.
5246 =head3 Interaction with Dependence Analysis
5248 During the dependence analysis, we frequently need to perform
5249 the following operation. Given a relation between sink iterations
5250 and potential source iterations from a particular source domain,
5251 what is the last potential source iteration corresponding to each
5252 sink iteration. It can sometimes be convenient to adjust
5253 the set of potential source iterations before or after each such operation.
5254 The prototypical example is fuzzy array dataflow analysis,
5255 where we need to analyze if, based on data-dependent constraints,
5256 the sink iteration can ever be executed without one or more of
5257 the corresponding potential source iterations being executed.
5258 If so, we can introduce extra parameters and select an unknown
5259 but fixed source iteration from the potential source iterations.
5260 To be able to perform such manipulations, C<isl> provides the following
5263 #include <isl/flow.h>
5265 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5266 __isl_keep isl_map *source_map,
5267 __isl_keep isl_set *sink, void *source_user,
5269 __isl_give isl_access_info *isl_access_info_set_restrict(
5270 __isl_take isl_access_info *acc,
5271 isl_access_restrict fn, void *user);
5273 The function C<isl_access_info_set_restrict> should be called
5274 before calling C<isl_access_info_compute_flow> and registers a callback function
5275 that will be called any time C<isl> is about to compute the last
5276 potential source. The first argument is the (reverse) proto-dependence,
5277 mapping sink iterations to potential source iterations.
5278 The second argument represents the sink iterations for which
5279 we want to compute the last source iteration.
5280 The third argument is the token corresponding to the source
5281 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5282 The callback is expected to return a restriction on either the input or
5283 the output of the operation computing the last potential source.
5284 If the input needs to be restricted then restrictions are needed
5285 for both the source and the sink iterations. The sink iterations
5286 and the potential source iterations will be intersected with these sets.
5287 If the output needs to be restricted then only a restriction on the source
5288 iterations is required.
5289 If any error occurs, the callback should return C<NULL>.
5290 An C<isl_restriction> object can be created, freed and inspected
5291 using the following functions.
5293 #include <isl/flow.h>
5295 __isl_give isl_restriction *isl_restriction_input(
5296 __isl_take isl_set *source_restr,
5297 __isl_take isl_set *sink_restr);
5298 __isl_give isl_restriction *isl_restriction_output(
5299 __isl_take isl_set *source_restr);
5300 __isl_give isl_restriction *isl_restriction_none(
5301 __isl_take isl_map *source_map);
5302 __isl_give isl_restriction *isl_restriction_empty(
5303 __isl_take isl_map *source_map);
5304 void *isl_restriction_free(
5305 __isl_take isl_restriction *restr);
5306 isl_ctx *isl_restriction_get_ctx(
5307 __isl_keep isl_restriction *restr);
5309 C<isl_restriction_none> and C<isl_restriction_empty> are special
5310 cases of C<isl_restriction_input>. C<isl_restriction_none>
5311 is essentially equivalent to
5313 isl_restriction_input(isl_set_universe(
5314 isl_space_range(isl_map_get_space(source_map))),
5316 isl_space_domain(isl_map_get_space(source_map))));
5318 whereas C<isl_restriction_empty> is essentially equivalent to
5320 isl_restriction_input(isl_set_empty(
5321 isl_space_range(isl_map_get_space(source_map))),
5323 isl_space_domain(isl_map_get_space(source_map))));
5327 B<The functionality described in this section is fairly new
5328 and may be subject to change.>
5330 The following function can be used to compute a schedule
5331 for a union of domains.
5332 By default, the algorithm used to construct the schedule is similar
5333 to that of C<Pluto>.
5334 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5336 The generated schedule respects all C<validity> dependences.
5337 That is, all dependence distances over these dependences in the
5338 scheduled space are lexicographically positive.
5339 The default algorithm tries to minimize the dependence distances over
5340 C<proximity> dependences.
5341 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5342 for groups of domains where the dependence distances have only
5343 non-negative values.
5344 When using Feautrier's algorithm, the C<proximity> dependence
5345 distances are only minimized during the extension to a
5346 full-dimensional schedule.
5348 #include <isl/schedule.h>
5349 __isl_give isl_schedule *isl_union_set_compute_schedule(
5350 __isl_take isl_union_set *domain,
5351 __isl_take isl_union_map *validity,
5352 __isl_take isl_union_map *proximity);
5353 void *isl_schedule_free(__isl_take isl_schedule *sched);
5355 A mapping from the domains to the scheduled space can be obtained
5356 from an C<isl_schedule> using the following function.
5358 __isl_give isl_union_map *isl_schedule_get_map(
5359 __isl_keep isl_schedule *sched);
5361 A representation of the schedule can be printed using
5363 __isl_give isl_printer *isl_printer_print_schedule(
5364 __isl_take isl_printer *p,
5365 __isl_keep isl_schedule *schedule);
5367 A representation of the schedule as a forest of bands can be obtained
5368 using the following function.
5370 __isl_give isl_band_list *isl_schedule_get_band_forest(
5371 __isl_keep isl_schedule *schedule);
5373 The individual bands can be visited in depth-first post-order
5374 using the following function.
5376 #include <isl/schedule.h>
5377 int isl_schedule_foreach_band(
5378 __isl_keep isl_schedule *sched,
5379 int (*fn)(__isl_keep isl_band *band, void *user),
5382 The list can be manipulated as explained in L<"Lists">.
5383 The bands inside the list can be copied and freed using the following
5386 #include <isl/band.h>
5387 __isl_give isl_band *isl_band_copy(
5388 __isl_keep isl_band *band);
5389 void *isl_band_free(__isl_take isl_band *band);
5391 Each band contains zero or more scheduling dimensions.
5392 These are referred to as the members of the band.
5393 The section of the schedule that corresponds to the band is
5394 referred to as the partial schedule of the band.
5395 For those nodes that participate in a band, the outer scheduling
5396 dimensions form the prefix schedule, while the inner scheduling
5397 dimensions form the suffix schedule.
5398 That is, if we take a cut of the band forest, then the union of
5399 the concatenations of the prefix, partial and suffix schedules of
5400 each band in the cut is equal to the entire schedule (modulo
5401 some possible padding at the end with zero scheduling dimensions).
5402 The properties of a band can be inspected using the following functions.
5404 #include <isl/band.h>
5405 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5407 int isl_band_has_children(__isl_keep isl_band *band);
5408 __isl_give isl_band_list *isl_band_get_children(
5409 __isl_keep isl_band *band);
5411 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5412 __isl_keep isl_band *band);
5413 __isl_give isl_union_map *isl_band_get_partial_schedule(
5414 __isl_keep isl_band *band);
5415 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5416 __isl_keep isl_band *band);
5418 int isl_band_n_member(__isl_keep isl_band *band);
5419 int isl_band_member_is_zero_distance(
5420 __isl_keep isl_band *band, int pos);
5422 int isl_band_list_foreach_band(
5423 __isl_keep isl_band_list *list,
5424 int (*fn)(__isl_keep isl_band *band, void *user),
5427 Note that a scheduling dimension is considered to be ``zero
5428 distance'' if it does not carry any proximity dependences
5430 That is, if the dependence distances of the proximity
5431 dependences are all zero in that direction (for fixed
5432 iterations of outer bands).
5433 Like C<isl_schedule_foreach_band>,
5434 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5435 in depth-first post-order.
5437 A band can be tiled using the following function.
5439 #include <isl/band.h>
5440 int isl_band_tile(__isl_keep isl_band *band,
5441 __isl_take isl_vec *sizes);
5443 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5445 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5446 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5448 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5450 The C<isl_band_tile> function tiles the band using the given tile sizes
5451 inside its schedule.
5452 A new child band is created to represent the point loops and it is
5453 inserted between the modified band and its children.
5454 The C<tile_scale_tile_loops> option specifies whether the tile
5455 loops iterators should be scaled by the tile sizes.
5456 If the C<tile_shift_point_loops> option is set, then the point loops
5457 are shifted to start at zero.
5459 A band can be split into two nested bands using the following function.
5461 int isl_band_split(__isl_keep isl_band *band, int pos);
5463 The resulting outer band contains the first C<pos> dimensions of C<band>
5464 while the inner band contains the remaining dimensions.
5466 A representation of the band can be printed using
5468 #include <isl/band.h>
5469 __isl_give isl_printer *isl_printer_print_band(
5470 __isl_take isl_printer *p,
5471 __isl_keep isl_band *band);
5475 #include <isl/schedule.h>
5476 int isl_options_set_schedule_max_coefficient(
5477 isl_ctx *ctx, int val);
5478 int isl_options_get_schedule_max_coefficient(
5480 int isl_options_set_schedule_max_constant_term(
5481 isl_ctx *ctx, int val);
5482 int isl_options_get_schedule_max_constant_term(
5484 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5485 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5486 int isl_options_set_schedule_maximize_band_depth(
5487 isl_ctx *ctx, int val);
5488 int isl_options_get_schedule_maximize_band_depth(
5490 int isl_options_set_schedule_outer_zero_distance(
5491 isl_ctx *ctx, int val);
5492 int isl_options_get_schedule_outer_zero_distance(
5494 int isl_options_set_schedule_split_scaled(
5495 isl_ctx *ctx, int val);
5496 int isl_options_get_schedule_split_scaled(
5498 int isl_options_set_schedule_algorithm(
5499 isl_ctx *ctx, int val);
5500 int isl_options_get_schedule_algorithm(
5502 int isl_options_set_schedule_separate_components(
5503 isl_ctx *ctx, int val);
5504 int isl_options_get_schedule_separate_components(
5509 =item * schedule_max_coefficient
5511 This option enforces that the coefficients for variable and parameter
5512 dimensions in the calculated schedule are not larger than the specified value.
5513 This option can significantly increase the speed of the scheduling calculation
5514 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5515 this option does not introduce bounds on the variable or parameter
5518 =item * schedule_max_constant_term
5520 This option enforces that the constant coefficients in the calculated schedule
5521 are not larger than the maximal constant term. This option can significantly
5522 increase the speed of the scheduling calculation and may also prevent fusing of
5523 unrelated dimensions. A value of -1 means that this option does not introduce
5524 bounds on the constant coefficients.
5526 =item * schedule_fuse
5528 This option controls the level of fusion.
5529 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5530 resulting schedule will be distributed as much as possible.
5531 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5532 try to fuse loops in the resulting schedule.
5534 =item * schedule_maximize_band_depth
5536 If this option is set, we do not split bands at the point
5537 where we detect splitting is necessary. Instead, we
5538 backtrack and split bands as early as possible. This
5539 reduces the number of splits and maximizes the width of
5540 the bands. Wider bands give more possibilities for tiling.
5541 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5542 then bands will be split as early as possible, even if there is no need.
5543 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5545 =item * schedule_outer_zero_distance
5547 If this option is set, then we try to construct schedules
5548 where the outermost scheduling dimension in each band
5549 results in a zero dependence distance over the proximity
5552 =item * schedule_split_scaled
5554 If this option is set, then we try to construct schedules in which the
5555 constant term is split off from the linear part if the linear parts of
5556 the scheduling rows for all nodes in the graphs have a common non-trivial
5558 The constant term is then placed in a separate band and the linear
5561 =item * schedule_algorithm
5563 Selects the scheduling algorithm to be used.
5564 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5565 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5567 =item * schedule_separate_components
5569 If at any point the dependence graph contains any (weakly connected) components,
5570 then these components are scheduled separately.
5571 If this option is not set, then some iterations of the domains
5572 in these components may be scheduled together.
5573 If this option is set, then the components are given consecutive
5578 =head2 AST Generation
5580 This section describes the C<isl> functionality for generating
5581 ASTs that visit all the elements
5582 in a domain in an order specified by a schedule.
5583 In particular, given a C<isl_union_map>, an AST is generated
5584 that visits all the elements in the domain of the C<isl_union_map>
5585 according to the lexicographic order of the corresponding image
5586 element(s). If the range of the C<isl_union_map> consists of
5587 elements in more than one space, then each of these spaces is handled
5588 separately in an arbitrary order.
5589 It should be noted that the image elements only specify the I<order>
5590 in which the corresponding domain elements should be visited.
5591 No direct relation between the image elements and the loop iterators
5592 in the generated AST should be assumed.
5594 Each AST is generated within a build. The initial build
5595 simply specifies the constraints on the parameters (if any)
5596 and can be created, inspected, copied and freed using the following functions.
5598 #include <isl/ast_build.h>
5599 __isl_give isl_ast_build *isl_ast_build_from_context(
5600 __isl_take isl_set *set);
5601 isl_ctx *isl_ast_build_get_ctx(
5602 __isl_keep isl_ast_build *build);
5603 __isl_give isl_ast_build *isl_ast_build_copy(
5604 __isl_keep isl_ast_build *build);
5605 void *isl_ast_build_free(
5606 __isl_take isl_ast_build *build);
5608 The C<set> argument is usually a parameter set with zero or more parameters.
5609 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5610 and L</"Fine-grained Control over AST Generation">.
5611 Finally, the AST itself can be constructed using the following
5614 #include <isl/ast_build.h>
5615 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5616 __isl_keep isl_ast_build *build,
5617 __isl_take isl_union_map *schedule);
5619 =head3 Inspecting the AST
5621 The basic properties of an AST node can be obtained as follows.
5623 #include <isl/ast.h>
5624 isl_ctx *isl_ast_node_get_ctx(
5625 __isl_keep isl_ast_node *node);
5626 enum isl_ast_node_type isl_ast_node_get_type(
5627 __isl_keep isl_ast_node *node);
5629 The type of an AST node is one of
5630 C<isl_ast_node_for>,
5632 C<isl_ast_node_block> or
5633 C<isl_ast_node_user>.
5634 An C<isl_ast_node_for> represents a for node.
5635 An C<isl_ast_node_if> represents an if node.
5636 An C<isl_ast_node_block> represents a compound node.
5637 An C<isl_ast_node_user> represents an expression statement.
5638 An expression statement typically corresponds to a domain element, i.e.,
5639 one of the elements that is visited by the AST.
5641 Each type of node has its own additional properties.
5643 #include <isl/ast.h>
5644 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5645 __isl_keep isl_ast_node *node);
5646 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5647 __isl_keep isl_ast_node *node);
5648 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5649 __isl_keep isl_ast_node *node);
5650 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5651 __isl_keep isl_ast_node *node);
5652 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5653 __isl_keep isl_ast_node *node);
5654 int isl_ast_node_for_is_degenerate(
5655 __isl_keep isl_ast_node *node);
5657 An C<isl_ast_for> is considered degenerate if it is known to execute
5660 #include <isl/ast.h>
5661 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5662 __isl_keep isl_ast_node *node);
5663 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5664 __isl_keep isl_ast_node *node);
5665 int isl_ast_node_if_has_else(
5666 __isl_keep isl_ast_node *node);
5667 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5668 __isl_keep isl_ast_node *node);
5670 __isl_give isl_ast_node_list *
5671 isl_ast_node_block_get_children(
5672 __isl_keep isl_ast_node *node);
5674 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5675 __isl_keep isl_ast_node *node);
5677 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5678 the following functions.
5680 #include <isl/ast.h>
5681 isl_ctx *isl_ast_expr_get_ctx(
5682 __isl_keep isl_ast_expr *expr);
5683 enum isl_ast_expr_type isl_ast_expr_get_type(
5684 __isl_keep isl_ast_expr *expr);
5686 The type of an AST expression is one of
5688 C<isl_ast_expr_id> or
5689 C<isl_ast_expr_int>.
5690 An C<isl_ast_expr_op> represents the result of an operation.
5691 An C<isl_ast_expr_id> represents an identifier.
5692 An C<isl_ast_expr_int> represents an integer value.
5694 Each type of expression has its own additional properties.
5696 #include <isl/ast.h>
5697 enum isl_ast_op_type isl_ast_expr_get_op_type(
5698 __isl_keep isl_ast_expr *expr);
5699 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5700 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5701 __isl_keep isl_ast_expr *expr, int pos);
5702 int isl_ast_node_foreach_ast_op_type(
5703 __isl_keep isl_ast_node *node,
5704 int (*fn)(enum isl_ast_op_type type, void *user),
5707 C<isl_ast_expr_get_op_type> returns the type of the operation
5708 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5709 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5711 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5712 C<isl_ast_op_type> that appears in C<node>.
5713 The operation type is one of the following.
5717 =item C<isl_ast_op_and>
5719 Logical I<and> of two arguments.
5720 Both arguments can be evaluated.
5722 =item C<isl_ast_op_and_then>
5724 Logical I<and> of two arguments.
5725 The second argument can only be evaluated if the first evaluates to true.
5727 =item C<isl_ast_op_or>
5729 Logical I<or> of two arguments.
5730 Both arguments can be evaluated.
5732 =item C<isl_ast_op_or_else>
5734 Logical I<or> of two arguments.
5735 The second argument can only be evaluated if the first evaluates to false.
5737 =item C<isl_ast_op_max>
5739 Maximum of two or more arguments.
5741 =item C<isl_ast_op_min>
5743 Minimum of two or more arguments.
5745 =item C<isl_ast_op_minus>
5749 =item C<isl_ast_op_add>
5751 Sum of two arguments.
5753 =item C<isl_ast_op_sub>
5755 Difference of two arguments.
5757 =item C<isl_ast_op_mul>
5759 Product of two arguments.
5761 =item C<isl_ast_op_div>
5763 Exact division. That is, the result is known to be an integer.
5765 =item C<isl_ast_op_fdiv_q>
5767 Result of integer division, rounded towards negative
5770 =item C<isl_ast_op_pdiv_q>
5772 Result of integer division, where dividend is known to be non-negative.
5774 =item C<isl_ast_op_pdiv_r>
5776 Remainder of integer division, where dividend is known to be non-negative.
5778 =item C<isl_ast_op_cond>
5780 Conditional operator defined on three arguments.
5781 If the first argument evaluates to true, then the result
5782 is equal to the second argument. Otherwise, the result
5783 is equal to the third argument.
5784 The second and third argument may only be evaluated if
5785 the first argument evaluates to true and false, respectively.
5786 Corresponds to C<a ? b : c> in C.
5788 =item C<isl_ast_op_select>
5790 Conditional operator defined on three arguments.
5791 If the first argument evaluates to true, then the result
5792 is equal to the second argument. Otherwise, the result
5793 is equal to the third argument.
5794 The second and third argument may be evaluated independently
5795 of the value of the first argument.
5796 Corresponds to C<a * b + (1 - a) * c> in C.
5798 =item C<isl_ast_op_eq>
5802 =item C<isl_ast_op_le>
5804 Less than or equal relation.
5806 =item C<isl_ast_op_lt>
5810 =item C<isl_ast_op_ge>
5812 Greater than or equal relation.
5814 =item C<isl_ast_op_gt>
5816 Greater than relation.
5818 =item C<isl_ast_op_call>
5821 The number of arguments of the C<isl_ast_expr> is one more than
5822 the number of arguments in the function call, the first argument
5823 representing the function being called.
5827 #include <isl/ast.h>
5828 __isl_give isl_id *isl_ast_expr_get_id(
5829 __isl_keep isl_ast_expr *expr);
5831 Return the identifier represented by the AST expression.
5833 #include <isl/ast.h>
5834 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5837 Return the integer represented by the AST expression.
5838 Note that the integer is returned through the C<v> argument.
5839 The return value of the function itself indicates whether the
5840 operation was performed successfully.
5842 =head3 Manipulating and printing the AST
5844 AST nodes can be copied and freed using the following functions.
5846 #include <isl/ast.h>
5847 __isl_give isl_ast_node *isl_ast_node_copy(
5848 __isl_keep isl_ast_node *node);
5849 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5851 AST expressions can be copied and freed using the following functions.
5853 #include <isl/ast.h>
5854 __isl_give isl_ast_expr *isl_ast_expr_copy(
5855 __isl_keep isl_ast_expr *expr);
5856 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5858 New AST expressions can be created either directly or within
5859 the context of an C<isl_ast_build>.
5861 #include <isl/ast.h>
5862 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5863 __isl_take isl_id *id);
5864 __isl_give isl_ast_expr *isl_ast_expr_neg(
5865 __isl_take isl_ast_expr *expr);
5866 __isl_give isl_ast_expr *isl_ast_expr_add(
5867 __isl_take isl_ast_expr *expr1,
5868 __isl_take isl_ast_expr *expr2);
5869 __isl_give isl_ast_expr *isl_ast_expr_sub(
5870 __isl_take isl_ast_expr *expr1,
5871 __isl_take isl_ast_expr *expr2);
5872 __isl_give isl_ast_expr *isl_ast_expr_mul(
5873 __isl_take isl_ast_expr *expr1,
5874 __isl_take isl_ast_expr *expr2);
5875 __isl_give isl_ast_expr *isl_ast_expr_div(
5876 __isl_take isl_ast_expr *expr1,
5877 __isl_take isl_ast_expr *expr2);
5878 __isl_give isl_ast_expr *isl_ast_expr_and(
5879 __isl_take isl_ast_expr *expr1,
5880 __isl_take isl_ast_expr *expr2)
5881 __isl_give isl_ast_expr *isl_ast_expr_or(
5882 __isl_take isl_ast_expr *expr1,
5883 __isl_take isl_ast_expr *expr2)
5885 #include <isl/ast_build.h>
5886 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5887 __isl_keep isl_ast_build *build,
5888 __isl_take isl_pw_aff *pa);
5889 __isl_give isl_ast_expr *
5890 isl_ast_build_call_from_pw_multi_aff(
5891 __isl_keep isl_ast_build *build,
5892 __isl_take isl_pw_multi_aff *pma);
5894 The domains of C<pa> and C<pma> should correspond
5895 to the schedule space of C<build>.
5896 The tuple id of C<pma> is used as the function being called.
5898 User specified data can be attached to an C<isl_ast_node> and obtained
5899 from the same C<isl_ast_node> using the following functions.
5901 #include <isl/ast.h>
5902 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5903 __isl_take isl_ast_node *node,
5904 __isl_take isl_id *annotation);
5905 __isl_give isl_id *isl_ast_node_get_annotation(
5906 __isl_keep isl_ast_node *node);
5908 Basic printing can be performed using the following functions.
5910 #include <isl/ast.h>
5911 __isl_give isl_printer *isl_printer_print_ast_expr(
5912 __isl_take isl_printer *p,
5913 __isl_keep isl_ast_expr *expr);
5914 __isl_give isl_printer *isl_printer_print_ast_node(
5915 __isl_take isl_printer *p,
5916 __isl_keep isl_ast_node *node);
5918 More advanced printing can be performed using the following functions.
5920 #include <isl/ast.h>
5921 __isl_give isl_printer *isl_ast_op_type_print_macro(
5922 enum isl_ast_op_type type,
5923 __isl_take isl_printer *p);
5924 __isl_give isl_printer *isl_ast_node_print_macros(
5925 __isl_keep isl_ast_node *node,
5926 __isl_take isl_printer *p);
5927 __isl_give isl_printer *isl_ast_node_print(
5928 __isl_keep isl_ast_node *node,
5929 __isl_take isl_printer *p,
5930 __isl_take isl_ast_print_options *options);
5931 __isl_give isl_printer *isl_ast_node_for_print(
5932 __isl_keep isl_ast_node *node,
5933 __isl_take isl_printer *p,
5934 __isl_take isl_ast_print_options *options);
5935 __isl_give isl_printer *isl_ast_node_if_print(
5936 __isl_keep isl_ast_node *node,
5937 __isl_take isl_printer *p,
5938 __isl_take isl_ast_print_options *options);
5940 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5941 C<isl> may print out an AST that makes use of macros such
5942 as C<floord>, C<min> and C<max>.
5943 C<isl_ast_op_type_print_macro> prints out the macro
5944 corresponding to a specific C<isl_ast_op_type>.
5945 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5946 for expressions where these macros would be used and prints
5947 out the required macro definitions.
5948 Essentially, C<isl_ast_node_print_macros> calls
5949 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5950 as function argument.
5951 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5952 C<isl_ast_node_if_print> print an C<isl_ast_node>
5953 in C<ISL_FORMAT_C>, but allow for some extra control
5954 through an C<isl_ast_print_options> object.
5955 This object can be created using the following functions.
5957 #include <isl/ast.h>
5958 __isl_give isl_ast_print_options *
5959 isl_ast_print_options_alloc(isl_ctx *ctx);
5960 __isl_give isl_ast_print_options *
5961 isl_ast_print_options_copy(
5962 __isl_keep isl_ast_print_options *options);
5963 void *isl_ast_print_options_free(
5964 __isl_take isl_ast_print_options *options);
5966 __isl_give isl_ast_print_options *
5967 isl_ast_print_options_set_print_user(
5968 __isl_take isl_ast_print_options *options,
5969 __isl_give isl_printer *(*print_user)(
5970 __isl_take isl_printer *p,
5971 __isl_take isl_ast_print_options *options,
5972 __isl_keep isl_ast_node *node, void *user),
5974 __isl_give isl_ast_print_options *
5975 isl_ast_print_options_set_print_for(
5976 __isl_take isl_ast_print_options *options,
5977 __isl_give isl_printer *(*print_for)(
5978 __isl_take isl_printer *p,
5979 __isl_take isl_ast_print_options *options,
5980 __isl_keep isl_ast_node *node, void *user),
5983 The callback set by C<isl_ast_print_options_set_print_user>
5984 is called whenever a node of type C<isl_ast_node_user> needs to
5986 The callback set by C<isl_ast_print_options_set_print_for>
5987 is called whenever a node of type C<isl_ast_node_for> needs to
5989 Note that C<isl_ast_node_for_print> will I<not> call the
5990 callback set by C<isl_ast_print_options_set_print_for> on the node
5991 on which C<isl_ast_node_for_print> is called, but only on nested
5992 nodes of type C<isl_ast_node_for>. It is therefore safe to
5993 call C<isl_ast_node_for_print> from within the callback set by
5994 C<isl_ast_print_options_set_print_for>.
5996 The following option determines the type to be used for iterators
5997 while printing the AST.
5999 int isl_options_set_ast_iterator_type(
6000 isl_ctx *ctx, const char *val);
6001 const char *isl_options_get_ast_iterator_type(
6006 #include <isl/ast_build.h>
6007 int isl_options_set_ast_build_atomic_upper_bound(
6008 isl_ctx *ctx, int val);
6009 int isl_options_get_ast_build_atomic_upper_bound(
6011 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6013 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6014 int isl_options_set_ast_build_exploit_nested_bounds(
6015 isl_ctx *ctx, int val);
6016 int isl_options_get_ast_build_exploit_nested_bounds(
6018 int isl_options_set_ast_build_group_coscheduled(
6019 isl_ctx *ctx, int val);
6020 int isl_options_get_ast_build_group_coscheduled(
6022 int isl_options_set_ast_build_scale_strides(
6023 isl_ctx *ctx, int val);
6024 int isl_options_get_ast_build_scale_strides(
6026 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6028 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6029 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6031 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6035 =item * ast_build_atomic_upper_bound
6037 Generate loop upper bounds that consist of the current loop iterator,
6038 an operator and an expression not involving the iterator.
6039 If this option is not set, then the current loop iterator may appear
6040 several times in the upper bound.
6041 For example, when this option is turned off, AST generation
6044 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6048 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6051 When the option is turned on, the following AST is generated
6053 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6056 =item * ast_build_prefer_pdiv
6058 If this option is turned off, then the AST generation will
6059 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6060 operators, but no C<isl_ast_op_pdiv_q> or
6061 C<isl_ast_op_pdiv_r> operators.
6062 If this options is turned on, then C<isl> will try to convert
6063 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6064 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6066 =item * ast_build_exploit_nested_bounds
6068 Simplify conditions based on bounds of nested for loops.
6069 In particular, remove conditions that are implied by the fact
6070 that one or more nested loops have at least one iteration,
6071 meaning that the upper bound is at least as large as the lower bound.
6072 For example, when this option is turned off, AST generation
6075 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6081 for (int c0 = 0; c0 <= N; c0 += 1)
6082 for (int c1 = 0; c1 <= M; c1 += 1)
6085 When the option is turned on, the following AST is generated
6087 for (int c0 = 0; c0 <= N; c0 += 1)
6088 for (int c1 = 0; c1 <= M; c1 += 1)
6091 =item * ast_build_group_coscheduled
6093 If two domain elements are assigned the same schedule point, then
6094 they may be executed in any order and they may even appear in different
6095 loops. If this options is set, then the AST generator will make
6096 sure that coscheduled domain elements do not appear in separate parts
6097 of the AST. This is useful in case of nested AST generation
6098 if the outer AST generation is given only part of a schedule
6099 and the inner AST generation should handle the domains that are
6100 coscheduled by this initial part of the schedule together.
6101 For example if an AST is generated for a schedule
6103 { A[i] -> [0]; B[i] -> [0] }
6105 then the C<isl_ast_build_set_create_leaf> callback described
6106 below may get called twice, once for each domain.
6107 Setting this option ensures that the callback is only called once
6108 on both domains together.
6110 =item * ast_build_separation_bounds
6112 This option specifies which bounds to use during separation.
6113 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6114 then all (possibly implicit) bounds on the current dimension will
6115 be used during separation.
6116 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6117 then only those bounds that are explicitly available will
6118 be used during separation.
6120 =item * ast_build_scale_strides
6122 This option specifies whether the AST generator is allowed
6123 to scale down iterators of strided loops.
6125 =item * ast_build_allow_else
6127 This option specifies whether the AST generator is allowed
6128 to construct if statements with else branches.
6130 =item * ast_build_allow_or
6132 This option specifies whether the AST generator is allowed
6133 to construct if conditions with disjunctions.
6137 =head3 Fine-grained Control over AST Generation
6139 Besides specifying the constraints on the parameters,
6140 an C<isl_ast_build> object can be used to control
6141 various aspects of the AST generation process.
6142 The most prominent way of control is through ``options'',
6143 which can be set using the following function.
6145 #include <isl/ast_build.h>
6146 __isl_give isl_ast_build *
6147 isl_ast_build_set_options(
6148 __isl_take isl_ast_build *control,
6149 __isl_take isl_union_map *options);
6151 The options are encoded in an <isl_union_map>.
6152 The domain of this union relation refers to the schedule domain,
6153 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6154 In the case of nested AST generation (see L</"Nested AST Generation">),
6155 the domain of C<options> should refer to the extra piece of the schedule.
6156 That is, it should be equal to the range of the wrapped relation in the
6157 range of the schedule.
6158 The range of the options can consist of elements in one or more spaces,
6159 the names of which determine the effect of the option.
6160 The values of the range typically also refer to the schedule dimension
6161 to which the option applies. In case of nested AST generation
6162 (see L</"Nested AST Generation">), these values refer to the position
6163 of the schedule dimension within the innermost AST generation.
6164 The constraints on the domain elements of
6165 the option should only refer to this dimension and earlier dimensions.
6166 We consider the following spaces.
6170 =item C<separation_class>
6172 This space is a wrapped relation between two one dimensional spaces.
6173 The input space represents the schedule dimension to which the option
6174 applies and the output space represents the separation class.
6175 While constructing a loop corresponding to the specified schedule
6176 dimension(s), the AST generator will try to generate separate loops
6177 for domain elements that are assigned different classes.
6178 If only some of the elements are assigned a class, then those elements
6179 that are not assigned any class will be treated as belonging to a class
6180 that is separate from the explicitly assigned classes.
6181 The typical use case for this option is to separate full tiles from
6183 The other options, described below, are applied after the separation
6186 As an example, consider the separation into full and partial tiles
6187 of a tiling of a triangular domain.
6188 Take, for example, the domain
6190 { A[i,j] : 0 <= i,j and i + j <= 100 }
6192 and a tiling into tiles of 10 by 10. The input to the AST generator
6193 is then the schedule
6195 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6198 Without any options, the following AST is generated
6200 for (int c0 = 0; c0 <= 10; c0 += 1)
6201 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6202 for (int c2 = 10 * c0;
6203 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6205 for (int c3 = 10 * c1;
6206 c3 <= min(10 * c1 + 9, -c2 + 100);
6210 Separation into full and partial tiles can be obtained by assigning
6211 a class, say C<0>, to the full tiles. The full tiles are represented by those
6212 values of the first and second schedule dimensions for which there are
6213 values of the third and fourth dimensions to cover an entire tile.
6214 That is, we need to specify the following option
6216 { [a,b,c,d] -> separation_class[[0]->[0]] :
6217 exists b': 0 <= 10a,10b' and
6218 10a+9+10b'+9 <= 100;
6219 [a,b,c,d] -> separation_class[[1]->[0]] :
6220 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6224 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6225 a >= 0 and b >= 0 and b <= 8 - a;
6226 [a, b, c, d] -> separation_class[[0] -> [0]] :
6229 With this option, the generated AST is as follows
6232 for (int c0 = 0; c0 <= 8; c0 += 1) {
6233 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6234 for (int c2 = 10 * c0;
6235 c2 <= 10 * c0 + 9; c2 += 1)
6236 for (int c3 = 10 * c1;
6237 c3 <= 10 * c1 + 9; c3 += 1)
6239 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6240 for (int c2 = 10 * c0;
6241 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6243 for (int c3 = 10 * c1;
6244 c3 <= min(-c2 + 100, 10 * c1 + 9);
6248 for (int c0 = 9; c0 <= 10; c0 += 1)
6249 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6250 for (int c2 = 10 * c0;
6251 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6253 for (int c3 = 10 * c1;
6254 c3 <= min(10 * c1 + 9, -c2 + 100);
6261 This is a single-dimensional space representing the schedule dimension(s)
6262 to which ``separation'' should be applied. Separation tries to split
6263 a loop into several pieces if this can avoid the generation of guards
6265 See also the C<atomic> option.
6269 This is a single-dimensional space representing the schedule dimension(s)
6270 for which the domains should be considered ``atomic''. That is, the
6271 AST generator will make sure that any given domain space will only appear
6272 in a single loop at the specified level.
6274 Consider the following schedule
6276 { a[i] -> [i] : 0 <= i < 10;
6277 b[i] -> [i+1] : 0 <= i < 10 }
6279 If the following option is specified
6281 { [i] -> separate[x] }
6283 then the following AST will be generated
6287 for (int c0 = 1; c0 <= 9; c0 += 1) {
6294 If, on the other hand, the following option is specified
6296 { [i] -> atomic[x] }
6298 then the following AST will be generated
6300 for (int c0 = 0; c0 <= 10; c0 += 1) {
6307 If neither C<atomic> nor C<separate> is specified, then the AST generator
6308 may produce either of these two results or some intermediate form.
6312 This is a single-dimensional space representing the schedule dimension(s)
6313 that should be I<completely> unrolled.
6314 To obtain a partial unrolling, the user should apply an additional
6315 strip-mining to the schedule and fully unroll the inner loop.
6319 Additional control is available through the following functions.
6321 #include <isl/ast_build.h>
6322 __isl_give isl_ast_build *
6323 isl_ast_build_set_iterators(
6324 __isl_take isl_ast_build *control,
6325 __isl_take isl_id_list *iterators);
6327 The function C<isl_ast_build_set_iterators> allows the user to
6328 specify a list of iterator C<isl_id>s to be used as iterators.
6329 If the input schedule is injective, then
6330 the number of elements in this list should be as large as the dimension
6331 of the schedule space, but no direct correspondence should be assumed
6332 between dimensions and elements.
6333 If the input schedule is not injective, then an additional number
6334 of C<isl_id>s equal to the largest dimension of the input domains
6336 If the number of provided C<isl_id>s is insufficient, then additional
6337 names are automatically generated.
6339 #include <isl/ast_build.h>
6340 __isl_give isl_ast_build *
6341 isl_ast_build_set_create_leaf(
6342 __isl_take isl_ast_build *control,
6343 __isl_give isl_ast_node *(*fn)(
6344 __isl_take isl_ast_build *build,
6345 void *user), void *user);
6348 C<isl_ast_build_set_create_leaf> function allows for the
6349 specification of a callback that should be called whenever the AST
6350 generator arrives at an element of the schedule domain.
6351 The callback should return an AST node that should be inserted
6352 at the corresponding position of the AST. The default action (when
6353 the callback is not set) is to continue generating parts of the AST to scan
6354 all the domain elements associated to the schedule domain element
6355 and to insert user nodes, ``calling'' the domain element, for each of them.
6356 The C<build> argument contains the current state of the C<isl_ast_build>.
6357 To ease nested AST generation (see L</"Nested AST Generation">),
6358 all control information that is
6359 specific to the current AST generation such as the options and
6360 the callbacks has been removed from this C<isl_ast_build>.
6361 The callback would typically return the result of a nested
6363 user defined node created using the following function.
6365 #include <isl/ast.h>
6366 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6367 __isl_take isl_ast_expr *expr);
6369 #include <isl/ast_build.h>
6370 __isl_give isl_ast_build *
6371 isl_ast_build_set_at_each_domain(
6372 __isl_take isl_ast_build *build,
6373 __isl_give isl_ast_node *(*fn)(
6374 __isl_take isl_ast_node *node,
6375 __isl_keep isl_ast_build *build,
6376 void *user), void *user);
6377 __isl_give isl_ast_build *
6378 isl_ast_build_set_before_each_for(
6379 __isl_take isl_ast_build *build,
6380 __isl_give isl_id *(*fn)(
6381 __isl_keep isl_ast_build *build,
6382 void *user), void *user);
6383 __isl_give isl_ast_build *
6384 isl_ast_build_set_after_each_for(
6385 __isl_take isl_ast_build *build,
6386 __isl_give isl_ast_node *(*fn)(
6387 __isl_take isl_ast_node *node,
6388 __isl_keep isl_ast_build *build,
6389 void *user), void *user);
6391 The callback set by C<isl_ast_build_set_at_each_domain> will
6392 be called for each domain AST node.
6393 The callbacks set by C<isl_ast_build_set_before_each_for>
6394 and C<isl_ast_build_set_after_each_for> will be called
6395 for each for AST node. The first will be called in depth-first
6396 pre-order, while the second will be called in depth-first post-order.
6397 Since C<isl_ast_build_set_before_each_for> is called before the for
6398 node is actually constructed, it is only passed an C<isl_ast_build>.
6399 The returned C<isl_id> will be added as an annotation (using
6400 C<isl_ast_node_set_annotation>) to the constructed for node.
6401 In particular, if the user has also specified an C<after_each_for>
6402 callback, then the annotation can be retrieved from the node passed to
6403 that callback using C<isl_ast_node_get_annotation>.
6404 All callbacks should C<NULL> on failure.
6405 The given C<isl_ast_build> can be used to create new
6406 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6407 or C<isl_ast_build_call_from_pw_multi_aff>.
6409 =head3 Nested AST Generation
6411 C<isl> allows the user to create an AST within the context
6412 of another AST. These nested ASTs are created using the
6413 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6414 outer AST. The C<build> argument should be an C<isl_ast_build>
6415 passed to a callback set by
6416 C<isl_ast_build_set_create_leaf>.
6417 The space of the range of the C<schedule> argument should refer
6418 to this build. In particular, the space should be a wrapped
6419 relation and the domain of this wrapped relation should be the
6420 same as that of the range of the schedule returned by
6421 C<isl_ast_build_get_schedule> below.
6422 In practice, the new schedule is typically
6423 created by calling C<isl_union_map_range_product> on the old schedule
6424 and some extra piece of the schedule.
6425 The space of the schedule domain is also available from
6426 the C<isl_ast_build>.
6428 #include <isl/ast_build.h>
6429 __isl_give isl_union_map *isl_ast_build_get_schedule(
6430 __isl_keep isl_ast_build *build);
6431 __isl_give isl_space *isl_ast_build_get_schedule_space(
6432 __isl_keep isl_ast_build *build);
6433 __isl_give isl_ast_build *isl_ast_build_restrict(
6434 __isl_take isl_ast_build *build,
6435 __isl_take isl_set *set);
6437 The C<isl_ast_build_get_schedule> function returns a (partial)
6438 schedule for the domains elements for which part of the AST still needs to
6439 be generated in the current build.
6440 In particular, the domain elements are mapped to those iterations of the loops
6441 enclosing the current point of the AST generation inside which
6442 the domain elements are executed.
6443 No direct correspondence between
6444 the input schedule and this schedule should be assumed.
6445 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6446 to create a set for C<isl_ast_build_restrict> to intersect
6447 with the current build. In particular, the set passed to
6448 C<isl_ast_build_restrict> can have additional parameters.
6449 The ids of the set dimensions in the space returned by
6450 C<isl_ast_build_get_schedule_space> correspond to the
6451 iterators of the already generated loops.
6452 The user should not rely on the ids of the output dimensions
6453 of the relations in the union relation returned by
6454 C<isl_ast_build_get_schedule> having any particular value.
6458 Although C<isl> is mainly meant to be used as a library,
6459 it also contains some basic applications that use some
6460 of the functionality of C<isl>.
6461 The input may be specified in either the L<isl format>
6462 or the L<PolyLib format>.
6464 =head2 C<isl_polyhedron_sample>
6466 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6467 an integer element of the polyhedron, if there is any.
6468 The first column in the output is the denominator and is always
6469 equal to 1. If the polyhedron contains no integer points,
6470 then a vector of length zero is printed.
6474 C<isl_pip> takes the same input as the C<example> program
6475 from the C<piplib> distribution, i.e., a set of constraints
6476 on the parameters, a line containing only -1 and finally a set
6477 of constraints on a parametric polyhedron.
6478 The coefficients of the parameters appear in the last columns
6479 (but before the final constant column).
6480 The output is the lexicographic minimum of the parametric polyhedron.
6481 As C<isl> currently does not have its own output format, the output
6482 is just a dump of the internal state.
6484 =head2 C<isl_polyhedron_minimize>
6486 C<isl_polyhedron_minimize> computes the minimum of some linear
6487 or affine objective function over the integer points in a polyhedron.
6488 If an affine objective function
6489 is given, then the constant should appear in the last column.
6491 =head2 C<isl_polytope_scan>
6493 Given a polytope, C<isl_polytope_scan> prints
6494 all integer points in the polytope.
6496 =head2 C<isl_codegen>
6498 Given a schedule, a context set and an options relation,
6499 C<isl_codegen> prints out an AST that scans the domain elements
6500 of the schedule in the order of their image(s) taking into account
6501 the constraints in the context set.