3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 int isl_constraint_involves_dims(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1805 The explicit representations of the existentially quantified
1806 variables can be inspected using the following function.
1807 Note that the user is only allowed to use this function
1808 if the inspected set or map is the result of a call
1809 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1810 The existentially quantified variable is equal to the floor
1811 of the returned affine expression. The affine expression
1812 itself can be inspected using the functions in
1813 L<"Piecewise Quasi Affine Expressions">.
1815 __isl_give isl_aff *isl_constraint_get_div(
1816 __isl_keep isl_constraint *constraint, int pos);
1818 To obtain the constraints of a basic set or map in matrix
1819 form, use the following functions.
1821 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1822 __isl_keep isl_basic_set *bset,
1823 enum isl_dim_type c1, enum isl_dim_type c2,
1824 enum isl_dim_type c3, enum isl_dim_type c4);
1825 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1826 __isl_keep isl_basic_set *bset,
1827 enum isl_dim_type c1, enum isl_dim_type c2,
1828 enum isl_dim_type c3, enum isl_dim_type c4);
1829 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1830 __isl_keep isl_basic_map *bmap,
1831 enum isl_dim_type c1,
1832 enum isl_dim_type c2, enum isl_dim_type c3,
1833 enum isl_dim_type c4, enum isl_dim_type c5);
1834 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1835 __isl_keep isl_basic_map *bmap,
1836 enum isl_dim_type c1,
1837 enum isl_dim_type c2, enum isl_dim_type c3,
1838 enum isl_dim_type c4, enum isl_dim_type c5);
1840 The C<isl_dim_type> arguments dictate the order in which
1841 different kinds of variables appear in the resulting matrix
1842 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1843 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1845 The number of parameters, input, output or set dimensions can
1846 be obtained using the following functions.
1848 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1849 enum isl_dim_type type);
1850 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1851 enum isl_dim_type type);
1852 unsigned isl_set_dim(__isl_keep isl_set *set,
1853 enum isl_dim_type type);
1854 unsigned isl_map_dim(__isl_keep isl_map *map,
1855 enum isl_dim_type type);
1857 To check whether the description of a set or relation depends
1858 on one or more given dimensions, it is not necessary to iterate over all
1859 constraints. Instead the following functions can be used.
1861 int isl_basic_set_involves_dims(
1862 __isl_keep isl_basic_set *bset,
1863 enum isl_dim_type type, unsigned first, unsigned n);
1864 int isl_set_involves_dims(__isl_keep isl_set *set,
1865 enum isl_dim_type type, unsigned first, unsigned n);
1866 int isl_basic_map_involves_dims(
1867 __isl_keep isl_basic_map *bmap,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_map_involves_dims(__isl_keep isl_map *map,
1870 enum isl_dim_type type, unsigned first, unsigned n);
1872 Similarly, the following functions can be used to check whether
1873 a given dimension is involved in any lower or upper bound.
1875 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1876 enum isl_dim_type type, unsigned pos);
1877 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1878 enum isl_dim_type type, unsigned pos);
1880 Note that these functions return true even if there is a bound on
1881 the dimension on only some of the basic sets of C<set>.
1882 To check if they have a bound for all of the basic sets in C<set>,
1883 use the following functions instead.
1885 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1886 enum isl_dim_type type, unsigned pos);
1887 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1888 enum isl_dim_type type, unsigned pos);
1890 The identifiers or names of the domain and range spaces of a set
1891 or relation can be read off or set using the following functions.
1893 __isl_give isl_set *isl_set_set_tuple_id(
1894 __isl_take isl_set *set, __isl_take isl_id *id);
1895 __isl_give isl_set *isl_set_reset_tuple_id(
1896 __isl_take isl_set *set);
1897 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1898 __isl_give isl_id *isl_set_get_tuple_id(
1899 __isl_keep isl_set *set);
1900 __isl_give isl_map *isl_map_set_tuple_id(
1901 __isl_take isl_map *map, enum isl_dim_type type,
1902 __isl_take isl_id *id);
1903 __isl_give isl_map *isl_map_reset_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type);
1905 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1906 enum isl_dim_type type);
1907 __isl_give isl_id *isl_map_get_tuple_id(
1908 __isl_keep isl_map *map, enum isl_dim_type type);
1910 const char *isl_basic_set_get_tuple_name(
1911 __isl_keep isl_basic_set *bset);
1912 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1913 __isl_take isl_basic_set *set, const char *s);
1914 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1915 const char *isl_set_get_tuple_name(
1916 __isl_keep isl_set *set);
1917 const char *isl_basic_map_get_tuple_name(
1918 __isl_keep isl_basic_map *bmap,
1919 enum isl_dim_type type);
1920 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1921 __isl_take isl_basic_map *bmap,
1922 enum isl_dim_type type, const char *s);
1923 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1924 enum isl_dim_type type);
1925 const char *isl_map_get_tuple_name(
1926 __isl_keep isl_map *map,
1927 enum isl_dim_type type);
1929 As with C<isl_space_get_tuple_name>, the value returned points to
1930 an internal data structure.
1931 The identifiers, positions or names of individual dimensions can be
1932 read off using the following functions.
1934 __isl_give isl_id *isl_basic_set_get_dim_id(
1935 __isl_keep isl_basic_set *bset,
1936 enum isl_dim_type type, unsigned pos);
1937 __isl_give isl_set *isl_set_set_dim_id(
1938 __isl_take isl_set *set, enum isl_dim_type type,
1939 unsigned pos, __isl_take isl_id *id);
1940 int isl_set_has_dim_id(__isl_keep isl_set *set,
1941 enum isl_dim_type type, unsigned pos);
1942 __isl_give isl_id *isl_set_get_dim_id(
1943 __isl_keep isl_set *set, enum isl_dim_type type,
1945 int isl_basic_map_has_dim_id(
1946 __isl_keep isl_basic_map *bmap,
1947 enum isl_dim_type type, unsigned pos);
1948 __isl_give isl_map *isl_map_set_dim_id(
1949 __isl_take isl_map *map, enum isl_dim_type type,
1950 unsigned pos, __isl_take isl_id *id);
1951 int isl_map_has_dim_id(__isl_keep isl_map *map,
1952 enum isl_dim_type type, unsigned pos);
1953 __isl_give isl_id *isl_map_get_dim_id(
1954 __isl_keep isl_map *map, enum isl_dim_type type,
1957 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1958 enum isl_dim_type type, __isl_keep isl_id *id);
1959 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1960 enum isl_dim_type type, __isl_keep isl_id *id);
1961 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1962 enum isl_dim_type type, const char *name);
1963 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1964 enum isl_dim_type type, const char *name);
1966 const char *isl_constraint_get_dim_name(
1967 __isl_keep isl_constraint *constraint,
1968 enum isl_dim_type type, unsigned pos);
1969 const char *isl_basic_set_get_dim_name(
1970 __isl_keep isl_basic_set *bset,
1971 enum isl_dim_type type, unsigned pos);
1972 int isl_set_has_dim_name(__isl_keep isl_set *set,
1973 enum isl_dim_type type, unsigned pos);
1974 const char *isl_set_get_dim_name(
1975 __isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_basic_map_get_dim_name(
1978 __isl_keep isl_basic_map *bmap,
1979 enum isl_dim_type type, unsigned pos);
1980 int isl_map_has_dim_name(__isl_keep isl_map *map,
1981 enum isl_dim_type type, unsigned pos);
1982 const char *isl_map_get_dim_name(
1983 __isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1986 These functions are mostly useful to obtain the identifiers, positions
1987 or names of the parameters. Identifiers of individual dimensions are
1988 essentially only useful for printing. They are ignored by all other
1989 operations and may not be preserved across those operations.
1993 =head3 Unary Properties
1999 The following functions test whether the given set or relation
2000 contains any integer points. The ``plain'' variants do not perform
2001 any computations, but simply check if the given set or relation
2002 is already known to be empty.
2004 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2005 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2006 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2007 int isl_set_is_empty(__isl_keep isl_set *set);
2008 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2009 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2010 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2011 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2012 int isl_map_is_empty(__isl_keep isl_map *map);
2013 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2015 =item * Universality
2017 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2018 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2019 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2021 =item * Single-valuedness
2023 int isl_basic_map_is_single_valued(
2024 __isl_keep isl_basic_map *bmap);
2025 int isl_map_plain_is_single_valued(
2026 __isl_keep isl_map *map);
2027 int isl_map_is_single_valued(__isl_keep isl_map *map);
2028 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2032 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2033 int isl_map_is_injective(__isl_keep isl_map *map);
2034 int isl_union_map_plain_is_injective(
2035 __isl_keep isl_union_map *umap);
2036 int isl_union_map_is_injective(
2037 __isl_keep isl_union_map *umap);
2041 int isl_map_is_bijective(__isl_keep isl_map *map);
2042 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2046 int isl_basic_map_plain_is_fixed(
2047 __isl_keep isl_basic_map *bmap,
2048 enum isl_dim_type type, unsigned pos,
2050 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2054 enum isl_dim_type type, unsigned pos,
2057 Check if the relation obviously lies on a hyperplane where the given dimension
2058 has a fixed value and if so, return that value in C<*val>.
2062 To check whether a set is a parameter domain, use this function:
2064 int isl_set_is_params(__isl_keep isl_set *set);
2065 int isl_union_set_is_params(
2066 __isl_keep isl_union_set *uset);
2070 The following functions check whether the domain of the given
2071 (basic) set is a wrapped relation.
2073 int isl_basic_set_is_wrapping(
2074 __isl_keep isl_basic_set *bset);
2075 int isl_set_is_wrapping(__isl_keep isl_set *set);
2077 =item * Internal Product
2079 int isl_basic_map_can_zip(
2080 __isl_keep isl_basic_map *bmap);
2081 int isl_map_can_zip(__isl_keep isl_map *map);
2083 Check whether the product of domain and range of the given relation
2085 i.e., whether both domain and range are nested relations.
2089 int isl_basic_map_can_curry(
2090 __isl_keep isl_basic_map *bmap);
2091 int isl_map_can_curry(__isl_keep isl_map *map);
2093 Check whether the domain of the (basic) relation is a wrapped relation.
2095 int isl_basic_map_can_uncurry(
2096 __isl_keep isl_basic_map *bmap);
2097 int isl_map_can_uncurry(__isl_keep isl_map *map);
2099 Check whether the range of the (basic) relation is a wrapped relation.
2103 =head3 Binary Properties
2109 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2110 __isl_keep isl_set *set2);
2111 int isl_set_is_equal(__isl_keep isl_set *set1,
2112 __isl_keep isl_set *set2);
2113 int isl_union_set_is_equal(
2114 __isl_keep isl_union_set *uset1,
2115 __isl_keep isl_union_set *uset2);
2116 int isl_basic_map_is_equal(
2117 __isl_keep isl_basic_map *bmap1,
2118 __isl_keep isl_basic_map *bmap2);
2119 int isl_map_is_equal(__isl_keep isl_map *map1,
2120 __isl_keep isl_map *map2);
2121 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2122 __isl_keep isl_map *map2);
2123 int isl_union_map_is_equal(
2124 __isl_keep isl_union_map *umap1,
2125 __isl_keep isl_union_map *umap2);
2127 =item * Disjointness
2129 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2130 __isl_keep isl_set *set2);
2131 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2132 __isl_keep isl_set *set2);
2133 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2134 __isl_keep isl_map *map2);
2138 int isl_basic_set_is_subset(
2139 __isl_keep isl_basic_set *bset1,
2140 __isl_keep isl_basic_set *bset2);
2141 int isl_set_is_subset(__isl_keep isl_set *set1,
2142 __isl_keep isl_set *set2);
2143 int isl_set_is_strict_subset(
2144 __isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_union_set_is_subset(
2147 __isl_keep isl_union_set *uset1,
2148 __isl_keep isl_union_set *uset2);
2149 int isl_union_set_is_strict_subset(
2150 __isl_keep isl_union_set *uset1,
2151 __isl_keep isl_union_set *uset2);
2152 int isl_basic_map_is_subset(
2153 __isl_keep isl_basic_map *bmap1,
2154 __isl_keep isl_basic_map *bmap2);
2155 int isl_basic_map_is_strict_subset(
2156 __isl_keep isl_basic_map *bmap1,
2157 __isl_keep isl_basic_map *bmap2);
2158 int isl_map_is_subset(
2159 __isl_keep isl_map *map1,
2160 __isl_keep isl_map *map2);
2161 int isl_map_is_strict_subset(
2162 __isl_keep isl_map *map1,
2163 __isl_keep isl_map *map2);
2164 int isl_union_map_is_subset(
2165 __isl_keep isl_union_map *umap1,
2166 __isl_keep isl_union_map *umap2);
2167 int isl_union_map_is_strict_subset(
2168 __isl_keep isl_union_map *umap1,
2169 __isl_keep isl_union_map *umap2);
2171 Check whether the first argument is a (strict) subset of the
2176 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2177 __isl_keep isl_set *set2);
2179 This function is useful for sorting C<isl_set>s.
2180 The order depends on the internal representation of the inputs.
2181 The order is fixed over different calls to the function (assuming
2182 the internal representation of the inputs has not changed), but may
2183 change over different versions of C<isl>.
2187 =head2 Unary Operations
2193 __isl_give isl_set *isl_set_complement(
2194 __isl_take isl_set *set);
2195 __isl_give isl_map *isl_map_complement(
2196 __isl_take isl_map *map);
2200 __isl_give isl_basic_map *isl_basic_map_reverse(
2201 __isl_take isl_basic_map *bmap);
2202 __isl_give isl_map *isl_map_reverse(
2203 __isl_take isl_map *map);
2204 __isl_give isl_union_map *isl_union_map_reverse(
2205 __isl_take isl_union_map *umap);
2209 __isl_give isl_basic_set *isl_basic_set_project_out(
2210 __isl_take isl_basic_set *bset,
2211 enum isl_dim_type type, unsigned first, unsigned n);
2212 __isl_give isl_basic_map *isl_basic_map_project_out(
2213 __isl_take isl_basic_map *bmap,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2216 enum isl_dim_type type, unsigned first, unsigned n);
2217 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2218 enum isl_dim_type type, unsigned first, unsigned n);
2219 __isl_give isl_basic_set *isl_basic_set_params(
2220 __isl_take isl_basic_set *bset);
2221 __isl_give isl_basic_set *isl_basic_map_domain(
2222 __isl_take isl_basic_map *bmap);
2223 __isl_give isl_basic_set *isl_basic_map_range(
2224 __isl_take isl_basic_map *bmap);
2225 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2226 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2227 __isl_give isl_set *isl_map_domain(
2228 __isl_take isl_map *bmap);
2229 __isl_give isl_set *isl_map_range(
2230 __isl_take isl_map *map);
2231 __isl_give isl_set *isl_union_set_params(
2232 __isl_take isl_union_set *uset);
2233 __isl_give isl_set *isl_union_map_params(
2234 __isl_take isl_union_map *umap);
2235 __isl_give isl_union_set *isl_union_map_domain(
2236 __isl_take isl_union_map *umap);
2237 __isl_give isl_union_set *isl_union_map_range(
2238 __isl_take isl_union_map *umap);
2240 __isl_give isl_basic_map *isl_basic_map_domain_map(
2241 __isl_take isl_basic_map *bmap);
2242 __isl_give isl_basic_map *isl_basic_map_range_map(
2243 __isl_take isl_basic_map *bmap);
2244 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2245 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2246 __isl_give isl_union_map *isl_union_map_domain_map(
2247 __isl_take isl_union_map *umap);
2248 __isl_give isl_union_map *isl_union_map_range_map(
2249 __isl_take isl_union_map *umap);
2251 The functions above construct a (basic, regular or union) relation
2252 that maps (a wrapped version of) the input relation to its domain or range.
2256 __isl_give isl_basic_set *isl_basic_set_eliminate(
2257 __isl_take isl_basic_set *bset,
2258 enum isl_dim_type type,
2259 unsigned first, unsigned n);
2260 __isl_give isl_set *isl_set_eliminate(
2261 __isl_take isl_set *set, enum isl_dim_type type,
2262 unsigned first, unsigned n);
2263 __isl_give isl_basic_map *isl_basic_map_eliminate(
2264 __isl_take isl_basic_map *bmap,
2265 enum isl_dim_type type,
2266 unsigned first, unsigned n);
2267 __isl_give isl_map *isl_map_eliminate(
2268 __isl_take isl_map *map, enum isl_dim_type type,
2269 unsigned first, unsigned n);
2271 Eliminate the coefficients for the given dimensions from the constraints,
2272 without removing the dimensions.
2276 __isl_give isl_basic_set *isl_basic_set_fix(
2277 __isl_take isl_basic_set *bset,
2278 enum isl_dim_type type, unsigned pos,
2280 __isl_give isl_basic_set *isl_basic_set_fix_si(
2281 __isl_take isl_basic_set *bset,
2282 enum isl_dim_type type, unsigned pos, int value);
2283 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2284 enum isl_dim_type type, unsigned pos,
2286 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2287 enum isl_dim_type type, unsigned pos, int value);
2288 __isl_give isl_basic_map *isl_basic_map_fix_si(
2289 __isl_take isl_basic_map *bmap,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2292 enum isl_dim_type type, unsigned pos,
2294 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos, int value);
2297 Intersect the set or relation with the hyperplane where the given
2298 dimension has the fixed given value.
2300 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2301 __isl_take isl_basic_map *bmap,
2302 enum isl_dim_type type, unsigned pos, int value);
2303 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_set *isl_set_lower_bound(
2307 __isl_take isl_set *set,
2308 enum isl_dim_type type, unsigned pos,
2310 __isl_give isl_set *isl_set_lower_bound_si(
2311 __isl_take isl_set *set,
2312 enum isl_dim_type type, unsigned pos, int value);
2313 __isl_give isl_map *isl_map_lower_bound_si(
2314 __isl_take isl_map *map,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_set *isl_set_upper_bound(
2317 __isl_take isl_set *set,
2318 enum isl_dim_type type, unsigned pos,
2320 __isl_give isl_set *isl_set_upper_bound_si(
2321 __isl_take isl_set *set,
2322 enum isl_dim_type type, unsigned pos, int value);
2323 __isl_give isl_map *isl_map_upper_bound_si(
2324 __isl_take isl_map *map,
2325 enum isl_dim_type type, unsigned pos, int value);
2327 Intersect the set or relation with the half-space where the given
2328 dimension has a value bounded by the fixed given value.
2330 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2331 enum isl_dim_type type1, int pos1,
2332 enum isl_dim_type type2, int pos2);
2333 __isl_give isl_basic_map *isl_basic_map_equate(
2334 __isl_take isl_basic_map *bmap,
2335 enum isl_dim_type type1, int pos1,
2336 enum isl_dim_type type2, int pos2);
2337 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2338 enum isl_dim_type type1, int pos1,
2339 enum isl_dim_type type2, int pos2);
2341 Intersect the set or relation with the hyperplane where the given
2342 dimensions are equal to each other.
2344 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2345 enum isl_dim_type type1, int pos1,
2346 enum isl_dim_type type2, int pos2);
2348 Intersect the relation with the hyperplane where the given
2349 dimensions have opposite values.
2351 __isl_give isl_basic_map *isl_basic_map_order_ge(
2352 __isl_take isl_basic_map *bmap,
2353 enum isl_dim_type type1, int pos1,
2354 enum isl_dim_type type2, int pos2);
2355 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2358 __isl_give isl_basic_map *isl_basic_map_order_gt(
2359 __isl_take isl_basic_map *bmap,
2360 enum isl_dim_type type1, int pos1,
2361 enum isl_dim_type type2, int pos2);
2362 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2366 Intersect the relation with the half-space where the given
2367 dimensions satisfy the given ordering.
2371 __isl_give isl_map *isl_set_identity(
2372 __isl_take isl_set *set);
2373 __isl_give isl_union_map *isl_union_set_identity(
2374 __isl_take isl_union_set *uset);
2376 Construct an identity relation on the given (union) set.
2380 __isl_give isl_basic_set *isl_basic_map_deltas(
2381 __isl_take isl_basic_map *bmap);
2382 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2383 __isl_give isl_union_set *isl_union_map_deltas(
2384 __isl_take isl_union_map *umap);
2386 These functions return a (basic) set containing the differences
2387 between image elements and corresponding domain elements in the input.
2389 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2390 __isl_take isl_basic_map *bmap);
2391 __isl_give isl_map *isl_map_deltas_map(
2392 __isl_take isl_map *map);
2393 __isl_give isl_union_map *isl_union_map_deltas_map(
2394 __isl_take isl_union_map *umap);
2396 The functions above construct a (basic, regular or union) relation
2397 that maps (a wrapped version of) the input relation to its delta set.
2401 Simplify the representation of a set or relation by trying
2402 to combine pairs of basic sets or relations into a single
2403 basic set or relation.
2405 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2406 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2407 __isl_give isl_union_set *isl_union_set_coalesce(
2408 __isl_take isl_union_set *uset);
2409 __isl_give isl_union_map *isl_union_map_coalesce(
2410 __isl_take isl_union_map *umap);
2412 One of the methods for combining pairs of basic sets or relations
2413 can result in coefficients that are much larger than those that appear
2414 in the constraints of the input. By default, the coefficients are
2415 not allowed to grow larger, but this can be changed by unsetting
2416 the following option.
2418 int isl_options_set_coalesce_bounded_wrapping(
2419 isl_ctx *ctx, int val);
2420 int isl_options_get_coalesce_bounded_wrapping(
2423 =item * Detecting equalities
2425 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2426 __isl_take isl_basic_set *bset);
2427 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2428 __isl_take isl_basic_map *bmap);
2429 __isl_give isl_set *isl_set_detect_equalities(
2430 __isl_take isl_set *set);
2431 __isl_give isl_map *isl_map_detect_equalities(
2432 __isl_take isl_map *map);
2433 __isl_give isl_union_set *isl_union_set_detect_equalities(
2434 __isl_take isl_union_set *uset);
2435 __isl_give isl_union_map *isl_union_map_detect_equalities(
2436 __isl_take isl_union_map *umap);
2438 Simplify the representation of a set or relation by detecting implicit
2441 =item * Removing redundant constraints
2443 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2444 __isl_take isl_basic_set *bset);
2445 __isl_give isl_set *isl_set_remove_redundancies(
2446 __isl_take isl_set *set);
2447 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2448 __isl_take isl_basic_map *bmap);
2449 __isl_give isl_map *isl_map_remove_redundancies(
2450 __isl_take isl_map *map);
2454 __isl_give isl_basic_set *isl_set_convex_hull(
2455 __isl_take isl_set *set);
2456 __isl_give isl_basic_map *isl_map_convex_hull(
2457 __isl_take isl_map *map);
2459 If the input set or relation has any existentially quantified
2460 variables, then the result of these operations is currently undefined.
2464 __isl_give isl_basic_set *
2465 isl_set_unshifted_simple_hull(
2466 __isl_take isl_set *set);
2467 __isl_give isl_basic_map *
2468 isl_map_unshifted_simple_hull(
2469 __isl_take isl_map *map);
2470 __isl_give isl_basic_set *isl_set_simple_hull(
2471 __isl_take isl_set *set);
2472 __isl_give isl_basic_map *isl_map_simple_hull(
2473 __isl_take isl_map *map);
2474 __isl_give isl_union_map *isl_union_map_simple_hull(
2475 __isl_take isl_union_map *umap);
2477 These functions compute a single basic set or relation
2478 that contains the whole input set or relation.
2479 In particular, the output is described by translates
2480 of the constraints describing the basic sets or relations in the input.
2481 In case of C<isl_set_unshifted_simple_hull>, only the original
2482 constraints are used, without any translation.
2486 (See \autoref{s:simple hull}.)
2492 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2493 __isl_take isl_basic_set *bset);
2494 __isl_give isl_basic_set *isl_set_affine_hull(
2495 __isl_take isl_set *set);
2496 __isl_give isl_union_set *isl_union_set_affine_hull(
2497 __isl_take isl_union_set *uset);
2498 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2499 __isl_take isl_basic_map *bmap);
2500 __isl_give isl_basic_map *isl_map_affine_hull(
2501 __isl_take isl_map *map);
2502 __isl_give isl_union_map *isl_union_map_affine_hull(
2503 __isl_take isl_union_map *umap);
2505 In case of union sets and relations, the affine hull is computed
2508 =item * Polyhedral hull
2510 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2511 __isl_take isl_set *set);
2512 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2513 __isl_take isl_map *map);
2514 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2515 __isl_take isl_union_set *uset);
2516 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2517 __isl_take isl_union_map *umap);
2519 These functions compute a single basic set or relation
2520 not involving any existentially quantified variables
2521 that contains the whole input set or relation.
2522 In case of union sets and relations, the polyhedral hull is computed
2525 =item * Other approximations
2527 __isl_give isl_basic_set *
2528 isl_basic_set_drop_constraints_involving_dims(
2529 __isl_take isl_basic_set *bset,
2530 enum isl_dim_type type,
2531 unsigned first, unsigned n);
2532 __isl_give isl_basic_map *
2533 isl_basic_map_drop_constraints_involving_dims(
2534 __isl_take isl_basic_map *bmap,
2535 enum isl_dim_type type,
2536 unsigned first, unsigned n);
2537 __isl_give isl_basic_set *
2538 isl_basic_set_drop_constraints_not_involving_dims(
2539 __isl_take isl_basic_set *bset,
2540 enum isl_dim_type type,
2541 unsigned first, unsigned n);
2542 __isl_give isl_set *
2543 isl_set_drop_constraints_involving_dims(
2544 __isl_take isl_set *set,
2545 enum isl_dim_type type,
2546 unsigned first, unsigned n);
2547 __isl_give isl_map *
2548 isl_map_drop_constraints_involving_dims(
2549 __isl_take isl_map *map,
2550 enum isl_dim_type type,
2551 unsigned first, unsigned n);
2553 These functions drop any constraints (not) involving the specified dimensions.
2554 Note that the result depends on the representation of the input.
2558 __isl_give isl_basic_set *isl_basic_set_sample(
2559 __isl_take isl_basic_set *bset);
2560 __isl_give isl_basic_set *isl_set_sample(
2561 __isl_take isl_set *set);
2562 __isl_give isl_basic_map *isl_basic_map_sample(
2563 __isl_take isl_basic_map *bmap);
2564 __isl_give isl_basic_map *isl_map_sample(
2565 __isl_take isl_map *map);
2567 If the input (basic) set or relation is non-empty, then return
2568 a singleton subset of the input. Otherwise, return an empty set.
2570 =item * Optimization
2572 #include <isl/ilp.h>
2573 enum isl_lp_result isl_basic_set_max(
2574 __isl_keep isl_basic_set *bset,
2575 __isl_keep isl_aff *obj, isl_int *opt)
2576 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2577 __isl_keep isl_aff *obj, isl_int *opt);
2578 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2579 __isl_keep isl_aff *obj, isl_int *opt);
2581 Compute the minimum or maximum of the integer affine expression C<obj>
2582 over the points in C<set>, returning the result in C<opt>.
2583 The return value may be one of C<isl_lp_error>,
2584 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2586 =item * Parametric optimization
2588 __isl_give isl_pw_aff *isl_set_dim_min(
2589 __isl_take isl_set *set, int pos);
2590 __isl_give isl_pw_aff *isl_set_dim_max(
2591 __isl_take isl_set *set, int pos);
2592 __isl_give isl_pw_aff *isl_map_dim_max(
2593 __isl_take isl_map *map, int pos);
2595 Compute the minimum or maximum of the given set or output dimension
2596 as a function of the parameters (and input dimensions), but independently
2597 of the other set or output dimensions.
2598 For lexicographic optimization, see L<"Lexicographic Optimization">.
2602 The following functions compute either the set of (rational) coefficient
2603 values of valid constraints for the given set or the set of (rational)
2604 values satisfying the constraints with coefficients from the given set.
2605 Internally, these two sets of functions perform essentially the
2606 same operations, except that the set of coefficients is assumed to
2607 be a cone, while the set of values may be any polyhedron.
2608 The current implementation is based on the Farkas lemma and
2609 Fourier-Motzkin elimination, but this may change or be made optional
2610 in future. In particular, future implementations may use different
2611 dualization algorithms or skip the elimination step.
2613 __isl_give isl_basic_set *isl_basic_set_coefficients(
2614 __isl_take isl_basic_set *bset);
2615 __isl_give isl_basic_set *isl_set_coefficients(
2616 __isl_take isl_set *set);
2617 __isl_give isl_union_set *isl_union_set_coefficients(
2618 __isl_take isl_union_set *bset);
2619 __isl_give isl_basic_set *isl_basic_set_solutions(
2620 __isl_take isl_basic_set *bset);
2621 __isl_give isl_basic_set *isl_set_solutions(
2622 __isl_take isl_set *set);
2623 __isl_give isl_union_set *isl_union_set_solutions(
2624 __isl_take isl_union_set *bset);
2628 __isl_give isl_map *isl_map_fixed_power(
2629 __isl_take isl_map *map, isl_int exp);
2630 __isl_give isl_union_map *isl_union_map_fixed_power(
2631 __isl_take isl_union_map *umap, isl_int exp);
2633 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2634 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2635 of C<map> is computed.
2637 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2639 __isl_give isl_union_map *isl_union_map_power(
2640 __isl_take isl_union_map *umap, int *exact);
2642 Compute a parametric representation for all positive powers I<k> of C<map>.
2643 The result maps I<k> to a nested relation corresponding to the
2644 I<k>th power of C<map>.
2645 The result may be an overapproximation. If the result is known to be exact,
2646 then C<*exact> is set to C<1>.
2648 =item * Transitive closure
2650 __isl_give isl_map *isl_map_transitive_closure(
2651 __isl_take isl_map *map, int *exact);
2652 __isl_give isl_union_map *isl_union_map_transitive_closure(
2653 __isl_take isl_union_map *umap, int *exact);
2655 Compute the transitive closure of C<map>.
2656 The result may be an overapproximation. If the result is known to be exact,
2657 then C<*exact> is set to C<1>.
2659 =item * Reaching path lengths
2661 __isl_give isl_map *isl_map_reaching_path_lengths(
2662 __isl_take isl_map *map, int *exact);
2664 Compute a relation that maps each element in the range of C<map>
2665 to the lengths of all paths composed of edges in C<map> that
2666 end up in the given element.
2667 The result may be an overapproximation. If the result is known to be exact,
2668 then C<*exact> is set to C<1>.
2669 To compute the I<maximal> path length, the resulting relation
2670 should be postprocessed by C<isl_map_lexmax>.
2671 In particular, if the input relation is a dependence relation
2672 (mapping sources to sinks), then the maximal path length corresponds
2673 to the free schedule.
2674 Note, however, that C<isl_map_lexmax> expects the maximum to be
2675 finite, so if the path lengths are unbounded (possibly due to
2676 the overapproximation), then you will get an error message.
2680 __isl_give isl_basic_set *isl_basic_map_wrap(
2681 __isl_take isl_basic_map *bmap);
2682 __isl_give isl_set *isl_map_wrap(
2683 __isl_take isl_map *map);
2684 __isl_give isl_union_set *isl_union_map_wrap(
2685 __isl_take isl_union_map *umap);
2686 __isl_give isl_basic_map *isl_basic_set_unwrap(
2687 __isl_take isl_basic_set *bset);
2688 __isl_give isl_map *isl_set_unwrap(
2689 __isl_take isl_set *set);
2690 __isl_give isl_union_map *isl_union_set_unwrap(
2691 __isl_take isl_union_set *uset);
2695 Remove any internal structure of domain (and range) of the given
2696 set or relation. If there is any such internal structure in the input,
2697 then the name of the space is also removed.
2699 __isl_give isl_basic_set *isl_basic_set_flatten(
2700 __isl_take isl_basic_set *bset);
2701 __isl_give isl_set *isl_set_flatten(
2702 __isl_take isl_set *set);
2703 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2704 __isl_take isl_basic_map *bmap);
2705 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2706 __isl_take isl_basic_map *bmap);
2707 __isl_give isl_map *isl_map_flatten_range(
2708 __isl_take isl_map *map);
2709 __isl_give isl_map *isl_map_flatten_domain(
2710 __isl_take isl_map *map);
2711 __isl_give isl_basic_map *isl_basic_map_flatten(
2712 __isl_take isl_basic_map *bmap);
2713 __isl_give isl_map *isl_map_flatten(
2714 __isl_take isl_map *map);
2716 __isl_give isl_map *isl_set_flatten_map(
2717 __isl_take isl_set *set);
2719 The function above constructs a relation
2720 that maps the input set to a flattened version of the set.
2724 Lift the input set to a space with extra dimensions corresponding
2725 to the existentially quantified variables in the input.
2726 In particular, the result lives in a wrapped map where the domain
2727 is the original space and the range corresponds to the original
2728 existentially quantified variables.
2730 __isl_give isl_basic_set *isl_basic_set_lift(
2731 __isl_take isl_basic_set *bset);
2732 __isl_give isl_set *isl_set_lift(
2733 __isl_take isl_set *set);
2734 __isl_give isl_union_set *isl_union_set_lift(
2735 __isl_take isl_union_set *uset);
2737 Given a local space that contains the existentially quantified
2738 variables of a set, a basic relation that, when applied to
2739 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2740 can be constructed using the following function.
2742 #include <isl/local_space.h>
2743 __isl_give isl_basic_map *isl_local_space_lifting(
2744 __isl_take isl_local_space *ls);
2746 =item * Internal Product
2748 __isl_give isl_basic_map *isl_basic_map_zip(
2749 __isl_take isl_basic_map *bmap);
2750 __isl_give isl_map *isl_map_zip(
2751 __isl_take isl_map *map);
2752 __isl_give isl_union_map *isl_union_map_zip(
2753 __isl_take isl_union_map *umap);
2755 Given a relation with nested relations for domain and range,
2756 interchange the range of the domain with the domain of the range.
2760 __isl_give isl_basic_map *isl_basic_map_curry(
2761 __isl_take isl_basic_map *bmap);
2762 __isl_give isl_basic_map *isl_basic_map_uncurry(
2763 __isl_take isl_basic_map *bmap);
2764 __isl_give isl_map *isl_map_curry(
2765 __isl_take isl_map *map);
2766 __isl_give isl_map *isl_map_uncurry(
2767 __isl_take isl_map *map);
2768 __isl_give isl_union_map *isl_union_map_curry(
2769 __isl_take isl_union_map *umap);
2770 __isl_give isl_union_map *isl_union_map_uncurry(
2771 __isl_take isl_union_map *umap);
2773 Given a relation with a nested relation for domain,
2774 the C<curry> functions
2775 move the range of the nested relation out of the domain
2776 and use it as the domain of a nested relation in the range,
2777 with the original range as range of this nested relation.
2778 The C<uncurry> functions perform the inverse operation.
2780 =item * Aligning parameters
2782 __isl_give isl_basic_set *isl_basic_set_align_params(
2783 __isl_take isl_basic_set *bset,
2784 __isl_take isl_space *model);
2785 __isl_give isl_set *isl_set_align_params(
2786 __isl_take isl_set *set,
2787 __isl_take isl_space *model);
2788 __isl_give isl_basic_map *isl_basic_map_align_params(
2789 __isl_take isl_basic_map *bmap,
2790 __isl_take isl_space *model);
2791 __isl_give isl_map *isl_map_align_params(
2792 __isl_take isl_map *map,
2793 __isl_take isl_space *model);
2795 Change the order of the parameters of the given set or relation
2796 such that the first parameters match those of C<model>.
2797 This may involve the introduction of extra parameters.
2798 All parameters need to be named.
2800 =item * Dimension manipulation
2802 __isl_give isl_basic_set *isl_basic_set_add_dims(
2803 __isl_take isl_basic_set *bset,
2804 enum isl_dim_type type, unsigned n);
2805 __isl_give isl_set *isl_set_add_dims(
2806 __isl_take isl_set *set,
2807 enum isl_dim_type type, unsigned n);
2808 __isl_give isl_map *isl_map_add_dims(
2809 __isl_take isl_map *map,
2810 enum isl_dim_type type, unsigned n);
2811 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2812 __isl_take isl_basic_set *bset,
2813 enum isl_dim_type type, unsigned pos,
2815 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2816 __isl_take isl_basic_map *bmap,
2817 enum isl_dim_type type, unsigned pos,
2819 __isl_give isl_set *isl_set_insert_dims(
2820 __isl_take isl_set *set,
2821 enum isl_dim_type type, unsigned pos, unsigned n);
2822 __isl_give isl_map *isl_map_insert_dims(
2823 __isl_take isl_map *map,
2824 enum isl_dim_type type, unsigned pos, unsigned n);
2825 __isl_give isl_basic_set *isl_basic_set_move_dims(
2826 __isl_take isl_basic_set *bset,
2827 enum isl_dim_type dst_type, unsigned dst_pos,
2828 enum isl_dim_type src_type, unsigned src_pos,
2830 __isl_give isl_basic_map *isl_basic_map_move_dims(
2831 __isl_take isl_basic_map *bmap,
2832 enum isl_dim_type dst_type, unsigned dst_pos,
2833 enum isl_dim_type src_type, unsigned src_pos,
2835 __isl_give isl_set *isl_set_move_dims(
2836 __isl_take isl_set *set,
2837 enum isl_dim_type dst_type, unsigned dst_pos,
2838 enum isl_dim_type src_type, unsigned src_pos,
2840 __isl_give isl_map *isl_map_move_dims(
2841 __isl_take isl_map *map,
2842 enum isl_dim_type dst_type, unsigned dst_pos,
2843 enum isl_dim_type src_type, unsigned src_pos,
2846 It is usually not advisable to directly change the (input or output)
2847 space of a set or a relation as this removes the name and the internal
2848 structure of the space. However, the above functions can be useful
2849 to add new parameters, assuming
2850 C<isl_set_align_params> and C<isl_map_align_params>
2855 =head2 Binary Operations
2857 The two arguments of a binary operation not only need to live
2858 in the same C<isl_ctx>, they currently also need to have
2859 the same (number of) parameters.
2861 =head3 Basic Operations
2865 =item * Intersection
2867 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2868 __isl_take isl_basic_set *bset1,
2869 __isl_take isl_basic_set *bset2);
2870 __isl_give isl_basic_set *isl_basic_set_intersect(
2871 __isl_take isl_basic_set *bset1,
2872 __isl_take isl_basic_set *bset2);
2873 __isl_give isl_set *isl_set_intersect_params(
2874 __isl_take isl_set *set,
2875 __isl_take isl_set *params);
2876 __isl_give isl_set *isl_set_intersect(
2877 __isl_take isl_set *set1,
2878 __isl_take isl_set *set2);
2879 __isl_give isl_union_set *isl_union_set_intersect_params(
2880 __isl_take isl_union_set *uset,
2881 __isl_take isl_set *set);
2882 __isl_give isl_union_map *isl_union_map_intersect_params(
2883 __isl_take isl_union_map *umap,
2884 __isl_take isl_set *set);
2885 __isl_give isl_union_set *isl_union_set_intersect(
2886 __isl_take isl_union_set *uset1,
2887 __isl_take isl_union_set *uset2);
2888 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2889 __isl_take isl_basic_map *bmap,
2890 __isl_take isl_basic_set *bset);
2891 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2892 __isl_take isl_basic_map *bmap,
2893 __isl_take isl_basic_set *bset);
2894 __isl_give isl_basic_map *isl_basic_map_intersect(
2895 __isl_take isl_basic_map *bmap1,
2896 __isl_take isl_basic_map *bmap2);
2897 __isl_give isl_map *isl_map_intersect_params(
2898 __isl_take isl_map *map,
2899 __isl_take isl_set *params);
2900 __isl_give isl_map *isl_map_intersect_domain(
2901 __isl_take isl_map *map,
2902 __isl_take isl_set *set);
2903 __isl_give isl_map *isl_map_intersect_range(
2904 __isl_take isl_map *map,
2905 __isl_take isl_set *set);
2906 __isl_give isl_map *isl_map_intersect(
2907 __isl_take isl_map *map1,
2908 __isl_take isl_map *map2);
2909 __isl_give isl_union_map *isl_union_map_intersect_domain(
2910 __isl_take isl_union_map *umap,
2911 __isl_take isl_union_set *uset);
2912 __isl_give isl_union_map *isl_union_map_intersect_range(
2913 __isl_take isl_union_map *umap,
2914 __isl_take isl_union_set *uset);
2915 __isl_give isl_union_map *isl_union_map_intersect(
2916 __isl_take isl_union_map *umap1,
2917 __isl_take isl_union_map *umap2);
2919 The second argument to the C<_params> functions needs to be
2920 a parametric (basic) set. For the other functions, a parametric set
2921 for either argument is only allowed if the other argument is
2922 a parametric set as well.
2926 __isl_give isl_set *isl_basic_set_union(
2927 __isl_take isl_basic_set *bset1,
2928 __isl_take isl_basic_set *bset2);
2929 __isl_give isl_map *isl_basic_map_union(
2930 __isl_take isl_basic_map *bmap1,
2931 __isl_take isl_basic_map *bmap2);
2932 __isl_give isl_set *isl_set_union(
2933 __isl_take isl_set *set1,
2934 __isl_take isl_set *set2);
2935 __isl_give isl_map *isl_map_union(
2936 __isl_take isl_map *map1,
2937 __isl_take isl_map *map2);
2938 __isl_give isl_union_set *isl_union_set_union(
2939 __isl_take isl_union_set *uset1,
2940 __isl_take isl_union_set *uset2);
2941 __isl_give isl_union_map *isl_union_map_union(
2942 __isl_take isl_union_map *umap1,
2943 __isl_take isl_union_map *umap2);
2945 =item * Set difference
2947 __isl_give isl_set *isl_set_subtract(
2948 __isl_take isl_set *set1,
2949 __isl_take isl_set *set2);
2950 __isl_give isl_map *isl_map_subtract(
2951 __isl_take isl_map *map1,
2952 __isl_take isl_map *map2);
2953 __isl_give isl_map *isl_map_subtract_domain(
2954 __isl_take isl_map *map,
2955 __isl_take isl_set *dom);
2956 __isl_give isl_map *isl_map_subtract_range(
2957 __isl_take isl_map *map,
2958 __isl_take isl_set *dom);
2959 __isl_give isl_union_set *isl_union_set_subtract(
2960 __isl_take isl_union_set *uset1,
2961 __isl_take isl_union_set *uset2);
2962 __isl_give isl_union_map *isl_union_map_subtract(
2963 __isl_take isl_union_map *umap1,
2964 __isl_take isl_union_map *umap2);
2965 __isl_give isl_union_map *isl_union_map_subtract_domain(
2966 __isl_take isl_union_map *umap,
2967 __isl_take isl_union_set *dom);
2968 __isl_give isl_union_map *isl_union_map_subtract_range(
2969 __isl_take isl_union_map *umap,
2970 __isl_take isl_union_set *dom);
2974 __isl_give isl_basic_set *isl_basic_set_apply(
2975 __isl_take isl_basic_set *bset,
2976 __isl_take isl_basic_map *bmap);
2977 __isl_give isl_set *isl_set_apply(
2978 __isl_take isl_set *set,
2979 __isl_take isl_map *map);
2980 __isl_give isl_union_set *isl_union_set_apply(
2981 __isl_take isl_union_set *uset,
2982 __isl_take isl_union_map *umap);
2983 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2984 __isl_take isl_basic_map *bmap1,
2985 __isl_take isl_basic_map *bmap2);
2986 __isl_give isl_basic_map *isl_basic_map_apply_range(
2987 __isl_take isl_basic_map *bmap1,
2988 __isl_take isl_basic_map *bmap2);
2989 __isl_give isl_map *isl_map_apply_domain(
2990 __isl_take isl_map *map1,
2991 __isl_take isl_map *map2);
2992 __isl_give isl_union_map *isl_union_map_apply_domain(
2993 __isl_take isl_union_map *umap1,
2994 __isl_take isl_union_map *umap2);
2995 __isl_give isl_map *isl_map_apply_range(
2996 __isl_take isl_map *map1,
2997 __isl_take isl_map *map2);
2998 __isl_give isl_union_map *isl_union_map_apply_range(
2999 __isl_take isl_union_map *umap1,
3000 __isl_take isl_union_map *umap2);
3004 __isl_give isl_basic_set *
3005 isl_basic_set_preimage_multi_aff(
3006 __isl_take isl_basic_set *bset,
3007 __isl_take isl_multi_aff *ma);
3008 __isl_give isl_set *isl_set_preimage_multi_aff(
3009 __isl_take isl_set *set,
3010 __isl_take isl_multi_aff *ma);
3011 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3012 __isl_take isl_set *set,
3013 __isl_take isl_pw_multi_aff *pma);
3014 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3015 __isl_take isl_map *map,
3016 __isl_take isl_multi_aff *ma);
3017 __isl_give isl_union_map *
3018 isl_union_map_preimage_domain_multi_aff(
3019 __isl_take isl_union_map *umap,
3020 __isl_take isl_multi_aff *ma);
3022 These functions compute the preimage of the given set or map domain under
3023 the given function. In other words, the expression is plugged
3024 into the set description or into the domain of the map.
3025 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3026 L</"Piecewise Multiple Quasi Affine Expressions">.
3028 =item * Cartesian Product
3030 __isl_give isl_set *isl_set_product(
3031 __isl_take isl_set *set1,
3032 __isl_take isl_set *set2);
3033 __isl_give isl_union_set *isl_union_set_product(
3034 __isl_take isl_union_set *uset1,
3035 __isl_take isl_union_set *uset2);
3036 __isl_give isl_basic_map *isl_basic_map_domain_product(
3037 __isl_take isl_basic_map *bmap1,
3038 __isl_take isl_basic_map *bmap2);
3039 __isl_give isl_basic_map *isl_basic_map_range_product(
3040 __isl_take isl_basic_map *bmap1,
3041 __isl_take isl_basic_map *bmap2);
3042 __isl_give isl_basic_map *isl_basic_map_product(
3043 __isl_take isl_basic_map *bmap1,
3044 __isl_take isl_basic_map *bmap2);
3045 __isl_give isl_map *isl_map_domain_product(
3046 __isl_take isl_map *map1,
3047 __isl_take isl_map *map2);
3048 __isl_give isl_map *isl_map_range_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_union_map *isl_union_map_domain_product(
3052 __isl_take isl_union_map *umap1,
3053 __isl_take isl_union_map *umap2);
3054 __isl_give isl_union_map *isl_union_map_range_product(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3057 __isl_give isl_map *isl_map_product(
3058 __isl_take isl_map *map1,
3059 __isl_take isl_map *map2);
3060 __isl_give isl_union_map *isl_union_map_product(
3061 __isl_take isl_union_map *umap1,
3062 __isl_take isl_union_map *umap2);
3064 The above functions compute the cross product of the given
3065 sets or relations. The domains and ranges of the results
3066 are wrapped maps between domains and ranges of the inputs.
3067 To obtain a ``flat'' product, use the following functions
3070 __isl_give isl_basic_set *isl_basic_set_flat_product(
3071 __isl_take isl_basic_set *bset1,
3072 __isl_take isl_basic_set *bset2);
3073 __isl_give isl_set *isl_set_flat_product(
3074 __isl_take isl_set *set1,
3075 __isl_take isl_set *set2);
3076 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3077 __isl_take isl_basic_map *bmap1,
3078 __isl_take isl_basic_map *bmap2);
3079 __isl_give isl_map *isl_map_flat_domain_product(
3080 __isl_take isl_map *map1,
3081 __isl_take isl_map *map2);
3082 __isl_give isl_map *isl_map_flat_range_product(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3085 __isl_give isl_union_map *isl_union_map_flat_range_product(
3086 __isl_take isl_union_map *umap1,
3087 __isl_take isl_union_map *umap2);
3088 __isl_give isl_basic_map *isl_basic_map_flat_product(
3089 __isl_take isl_basic_map *bmap1,
3090 __isl_take isl_basic_map *bmap2);
3091 __isl_give isl_map *isl_map_flat_product(
3092 __isl_take isl_map *map1,
3093 __isl_take isl_map *map2);
3095 =item * Simplification
3097 __isl_give isl_basic_set *isl_basic_set_gist(
3098 __isl_take isl_basic_set *bset,
3099 __isl_take isl_basic_set *context);
3100 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3101 __isl_take isl_set *context);
3102 __isl_give isl_set *isl_set_gist_params(
3103 __isl_take isl_set *set,
3104 __isl_take isl_set *context);
3105 __isl_give isl_union_set *isl_union_set_gist(
3106 __isl_take isl_union_set *uset,
3107 __isl_take isl_union_set *context);
3108 __isl_give isl_union_set *isl_union_set_gist_params(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_set *set);
3111 __isl_give isl_basic_map *isl_basic_map_gist(
3112 __isl_take isl_basic_map *bmap,
3113 __isl_take isl_basic_map *context);
3114 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3115 __isl_take isl_map *context);
3116 __isl_give isl_map *isl_map_gist_params(
3117 __isl_take isl_map *map,
3118 __isl_take isl_set *context);
3119 __isl_give isl_map *isl_map_gist_domain(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_map *isl_map_gist_range(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_union_map *isl_union_map_gist(
3126 __isl_take isl_union_map *umap,
3127 __isl_take isl_union_map *context);
3128 __isl_give isl_union_map *isl_union_map_gist_params(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_set *set);
3131 __isl_give isl_union_map *isl_union_map_gist_domain(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_union_set *uset);
3134 __isl_give isl_union_map *isl_union_map_gist_range(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_union_set *uset);
3138 The gist operation returns a set or relation that has the
3139 same intersection with the context as the input set or relation.
3140 Any implicit equality in the intersection is made explicit in the result,
3141 while all inequalities that are redundant with respect to the intersection
3143 In case of union sets and relations, the gist operation is performed
3148 =head3 Lexicographic Optimization
3150 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3151 the following functions
3152 compute a set that contains the lexicographic minimum or maximum
3153 of the elements in C<set> (or C<bset>) for those values of the parameters
3154 that satisfy C<dom>.
3155 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3156 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3158 In other words, the union of the parameter values
3159 for which the result is non-empty and of C<*empty>
3162 __isl_give isl_set *isl_basic_set_partial_lexmin(
3163 __isl_take isl_basic_set *bset,
3164 __isl_take isl_basic_set *dom,
3165 __isl_give isl_set **empty);
3166 __isl_give isl_set *isl_basic_set_partial_lexmax(
3167 __isl_take isl_basic_set *bset,
3168 __isl_take isl_basic_set *dom,
3169 __isl_give isl_set **empty);
3170 __isl_give isl_set *isl_set_partial_lexmin(
3171 __isl_take isl_set *set, __isl_take isl_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_set *isl_set_partial_lexmax(
3174 __isl_take isl_set *set, __isl_take isl_set *dom,
3175 __isl_give isl_set **empty);
3177 Given a (basic) set C<set> (or C<bset>), the following functions simply
3178 return a set containing the lexicographic minimum or maximum
3179 of the elements in C<set> (or C<bset>).
3180 In case of union sets, the optimum is computed per space.
3182 __isl_give isl_set *isl_basic_set_lexmin(
3183 __isl_take isl_basic_set *bset);
3184 __isl_give isl_set *isl_basic_set_lexmax(
3185 __isl_take isl_basic_set *bset);
3186 __isl_give isl_set *isl_set_lexmin(
3187 __isl_take isl_set *set);
3188 __isl_give isl_set *isl_set_lexmax(
3189 __isl_take isl_set *set);
3190 __isl_give isl_union_set *isl_union_set_lexmin(
3191 __isl_take isl_union_set *uset);
3192 __isl_give isl_union_set *isl_union_set_lexmax(
3193 __isl_take isl_union_set *uset);
3195 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3196 the following functions
3197 compute a relation that maps each element of C<dom>
3198 to the single lexicographic minimum or maximum
3199 of the elements that are associated to that same
3200 element in C<map> (or C<bmap>).
3201 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3202 that contains the elements in C<dom> that do not map
3203 to any elements in C<map> (or C<bmap>).
3204 In other words, the union of the domain of the result and of C<*empty>
3207 __isl_give isl_map *isl_basic_map_partial_lexmax(
3208 __isl_take isl_basic_map *bmap,
3209 __isl_take isl_basic_set *dom,
3210 __isl_give isl_set **empty);
3211 __isl_give isl_map *isl_basic_map_partial_lexmin(
3212 __isl_take isl_basic_map *bmap,
3213 __isl_take isl_basic_set *dom,
3214 __isl_give isl_set **empty);
3215 __isl_give isl_map *isl_map_partial_lexmax(
3216 __isl_take isl_map *map, __isl_take isl_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_map *isl_map_partial_lexmin(
3219 __isl_take isl_map *map, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3222 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3223 return a map mapping each element in the domain of
3224 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3225 of all elements associated to that element.
3226 In case of union relations, the optimum is computed per space.
3228 __isl_give isl_map *isl_basic_map_lexmin(
3229 __isl_take isl_basic_map *bmap);
3230 __isl_give isl_map *isl_basic_map_lexmax(
3231 __isl_take isl_basic_map *bmap);
3232 __isl_give isl_map *isl_map_lexmin(
3233 __isl_take isl_map *map);
3234 __isl_give isl_map *isl_map_lexmax(
3235 __isl_take isl_map *map);
3236 __isl_give isl_union_map *isl_union_map_lexmin(
3237 __isl_take isl_union_map *umap);
3238 __isl_give isl_union_map *isl_union_map_lexmax(
3239 __isl_take isl_union_map *umap);
3241 The following functions return their result in the form of
3242 a piecewise multi-affine expression
3243 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3244 but are otherwise equivalent to the corresponding functions
3245 returning a basic set or relation.
3247 __isl_give isl_pw_multi_aff *
3248 isl_basic_map_lexmin_pw_multi_aff(
3249 __isl_take isl_basic_map *bmap);
3250 __isl_give isl_pw_multi_aff *
3251 isl_basic_set_partial_lexmin_pw_multi_aff(
3252 __isl_take isl_basic_set *bset,
3253 __isl_take isl_basic_set *dom,
3254 __isl_give isl_set **empty);
3255 __isl_give isl_pw_multi_aff *
3256 isl_basic_set_partial_lexmax_pw_multi_aff(
3257 __isl_take isl_basic_set *bset,
3258 __isl_take isl_basic_set *dom,
3259 __isl_give isl_set **empty);
3260 __isl_give isl_pw_multi_aff *
3261 isl_basic_map_partial_lexmin_pw_multi_aff(
3262 __isl_take isl_basic_map *bmap,
3263 __isl_take isl_basic_set *dom,
3264 __isl_give isl_set **empty);
3265 __isl_give isl_pw_multi_aff *
3266 isl_basic_map_partial_lexmax_pw_multi_aff(
3267 __isl_take isl_basic_map *bmap,
3268 __isl_take isl_basic_set *dom,
3269 __isl_give isl_set **empty);
3270 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3271 __isl_take isl_set *set);
3272 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3273 __isl_take isl_set *set);
3274 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3275 __isl_take isl_map *map);
3276 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3277 __isl_take isl_map *map);
3281 Lists are defined over several element types, including
3282 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3283 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3284 Here we take lists of C<isl_set>s as an example.
3285 Lists can be created, copied, modified and freed using the following functions.
3287 #include <isl/list.h>
3288 __isl_give isl_set_list *isl_set_list_from_set(
3289 __isl_take isl_set *el);
3290 __isl_give isl_set_list *isl_set_list_alloc(
3291 isl_ctx *ctx, int n);
3292 __isl_give isl_set_list *isl_set_list_copy(
3293 __isl_keep isl_set_list *list);
3294 __isl_give isl_set_list *isl_set_list_insert(
3295 __isl_take isl_set_list *list, unsigned pos,
3296 __isl_take isl_set *el);
3297 __isl_give isl_set_list *isl_set_list_add(
3298 __isl_take isl_set_list *list,
3299 __isl_take isl_set *el);
3300 __isl_give isl_set_list *isl_set_list_drop(
3301 __isl_take isl_set_list *list,
3302 unsigned first, unsigned n);
3303 __isl_give isl_set_list *isl_set_list_set_set(
3304 __isl_take isl_set_list *list, int index,
3305 __isl_take isl_set *set);
3306 __isl_give isl_set_list *isl_set_list_concat(
3307 __isl_take isl_set_list *list1,
3308 __isl_take isl_set_list *list2);
3309 __isl_give isl_set_list *isl_set_list_sort(
3310 __isl_take isl_set_list *list,
3311 int (*cmp)(__isl_keep isl_set *a,
3312 __isl_keep isl_set *b, void *user),
3314 void *isl_set_list_free(__isl_take isl_set_list *list);
3316 C<isl_set_list_alloc> creates an empty list with a capacity for
3317 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3320 Lists can be inspected using the following functions.
3322 #include <isl/list.h>
3323 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3324 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3325 __isl_give isl_set *isl_set_list_get_set(
3326 __isl_keep isl_set_list *list, int index);
3327 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3328 int (*fn)(__isl_take isl_set *el, void *user),
3330 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3331 int (*follows)(__isl_keep isl_set *a,
3332 __isl_keep isl_set *b, void *user),
3334 int (*fn)(__isl_take isl_set *el, void *user),
3337 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3338 strongly connected components of the graph with as vertices the elements
3339 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3340 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3341 should return C<-1> on error.
3343 Lists can be printed using
3345 #include <isl/list.h>
3346 __isl_give isl_printer *isl_printer_print_set_list(
3347 __isl_take isl_printer *p,
3348 __isl_keep isl_set_list *list);
3350 =head2 Multiple Values
3352 An C<isl_multi_val> object represents a sequence of zero or more values,
3353 living in a set space.
3355 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3356 using the following function
3358 #include <isl/val.h>
3359 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3360 __isl_take isl_space *space,
3361 __isl_take isl_val_list *list);
3363 The zero multiple value (with value zero for each set dimension)
3364 can be created using the following function.
3366 #include <isl/val.h>
3367 __isl_give isl_multi_val *isl_multi_val_zero(
3368 __isl_take isl_space *space);
3370 Multiple values can be copied and freed using
3372 #include <isl/val.h>
3373 __isl_give isl_multi_val *isl_multi_val_copy(
3374 __isl_keep isl_multi_val *mv);
3375 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3377 They can be inspected using
3379 #include <isl/val.h>
3380 isl_ctx *isl_multi_val_get_ctx(
3381 __isl_keep isl_multi_val *mv);
3382 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3383 enum isl_dim_type type);
3384 __isl_give isl_val *isl_multi_val_get_val(
3385 __isl_keep isl_multi_val *mv, int pos);
3386 const char *isl_multi_val_get_tuple_name(
3387 __isl_keep isl_multi_val *mv,
3388 enum isl_dim_type type);
3390 They can be modified using
3392 #include <isl/val.h>
3393 __isl_give isl_multi_val *isl_multi_val_set_val(
3394 __isl_take isl_multi_val *mv, int pos,
3395 __isl_take isl_val *val);
3396 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3397 __isl_take isl_multi_val *mv,
3398 enum isl_dim_type type, unsigned pos, const char *s);
3399 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3400 __isl_take isl_multi_val *mv,
3401 enum isl_dim_type type, const char *s);
3402 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3403 __isl_take isl_multi_val *mv,
3404 enum isl_dim_type type, __isl_take isl_id *id);
3406 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3407 __isl_take isl_multi_val *mv,
3408 enum isl_dim_type type, unsigned first, unsigned n);
3409 __isl_give isl_multi_val *isl_multi_val_add_dims(
3410 __isl_take isl_multi_val *mv,
3411 enum isl_dim_type type, unsigned n);
3412 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3413 __isl_take isl_multi_val *mv,
3414 enum isl_dim_type type, unsigned first, unsigned n);
3418 #include <isl/val.h>
3419 __isl_give isl_multi_val *isl_multi_val_align_params(
3420 __isl_take isl_multi_val *mv,
3421 __isl_take isl_space *model);
3422 __isl_give isl_multi_val *isl_multi_val_range_splice(
3423 __isl_take isl_multi_val *mv1, unsigned pos,
3424 __isl_take isl_multi_val *mv2);
3425 __isl_give isl_multi_val *isl_multi_val_range_product(
3426 __isl_take isl_multi_val *mv1,
3427 __isl_take isl_multi_val *mv2);
3428 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3429 __isl_take isl_multi_val *mv1,
3430 __isl_take isl_multi_aff *mv2);
3431 __isl_give isl_multi_val *isl_multi_val_add_val(
3432 __isl_take isl_multi_val *mv,
3433 __isl_take isl_val *v);
3434 __isl_give isl_multi_val *isl_multi_val_mod_val(
3435 __isl_take isl_multi_val *mv,
3436 __isl_take isl_val *v);
3440 Vectors can be created, copied and freed using the following functions.
3442 #include <isl/vec.h>
3443 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3445 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3446 void *isl_vec_free(__isl_take isl_vec *vec);
3448 Note that the elements of a newly created vector may have arbitrary values.
3449 The elements can be changed and inspected using the following functions.
3451 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3452 int isl_vec_size(__isl_keep isl_vec *vec);
3453 int isl_vec_get_element(__isl_keep isl_vec *vec,
3454 int pos, isl_int *v);
3455 __isl_give isl_val *isl_vec_get_element_val(
3456 __isl_keep isl_vec *vec, int pos);
3457 __isl_give isl_vec *isl_vec_set_element(
3458 __isl_take isl_vec *vec, int pos, isl_int v);
3459 __isl_give isl_vec *isl_vec_set_element_si(
3460 __isl_take isl_vec *vec, int pos, int v);
3461 __isl_give isl_vec *isl_vec_set_element_val(
3462 __isl_take isl_vec *vec, int pos,
3463 __isl_take isl_val *v);
3464 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3466 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3468 __isl_give isl_vec *isl_vec_set_val(
3469 __isl_take isl_vec *vec, __isl_take isl_val *v);
3470 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3473 C<isl_vec_get_element> will return a negative value if anything went wrong.
3474 In that case, the value of C<*v> is undefined.
3476 The following function can be used to concatenate two vectors.
3478 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3479 __isl_take isl_vec *vec2);
3483 Matrices can be created, copied and freed using the following functions.
3485 #include <isl/mat.h>
3486 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3487 unsigned n_row, unsigned n_col);
3488 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3489 void *isl_mat_free(__isl_take isl_mat *mat);
3491 Note that the elements of a newly created matrix may have arbitrary values.
3492 The elements can be changed and inspected using the following functions.
3494 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3495 int isl_mat_rows(__isl_keep isl_mat *mat);
3496 int isl_mat_cols(__isl_keep isl_mat *mat);
3497 int isl_mat_get_element(__isl_keep isl_mat *mat,
3498 int row, int col, isl_int *v);
3499 __isl_give isl_val *isl_mat_get_element_val(
3500 __isl_keep isl_mat *mat, int row, int col);
3501 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3502 int row, int col, isl_int v);
3503 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3504 int row, int col, int v);
3505 __isl_give isl_mat *isl_mat_set_element_val(
3506 __isl_take isl_mat *mat, int row, int col,
3507 __isl_take isl_val *v);
3509 C<isl_mat_get_element> will return a negative value if anything went wrong.
3510 In that case, the value of C<*v> is undefined.
3512 The following function can be used to compute the (right) inverse
3513 of a matrix, i.e., a matrix such that the product of the original
3514 and the inverse (in that order) is a multiple of the identity matrix.
3515 The input matrix is assumed to be of full row-rank.
3517 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3519 The following function can be used to compute the (right) kernel
3520 (or null space) of a matrix, i.e., a matrix such that the product of
3521 the original and the kernel (in that order) is the zero matrix.
3523 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3525 =head2 Piecewise Quasi Affine Expressions
3527 The zero quasi affine expression or the quasi affine expression
3528 that is equal to a specified dimension on a given domain can be created using
3530 __isl_give isl_aff *isl_aff_zero_on_domain(
3531 __isl_take isl_local_space *ls);
3532 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3533 __isl_take isl_local_space *ls);
3534 __isl_give isl_aff *isl_aff_var_on_domain(
3535 __isl_take isl_local_space *ls,
3536 enum isl_dim_type type, unsigned pos);
3537 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3538 __isl_take isl_local_space *ls,
3539 enum isl_dim_type type, unsigned pos);
3541 Note that the space in which the resulting objects live is a map space
3542 with the given space as domain and a one-dimensional range.
3544 An empty piecewise quasi affine expression (one with no cells)
3545 or a piecewise quasi affine expression with a single cell can
3546 be created using the following functions.
3548 #include <isl/aff.h>
3549 __isl_give isl_pw_aff *isl_pw_aff_empty(
3550 __isl_take isl_space *space);
3551 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3552 __isl_take isl_set *set, __isl_take isl_aff *aff);
3553 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3554 __isl_take isl_aff *aff);
3556 A piecewise quasi affine expression that is equal to 1 on a set
3557 and 0 outside the set can be created using the following function.
3559 #include <isl/aff.h>
3560 __isl_give isl_pw_aff *isl_set_indicator_function(
3561 __isl_take isl_set *set);
3563 Quasi affine expressions can be copied and freed using
3565 #include <isl/aff.h>
3566 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3567 void *isl_aff_free(__isl_take isl_aff *aff);
3569 __isl_give isl_pw_aff *isl_pw_aff_copy(
3570 __isl_keep isl_pw_aff *pwaff);
3571 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3573 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3574 using the following function. The constraint is required to have
3575 a non-zero coefficient for the specified dimension.
3577 #include <isl/constraint.h>
3578 __isl_give isl_aff *isl_constraint_get_bound(
3579 __isl_keep isl_constraint *constraint,
3580 enum isl_dim_type type, int pos);
3582 The entire affine expression of the constraint can also be extracted
3583 using the following function.
3585 #include <isl/constraint.h>
3586 __isl_give isl_aff *isl_constraint_get_aff(
3587 __isl_keep isl_constraint *constraint);
3589 Conversely, an equality constraint equating
3590 the affine expression to zero or an inequality constraint enforcing
3591 the affine expression to be non-negative, can be constructed using
3593 __isl_give isl_constraint *isl_equality_from_aff(
3594 __isl_take isl_aff *aff);
3595 __isl_give isl_constraint *isl_inequality_from_aff(
3596 __isl_take isl_aff *aff);
3598 The expression can be inspected using
3600 #include <isl/aff.h>
3601 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3602 int isl_aff_dim(__isl_keep isl_aff *aff,
3603 enum isl_dim_type type);
3604 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3605 __isl_keep isl_aff *aff);
3606 __isl_give isl_local_space *isl_aff_get_local_space(
3607 __isl_keep isl_aff *aff);
3608 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3609 enum isl_dim_type type, unsigned pos);
3610 const char *isl_pw_aff_get_dim_name(
3611 __isl_keep isl_pw_aff *pa,
3612 enum isl_dim_type type, unsigned pos);
3613 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3614 enum isl_dim_type type, unsigned pos);
3615 __isl_give isl_id *isl_pw_aff_get_dim_id(
3616 __isl_keep isl_pw_aff *pa,
3617 enum isl_dim_type type, unsigned pos);
3618 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3619 __isl_keep isl_pw_aff *pa,
3620 enum isl_dim_type type);
3621 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3623 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3624 enum isl_dim_type type, int pos, isl_int *v);
3625 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3627 __isl_give isl_aff *isl_aff_get_div(
3628 __isl_keep isl_aff *aff, int pos);
3630 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3631 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3632 int (*fn)(__isl_take isl_set *set,
3633 __isl_take isl_aff *aff,
3634 void *user), void *user);
3636 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3637 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3639 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3640 enum isl_dim_type type, unsigned first, unsigned n);
3641 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3642 enum isl_dim_type type, unsigned first, unsigned n);
3644 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3645 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3646 enum isl_dim_type type);
3647 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3649 It can be modified using
3651 #include <isl/aff.h>
3652 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3653 __isl_take isl_pw_aff *pwaff,
3654 enum isl_dim_type type, __isl_take isl_id *id);
3655 __isl_give isl_aff *isl_aff_set_dim_name(
3656 __isl_take isl_aff *aff, enum isl_dim_type type,
3657 unsigned pos, const char *s);
3658 __isl_give isl_aff *isl_aff_set_dim_id(
3659 __isl_take isl_aff *aff, enum isl_dim_type type,
3660 unsigned pos, __isl_take isl_id *id);
3661 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3662 __isl_take isl_pw_aff *pma,
3663 enum isl_dim_type type, unsigned pos,
3664 __isl_take isl_id *id);
3665 __isl_give isl_aff *isl_aff_set_constant(
3666 __isl_take isl_aff *aff, isl_int v);
3667 __isl_give isl_aff *isl_aff_set_constant_si(
3668 __isl_take isl_aff *aff, int v);
3669 __isl_give isl_aff *isl_aff_set_coefficient(
3670 __isl_take isl_aff *aff,
3671 enum isl_dim_type type, int pos, isl_int v);
3672 __isl_give isl_aff *isl_aff_set_coefficient_si(
3673 __isl_take isl_aff *aff,
3674 enum isl_dim_type type, int pos, int v);
3675 __isl_give isl_aff *isl_aff_set_denominator(
3676 __isl_take isl_aff *aff, isl_int v);
3678 __isl_give isl_aff *isl_aff_add_constant(
3679 __isl_take isl_aff *aff, isl_int v);
3680 __isl_give isl_aff *isl_aff_add_constant_si(
3681 __isl_take isl_aff *aff, int v);
3682 __isl_give isl_aff *isl_aff_add_constant_num(
3683 __isl_take isl_aff *aff, isl_int v);
3684 __isl_give isl_aff *isl_aff_add_constant_num_si(
3685 __isl_take isl_aff *aff, int v);
3686 __isl_give isl_aff *isl_aff_add_coefficient(
3687 __isl_take isl_aff *aff,
3688 enum isl_dim_type type, int pos, isl_int v);
3689 __isl_give isl_aff *isl_aff_add_coefficient_si(
3690 __isl_take isl_aff *aff,
3691 enum isl_dim_type type, int pos, int v);
3693 __isl_give isl_aff *isl_aff_insert_dims(
3694 __isl_take isl_aff *aff,
3695 enum isl_dim_type type, unsigned first, unsigned n);
3696 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3697 __isl_take isl_pw_aff *pwaff,
3698 enum isl_dim_type type, unsigned first, unsigned n);
3699 __isl_give isl_aff *isl_aff_add_dims(
3700 __isl_take isl_aff *aff,
3701 enum isl_dim_type type, unsigned n);
3702 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3703 __isl_take isl_pw_aff *pwaff,
3704 enum isl_dim_type type, unsigned n);
3705 __isl_give isl_aff *isl_aff_drop_dims(
3706 __isl_take isl_aff *aff,
3707 enum isl_dim_type type, unsigned first, unsigned n);
3708 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3709 __isl_take isl_pw_aff *pwaff,
3710 enum isl_dim_type type, unsigned first, unsigned n);
3712 Note that the C<set_constant> and C<set_coefficient> functions
3713 set the I<numerator> of the constant or coefficient, while
3714 C<add_constant> and C<add_coefficient> add an integer value to
3715 the possibly rational constant or coefficient.
3716 The C<add_constant_num> functions add an integer value to
3719 To check whether an affine expressions is obviously zero
3720 or obviously equal to some other affine expression, use
3722 #include <isl/aff.h>
3723 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3724 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3725 __isl_keep isl_aff *aff2);
3726 int isl_pw_aff_plain_is_equal(
3727 __isl_keep isl_pw_aff *pwaff1,
3728 __isl_keep isl_pw_aff *pwaff2);
3732 #include <isl/aff.h>
3733 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3734 __isl_take isl_aff *aff2);
3735 __isl_give isl_pw_aff *isl_pw_aff_add(
3736 __isl_take isl_pw_aff *pwaff1,
3737 __isl_take isl_pw_aff *pwaff2);
3738 __isl_give isl_pw_aff *isl_pw_aff_min(
3739 __isl_take isl_pw_aff *pwaff1,
3740 __isl_take isl_pw_aff *pwaff2);
3741 __isl_give isl_pw_aff *isl_pw_aff_max(
3742 __isl_take isl_pw_aff *pwaff1,
3743 __isl_take isl_pw_aff *pwaff2);
3744 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3745 __isl_take isl_aff *aff2);
3746 __isl_give isl_pw_aff *isl_pw_aff_sub(
3747 __isl_take isl_pw_aff *pwaff1,
3748 __isl_take isl_pw_aff *pwaff2);
3749 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3750 __isl_give isl_pw_aff *isl_pw_aff_neg(
3751 __isl_take isl_pw_aff *pwaff);
3752 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3753 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3754 __isl_take isl_pw_aff *pwaff);
3755 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3756 __isl_give isl_pw_aff *isl_pw_aff_floor(
3757 __isl_take isl_pw_aff *pwaff);
3758 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3760 __isl_give isl_pw_aff *isl_pw_aff_mod(
3761 __isl_take isl_pw_aff *pwaff, isl_int mod);
3762 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3764 __isl_give isl_pw_aff *isl_pw_aff_scale(
3765 __isl_take isl_pw_aff *pwaff, isl_int f);
3766 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3768 __isl_give isl_aff *isl_aff_scale_down_ui(
3769 __isl_take isl_aff *aff, unsigned f);
3770 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3771 __isl_take isl_pw_aff *pwaff, isl_int f);
3773 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3774 __isl_take isl_pw_aff_list *list);
3775 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3776 __isl_take isl_pw_aff_list *list);
3778 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3779 __isl_take isl_pw_aff *pwqp);
3781 __isl_give isl_aff *isl_aff_align_params(
3782 __isl_take isl_aff *aff,
3783 __isl_take isl_space *model);
3784 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3785 __isl_take isl_pw_aff *pwaff,
3786 __isl_take isl_space *model);
3788 __isl_give isl_aff *isl_aff_project_domain_on_params(
3789 __isl_take isl_aff *aff);
3791 __isl_give isl_aff *isl_aff_gist_params(
3792 __isl_take isl_aff *aff,
3793 __isl_take isl_set *context);
3794 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3795 __isl_take isl_set *context);
3796 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3797 __isl_take isl_pw_aff *pwaff,
3798 __isl_take isl_set *context);
3799 __isl_give isl_pw_aff *isl_pw_aff_gist(
3800 __isl_take isl_pw_aff *pwaff,
3801 __isl_take isl_set *context);
3803 __isl_give isl_set *isl_pw_aff_domain(
3804 __isl_take isl_pw_aff *pwaff);
3805 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3806 __isl_take isl_pw_aff *pa,
3807 __isl_take isl_set *set);
3808 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3809 __isl_take isl_pw_aff *pa,
3810 __isl_take isl_set *set);
3812 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3813 __isl_take isl_aff *aff2);
3814 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3815 __isl_take isl_aff *aff2);
3816 __isl_give isl_pw_aff *isl_pw_aff_mul(
3817 __isl_take isl_pw_aff *pwaff1,
3818 __isl_take isl_pw_aff *pwaff2);
3819 __isl_give isl_pw_aff *isl_pw_aff_div(
3820 __isl_take isl_pw_aff *pa1,
3821 __isl_take isl_pw_aff *pa2);
3822 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3823 __isl_take isl_pw_aff *pa1,
3824 __isl_take isl_pw_aff *pa2);
3825 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3826 __isl_take isl_pw_aff *pa1,
3827 __isl_take isl_pw_aff *pa2);
3829 When multiplying two affine expressions, at least one of the two needs
3830 to be a constant. Similarly, when dividing an affine expression by another,
3831 the second expression needs to be a constant.
3832 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3833 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3836 #include <isl/aff.h>
3837 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3838 __isl_take isl_aff *aff,
3839 __isl_take isl_multi_aff *ma);
3840 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3841 __isl_take isl_pw_aff *pa,
3842 __isl_take isl_multi_aff *ma);
3843 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3844 __isl_take isl_pw_aff *pa,
3845 __isl_take isl_pw_multi_aff *pma);
3847 These functions precompose the input expression by the given
3848 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3849 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3850 into the (piecewise) affine expression.
3851 Objects of type C<isl_multi_aff> are described in
3852 L</"Piecewise Multiple Quasi Affine Expressions">.
3854 #include <isl/aff.h>
3855 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3856 __isl_take isl_aff *aff);
3857 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3858 __isl_take isl_aff *aff);
3859 __isl_give isl_basic_set *isl_aff_le_basic_set(
3860 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3861 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3862 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3863 __isl_give isl_set *isl_pw_aff_eq_set(
3864 __isl_take isl_pw_aff *pwaff1,
3865 __isl_take isl_pw_aff *pwaff2);
3866 __isl_give isl_set *isl_pw_aff_ne_set(
3867 __isl_take isl_pw_aff *pwaff1,
3868 __isl_take isl_pw_aff *pwaff2);
3869 __isl_give isl_set *isl_pw_aff_le_set(
3870 __isl_take isl_pw_aff *pwaff1,
3871 __isl_take isl_pw_aff *pwaff2);
3872 __isl_give isl_set *isl_pw_aff_lt_set(
3873 __isl_take isl_pw_aff *pwaff1,
3874 __isl_take isl_pw_aff *pwaff2);
3875 __isl_give isl_set *isl_pw_aff_ge_set(
3876 __isl_take isl_pw_aff *pwaff1,
3877 __isl_take isl_pw_aff *pwaff2);
3878 __isl_give isl_set *isl_pw_aff_gt_set(
3879 __isl_take isl_pw_aff *pwaff1,
3880 __isl_take isl_pw_aff *pwaff2);
3882 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_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_lt_set(
3892 __isl_take isl_pw_aff_list *list1,
3893 __isl_take isl_pw_aff_list *list2);
3894 __isl_give isl_set *isl_pw_aff_list_ge_set(
3895 __isl_take isl_pw_aff_list *list1,
3896 __isl_take isl_pw_aff_list *list2);
3897 __isl_give isl_set *isl_pw_aff_list_gt_set(
3898 __isl_take isl_pw_aff_list *list1,
3899 __isl_take isl_pw_aff_list *list2);
3901 The function C<isl_aff_neg_basic_set> returns a basic set
3902 containing those elements in the domain space
3903 of C<aff> where C<aff> is negative.
3904 The function C<isl_aff_ge_basic_set> returns a basic set
3905 containing those elements in the shared space
3906 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3907 The function C<isl_pw_aff_ge_set> returns a set
3908 containing those elements in the shared domain
3909 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3910 The functions operating on C<isl_pw_aff_list> apply the corresponding
3911 C<isl_pw_aff> function to each pair of elements in the two lists.
3913 #include <isl/aff.h>
3914 __isl_give isl_set *isl_pw_aff_nonneg_set(
3915 __isl_take isl_pw_aff *pwaff);
3916 __isl_give isl_set *isl_pw_aff_zero_set(
3917 __isl_take isl_pw_aff *pwaff);
3918 __isl_give isl_set *isl_pw_aff_non_zero_set(
3919 __isl_take isl_pw_aff *pwaff);
3921 The function C<isl_pw_aff_nonneg_set> returns a set
3922 containing those elements in the domain
3923 of C<pwaff> where C<pwaff> is non-negative.
3925 #include <isl/aff.h>
3926 __isl_give isl_pw_aff *isl_pw_aff_cond(
3927 __isl_take isl_pw_aff *cond,
3928 __isl_take isl_pw_aff *pwaff_true,
3929 __isl_take isl_pw_aff *pwaff_false);
3931 The function C<isl_pw_aff_cond> performs a conditional operator
3932 and returns an expression that is equal to C<pwaff_true>
3933 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3934 where C<cond> is zero.
3936 #include <isl/aff.h>
3937 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3938 __isl_take isl_pw_aff *pwaff1,
3939 __isl_take isl_pw_aff *pwaff2);
3940 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3941 __isl_take isl_pw_aff *pwaff1,
3942 __isl_take isl_pw_aff *pwaff2);
3943 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3944 __isl_take isl_pw_aff *pwaff1,
3945 __isl_take isl_pw_aff *pwaff2);
3947 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3948 expression with a domain that is the union of those of C<pwaff1> and
3949 C<pwaff2> and such that on each cell, the quasi-affine expression is
3950 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3951 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3952 associated expression is the defined one.
3954 An expression can be read from input using
3956 #include <isl/aff.h>
3957 __isl_give isl_aff *isl_aff_read_from_str(
3958 isl_ctx *ctx, const char *str);
3959 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3960 isl_ctx *ctx, const char *str);
3962 An expression can be printed using
3964 #include <isl/aff.h>
3965 __isl_give isl_printer *isl_printer_print_aff(
3966 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3968 __isl_give isl_printer *isl_printer_print_pw_aff(
3969 __isl_take isl_printer *p,
3970 __isl_keep isl_pw_aff *pwaff);
3972 =head2 Piecewise Multiple Quasi Affine Expressions
3974 An C<isl_multi_aff> object represents a sequence of
3975 zero or more affine expressions, all defined on the same domain space.
3976 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3977 zero or more piecewise affine expressions.
3979 An C<isl_multi_aff> can be constructed from a single
3980 C<isl_aff> or an C<isl_aff_list> using the
3981 following functions. Similarly for C<isl_multi_pw_aff>.
3983 #include <isl/aff.h>
3984 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3985 __isl_take isl_aff *aff);
3986 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3987 __isl_take isl_pw_aff *pa);
3988 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3989 __isl_take isl_space *space,
3990 __isl_take isl_aff_list *list);
3992 An empty piecewise multiple quasi affine expression (one with no cells),
3993 the zero piecewise multiple quasi affine expression (with value zero
3994 for each output dimension),
3995 a piecewise multiple quasi affine expression with a single cell (with
3996 either a universe or a specified domain) or
3997 a zero-dimensional piecewise multiple quasi affine expression
3999 can be created using the following functions.
4001 #include <isl/aff.h>
4002 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4003 __isl_take isl_space *space);
4004 __isl_give isl_multi_aff *isl_multi_aff_zero(
4005 __isl_take isl_space *space);
4006 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4007 __isl_take isl_space *space);
4008 __isl_give isl_multi_aff *isl_multi_aff_identity(
4009 __isl_take isl_space *space);
4010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4011 __isl_take isl_space *space);
4012 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4013 __isl_take isl_space *space);
4014 __isl_give isl_pw_multi_aff *
4015 isl_pw_multi_aff_from_multi_aff(
4016 __isl_take isl_multi_aff *ma);
4017 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4018 __isl_take isl_set *set,
4019 __isl_take isl_multi_aff *maff);
4020 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4021 __isl_take isl_set *set);
4023 __isl_give isl_union_pw_multi_aff *
4024 isl_union_pw_multi_aff_empty(
4025 __isl_take isl_space *space);
4026 __isl_give isl_union_pw_multi_aff *
4027 isl_union_pw_multi_aff_add_pw_multi_aff(
4028 __isl_take isl_union_pw_multi_aff *upma,
4029 __isl_take isl_pw_multi_aff *pma);
4030 __isl_give isl_union_pw_multi_aff *
4031 isl_union_pw_multi_aff_from_domain(
4032 __isl_take isl_union_set *uset);
4034 A piecewise multiple quasi affine expression can also be initialized
4035 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4036 and the C<isl_map> is single-valued.
4037 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4038 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4040 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4041 __isl_take isl_set *set);
4042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4043 __isl_take isl_map *map);
4045 __isl_give isl_union_pw_multi_aff *
4046 isl_union_pw_multi_aff_from_union_set(
4047 __isl_take isl_union_set *uset);
4048 __isl_give isl_union_pw_multi_aff *
4049 isl_union_pw_multi_aff_from_union_map(
4050 __isl_take isl_union_map *umap);
4052 Multiple quasi affine expressions can be copied and freed using
4054 #include <isl/aff.h>
4055 __isl_give isl_multi_aff *isl_multi_aff_copy(
4056 __isl_keep isl_multi_aff *maff);
4057 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4059 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4060 __isl_keep isl_pw_multi_aff *pma);
4061 void *isl_pw_multi_aff_free(
4062 __isl_take isl_pw_multi_aff *pma);
4064 __isl_give isl_union_pw_multi_aff *
4065 isl_union_pw_multi_aff_copy(
4066 __isl_keep isl_union_pw_multi_aff *upma);
4067 void *isl_union_pw_multi_aff_free(
4068 __isl_take isl_union_pw_multi_aff *upma);
4070 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4071 __isl_keep isl_multi_pw_aff *mpa);
4072 void *isl_multi_pw_aff_free(
4073 __isl_take isl_multi_pw_aff *mpa);
4075 The expression can be inspected using
4077 #include <isl/aff.h>
4078 isl_ctx *isl_multi_aff_get_ctx(
4079 __isl_keep isl_multi_aff *maff);
4080 isl_ctx *isl_pw_multi_aff_get_ctx(
4081 __isl_keep isl_pw_multi_aff *pma);
4082 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4083 __isl_keep isl_union_pw_multi_aff *upma);
4084 isl_ctx *isl_multi_pw_aff_get_ctx(
4085 __isl_keep isl_multi_pw_aff *mpa);
4086 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4087 enum isl_dim_type type);
4088 unsigned isl_pw_multi_aff_dim(
4089 __isl_keep isl_pw_multi_aff *pma,
4090 enum isl_dim_type type);
4091 unsigned isl_multi_pw_aff_dim(
4092 __isl_keep isl_multi_pw_aff *mpa,
4093 enum isl_dim_type type);
4094 __isl_give isl_aff *isl_multi_aff_get_aff(
4095 __isl_keep isl_multi_aff *multi, int pos);
4096 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4097 __isl_keep isl_pw_multi_aff *pma, int pos);
4098 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4099 __isl_keep isl_multi_pw_aff *mpa, int pos);
4100 const char *isl_pw_multi_aff_get_dim_name(
4101 __isl_keep isl_pw_multi_aff *pma,
4102 enum isl_dim_type type, unsigned pos);
4103 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4104 __isl_keep isl_pw_multi_aff *pma,
4105 enum isl_dim_type type, unsigned pos);
4106 const char *isl_multi_aff_get_tuple_name(
4107 __isl_keep isl_multi_aff *multi,
4108 enum isl_dim_type type);
4109 int isl_pw_multi_aff_has_tuple_name(
4110 __isl_keep isl_pw_multi_aff *pma,
4111 enum isl_dim_type type);
4112 const char *isl_pw_multi_aff_get_tuple_name(
4113 __isl_keep isl_pw_multi_aff *pma,
4114 enum isl_dim_type type);
4115 int isl_pw_multi_aff_has_tuple_id(
4116 __isl_keep isl_pw_multi_aff *pma,
4117 enum isl_dim_type type);
4118 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4119 __isl_keep isl_pw_multi_aff *pma,
4120 enum isl_dim_type type);
4122 int isl_pw_multi_aff_foreach_piece(
4123 __isl_keep isl_pw_multi_aff *pma,
4124 int (*fn)(__isl_take isl_set *set,
4125 __isl_take isl_multi_aff *maff,
4126 void *user), void *user);
4128 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4129 __isl_keep isl_union_pw_multi_aff *upma,
4130 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4131 void *user), void *user);
4133 It can be modified using
4135 #include <isl/aff.h>
4136 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4137 __isl_take isl_multi_aff *multi, int pos,
4138 __isl_take isl_aff *aff);
4139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4140 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4141 __isl_take isl_pw_aff *pa);
4142 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4143 __isl_take isl_multi_aff *maff,
4144 enum isl_dim_type type, unsigned pos, const char *s);
4145 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4146 __isl_take isl_multi_aff *maff,
4147 enum isl_dim_type type, const char *s);
4148 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4149 __isl_take isl_multi_aff *maff,
4150 enum isl_dim_type type, __isl_take isl_id *id);
4151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4152 __isl_take isl_pw_multi_aff *pma,
4153 enum isl_dim_type type, __isl_take isl_id *id);
4155 __isl_give isl_multi_pw_aff *
4156 isl_multi_pw_aff_set_dim_name(
4157 __isl_take isl_multi_pw_aff *mpa,
4158 enum isl_dim_type type, unsigned pos, const char *s);
4159 __isl_give isl_multi_pw_aff *
4160 isl_multi_pw_aff_set_tuple_name(
4161 __isl_take isl_multi_pw_aff *mpa,
4162 enum isl_dim_type type, const char *s);
4164 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4165 __isl_take isl_multi_aff *ma,
4166 enum isl_dim_type type, unsigned first, unsigned n);
4167 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4168 __isl_take isl_multi_aff *ma,
4169 enum isl_dim_type type, unsigned n);
4170 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4171 __isl_take isl_multi_aff *maff,
4172 enum isl_dim_type type, unsigned first, unsigned n);
4173 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4174 __isl_take isl_pw_multi_aff *pma,
4175 enum isl_dim_type type, unsigned first, unsigned n);
4177 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4178 __isl_take isl_multi_pw_aff *mpa,
4179 enum isl_dim_type type, unsigned first, unsigned n);
4180 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4181 __isl_take isl_multi_pw_aff *mpa,
4182 enum isl_dim_type type, unsigned n);
4184 To check whether two multiple affine expressions are
4185 obviously equal to each other, use
4187 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4188 __isl_keep isl_multi_aff *maff2);
4189 int isl_pw_multi_aff_plain_is_equal(
4190 __isl_keep isl_pw_multi_aff *pma1,
4191 __isl_keep isl_pw_multi_aff *pma2);
4195 #include <isl/aff.h>
4196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4197 __isl_take isl_pw_multi_aff *pma1,
4198 __isl_take isl_pw_multi_aff *pma2);
4199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4200 __isl_take isl_pw_multi_aff *pma1,
4201 __isl_take isl_pw_multi_aff *pma2);
4202 __isl_give isl_multi_aff *isl_multi_aff_add(
4203 __isl_take isl_multi_aff *maff1,
4204 __isl_take isl_multi_aff *maff2);
4205 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4206 __isl_take isl_pw_multi_aff *pma1,
4207 __isl_take isl_pw_multi_aff *pma2);
4208 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4209 __isl_take isl_union_pw_multi_aff *upma1,
4210 __isl_take isl_union_pw_multi_aff *upma2);
4211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4212 __isl_take isl_pw_multi_aff *pma1,
4213 __isl_take isl_pw_multi_aff *pma2);
4214 __isl_give isl_multi_aff *isl_multi_aff_sub(
4215 __isl_take isl_multi_aff *ma1,
4216 __isl_take isl_multi_aff *ma2);
4217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4218 __isl_take isl_pw_multi_aff *pma1,
4219 __isl_take isl_pw_multi_aff *pma2);
4220 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4221 __isl_take isl_union_pw_multi_aff *upma1,
4222 __isl_take isl_union_pw_multi_aff *upma2);
4224 C<isl_multi_aff_sub> subtracts the second argument from the first.
4226 __isl_give isl_multi_aff *isl_multi_aff_scale(
4227 __isl_take isl_multi_aff *maff,
4229 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4230 __isl_take isl_multi_aff *ma,
4231 __isl_take isl_vec *v);
4232 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4233 __isl_take isl_pw_multi_aff *pma,
4234 __isl_take isl_vec *v);
4235 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4236 __isl_take isl_union_pw_multi_aff *upma,
4237 __isl_take isl_vec *v);
4239 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4240 by the corresponding elements of C<v>.
4242 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4243 __isl_take isl_pw_multi_aff *pma,
4244 __isl_take isl_set *set);
4245 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4246 __isl_take isl_pw_multi_aff *pma,
4247 __isl_take isl_set *set);
4248 __isl_give isl_union_pw_multi_aff *
4249 isl_union_pw_multi_aff_intersect_domain(
4250 __isl_take isl_union_pw_multi_aff *upma,
4251 __isl_take isl_union_set *uset);
4252 __isl_give isl_multi_aff *isl_multi_aff_lift(
4253 __isl_take isl_multi_aff *maff,
4254 __isl_give isl_local_space **ls);
4255 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4256 __isl_take isl_pw_multi_aff *pma);
4257 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4258 __isl_take isl_multi_aff *multi,
4259 __isl_take isl_space *model);
4260 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4261 __isl_take isl_pw_multi_aff *pma,
4262 __isl_take isl_space *model);
4263 __isl_give isl_pw_multi_aff *
4264 isl_pw_multi_aff_project_domain_on_params(
4265 __isl_take isl_pw_multi_aff *pma);
4266 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4267 __isl_take isl_multi_aff *maff,
4268 __isl_take isl_set *context);
4269 __isl_give isl_multi_aff *isl_multi_aff_gist(
4270 __isl_take isl_multi_aff *maff,
4271 __isl_take isl_set *context);
4272 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4273 __isl_take isl_pw_multi_aff *pma,
4274 __isl_take isl_set *set);
4275 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4276 __isl_take isl_pw_multi_aff *pma,
4277 __isl_take isl_set *set);
4278 __isl_give isl_set *isl_pw_multi_aff_domain(
4279 __isl_take isl_pw_multi_aff *pma);
4280 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4281 __isl_take isl_union_pw_multi_aff *upma);
4282 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4283 __isl_take isl_multi_aff *ma1, unsigned pos,
4284 __isl_take isl_multi_aff *ma2);
4285 __isl_give isl_multi_aff *isl_multi_aff_splice(
4286 __isl_take isl_multi_aff *ma1,
4287 unsigned in_pos, unsigned out_pos,
4288 __isl_take isl_multi_aff *ma2);
4289 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4290 __isl_take isl_multi_aff *ma1,
4291 __isl_take isl_multi_aff *ma2);
4292 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4293 __isl_take isl_multi_aff *ma1,
4294 __isl_take isl_multi_aff *ma2);
4295 __isl_give isl_multi_aff *isl_multi_aff_product(
4296 __isl_take isl_multi_aff *ma1,
4297 __isl_take isl_multi_aff *ma2);
4298 __isl_give isl_pw_multi_aff *
4299 isl_pw_multi_aff_range_product(
4300 __isl_take isl_pw_multi_aff *pma1,
4301 __isl_take isl_pw_multi_aff *pma2);
4302 __isl_give isl_pw_multi_aff *
4303 isl_pw_multi_aff_flat_range_product(
4304 __isl_take isl_pw_multi_aff *pma1,
4305 __isl_take isl_pw_multi_aff *pma2);
4306 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4307 __isl_take isl_pw_multi_aff *pma1,
4308 __isl_take isl_pw_multi_aff *pma2);
4309 __isl_give isl_union_pw_multi_aff *
4310 isl_union_pw_multi_aff_flat_range_product(
4311 __isl_take isl_union_pw_multi_aff *upma1,
4312 __isl_take isl_union_pw_multi_aff *upma2);
4313 __isl_give isl_multi_pw_aff *
4314 isl_multi_pw_aff_range_splice(
4315 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4316 __isl_take isl_multi_pw_aff *mpa2);
4317 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4318 __isl_take isl_multi_pw_aff *mpa1,
4319 unsigned in_pos, unsigned out_pos,
4320 __isl_take isl_multi_pw_aff *mpa2);
4321 __isl_give isl_multi_pw_aff *
4322 isl_multi_pw_aff_range_product(
4323 __isl_take isl_multi_pw_aff *mpa1,
4324 __isl_take isl_multi_pw_aff *mpa2);
4325 __isl_give isl_multi_pw_aff *
4326 isl_multi_pw_aff_flat_range_product(
4327 __isl_take isl_multi_pw_aff *mpa1,
4328 __isl_take isl_multi_pw_aff *mpa2);
4330 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4331 then it is assigned the local space that lies at the basis of
4332 the lifting applied.
4334 #include <isl/aff.h>
4335 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4336 __isl_take isl_multi_aff *ma1,
4337 __isl_take isl_multi_aff *ma2);
4338 __isl_give isl_pw_multi_aff *
4339 isl_pw_multi_aff_pullback_multi_aff(
4340 __isl_take isl_pw_multi_aff *pma,
4341 __isl_take isl_multi_aff *ma);
4342 __isl_give isl_pw_multi_aff *
4343 isl_pw_multi_aff_pullback_pw_multi_aff(
4344 __isl_take isl_pw_multi_aff *pma1,
4345 __isl_take isl_pw_multi_aff *pma2);
4347 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4348 In other words, C<ma2> is plugged
4351 __isl_give isl_set *isl_multi_aff_lex_le_set(
4352 __isl_take isl_multi_aff *ma1,
4353 __isl_take isl_multi_aff *ma2);
4354 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4355 __isl_take isl_multi_aff *ma1,
4356 __isl_take isl_multi_aff *ma2);
4358 The function C<isl_multi_aff_lex_le_set> returns a set
4359 containing those elements in the shared domain space
4360 where C<ma1> is lexicographically smaller than or
4363 An expression can be read from input using
4365 #include <isl/aff.h>
4366 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4367 isl_ctx *ctx, const char *str);
4368 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4369 isl_ctx *ctx, const char *str);
4370 __isl_give isl_union_pw_multi_aff *
4371 isl_union_pw_multi_aff_read_from_str(
4372 isl_ctx *ctx, const char *str);
4374 An expression can be printed using
4376 #include <isl/aff.h>
4377 __isl_give isl_printer *isl_printer_print_multi_aff(
4378 __isl_take isl_printer *p,
4379 __isl_keep isl_multi_aff *maff);
4380 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4381 __isl_take isl_printer *p,
4382 __isl_keep isl_pw_multi_aff *pma);
4383 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4384 __isl_take isl_printer *p,
4385 __isl_keep isl_union_pw_multi_aff *upma);
4386 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4387 __isl_take isl_printer *p,
4388 __isl_keep isl_multi_pw_aff *mpa);
4392 Points are elements of a set. They can be used to construct
4393 simple sets (boxes) or they can be used to represent the
4394 individual elements of a set.
4395 The zero point (the origin) can be created using
4397 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4399 The coordinates of a point can be inspected, set and changed
4402 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4403 enum isl_dim_type type, int pos, isl_int *v);
4404 __isl_give isl_val *isl_point_get_coordinate_val(
4405 __isl_keep isl_point *pnt,
4406 enum isl_dim_type type, int pos);
4407 __isl_give isl_point *isl_point_set_coordinate(
4408 __isl_take isl_point *pnt,
4409 enum isl_dim_type type, int pos, isl_int v);
4410 __isl_give isl_point *isl_point_set_coordinate_val(
4411 __isl_take isl_point *pnt,
4412 enum isl_dim_type type, int pos,
4413 __isl_take isl_val *v);
4415 __isl_give isl_point *isl_point_add_ui(
4416 __isl_take isl_point *pnt,
4417 enum isl_dim_type type, int pos, unsigned val);
4418 __isl_give isl_point *isl_point_sub_ui(
4419 __isl_take isl_point *pnt,
4420 enum isl_dim_type type, int pos, unsigned val);
4422 Other properties can be obtained using
4424 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4426 Points can be copied or freed using
4428 __isl_give isl_point *isl_point_copy(
4429 __isl_keep isl_point *pnt);
4430 void isl_point_free(__isl_take isl_point *pnt);
4432 A singleton set can be created from a point using
4434 __isl_give isl_basic_set *isl_basic_set_from_point(
4435 __isl_take isl_point *pnt);
4436 __isl_give isl_set *isl_set_from_point(
4437 __isl_take isl_point *pnt);
4439 and a box can be created from two opposite extremal points using
4441 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4442 __isl_take isl_point *pnt1,
4443 __isl_take isl_point *pnt2);
4444 __isl_give isl_set *isl_set_box_from_points(
4445 __isl_take isl_point *pnt1,
4446 __isl_take isl_point *pnt2);
4448 All elements of a B<bounded> (union) set can be enumerated using
4449 the following functions.
4451 int isl_set_foreach_point(__isl_keep isl_set *set,
4452 int (*fn)(__isl_take isl_point *pnt, void *user),
4454 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4455 int (*fn)(__isl_take isl_point *pnt, void *user),
4458 The function C<fn> is called for each integer point in
4459 C<set> with as second argument the last argument of
4460 the C<isl_set_foreach_point> call. The function C<fn>
4461 should return C<0> on success and C<-1> on failure.
4462 In the latter case, C<isl_set_foreach_point> will stop
4463 enumerating and return C<-1> as well.
4464 If the enumeration is performed successfully and to completion,
4465 then C<isl_set_foreach_point> returns C<0>.
4467 To obtain a single point of a (basic) set, use
4469 __isl_give isl_point *isl_basic_set_sample_point(
4470 __isl_take isl_basic_set *bset);
4471 __isl_give isl_point *isl_set_sample_point(
4472 __isl_take isl_set *set);
4474 If C<set> does not contain any (integer) points, then the
4475 resulting point will be ``void'', a property that can be
4478 int isl_point_is_void(__isl_keep isl_point *pnt);
4480 =head2 Piecewise Quasipolynomials
4482 A piecewise quasipolynomial is a particular kind of function that maps
4483 a parametric point to a rational value.
4484 More specifically, a quasipolynomial is a polynomial expression in greatest
4485 integer parts of affine expressions of parameters and variables.
4486 A piecewise quasipolynomial is a subdivision of a given parametric
4487 domain into disjoint cells with a quasipolynomial associated to
4488 each cell. The value of the piecewise quasipolynomial at a given
4489 point is the value of the quasipolynomial associated to the cell
4490 that contains the point. Outside of the union of cells,
4491 the value is assumed to be zero.
4492 For example, the piecewise quasipolynomial
4494 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4496 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4497 A given piecewise quasipolynomial has a fixed domain dimension.
4498 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4499 defined over different domains.
4500 Piecewise quasipolynomials are mainly used by the C<barvinok>
4501 library for representing the number of elements in a parametric set or map.
4502 For example, the piecewise quasipolynomial above represents
4503 the number of points in the map
4505 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4507 =head3 Input and Output
4509 Piecewise quasipolynomials can be read from input using
4511 __isl_give isl_union_pw_qpolynomial *
4512 isl_union_pw_qpolynomial_read_from_str(
4513 isl_ctx *ctx, const char *str);
4515 Quasipolynomials and piecewise quasipolynomials can be printed
4516 using the following functions.
4518 __isl_give isl_printer *isl_printer_print_qpolynomial(
4519 __isl_take isl_printer *p,
4520 __isl_keep isl_qpolynomial *qp);
4522 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4523 __isl_take isl_printer *p,
4524 __isl_keep isl_pw_qpolynomial *pwqp);
4526 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4527 __isl_take isl_printer *p,
4528 __isl_keep isl_union_pw_qpolynomial *upwqp);
4530 The output format of the printer
4531 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4532 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4534 In case of printing in C<ISL_FORMAT_C>, the user may want
4535 to set the names of all dimensions
4537 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4538 __isl_take isl_qpolynomial *qp,
4539 enum isl_dim_type type, unsigned pos,
4541 __isl_give isl_pw_qpolynomial *
4542 isl_pw_qpolynomial_set_dim_name(
4543 __isl_take isl_pw_qpolynomial *pwqp,
4544 enum isl_dim_type type, unsigned pos,
4547 =head3 Creating New (Piecewise) Quasipolynomials
4549 Some simple quasipolynomials can be created using the following functions.
4550 More complicated quasipolynomials can be created by applying
4551 operations such as addition and multiplication
4552 on the resulting quasipolynomials
4554 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4555 __isl_take isl_space *domain);
4556 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4557 __isl_take isl_space *domain);
4558 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4559 __isl_take isl_space *domain);
4560 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4561 __isl_take isl_space *domain);
4562 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4563 __isl_take isl_space *domain);
4564 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4565 __isl_take isl_space *domain,
4566 const isl_int n, const isl_int d);
4567 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4568 __isl_take isl_space *domain,
4569 enum isl_dim_type type, unsigned pos);
4570 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4571 __isl_take isl_aff *aff);
4573 Note that the space in which a quasipolynomial lives is a map space
4574 with a one-dimensional range. The C<domain> argument in some of
4575 the functions above corresponds to the domain of this map space.
4577 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4578 with a single cell can be created using the following functions.
4579 Multiple of these single cell piecewise quasipolynomials can
4580 be combined to create more complicated piecewise quasipolynomials.
4582 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4583 __isl_take isl_space *space);
4584 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4585 __isl_take isl_set *set,
4586 __isl_take isl_qpolynomial *qp);
4587 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4588 __isl_take isl_qpolynomial *qp);
4589 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4590 __isl_take isl_pw_aff *pwaff);
4592 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4593 __isl_take isl_space *space);
4594 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4595 __isl_take isl_pw_qpolynomial *pwqp);
4596 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4597 __isl_take isl_union_pw_qpolynomial *upwqp,
4598 __isl_take isl_pw_qpolynomial *pwqp);
4600 Quasipolynomials can be copied and freed again using the following
4603 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4604 __isl_keep isl_qpolynomial *qp);
4605 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4607 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4608 __isl_keep isl_pw_qpolynomial *pwqp);
4609 void *isl_pw_qpolynomial_free(
4610 __isl_take isl_pw_qpolynomial *pwqp);
4612 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4613 __isl_keep isl_union_pw_qpolynomial *upwqp);
4614 void *isl_union_pw_qpolynomial_free(
4615 __isl_take isl_union_pw_qpolynomial *upwqp);
4617 =head3 Inspecting (Piecewise) Quasipolynomials
4619 To iterate over all piecewise quasipolynomials in a union
4620 piecewise quasipolynomial, use the following function
4622 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4623 __isl_keep isl_union_pw_qpolynomial *upwqp,
4624 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4627 To extract the piecewise quasipolynomial in a given space from a union, use
4629 __isl_give isl_pw_qpolynomial *
4630 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4631 __isl_keep isl_union_pw_qpolynomial *upwqp,
4632 __isl_take isl_space *space);
4634 To iterate over the cells in a piecewise quasipolynomial,
4635 use either of the following two functions
4637 int isl_pw_qpolynomial_foreach_piece(
4638 __isl_keep isl_pw_qpolynomial *pwqp,
4639 int (*fn)(__isl_take isl_set *set,
4640 __isl_take isl_qpolynomial *qp,
4641 void *user), void *user);
4642 int isl_pw_qpolynomial_foreach_lifted_piece(
4643 __isl_keep isl_pw_qpolynomial *pwqp,
4644 int (*fn)(__isl_take isl_set *set,
4645 __isl_take isl_qpolynomial *qp,
4646 void *user), void *user);
4648 As usual, the function C<fn> should return C<0> on success
4649 and C<-1> on failure. The difference between
4650 C<isl_pw_qpolynomial_foreach_piece> and
4651 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4652 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4653 compute unique representations for all existentially quantified
4654 variables and then turn these existentially quantified variables
4655 into extra set variables, adapting the associated quasipolynomial
4656 accordingly. This means that the C<set> passed to C<fn>
4657 will not have any existentially quantified variables, but that
4658 the dimensions of the sets may be different for different
4659 invocations of C<fn>.
4661 To iterate over all terms in a quasipolynomial,
4664 int isl_qpolynomial_foreach_term(
4665 __isl_keep isl_qpolynomial *qp,
4666 int (*fn)(__isl_take isl_term *term,
4667 void *user), void *user);
4669 The terms themselves can be inspected and freed using
4672 unsigned isl_term_dim(__isl_keep isl_term *term,
4673 enum isl_dim_type type);
4674 void isl_term_get_num(__isl_keep isl_term *term,
4676 void isl_term_get_den(__isl_keep isl_term *term,
4678 int isl_term_get_exp(__isl_keep isl_term *term,
4679 enum isl_dim_type type, unsigned pos);
4680 __isl_give isl_aff *isl_term_get_div(
4681 __isl_keep isl_term *term, unsigned pos);
4682 void isl_term_free(__isl_take isl_term *term);
4684 Each term is a product of parameters, set variables and
4685 integer divisions. The function C<isl_term_get_exp>
4686 returns the exponent of a given dimensions in the given term.
4687 The C<isl_int>s in the arguments of C<isl_term_get_num>
4688 and C<isl_term_get_den> need to have been initialized
4689 using C<isl_int_init> before calling these functions.
4691 =head3 Properties of (Piecewise) Quasipolynomials
4693 To check whether a quasipolynomial is actually a constant,
4694 use the following function.
4696 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4697 isl_int *n, isl_int *d);
4699 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4700 then the numerator and denominator of the constant
4701 are returned in C<*n> and C<*d>, respectively.
4703 To check whether two union piecewise quasipolynomials are
4704 obviously equal, use
4706 int isl_union_pw_qpolynomial_plain_is_equal(
4707 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4708 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4710 =head3 Operations on (Piecewise) Quasipolynomials
4712 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4713 __isl_take isl_qpolynomial *qp, isl_int v);
4714 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4715 __isl_take isl_qpolynomial *qp);
4716 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4717 __isl_take isl_qpolynomial *qp1,
4718 __isl_take isl_qpolynomial *qp2);
4719 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4720 __isl_take isl_qpolynomial *qp1,
4721 __isl_take isl_qpolynomial *qp2);
4722 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4723 __isl_take isl_qpolynomial *qp1,
4724 __isl_take isl_qpolynomial *qp2);
4725 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4726 __isl_take isl_qpolynomial *qp, unsigned exponent);
4728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4729 __isl_take isl_pw_qpolynomial *pwqp1,
4730 __isl_take isl_pw_qpolynomial *pwqp2);
4731 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4732 __isl_take isl_pw_qpolynomial *pwqp1,
4733 __isl_take isl_pw_qpolynomial *pwqp2);
4734 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4735 __isl_take isl_pw_qpolynomial *pwqp1,
4736 __isl_take isl_pw_qpolynomial *pwqp2);
4737 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4738 __isl_take isl_pw_qpolynomial *pwqp);
4739 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4740 __isl_take isl_pw_qpolynomial *pwqp1,
4741 __isl_take isl_pw_qpolynomial *pwqp2);
4742 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4743 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4745 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4746 __isl_take isl_union_pw_qpolynomial *upwqp1,
4747 __isl_take isl_union_pw_qpolynomial *upwqp2);
4748 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4749 __isl_take isl_union_pw_qpolynomial *upwqp1,
4750 __isl_take isl_union_pw_qpolynomial *upwqp2);
4751 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4752 __isl_take isl_union_pw_qpolynomial *upwqp1,
4753 __isl_take isl_union_pw_qpolynomial *upwqp2);
4755 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4756 __isl_take isl_pw_qpolynomial *pwqp,
4757 __isl_take isl_point *pnt);
4759 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4760 __isl_take isl_union_pw_qpolynomial *upwqp,
4761 __isl_take isl_point *pnt);
4763 __isl_give isl_set *isl_pw_qpolynomial_domain(
4764 __isl_take isl_pw_qpolynomial *pwqp);
4765 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4766 __isl_take isl_pw_qpolynomial *pwpq,
4767 __isl_take isl_set *set);
4768 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4769 __isl_take isl_pw_qpolynomial *pwpq,
4770 __isl_take isl_set *set);
4772 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4773 __isl_take isl_union_pw_qpolynomial *upwqp);
4774 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4775 __isl_take isl_union_pw_qpolynomial *upwpq,
4776 __isl_take isl_union_set *uset);
4777 __isl_give isl_union_pw_qpolynomial *
4778 isl_union_pw_qpolynomial_intersect_params(
4779 __isl_take isl_union_pw_qpolynomial *upwpq,
4780 __isl_take isl_set *set);
4782 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4783 __isl_take isl_qpolynomial *qp,
4784 __isl_take isl_space *model);
4786 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4787 __isl_take isl_qpolynomial *qp);
4788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4789 __isl_take isl_pw_qpolynomial *pwqp);
4791 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4792 __isl_take isl_union_pw_qpolynomial *upwqp);
4794 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4795 __isl_take isl_qpolynomial *qp,
4796 __isl_take isl_set *context);
4797 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4798 __isl_take isl_qpolynomial *qp,
4799 __isl_take isl_set *context);
4801 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4802 __isl_take isl_pw_qpolynomial *pwqp,
4803 __isl_take isl_set *context);
4804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4805 __isl_take isl_pw_qpolynomial *pwqp,
4806 __isl_take isl_set *context);
4808 __isl_give isl_union_pw_qpolynomial *
4809 isl_union_pw_qpolynomial_gist_params(
4810 __isl_take isl_union_pw_qpolynomial *upwqp,
4811 __isl_take isl_set *context);
4812 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4813 __isl_take isl_union_pw_qpolynomial *upwqp,
4814 __isl_take isl_union_set *context);
4816 The gist operation applies the gist operation to each of
4817 the cells in the domain of the input piecewise quasipolynomial.
4818 The context is also exploited
4819 to simplify the quasipolynomials associated to each cell.
4821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4822 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4823 __isl_give isl_union_pw_qpolynomial *
4824 isl_union_pw_qpolynomial_to_polynomial(
4825 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4827 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4828 the polynomial will be an overapproximation. If C<sign> is negative,
4829 it will be an underapproximation. If C<sign> is zero, the approximation
4830 will lie somewhere in between.
4832 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4834 A piecewise quasipolynomial reduction is a piecewise
4835 reduction (or fold) of quasipolynomials.
4836 In particular, the reduction can be maximum or a minimum.
4837 The objects are mainly used to represent the result of
4838 an upper or lower bound on a quasipolynomial over its domain,
4839 i.e., as the result of the following function.
4841 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4842 __isl_take isl_pw_qpolynomial *pwqp,
4843 enum isl_fold type, int *tight);
4845 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4846 __isl_take isl_union_pw_qpolynomial *upwqp,
4847 enum isl_fold type, int *tight);
4849 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4850 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4851 is the returned bound is known be tight, i.e., for each value
4852 of the parameters there is at least
4853 one element in the domain that reaches the bound.
4854 If the domain of C<pwqp> is not wrapping, then the bound is computed
4855 over all elements in that domain and the result has a purely parametric
4856 domain. If the domain of C<pwqp> is wrapping, then the bound is
4857 computed over the range of the wrapped relation. The domain of the
4858 wrapped relation becomes the domain of the result.
4860 A (piecewise) quasipolynomial reduction can be copied or freed using the
4861 following functions.
4863 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4864 __isl_keep isl_qpolynomial_fold *fold);
4865 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4866 __isl_keep isl_pw_qpolynomial_fold *pwf);
4867 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4868 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4869 void isl_qpolynomial_fold_free(
4870 __isl_take isl_qpolynomial_fold *fold);
4871 void *isl_pw_qpolynomial_fold_free(
4872 __isl_take isl_pw_qpolynomial_fold *pwf);
4873 void *isl_union_pw_qpolynomial_fold_free(
4874 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4876 =head3 Printing Piecewise Quasipolynomial Reductions
4878 Piecewise quasipolynomial reductions can be printed
4879 using the following function.
4881 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4882 __isl_take isl_printer *p,
4883 __isl_keep isl_pw_qpolynomial_fold *pwf);
4884 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4885 __isl_take isl_printer *p,
4886 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4888 For C<isl_printer_print_pw_qpolynomial_fold>,
4889 output format of the printer
4890 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4891 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4892 output format of the printer
4893 needs to be set to C<ISL_FORMAT_ISL>.
4894 In case of printing in C<ISL_FORMAT_C>, the user may want
4895 to set the names of all dimensions
4897 __isl_give isl_pw_qpolynomial_fold *
4898 isl_pw_qpolynomial_fold_set_dim_name(
4899 __isl_take isl_pw_qpolynomial_fold *pwf,
4900 enum isl_dim_type type, unsigned pos,
4903 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4905 To iterate over all piecewise quasipolynomial reductions in a union
4906 piecewise quasipolynomial reduction, use the following function
4908 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4909 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4910 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4911 void *user), void *user);
4913 To iterate over the cells in a piecewise quasipolynomial reduction,
4914 use either of the following two functions
4916 int isl_pw_qpolynomial_fold_foreach_piece(
4917 __isl_keep isl_pw_qpolynomial_fold *pwf,
4918 int (*fn)(__isl_take isl_set *set,
4919 __isl_take isl_qpolynomial_fold *fold,
4920 void *user), void *user);
4921 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4922 __isl_keep isl_pw_qpolynomial_fold *pwf,
4923 int (*fn)(__isl_take isl_set *set,
4924 __isl_take isl_qpolynomial_fold *fold,
4925 void *user), void *user);
4927 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4928 of the difference between these two functions.
4930 To iterate over all quasipolynomials in a reduction, use
4932 int isl_qpolynomial_fold_foreach_qpolynomial(
4933 __isl_keep isl_qpolynomial_fold *fold,
4934 int (*fn)(__isl_take isl_qpolynomial *qp,
4935 void *user), void *user);
4937 =head3 Properties of Piecewise Quasipolynomial Reductions
4939 To check whether two union piecewise quasipolynomial reductions are
4940 obviously equal, use
4942 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4943 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4944 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4946 =head3 Operations on Piecewise Quasipolynomial Reductions
4948 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4949 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4951 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4952 __isl_take isl_pw_qpolynomial_fold *pwf1,
4953 __isl_take isl_pw_qpolynomial_fold *pwf2);
4955 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4956 __isl_take isl_pw_qpolynomial_fold *pwf1,
4957 __isl_take isl_pw_qpolynomial_fold *pwf2);
4959 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4960 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4961 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4963 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4964 __isl_take isl_pw_qpolynomial_fold *pwf,
4965 __isl_take isl_point *pnt);
4967 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4968 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4969 __isl_take isl_point *pnt);
4971 __isl_give isl_pw_qpolynomial_fold *
4972 isl_pw_qpolynomial_fold_intersect_params(
4973 __isl_take isl_pw_qpolynomial_fold *pwf,
4974 __isl_take isl_set *set);
4976 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4977 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4978 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4979 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4980 __isl_take isl_union_set *uset);
4981 __isl_give isl_union_pw_qpolynomial_fold *
4982 isl_union_pw_qpolynomial_fold_intersect_params(
4983 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4984 __isl_take isl_set *set);
4986 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4987 __isl_take isl_pw_qpolynomial_fold *pwf);
4989 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4990 __isl_take isl_pw_qpolynomial_fold *pwf);
4992 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4993 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4995 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4996 __isl_take isl_qpolynomial_fold *fold,
4997 __isl_take isl_set *context);
4998 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4999 __isl_take isl_qpolynomial_fold *fold,
5000 __isl_take isl_set *context);
5002 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5003 __isl_take isl_pw_qpolynomial_fold *pwf,
5004 __isl_take isl_set *context);
5005 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5006 __isl_take isl_pw_qpolynomial_fold *pwf,
5007 __isl_take isl_set *context);
5009 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5010 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5011 __isl_take isl_union_set *context);
5012 __isl_give isl_union_pw_qpolynomial_fold *
5013 isl_union_pw_qpolynomial_fold_gist_params(
5014 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5015 __isl_take isl_set *context);
5017 The gist operation applies the gist operation to each of
5018 the cells in the domain of the input piecewise quasipolynomial reduction.
5019 In future, the operation will also exploit the context
5020 to simplify the quasipolynomial reductions associated to each cell.
5022 __isl_give isl_pw_qpolynomial_fold *
5023 isl_set_apply_pw_qpolynomial_fold(
5024 __isl_take isl_set *set,
5025 __isl_take isl_pw_qpolynomial_fold *pwf,
5027 __isl_give isl_pw_qpolynomial_fold *
5028 isl_map_apply_pw_qpolynomial_fold(
5029 __isl_take isl_map *map,
5030 __isl_take isl_pw_qpolynomial_fold *pwf,
5032 __isl_give isl_union_pw_qpolynomial_fold *
5033 isl_union_set_apply_union_pw_qpolynomial_fold(
5034 __isl_take isl_union_set *uset,
5035 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5037 __isl_give isl_union_pw_qpolynomial_fold *
5038 isl_union_map_apply_union_pw_qpolynomial_fold(
5039 __isl_take isl_union_map *umap,
5040 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5043 The functions taking a map
5044 compose the given map with the given piecewise quasipolynomial reduction.
5045 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5046 over all elements in the intersection of the range of the map
5047 and the domain of the piecewise quasipolynomial reduction
5048 as a function of an element in the domain of the map.
5049 The functions taking a set compute a bound over all elements in the
5050 intersection of the set and the domain of the
5051 piecewise quasipolynomial reduction.
5053 =head2 Parametric Vertex Enumeration
5055 The parametric vertex enumeration described in this section
5056 is mainly intended to be used internally and by the C<barvinok>
5059 #include <isl/vertices.h>
5060 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5061 __isl_keep isl_basic_set *bset);
5063 The function C<isl_basic_set_compute_vertices> performs the
5064 actual computation of the parametric vertices and the chamber
5065 decomposition and store the result in an C<isl_vertices> object.
5066 This information can be queried by either iterating over all
5067 the vertices or iterating over all the chambers or cells
5068 and then iterating over all vertices that are active on the chamber.
5070 int isl_vertices_foreach_vertex(
5071 __isl_keep isl_vertices *vertices,
5072 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5075 int isl_vertices_foreach_cell(
5076 __isl_keep isl_vertices *vertices,
5077 int (*fn)(__isl_take isl_cell *cell, void *user),
5079 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5080 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5083 Other operations that can be performed on an C<isl_vertices> object are
5086 isl_ctx *isl_vertices_get_ctx(
5087 __isl_keep isl_vertices *vertices);
5088 int isl_vertices_get_n_vertices(
5089 __isl_keep isl_vertices *vertices);
5090 void isl_vertices_free(__isl_take isl_vertices *vertices);
5092 Vertices can be inspected and destroyed using the following functions.
5094 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5095 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5096 __isl_give isl_basic_set *isl_vertex_get_domain(
5097 __isl_keep isl_vertex *vertex);
5098 __isl_give isl_basic_set *isl_vertex_get_expr(
5099 __isl_keep isl_vertex *vertex);
5100 void isl_vertex_free(__isl_take isl_vertex *vertex);
5102 C<isl_vertex_get_expr> returns a singleton parametric set describing
5103 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5105 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5106 B<rational> basic sets, so they should mainly be used for inspection
5107 and should not be mixed with integer sets.
5109 Chambers can be inspected and destroyed using the following functions.
5111 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5112 __isl_give isl_basic_set *isl_cell_get_domain(
5113 __isl_keep isl_cell *cell);
5114 void isl_cell_free(__isl_take isl_cell *cell);
5116 =head1 Polyhedral Compilation Library
5118 This section collects functionality in C<isl> that has been specifically
5119 designed for use during polyhedral compilation.
5121 =head2 Dependence Analysis
5123 C<isl> contains specialized functionality for performing
5124 array dataflow analysis. That is, given a I<sink> access relation
5125 and a collection of possible I<source> access relations,
5126 C<isl> can compute relations that describe
5127 for each iteration of the sink access, which iteration
5128 of which of the source access relations was the last
5129 to access the same data element before the given iteration
5131 The resulting dependence relations map source iterations
5132 to the corresponding sink iterations.
5133 To compute standard flow dependences, the sink should be
5134 a read, while the sources should be writes.
5135 If any of the source accesses are marked as being I<may>
5136 accesses, then there will be a dependence from the last
5137 I<must> access B<and> from any I<may> access that follows
5138 this last I<must> access.
5139 In particular, if I<all> sources are I<may> accesses,
5140 then memory based dependence analysis is performed.
5141 If, on the other hand, all sources are I<must> accesses,
5142 then value based dependence analysis is performed.
5144 #include <isl/flow.h>
5146 typedef int (*isl_access_level_before)(void *first, void *second);
5148 __isl_give isl_access_info *isl_access_info_alloc(
5149 __isl_take isl_map *sink,
5150 void *sink_user, isl_access_level_before fn,
5152 __isl_give isl_access_info *isl_access_info_add_source(
5153 __isl_take isl_access_info *acc,
5154 __isl_take isl_map *source, int must,
5156 void *isl_access_info_free(__isl_take isl_access_info *acc);
5158 __isl_give isl_flow *isl_access_info_compute_flow(
5159 __isl_take isl_access_info *acc);
5161 int isl_flow_foreach(__isl_keep isl_flow *deps,
5162 int (*fn)(__isl_take isl_map *dep, int must,
5163 void *dep_user, void *user),
5165 __isl_give isl_map *isl_flow_get_no_source(
5166 __isl_keep isl_flow *deps, int must);
5167 void isl_flow_free(__isl_take isl_flow *deps);
5169 The function C<isl_access_info_compute_flow> performs the actual
5170 dependence analysis. The other functions are used to construct
5171 the input for this function or to read off the output.
5173 The input is collected in an C<isl_access_info>, which can
5174 be created through a call to C<isl_access_info_alloc>.
5175 The arguments to this functions are the sink access relation
5176 C<sink>, a token C<sink_user> used to identify the sink
5177 access to the user, a callback function for specifying the
5178 relative order of source and sink accesses, and the number
5179 of source access relations that will be added.
5180 The callback function has type C<int (*)(void *first, void *second)>.
5181 The function is called with two user supplied tokens identifying
5182 either a source or the sink and it should return the shared nesting
5183 level and the relative order of the two accesses.
5184 In particular, let I<n> be the number of loops shared by
5185 the two accesses. If C<first> precedes C<second> textually,
5186 then the function should return I<2 * n + 1>; otherwise,
5187 it should return I<2 * n>.
5188 The sources can be added to the C<isl_access_info> by performing
5189 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5190 C<must> indicates whether the source is a I<must> access
5191 or a I<may> access. Note that a multi-valued access relation
5192 should only be marked I<must> if every iteration in the domain
5193 of the relation accesses I<all> elements in its image.
5194 The C<source_user> token is again used to identify
5195 the source access. The range of the source access relation
5196 C<source> should have the same dimension as the range
5197 of the sink access relation.
5198 The C<isl_access_info_free> function should usually not be
5199 called explicitly, because it is called implicitly by
5200 C<isl_access_info_compute_flow>.
5202 The result of the dependence analysis is collected in an
5203 C<isl_flow>. There may be elements of
5204 the sink access for which no preceding source access could be
5205 found or for which all preceding sources are I<may> accesses.
5206 The relations containing these elements can be obtained through
5207 calls to C<isl_flow_get_no_source>, the first with C<must> set
5208 and the second with C<must> unset.
5209 In the case of standard flow dependence analysis,
5210 with the sink a read and the sources I<must> writes,
5211 the first relation corresponds to the reads from uninitialized
5212 array elements and the second relation is empty.
5213 The actual flow dependences can be extracted using
5214 C<isl_flow_foreach>. This function will call the user-specified
5215 callback function C<fn> for each B<non-empty> dependence between
5216 a source and the sink. The callback function is called
5217 with four arguments, the actual flow dependence relation
5218 mapping source iterations to sink iterations, a boolean that
5219 indicates whether it is a I<must> or I<may> dependence, a token
5220 identifying the source and an additional C<void *> with value
5221 equal to the third argument of the C<isl_flow_foreach> call.
5222 A dependence is marked I<must> if it originates from a I<must>
5223 source and if it is not followed by any I<may> sources.
5225 After finishing with an C<isl_flow>, the user should call
5226 C<isl_flow_free> to free all associated memory.
5228 A higher-level interface to dependence analysis is provided
5229 by the following function.
5231 #include <isl/flow.h>
5233 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5234 __isl_take isl_union_map *must_source,
5235 __isl_take isl_union_map *may_source,
5236 __isl_take isl_union_map *schedule,
5237 __isl_give isl_union_map **must_dep,
5238 __isl_give isl_union_map **may_dep,
5239 __isl_give isl_union_map **must_no_source,
5240 __isl_give isl_union_map **may_no_source);
5242 The arrays are identified by the tuple names of the ranges
5243 of the accesses. The iteration domains by the tuple names
5244 of the domains of the accesses and of the schedule.
5245 The relative order of the iteration domains is given by the
5246 schedule. The relations returned through C<must_no_source>
5247 and C<may_no_source> are subsets of C<sink>.
5248 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5249 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5250 any of the other arguments is treated as an error.
5252 =head3 Interaction with Dependence Analysis
5254 During the dependence analysis, we frequently need to perform
5255 the following operation. Given a relation between sink iterations
5256 and potential source iterations from a particular source domain,
5257 what is the last potential source iteration corresponding to each
5258 sink iteration. It can sometimes be convenient to adjust
5259 the set of potential source iterations before or after each such operation.
5260 The prototypical example is fuzzy array dataflow analysis,
5261 where we need to analyze if, based on data-dependent constraints,
5262 the sink iteration can ever be executed without one or more of
5263 the corresponding potential source iterations being executed.
5264 If so, we can introduce extra parameters and select an unknown
5265 but fixed source iteration from the potential source iterations.
5266 To be able to perform such manipulations, C<isl> provides the following
5269 #include <isl/flow.h>
5271 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5272 __isl_keep isl_map *source_map,
5273 __isl_keep isl_set *sink, void *source_user,
5275 __isl_give isl_access_info *isl_access_info_set_restrict(
5276 __isl_take isl_access_info *acc,
5277 isl_access_restrict fn, void *user);
5279 The function C<isl_access_info_set_restrict> should be called
5280 before calling C<isl_access_info_compute_flow> and registers a callback function
5281 that will be called any time C<isl> is about to compute the last
5282 potential source. The first argument is the (reverse) proto-dependence,
5283 mapping sink iterations to potential source iterations.
5284 The second argument represents the sink iterations for which
5285 we want to compute the last source iteration.
5286 The third argument is the token corresponding to the source
5287 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5288 The callback is expected to return a restriction on either the input or
5289 the output of the operation computing the last potential source.
5290 If the input needs to be restricted then restrictions are needed
5291 for both the source and the sink iterations. The sink iterations
5292 and the potential source iterations will be intersected with these sets.
5293 If the output needs to be restricted then only a restriction on the source
5294 iterations is required.
5295 If any error occurs, the callback should return C<NULL>.
5296 An C<isl_restriction> object can be created, freed and inspected
5297 using the following functions.
5299 #include <isl/flow.h>
5301 __isl_give isl_restriction *isl_restriction_input(
5302 __isl_take isl_set *source_restr,
5303 __isl_take isl_set *sink_restr);
5304 __isl_give isl_restriction *isl_restriction_output(
5305 __isl_take isl_set *source_restr);
5306 __isl_give isl_restriction *isl_restriction_none(
5307 __isl_take isl_map *source_map);
5308 __isl_give isl_restriction *isl_restriction_empty(
5309 __isl_take isl_map *source_map);
5310 void *isl_restriction_free(
5311 __isl_take isl_restriction *restr);
5312 isl_ctx *isl_restriction_get_ctx(
5313 __isl_keep isl_restriction *restr);
5315 C<isl_restriction_none> and C<isl_restriction_empty> are special
5316 cases of C<isl_restriction_input>. C<isl_restriction_none>
5317 is essentially equivalent to
5319 isl_restriction_input(isl_set_universe(
5320 isl_space_range(isl_map_get_space(source_map))),
5322 isl_space_domain(isl_map_get_space(source_map))));
5324 whereas C<isl_restriction_empty> is essentially equivalent to
5326 isl_restriction_input(isl_set_empty(
5327 isl_space_range(isl_map_get_space(source_map))),
5329 isl_space_domain(isl_map_get_space(source_map))));
5333 B<The functionality described in this section is fairly new
5334 and may be subject to change.>
5336 The following function can be used to compute a schedule
5337 for a union of domains.
5338 By default, the algorithm used to construct the schedule is similar
5339 to that of C<Pluto>.
5340 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5342 The generated schedule respects all C<validity> dependences.
5343 That is, all dependence distances over these dependences in the
5344 scheduled space are lexicographically positive.
5345 The default algorithm tries to minimize the dependence distances over
5346 C<proximity> dependences.
5347 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5348 for groups of domains where the dependence distances have only
5349 non-negative values.
5350 When using Feautrier's algorithm, the C<proximity> dependence
5351 distances are only minimized during the extension to a
5352 full-dimensional schedule.
5354 #include <isl/schedule.h>
5355 __isl_give isl_schedule *isl_union_set_compute_schedule(
5356 __isl_take isl_union_set *domain,
5357 __isl_take isl_union_map *validity,
5358 __isl_take isl_union_map *proximity);
5359 void *isl_schedule_free(__isl_take isl_schedule *sched);
5361 A mapping from the domains to the scheduled space can be obtained
5362 from an C<isl_schedule> using the following function.
5364 __isl_give isl_union_map *isl_schedule_get_map(
5365 __isl_keep isl_schedule *sched);
5367 A representation of the schedule can be printed using
5369 __isl_give isl_printer *isl_printer_print_schedule(
5370 __isl_take isl_printer *p,
5371 __isl_keep isl_schedule *schedule);
5373 A representation of the schedule as a forest of bands can be obtained
5374 using the following function.
5376 __isl_give isl_band_list *isl_schedule_get_band_forest(
5377 __isl_keep isl_schedule *schedule);
5379 The individual bands can be visited in depth-first post-order
5380 using the following function.
5382 #include <isl/schedule.h>
5383 int isl_schedule_foreach_band(
5384 __isl_keep isl_schedule *sched,
5385 int (*fn)(__isl_keep isl_band *band, void *user),
5388 The list can be manipulated as explained in L<"Lists">.
5389 The bands inside the list can be copied and freed using the following
5392 #include <isl/band.h>
5393 __isl_give isl_band *isl_band_copy(
5394 __isl_keep isl_band *band);
5395 void *isl_band_free(__isl_take isl_band *band);
5397 Each band contains zero or more scheduling dimensions.
5398 These are referred to as the members of the band.
5399 The section of the schedule that corresponds to the band is
5400 referred to as the partial schedule of the band.
5401 For those nodes that participate in a band, the outer scheduling
5402 dimensions form the prefix schedule, while the inner scheduling
5403 dimensions form the suffix schedule.
5404 That is, if we take a cut of the band forest, then the union of
5405 the concatenations of the prefix, partial and suffix schedules of
5406 each band in the cut is equal to the entire schedule (modulo
5407 some possible padding at the end with zero scheduling dimensions).
5408 The properties of a band can be inspected using the following functions.
5410 #include <isl/band.h>
5411 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5413 int isl_band_has_children(__isl_keep isl_band *band);
5414 __isl_give isl_band_list *isl_band_get_children(
5415 __isl_keep isl_band *band);
5417 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5418 __isl_keep isl_band *band);
5419 __isl_give isl_union_map *isl_band_get_partial_schedule(
5420 __isl_keep isl_band *band);
5421 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5422 __isl_keep isl_band *band);
5424 int isl_band_n_member(__isl_keep isl_band *band);
5425 int isl_band_member_is_zero_distance(
5426 __isl_keep isl_band *band, int pos);
5428 int isl_band_list_foreach_band(
5429 __isl_keep isl_band_list *list,
5430 int (*fn)(__isl_keep isl_band *band, void *user),
5433 Note that a scheduling dimension is considered to be ``zero
5434 distance'' if it does not carry any proximity dependences
5436 That is, if the dependence distances of the proximity
5437 dependences are all zero in that direction (for fixed
5438 iterations of outer bands).
5439 Like C<isl_schedule_foreach_band>,
5440 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5441 in depth-first post-order.
5443 A band can be tiled using the following function.
5445 #include <isl/band.h>
5446 int isl_band_tile(__isl_keep isl_band *band,
5447 __isl_take isl_vec *sizes);
5449 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5451 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5452 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5454 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5456 The C<isl_band_tile> function tiles the band using the given tile sizes
5457 inside its schedule.
5458 A new child band is created to represent the point loops and it is
5459 inserted between the modified band and its children.
5460 The C<tile_scale_tile_loops> option specifies whether the tile
5461 loops iterators should be scaled by the tile sizes.
5462 If the C<tile_shift_point_loops> option is set, then the point loops
5463 are shifted to start at zero.
5465 A band can be split into two nested bands using the following function.
5467 int isl_band_split(__isl_keep isl_band *band, int pos);
5469 The resulting outer band contains the first C<pos> dimensions of C<band>
5470 while the inner band contains the remaining dimensions.
5472 A representation of the band can be printed using
5474 #include <isl/band.h>
5475 __isl_give isl_printer *isl_printer_print_band(
5476 __isl_take isl_printer *p,
5477 __isl_keep isl_band *band);
5481 #include <isl/schedule.h>
5482 int isl_options_set_schedule_max_coefficient(
5483 isl_ctx *ctx, int val);
5484 int isl_options_get_schedule_max_coefficient(
5486 int isl_options_set_schedule_max_constant_term(
5487 isl_ctx *ctx, int val);
5488 int isl_options_get_schedule_max_constant_term(
5490 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5491 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5492 int isl_options_set_schedule_maximize_band_depth(
5493 isl_ctx *ctx, int val);
5494 int isl_options_get_schedule_maximize_band_depth(
5496 int isl_options_set_schedule_outer_zero_distance(
5497 isl_ctx *ctx, int val);
5498 int isl_options_get_schedule_outer_zero_distance(
5500 int isl_options_set_schedule_split_scaled(
5501 isl_ctx *ctx, int val);
5502 int isl_options_get_schedule_split_scaled(
5504 int isl_options_set_schedule_algorithm(
5505 isl_ctx *ctx, int val);
5506 int isl_options_get_schedule_algorithm(
5508 int isl_options_set_schedule_separate_components(
5509 isl_ctx *ctx, int val);
5510 int isl_options_get_schedule_separate_components(
5515 =item * schedule_max_coefficient
5517 This option enforces that the coefficients for variable and parameter
5518 dimensions in the calculated schedule are not larger than the specified value.
5519 This option can significantly increase the speed of the scheduling calculation
5520 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5521 this option does not introduce bounds on the variable or parameter
5524 =item * schedule_max_constant_term
5526 This option enforces that the constant coefficients in the calculated schedule
5527 are not larger than the maximal constant term. This option can significantly
5528 increase the speed of the scheduling calculation and may also prevent fusing of
5529 unrelated dimensions. A value of -1 means that this option does not introduce
5530 bounds on the constant coefficients.
5532 =item * schedule_fuse
5534 This option controls the level of fusion.
5535 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5536 resulting schedule will be distributed as much as possible.
5537 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5538 try to fuse loops in the resulting schedule.
5540 =item * schedule_maximize_band_depth
5542 If this option is set, we do not split bands at the point
5543 where we detect splitting is necessary. Instead, we
5544 backtrack and split bands as early as possible. This
5545 reduces the number of splits and maximizes the width of
5546 the bands. Wider bands give more possibilities for tiling.
5547 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5548 then bands will be split as early as possible, even if there is no need.
5549 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5551 =item * schedule_outer_zero_distance
5553 If this option is set, then we try to construct schedules
5554 where the outermost scheduling dimension in each band
5555 results in a zero dependence distance over the proximity
5558 =item * schedule_split_scaled
5560 If this option is set, then we try to construct schedules in which the
5561 constant term is split off from the linear part if the linear parts of
5562 the scheduling rows for all nodes in the graphs have a common non-trivial
5564 The constant term is then placed in a separate band and the linear
5567 =item * schedule_algorithm
5569 Selects the scheduling algorithm to be used.
5570 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5571 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5573 =item * schedule_separate_components
5575 If at any point the dependence graph contains any (weakly connected) components,
5576 then these components are scheduled separately.
5577 If this option is not set, then some iterations of the domains
5578 in these components may be scheduled together.
5579 If this option is set, then the components are given consecutive
5584 =head2 AST Generation
5586 This section describes the C<isl> functionality for generating
5587 ASTs that visit all the elements
5588 in a domain in an order specified by a schedule.
5589 In particular, given a C<isl_union_map>, an AST is generated
5590 that visits all the elements in the domain of the C<isl_union_map>
5591 according to the lexicographic order of the corresponding image
5592 element(s). If the range of the C<isl_union_map> consists of
5593 elements in more than one space, then each of these spaces is handled
5594 separately in an arbitrary order.
5595 It should be noted that the image elements only specify the I<order>
5596 in which the corresponding domain elements should be visited.
5597 No direct relation between the image elements and the loop iterators
5598 in the generated AST should be assumed.
5600 Each AST is generated within a build. The initial build
5601 simply specifies the constraints on the parameters (if any)
5602 and can be created, inspected, copied and freed using the following functions.
5604 #include <isl/ast_build.h>
5605 __isl_give isl_ast_build *isl_ast_build_from_context(
5606 __isl_take isl_set *set);
5607 isl_ctx *isl_ast_build_get_ctx(
5608 __isl_keep isl_ast_build *build);
5609 __isl_give isl_ast_build *isl_ast_build_copy(
5610 __isl_keep isl_ast_build *build);
5611 void *isl_ast_build_free(
5612 __isl_take isl_ast_build *build);
5614 The C<set> argument is usually a parameter set with zero or more parameters.
5615 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5616 and L</"Fine-grained Control over AST Generation">.
5617 Finally, the AST itself can be constructed using the following
5620 #include <isl/ast_build.h>
5621 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5622 __isl_keep isl_ast_build *build,
5623 __isl_take isl_union_map *schedule);
5625 =head3 Inspecting the AST
5627 The basic properties of an AST node can be obtained as follows.
5629 #include <isl/ast.h>
5630 isl_ctx *isl_ast_node_get_ctx(
5631 __isl_keep isl_ast_node *node);
5632 enum isl_ast_node_type isl_ast_node_get_type(
5633 __isl_keep isl_ast_node *node);
5635 The type of an AST node is one of
5636 C<isl_ast_node_for>,
5638 C<isl_ast_node_block> or
5639 C<isl_ast_node_user>.
5640 An C<isl_ast_node_for> represents a for node.
5641 An C<isl_ast_node_if> represents an if node.
5642 An C<isl_ast_node_block> represents a compound node.
5643 An C<isl_ast_node_user> represents an expression statement.
5644 An expression statement typically corresponds to a domain element, i.e.,
5645 one of the elements that is visited by the AST.
5647 Each type of node has its own additional properties.
5649 #include <isl/ast.h>
5650 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5651 __isl_keep isl_ast_node *node);
5652 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5653 __isl_keep isl_ast_node *node);
5654 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5655 __isl_keep isl_ast_node *node);
5656 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5657 __isl_keep isl_ast_node *node);
5658 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5659 __isl_keep isl_ast_node *node);
5660 int isl_ast_node_for_is_degenerate(
5661 __isl_keep isl_ast_node *node);
5663 An C<isl_ast_for> is considered degenerate if it is known to execute
5666 #include <isl/ast.h>
5667 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5668 __isl_keep isl_ast_node *node);
5669 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5670 __isl_keep isl_ast_node *node);
5671 int isl_ast_node_if_has_else(
5672 __isl_keep isl_ast_node *node);
5673 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5674 __isl_keep isl_ast_node *node);
5676 __isl_give isl_ast_node_list *
5677 isl_ast_node_block_get_children(
5678 __isl_keep isl_ast_node *node);
5680 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5681 __isl_keep isl_ast_node *node);
5683 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5684 the following functions.
5686 #include <isl/ast.h>
5687 isl_ctx *isl_ast_expr_get_ctx(
5688 __isl_keep isl_ast_expr *expr);
5689 enum isl_ast_expr_type isl_ast_expr_get_type(
5690 __isl_keep isl_ast_expr *expr);
5692 The type of an AST expression is one of
5694 C<isl_ast_expr_id> or
5695 C<isl_ast_expr_int>.
5696 An C<isl_ast_expr_op> represents the result of an operation.
5697 An C<isl_ast_expr_id> represents an identifier.
5698 An C<isl_ast_expr_int> represents an integer value.
5700 Each type of expression has its own additional properties.
5702 #include <isl/ast.h>
5703 enum isl_ast_op_type isl_ast_expr_get_op_type(
5704 __isl_keep isl_ast_expr *expr);
5705 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5706 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5707 __isl_keep isl_ast_expr *expr, int pos);
5708 int isl_ast_node_foreach_ast_op_type(
5709 __isl_keep isl_ast_node *node,
5710 int (*fn)(enum isl_ast_op_type type, void *user),
5713 C<isl_ast_expr_get_op_type> returns the type of the operation
5714 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5715 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5717 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5718 C<isl_ast_op_type> that appears in C<node>.
5719 The operation type is one of the following.
5723 =item C<isl_ast_op_and>
5725 Logical I<and> of two arguments.
5726 Both arguments can be evaluated.
5728 =item C<isl_ast_op_and_then>
5730 Logical I<and> of two arguments.
5731 The second argument can only be evaluated if the first evaluates to true.
5733 =item C<isl_ast_op_or>
5735 Logical I<or> of two arguments.
5736 Both arguments can be evaluated.
5738 =item C<isl_ast_op_or_else>
5740 Logical I<or> of two arguments.
5741 The second argument can only be evaluated if the first evaluates to false.
5743 =item C<isl_ast_op_max>
5745 Maximum of two or more arguments.
5747 =item C<isl_ast_op_min>
5749 Minimum of two or more arguments.
5751 =item C<isl_ast_op_minus>
5755 =item C<isl_ast_op_add>
5757 Sum of two arguments.
5759 =item C<isl_ast_op_sub>
5761 Difference of two arguments.
5763 =item C<isl_ast_op_mul>
5765 Product of two arguments.
5767 =item C<isl_ast_op_div>
5769 Exact division. That is, the result is known to be an integer.
5771 =item C<isl_ast_op_fdiv_q>
5773 Result of integer division, rounded towards negative
5776 =item C<isl_ast_op_pdiv_q>
5778 Result of integer division, where dividend is known to be non-negative.
5780 =item C<isl_ast_op_pdiv_r>
5782 Remainder of integer division, where dividend is known to be non-negative.
5784 =item C<isl_ast_op_cond>
5786 Conditional operator defined on three arguments.
5787 If the first argument evaluates to true, then the result
5788 is equal to the second argument. Otherwise, the result
5789 is equal to the third argument.
5790 The second and third argument may only be evaluated if
5791 the first argument evaluates to true and false, respectively.
5792 Corresponds to C<a ? b : c> in C.
5794 =item C<isl_ast_op_select>
5796 Conditional operator defined on three arguments.
5797 If the first argument evaluates to true, then the result
5798 is equal to the second argument. Otherwise, the result
5799 is equal to the third argument.
5800 The second and third argument may be evaluated independently
5801 of the value of the first argument.
5802 Corresponds to C<a * b + (1 - a) * c> in C.
5804 =item C<isl_ast_op_eq>
5808 =item C<isl_ast_op_le>
5810 Less than or equal relation.
5812 =item C<isl_ast_op_lt>
5816 =item C<isl_ast_op_ge>
5818 Greater than or equal relation.
5820 =item C<isl_ast_op_gt>
5822 Greater than relation.
5824 =item C<isl_ast_op_call>
5827 The number of arguments of the C<isl_ast_expr> is one more than
5828 the number of arguments in the function call, the first argument
5829 representing the function being called.
5833 #include <isl/ast.h>
5834 __isl_give isl_id *isl_ast_expr_get_id(
5835 __isl_keep isl_ast_expr *expr);
5837 Return the identifier represented by the AST expression.
5839 #include <isl/ast.h>
5840 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5843 Return the integer represented by the AST expression.
5844 Note that the integer is returned through the C<v> argument.
5845 The return value of the function itself indicates whether the
5846 operation was performed successfully.
5848 =head3 Manipulating and printing the AST
5850 AST nodes can be copied and freed using the following functions.
5852 #include <isl/ast.h>
5853 __isl_give isl_ast_node *isl_ast_node_copy(
5854 __isl_keep isl_ast_node *node);
5855 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5857 AST expressions can be copied and freed using the following functions.
5859 #include <isl/ast.h>
5860 __isl_give isl_ast_expr *isl_ast_expr_copy(
5861 __isl_keep isl_ast_expr *expr);
5862 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5864 New AST expressions can be created either directly or within
5865 the context of an C<isl_ast_build>.
5867 #include <isl/ast.h>
5868 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5869 __isl_take isl_id *id);
5870 __isl_give isl_ast_expr *isl_ast_expr_neg(
5871 __isl_take isl_ast_expr *expr);
5872 __isl_give isl_ast_expr *isl_ast_expr_add(
5873 __isl_take isl_ast_expr *expr1,
5874 __isl_take isl_ast_expr *expr2);
5875 __isl_give isl_ast_expr *isl_ast_expr_sub(
5876 __isl_take isl_ast_expr *expr1,
5877 __isl_take isl_ast_expr *expr2);
5878 __isl_give isl_ast_expr *isl_ast_expr_mul(
5879 __isl_take isl_ast_expr *expr1,
5880 __isl_take isl_ast_expr *expr2);
5881 __isl_give isl_ast_expr *isl_ast_expr_div(
5882 __isl_take isl_ast_expr *expr1,
5883 __isl_take isl_ast_expr *expr2);
5884 __isl_give isl_ast_expr *isl_ast_expr_and(
5885 __isl_take isl_ast_expr *expr1,
5886 __isl_take isl_ast_expr *expr2)
5887 __isl_give isl_ast_expr *isl_ast_expr_or(
5888 __isl_take isl_ast_expr *expr1,
5889 __isl_take isl_ast_expr *expr2)
5891 #include <isl/ast_build.h>
5892 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5893 __isl_keep isl_ast_build *build,
5894 __isl_take isl_pw_aff *pa);
5895 __isl_give isl_ast_expr *
5896 isl_ast_build_call_from_pw_multi_aff(
5897 __isl_keep isl_ast_build *build,
5898 __isl_take isl_pw_multi_aff *pma);
5900 The domains of C<pa> and C<pma> should correspond
5901 to the schedule space of C<build>.
5902 The tuple id of C<pma> is used as the function being called.
5904 User specified data can be attached to an C<isl_ast_node> and obtained
5905 from the same C<isl_ast_node> using the following functions.
5907 #include <isl/ast.h>
5908 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5909 __isl_take isl_ast_node *node,
5910 __isl_take isl_id *annotation);
5911 __isl_give isl_id *isl_ast_node_get_annotation(
5912 __isl_keep isl_ast_node *node);
5914 Basic printing can be performed using the following functions.
5916 #include <isl/ast.h>
5917 __isl_give isl_printer *isl_printer_print_ast_expr(
5918 __isl_take isl_printer *p,
5919 __isl_keep isl_ast_expr *expr);
5920 __isl_give isl_printer *isl_printer_print_ast_node(
5921 __isl_take isl_printer *p,
5922 __isl_keep isl_ast_node *node);
5924 More advanced printing can be performed using the following functions.
5926 #include <isl/ast.h>
5927 __isl_give isl_printer *isl_ast_op_type_print_macro(
5928 enum isl_ast_op_type type,
5929 __isl_take isl_printer *p);
5930 __isl_give isl_printer *isl_ast_node_print_macros(
5931 __isl_keep isl_ast_node *node,
5932 __isl_take isl_printer *p);
5933 __isl_give isl_printer *isl_ast_node_print(
5934 __isl_keep isl_ast_node *node,
5935 __isl_take isl_printer *p,
5936 __isl_take isl_ast_print_options *options);
5937 __isl_give isl_printer *isl_ast_node_for_print(
5938 __isl_keep isl_ast_node *node,
5939 __isl_take isl_printer *p,
5940 __isl_take isl_ast_print_options *options);
5941 __isl_give isl_printer *isl_ast_node_if_print(
5942 __isl_keep isl_ast_node *node,
5943 __isl_take isl_printer *p,
5944 __isl_take isl_ast_print_options *options);
5946 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5947 C<isl> may print out an AST that makes use of macros such
5948 as C<floord>, C<min> and C<max>.
5949 C<isl_ast_op_type_print_macro> prints out the macro
5950 corresponding to a specific C<isl_ast_op_type>.
5951 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5952 for expressions where these macros would be used and prints
5953 out the required macro definitions.
5954 Essentially, C<isl_ast_node_print_macros> calls
5955 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5956 as function argument.
5957 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5958 C<isl_ast_node_if_print> print an C<isl_ast_node>
5959 in C<ISL_FORMAT_C>, but allow for some extra control
5960 through an C<isl_ast_print_options> object.
5961 This object can be created using the following functions.
5963 #include <isl/ast.h>
5964 __isl_give isl_ast_print_options *
5965 isl_ast_print_options_alloc(isl_ctx *ctx);
5966 __isl_give isl_ast_print_options *
5967 isl_ast_print_options_copy(
5968 __isl_keep isl_ast_print_options *options);
5969 void *isl_ast_print_options_free(
5970 __isl_take isl_ast_print_options *options);
5972 __isl_give isl_ast_print_options *
5973 isl_ast_print_options_set_print_user(
5974 __isl_take isl_ast_print_options *options,
5975 __isl_give isl_printer *(*print_user)(
5976 __isl_take isl_printer *p,
5977 __isl_take isl_ast_print_options *options,
5978 __isl_keep isl_ast_node *node, void *user),
5980 __isl_give isl_ast_print_options *
5981 isl_ast_print_options_set_print_for(
5982 __isl_take isl_ast_print_options *options,
5983 __isl_give isl_printer *(*print_for)(
5984 __isl_take isl_printer *p,
5985 __isl_take isl_ast_print_options *options,
5986 __isl_keep isl_ast_node *node, void *user),
5989 The callback set by C<isl_ast_print_options_set_print_user>
5990 is called whenever a node of type C<isl_ast_node_user> needs to
5992 The callback set by C<isl_ast_print_options_set_print_for>
5993 is called whenever a node of type C<isl_ast_node_for> needs to
5995 Note that C<isl_ast_node_for_print> will I<not> call the
5996 callback set by C<isl_ast_print_options_set_print_for> on the node
5997 on which C<isl_ast_node_for_print> is called, but only on nested
5998 nodes of type C<isl_ast_node_for>. It is therefore safe to
5999 call C<isl_ast_node_for_print> from within the callback set by
6000 C<isl_ast_print_options_set_print_for>.
6002 The following option determines the type to be used for iterators
6003 while printing the AST.
6005 int isl_options_set_ast_iterator_type(
6006 isl_ctx *ctx, const char *val);
6007 const char *isl_options_get_ast_iterator_type(
6012 #include <isl/ast_build.h>
6013 int isl_options_set_ast_build_atomic_upper_bound(
6014 isl_ctx *ctx, int val);
6015 int isl_options_get_ast_build_atomic_upper_bound(
6017 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6019 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6020 int isl_options_set_ast_build_exploit_nested_bounds(
6021 isl_ctx *ctx, int val);
6022 int isl_options_get_ast_build_exploit_nested_bounds(
6024 int isl_options_set_ast_build_group_coscheduled(
6025 isl_ctx *ctx, int val);
6026 int isl_options_get_ast_build_group_coscheduled(
6028 int isl_options_set_ast_build_scale_strides(
6029 isl_ctx *ctx, int val);
6030 int isl_options_get_ast_build_scale_strides(
6032 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6034 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6035 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6037 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6041 =item * ast_build_atomic_upper_bound
6043 Generate loop upper bounds that consist of the current loop iterator,
6044 an operator and an expression not involving the iterator.
6045 If this option is not set, then the current loop iterator may appear
6046 several times in the upper bound.
6047 For example, when this option is turned off, AST generation
6050 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6054 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6057 When the option is turned on, the following AST is generated
6059 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6062 =item * ast_build_prefer_pdiv
6064 If this option is turned off, then the AST generation will
6065 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6066 operators, but no C<isl_ast_op_pdiv_q> or
6067 C<isl_ast_op_pdiv_r> operators.
6068 If this options is turned on, then C<isl> will try to convert
6069 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6070 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6072 =item * ast_build_exploit_nested_bounds
6074 Simplify conditions based on bounds of nested for loops.
6075 In particular, remove conditions that are implied by the fact
6076 that one or more nested loops have at least one iteration,
6077 meaning that the upper bound is at least as large as the lower bound.
6078 For example, when this option is turned off, AST generation
6081 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6087 for (int c0 = 0; c0 <= N; c0 += 1)
6088 for (int c1 = 0; c1 <= M; c1 += 1)
6091 When the option is turned on, the following AST is generated
6093 for (int c0 = 0; c0 <= N; c0 += 1)
6094 for (int c1 = 0; c1 <= M; c1 += 1)
6097 =item * ast_build_group_coscheduled
6099 If two domain elements are assigned the same schedule point, then
6100 they may be executed in any order and they may even appear in different
6101 loops. If this options is set, then the AST generator will make
6102 sure that coscheduled domain elements do not appear in separate parts
6103 of the AST. This is useful in case of nested AST generation
6104 if the outer AST generation is given only part of a schedule
6105 and the inner AST generation should handle the domains that are
6106 coscheduled by this initial part of the schedule together.
6107 For example if an AST is generated for a schedule
6109 { A[i] -> [0]; B[i] -> [0] }
6111 then the C<isl_ast_build_set_create_leaf> callback described
6112 below may get called twice, once for each domain.
6113 Setting this option ensures that the callback is only called once
6114 on both domains together.
6116 =item * ast_build_separation_bounds
6118 This option specifies which bounds to use during separation.
6119 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6120 then all (possibly implicit) bounds on the current dimension will
6121 be used during separation.
6122 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6123 then only those bounds that are explicitly available will
6124 be used during separation.
6126 =item * ast_build_scale_strides
6128 This option specifies whether the AST generator is allowed
6129 to scale down iterators of strided loops.
6131 =item * ast_build_allow_else
6133 This option specifies whether the AST generator is allowed
6134 to construct if statements with else branches.
6136 =item * ast_build_allow_or
6138 This option specifies whether the AST generator is allowed
6139 to construct if conditions with disjunctions.
6143 =head3 Fine-grained Control over AST Generation
6145 Besides specifying the constraints on the parameters,
6146 an C<isl_ast_build> object can be used to control
6147 various aspects of the AST generation process.
6148 The most prominent way of control is through ``options'',
6149 which can be set using the following function.
6151 #include <isl/ast_build.h>
6152 __isl_give isl_ast_build *
6153 isl_ast_build_set_options(
6154 __isl_take isl_ast_build *control,
6155 __isl_take isl_union_map *options);
6157 The options are encoded in an <isl_union_map>.
6158 The domain of this union relation refers to the schedule domain,
6159 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6160 In the case of nested AST generation (see L</"Nested AST Generation">),
6161 the domain of C<options> should refer to the extra piece of the schedule.
6162 That is, it should be equal to the range of the wrapped relation in the
6163 range of the schedule.
6164 The range of the options can consist of elements in one or more spaces,
6165 the names of which determine the effect of the option.
6166 The values of the range typically also refer to the schedule dimension
6167 to which the option applies. In case of nested AST generation
6168 (see L</"Nested AST Generation">), these values refer to the position
6169 of the schedule dimension within the innermost AST generation.
6170 The constraints on the domain elements of
6171 the option should only refer to this dimension and earlier dimensions.
6172 We consider the following spaces.
6176 =item C<separation_class>
6178 This space is a wrapped relation between two one dimensional spaces.
6179 The input space represents the schedule dimension to which the option
6180 applies and the output space represents the separation class.
6181 While constructing a loop corresponding to the specified schedule
6182 dimension(s), the AST generator will try to generate separate loops
6183 for domain elements that are assigned different classes.
6184 If only some of the elements are assigned a class, then those elements
6185 that are not assigned any class will be treated as belonging to a class
6186 that is separate from the explicitly assigned classes.
6187 The typical use case for this option is to separate full tiles from
6189 The other options, described below, are applied after the separation
6192 As an example, consider the separation into full and partial tiles
6193 of a tiling of a triangular domain.
6194 Take, for example, the domain
6196 { A[i,j] : 0 <= i,j and i + j <= 100 }
6198 and a tiling into tiles of 10 by 10. The input to the AST generator
6199 is then the schedule
6201 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6204 Without any options, the following AST is generated
6206 for (int c0 = 0; c0 <= 10; c0 += 1)
6207 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6208 for (int c2 = 10 * c0;
6209 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6211 for (int c3 = 10 * c1;
6212 c3 <= min(10 * c1 + 9, -c2 + 100);
6216 Separation into full and partial tiles can be obtained by assigning
6217 a class, say C<0>, to the full tiles. The full tiles are represented by those
6218 values of the first and second schedule dimensions for which there are
6219 values of the third and fourth dimensions to cover an entire tile.
6220 That is, we need to specify the following option
6222 { [a,b,c,d] -> separation_class[[0]->[0]] :
6223 exists b': 0 <= 10a,10b' and
6224 10a+9+10b'+9 <= 100;
6225 [a,b,c,d] -> separation_class[[1]->[0]] :
6226 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6230 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6231 a >= 0 and b >= 0 and b <= 8 - a;
6232 [a, b, c, d] -> separation_class[[0] -> [0]] :
6235 With this option, the generated AST is as follows
6238 for (int c0 = 0; c0 <= 8; c0 += 1) {
6239 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6240 for (int c2 = 10 * c0;
6241 c2 <= 10 * c0 + 9; c2 += 1)
6242 for (int c3 = 10 * c1;
6243 c3 <= 10 * c1 + 9; c3 += 1)
6245 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6246 for (int c2 = 10 * c0;
6247 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6249 for (int c3 = 10 * c1;
6250 c3 <= min(-c2 + 100, 10 * c1 + 9);
6254 for (int c0 = 9; c0 <= 10; c0 += 1)
6255 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6256 for (int c2 = 10 * c0;
6257 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6259 for (int c3 = 10 * c1;
6260 c3 <= min(10 * c1 + 9, -c2 + 100);
6267 This is a single-dimensional space representing the schedule dimension(s)
6268 to which ``separation'' should be applied. Separation tries to split
6269 a loop into several pieces if this can avoid the generation of guards
6271 See also the C<atomic> option.
6275 This is a single-dimensional space representing the schedule dimension(s)
6276 for which the domains should be considered ``atomic''. That is, the
6277 AST generator will make sure that any given domain space will only appear
6278 in a single loop at the specified level.
6280 Consider the following schedule
6282 { a[i] -> [i] : 0 <= i < 10;
6283 b[i] -> [i+1] : 0 <= i < 10 }
6285 If the following option is specified
6287 { [i] -> separate[x] }
6289 then the following AST will be generated
6293 for (int c0 = 1; c0 <= 9; c0 += 1) {
6300 If, on the other hand, the following option is specified
6302 { [i] -> atomic[x] }
6304 then the following AST will be generated
6306 for (int c0 = 0; c0 <= 10; c0 += 1) {
6313 If neither C<atomic> nor C<separate> is specified, then the AST generator
6314 may produce either of these two results or some intermediate form.
6318 This is a single-dimensional space representing the schedule dimension(s)
6319 that should be I<completely> unrolled.
6320 To obtain a partial unrolling, the user should apply an additional
6321 strip-mining to the schedule and fully unroll the inner loop.
6325 Additional control is available through the following functions.
6327 #include <isl/ast_build.h>
6328 __isl_give isl_ast_build *
6329 isl_ast_build_set_iterators(
6330 __isl_take isl_ast_build *control,
6331 __isl_take isl_id_list *iterators);
6333 The function C<isl_ast_build_set_iterators> allows the user to
6334 specify a list of iterator C<isl_id>s to be used as iterators.
6335 If the input schedule is injective, then
6336 the number of elements in this list should be as large as the dimension
6337 of the schedule space, but no direct correspondence should be assumed
6338 between dimensions and elements.
6339 If the input schedule is not injective, then an additional number
6340 of C<isl_id>s equal to the largest dimension of the input domains
6342 If the number of provided C<isl_id>s is insufficient, then additional
6343 names are automatically generated.
6345 #include <isl/ast_build.h>
6346 __isl_give isl_ast_build *
6347 isl_ast_build_set_create_leaf(
6348 __isl_take isl_ast_build *control,
6349 __isl_give isl_ast_node *(*fn)(
6350 __isl_take isl_ast_build *build,
6351 void *user), void *user);
6354 C<isl_ast_build_set_create_leaf> function allows for the
6355 specification of a callback that should be called whenever the AST
6356 generator arrives at an element of the schedule domain.
6357 The callback should return an AST node that should be inserted
6358 at the corresponding position of the AST. The default action (when
6359 the callback is not set) is to continue generating parts of the AST to scan
6360 all the domain elements associated to the schedule domain element
6361 and to insert user nodes, ``calling'' the domain element, for each of them.
6362 The C<build> argument contains the current state of the C<isl_ast_build>.
6363 To ease nested AST generation (see L</"Nested AST Generation">),
6364 all control information that is
6365 specific to the current AST generation such as the options and
6366 the callbacks has been removed from this C<isl_ast_build>.
6367 The callback would typically return the result of a nested
6369 user defined node created using the following function.
6371 #include <isl/ast.h>
6372 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6373 __isl_take isl_ast_expr *expr);
6375 #include <isl/ast_build.h>
6376 __isl_give isl_ast_build *
6377 isl_ast_build_set_at_each_domain(
6378 __isl_take isl_ast_build *build,
6379 __isl_give isl_ast_node *(*fn)(
6380 __isl_take isl_ast_node *node,
6381 __isl_keep isl_ast_build *build,
6382 void *user), void *user);
6383 __isl_give isl_ast_build *
6384 isl_ast_build_set_before_each_for(
6385 __isl_take isl_ast_build *build,
6386 __isl_give isl_id *(*fn)(
6387 __isl_keep isl_ast_build *build,
6388 void *user), void *user);
6389 __isl_give isl_ast_build *
6390 isl_ast_build_set_after_each_for(
6391 __isl_take isl_ast_build *build,
6392 __isl_give isl_ast_node *(*fn)(
6393 __isl_take isl_ast_node *node,
6394 __isl_keep isl_ast_build *build,
6395 void *user), void *user);
6397 The callback set by C<isl_ast_build_set_at_each_domain> will
6398 be called for each domain AST node.
6399 The callbacks set by C<isl_ast_build_set_before_each_for>
6400 and C<isl_ast_build_set_after_each_for> will be called
6401 for each for AST node. The first will be called in depth-first
6402 pre-order, while the second will be called in depth-first post-order.
6403 Since C<isl_ast_build_set_before_each_for> is called before the for
6404 node is actually constructed, it is only passed an C<isl_ast_build>.
6405 The returned C<isl_id> will be added as an annotation (using
6406 C<isl_ast_node_set_annotation>) to the constructed for node.
6407 In particular, if the user has also specified an C<after_each_for>
6408 callback, then the annotation can be retrieved from the node passed to
6409 that callback using C<isl_ast_node_get_annotation>.
6410 All callbacks should C<NULL> on failure.
6411 The given C<isl_ast_build> can be used to create new
6412 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6413 or C<isl_ast_build_call_from_pw_multi_aff>.
6415 =head3 Nested AST Generation
6417 C<isl> allows the user to create an AST within the context
6418 of another AST. These nested ASTs are created using the
6419 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6420 outer AST. The C<build> argument should be an C<isl_ast_build>
6421 passed to a callback set by
6422 C<isl_ast_build_set_create_leaf>.
6423 The space of the range of the C<schedule> argument should refer
6424 to this build. In particular, the space should be a wrapped
6425 relation and the domain of this wrapped relation should be the
6426 same as that of the range of the schedule returned by
6427 C<isl_ast_build_get_schedule> below.
6428 In practice, the new schedule is typically
6429 created by calling C<isl_union_map_range_product> on the old schedule
6430 and some extra piece of the schedule.
6431 The space of the schedule domain is also available from
6432 the C<isl_ast_build>.
6434 #include <isl/ast_build.h>
6435 __isl_give isl_union_map *isl_ast_build_get_schedule(
6436 __isl_keep isl_ast_build *build);
6437 __isl_give isl_space *isl_ast_build_get_schedule_space(
6438 __isl_keep isl_ast_build *build);
6439 __isl_give isl_ast_build *isl_ast_build_restrict(
6440 __isl_take isl_ast_build *build,
6441 __isl_take isl_set *set);
6443 The C<isl_ast_build_get_schedule> function returns a (partial)
6444 schedule for the domains elements for which part of the AST still needs to
6445 be generated in the current build.
6446 In particular, the domain elements are mapped to those iterations of the loops
6447 enclosing the current point of the AST generation inside which
6448 the domain elements are executed.
6449 No direct correspondence between
6450 the input schedule and this schedule should be assumed.
6451 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6452 to create a set for C<isl_ast_build_restrict> to intersect
6453 with the current build. In particular, the set passed to
6454 C<isl_ast_build_restrict> can have additional parameters.
6455 The ids of the set dimensions in the space returned by
6456 C<isl_ast_build_get_schedule_space> correspond to the
6457 iterators of the already generated loops.
6458 The user should not rely on the ids of the output dimensions
6459 of the relations in the union relation returned by
6460 C<isl_ast_build_get_schedule> having any particular value.
6464 Although C<isl> is mainly meant to be used as a library,
6465 it also contains some basic applications that use some
6466 of the functionality of C<isl>.
6467 The input may be specified in either the L<isl format>
6468 or the L<PolyLib format>.
6470 =head2 C<isl_polyhedron_sample>
6472 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6473 an integer element of the polyhedron, if there is any.
6474 The first column in the output is the denominator and is always
6475 equal to 1. If the polyhedron contains no integer points,
6476 then a vector of length zero is printed.
6480 C<isl_pip> takes the same input as the C<example> program
6481 from the C<piplib> distribution, i.e., a set of constraints
6482 on the parameters, a line containing only -1 and finally a set
6483 of constraints on a parametric polyhedron.
6484 The coefficients of the parameters appear in the last columns
6485 (but before the final constant column).
6486 The output is the lexicographic minimum of the parametric polyhedron.
6487 As C<isl> currently does not have its own output format, the output
6488 is just a dump of the internal state.
6490 =head2 C<isl_polyhedron_minimize>
6492 C<isl_polyhedron_minimize> computes the minimum of some linear
6493 or affine objective function over the integer points in a polyhedron.
6494 If an affine objective function
6495 is given, then the constant should appear in the last column.
6497 =head2 C<isl_polytope_scan>
6499 Given a polytope, C<isl_polytope_scan> prints
6500 all integer points in the polytope.
6502 =head2 C<isl_codegen>
6504 Given a schedule, a context set and an options relation,
6505 C<isl_codegen> prints out an AST that scans the domain elements
6506 of the schedule in the order of their image(s) taking into account
6507 the constraints in the context set.