3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 __isl_give isl_val *isl_constraint_get_coefficient_val(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, int pos);
1804 int isl_constraint_involves_dims(
1805 __isl_keep isl_constraint *constraint,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1808 The explicit representations of the existentially quantified
1809 variables can be inspected using the following function.
1810 Note that the user is only allowed to use this function
1811 if the inspected set or map is the result of a call
1812 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1813 The existentially quantified variable is equal to the floor
1814 of the returned affine expression. The affine expression
1815 itself can be inspected using the functions in
1816 L<"Piecewise Quasi Affine Expressions">.
1818 __isl_give isl_aff *isl_constraint_get_div(
1819 __isl_keep isl_constraint *constraint, int pos);
1821 To obtain the constraints of a basic set or map in matrix
1822 form, use the following functions.
1824 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1825 __isl_keep isl_basic_set *bset,
1826 enum isl_dim_type c1, enum isl_dim_type c2,
1827 enum isl_dim_type c3, enum isl_dim_type c4);
1828 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1829 __isl_keep isl_basic_set *bset,
1830 enum isl_dim_type c1, enum isl_dim_type c2,
1831 enum isl_dim_type c3, enum isl_dim_type c4);
1832 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type c1,
1835 enum isl_dim_type c2, enum isl_dim_type c3,
1836 enum isl_dim_type c4, enum isl_dim_type c5);
1837 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type c1,
1840 enum isl_dim_type c2, enum isl_dim_type c3,
1841 enum isl_dim_type c4, enum isl_dim_type c5);
1843 The C<isl_dim_type> arguments dictate the order in which
1844 different kinds of variables appear in the resulting matrix
1845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1846 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1848 The number of parameters, input, output or set dimensions can
1849 be obtained using the following functions.
1851 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type);
1853 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1854 enum isl_dim_type type);
1855 unsigned isl_set_dim(__isl_keep isl_set *set,
1856 enum isl_dim_type type);
1857 unsigned isl_map_dim(__isl_keep isl_map *map,
1858 enum isl_dim_type type);
1860 To check whether the description of a set or relation depends
1861 on one or more given dimensions, it is not necessary to iterate over all
1862 constraints. Instead the following functions can be used.
1864 int isl_basic_set_involves_dims(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned first, unsigned n);
1867 int isl_set_involves_dims(__isl_keep isl_set *set,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_basic_map_involves_dims(
1870 __isl_keep isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 int isl_map_involves_dims(__isl_keep isl_map *map,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1875 Similarly, the following functions can be used to check whether
1876 a given dimension is involved in any lower or upper bound.
1878 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1880 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1881 enum isl_dim_type type, unsigned pos);
1883 Note that these functions return true even if there is a bound on
1884 the dimension on only some of the basic sets of C<set>.
1885 To check if they have a bound for all of the basic sets in C<set>,
1886 use the following functions instead.
1888 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1893 The identifiers or names of the domain and range spaces of a set
1894 or relation can be read off or set using the following functions.
1896 __isl_give isl_set *isl_set_set_tuple_id(
1897 __isl_take isl_set *set, __isl_take isl_id *id);
1898 __isl_give isl_set *isl_set_reset_tuple_id(
1899 __isl_take isl_set *set);
1900 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1901 __isl_give isl_id *isl_set_get_tuple_id(
1902 __isl_keep isl_set *set);
1903 __isl_give isl_map *isl_map_set_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 __isl_take isl_id *id);
1906 __isl_give isl_map *isl_map_reset_tuple_id(
1907 __isl_take isl_map *map, enum isl_dim_type type);
1908 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type);
1910 __isl_give isl_id *isl_map_get_tuple_id(
1911 __isl_keep isl_map *map, enum isl_dim_type type);
1913 const char *isl_basic_set_get_tuple_name(
1914 __isl_keep isl_basic_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1916 __isl_take isl_basic_set *set, const char *s);
1917 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1918 const char *isl_set_get_tuple_name(
1919 __isl_keep isl_set *set);
1920 const char *isl_basic_map_get_tuple_name(
1921 __isl_keep isl_basic_map *bmap,
1922 enum isl_dim_type type);
1923 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1924 __isl_take isl_basic_map *bmap,
1925 enum isl_dim_type type, const char *s);
1926 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1927 enum isl_dim_type type);
1928 const char *isl_map_get_tuple_name(
1929 __isl_keep isl_map *map,
1930 enum isl_dim_type type);
1932 As with C<isl_space_get_tuple_name>, the value returned points to
1933 an internal data structure.
1934 The identifiers, positions or names of individual dimensions can be
1935 read off using the following functions.
1937 __isl_give isl_id *isl_basic_set_get_dim_id(
1938 __isl_keep isl_basic_set *bset,
1939 enum isl_dim_type type, unsigned pos);
1940 __isl_give isl_set *isl_set_set_dim_id(
1941 __isl_take isl_set *set, enum isl_dim_type type,
1942 unsigned pos, __isl_take isl_id *id);
1943 int isl_set_has_dim_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, unsigned pos);
1945 __isl_give isl_id *isl_set_get_dim_id(
1946 __isl_keep isl_set *set, enum isl_dim_type type,
1948 int isl_basic_map_has_dim_id(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned pos);
1951 __isl_give isl_map *isl_map_set_dim_id(
1952 __isl_take isl_map *map, enum isl_dim_type type,
1953 unsigned pos, __isl_take isl_id *id);
1954 int isl_map_has_dim_id(__isl_keep isl_map *map,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_id *isl_map_get_dim_id(
1957 __isl_keep isl_map *map, enum isl_dim_type type,
1960 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1961 enum isl_dim_type type, __isl_keep isl_id *id);
1962 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1963 enum isl_dim_type type, __isl_keep isl_id *id);
1964 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1965 enum isl_dim_type type, const char *name);
1966 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, const char *name);
1969 const char *isl_constraint_get_dim_name(
1970 __isl_keep isl_constraint *constraint,
1971 enum isl_dim_type type, unsigned pos);
1972 const char *isl_basic_set_get_dim_name(
1973 __isl_keep isl_basic_set *bset,
1974 enum isl_dim_type type, unsigned pos);
1975 int isl_set_has_dim_name(__isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_set_get_dim_name(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 const char *isl_basic_map_get_dim_name(
1981 __isl_keep isl_basic_map *bmap,
1982 enum isl_dim_type type, unsigned pos);
1983 int isl_map_has_dim_name(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 const char *isl_map_get_dim_name(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 These functions are mostly useful to obtain the identifiers, positions
1990 or names of the parameters. Identifiers of individual dimensions are
1991 essentially only useful for printing. They are ignored by all other
1992 operations and may not be preserved across those operations.
1996 =head3 Unary Properties
2002 The following functions test whether the given set or relation
2003 contains any integer points. The ``plain'' variants do not perform
2004 any computations, but simply check if the given set or relation
2005 is already known to be empty.
2007 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2009 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2010 int isl_set_is_empty(__isl_keep isl_set *set);
2011 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2012 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2014 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2015 int isl_map_is_empty(__isl_keep isl_map *map);
2016 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2018 =item * Universality
2020 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2021 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2022 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2024 =item * Single-valuedness
2026 int isl_basic_map_is_single_valued(
2027 __isl_keep isl_basic_map *bmap);
2028 int isl_map_plain_is_single_valued(
2029 __isl_keep isl_map *map);
2030 int isl_map_is_single_valued(__isl_keep isl_map *map);
2031 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2035 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2036 int isl_map_is_injective(__isl_keep isl_map *map);
2037 int isl_union_map_plain_is_injective(
2038 __isl_keep isl_union_map *umap);
2039 int isl_union_map_is_injective(
2040 __isl_keep isl_union_map *umap);
2044 int isl_map_is_bijective(__isl_keep isl_map *map);
2045 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2049 int isl_basic_map_plain_is_fixed(
2050 __isl_keep isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2054 enum isl_dim_type type, unsigned pos,
2056 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2057 enum isl_dim_type type, unsigned pos,
2060 Check if the relation obviously lies on a hyperplane where the given dimension
2061 has a fixed value and if so, return that value in C<*val>.
2065 To check whether a set is a parameter domain, use this function:
2067 int isl_set_is_params(__isl_keep isl_set *set);
2068 int isl_union_set_is_params(
2069 __isl_keep isl_union_set *uset);
2073 The following functions check whether the domain of the given
2074 (basic) set is a wrapped relation.
2076 int isl_basic_set_is_wrapping(
2077 __isl_keep isl_basic_set *bset);
2078 int isl_set_is_wrapping(__isl_keep isl_set *set);
2080 =item * Internal Product
2082 int isl_basic_map_can_zip(
2083 __isl_keep isl_basic_map *bmap);
2084 int isl_map_can_zip(__isl_keep isl_map *map);
2086 Check whether the product of domain and range of the given relation
2088 i.e., whether both domain and range are nested relations.
2092 int isl_basic_map_can_curry(
2093 __isl_keep isl_basic_map *bmap);
2094 int isl_map_can_curry(__isl_keep isl_map *map);
2096 Check whether the domain of the (basic) relation is a wrapped relation.
2098 int isl_basic_map_can_uncurry(
2099 __isl_keep isl_basic_map *bmap);
2100 int isl_map_can_uncurry(__isl_keep isl_map *map);
2102 Check whether the range of the (basic) relation is a wrapped relation.
2106 =head3 Binary Properties
2112 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_set_is_equal(__isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_equal(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_equal(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_equal(__isl_keep isl_map *map1,
2123 __isl_keep isl_map *map2);
2124 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2125 __isl_keep isl_map *map2);
2126 int isl_union_map_is_equal(
2127 __isl_keep isl_union_map *umap1,
2128 __isl_keep isl_union_map *umap2);
2130 =item * Disjointness
2132 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2133 __isl_keep isl_set *set2);
2134 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2135 __isl_keep isl_set *set2);
2136 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2141 int isl_basic_set_is_subset(
2142 __isl_keep isl_basic_set *bset1,
2143 __isl_keep isl_basic_set *bset2);
2144 int isl_set_is_subset(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_set_is_strict_subset(
2147 __isl_keep isl_set *set1,
2148 __isl_keep isl_set *set2);
2149 int isl_union_set_is_subset(
2150 __isl_keep isl_union_set *uset1,
2151 __isl_keep isl_union_set *uset2);
2152 int isl_union_set_is_strict_subset(
2153 __isl_keep isl_union_set *uset1,
2154 __isl_keep isl_union_set *uset2);
2155 int isl_basic_map_is_subset(
2156 __isl_keep isl_basic_map *bmap1,
2157 __isl_keep isl_basic_map *bmap2);
2158 int isl_basic_map_is_strict_subset(
2159 __isl_keep isl_basic_map *bmap1,
2160 __isl_keep isl_basic_map *bmap2);
2161 int isl_map_is_subset(
2162 __isl_keep isl_map *map1,
2163 __isl_keep isl_map *map2);
2164 int isl_map_is_strict_subset(
2165 __isl_keep isl_map *map1,
2166 __isl_keep isl_map *map2);
2167 int isl_union_map_is_subset(
2168 __isl_keep isl_union_map *umap1,
2169 __isl_keep isl_union_map *umap2);
2170 int isl_union_map_is_strict_subset(
2171 __isl_keep isl_union_map *umap1,
2172 __isl_keep isl_union_map *umap2);
2174 Check whether the first argument is a (strict) subset of the
2179 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2180 __isl_keep isl_set *set2);
2182 This function is useful for sorting C<isl_set>s.
2183 The order depends on the internal representation of the inputs.
2184 The order is fixed over different calls to the function (assuming
2185 the internal representation of the inputs has not changed), but may
2186 change over different versions of C<isl>.
2190 =head2 Unary Operations
2196 __isl_give isl_set *isl_set_complement(
2197 __isl_take isl_set *set);
2198 __isl_give isl_map *isl_map_complement(
2199 __isl_take isl_map *map);
2203 __isl_give isl_basic_map *isl_basic_map_reverse(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_map *isl_map_reverse(
2206 __isl_take isl_map *map);
2207 __isl_give isl_union_map *isl_union_map_reverse(
2208 __isl_take isl_union_map *umap);
2212 __isl_give isl_basic_set *isl_basic_set_project_out(
2213 __isl_take isl_basic_set *bset,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_map *isl_basic_map_project_out(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned first, unsigned n);
2218 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned first, unsigned n);
2220 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2221 enum isl_dim_type type, unsigned first, unsigned n);
2222 __isl_give isl_basic_set *isl_basic_set_params(
2223 __isl_take isl_basic_set *bset);
2224 __isl_give isl_basic_set *isl_basic_map_domain(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_set *isl_basic_map_range(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2229 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2230 __isl_give isl_set *isl_map_domain(
2231 __isl_take isl_map *bmap);
2232 __isl_give isl_set *isl_map_range(
2233 __isl_take isl_map *map);
2234 __isl_give isl_set *isl_union_set_params(
2235 __isl_take isl_union_set *uset);
2236 __isl_give isl_set *isl_union_map_params(
2237 __isl_take isl_union_map *umap);
2238 __isl_give isl_union_set *isl_union_map_domain(
2239 __isl_take isl_union_map *umap);
2240 __isl_give isl_union_set *isl_union_map_range(
2241 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_map_domain_map(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_basic_map *isl_basic_map_range_map(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2248 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2249 __isl_give isl_union_map *isl_union_map_domain_map(
2250 __isl_take isl_union_map *umap);
2251 __isl_give isl_union_map *isl_union_map_range_map(
2252 __isl_take isl_union_map *umap);
2254 The functions above construct a (basic, regular or union) relation
2255 that maps (a wrapped version of) the input relation to its domain or range.
2259 __isl_give isl_basic_set *isl_basic_set_eliminate(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type type,
2262 unsigned first, unsigned n);
2263 __isl_give isl_set *isl_set_eliminate(
2264 __isl_take isl_set *set, enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_basic_map *isl_basic_map_eliminate(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type,
2269 unsigned first, unsigned n);
2270 __isl_give isl_map *isl_map_eliminate(
2271 __isl_take isl_map *map, enum isl_dim_type type,
2272 unsigned first, unsigned n);
2274 Eliminate the coefficients for the given dimensions from the constraints,
2275 without removing the dimensions.
2279 __isl_give isl_basic_set *isl_basic_set_fix(
2280 __isl_take isl_basic_set *bset,
2281 enum isl_dim_type type, unsigned pos,
2283 __isl_give isl_basic_set *isl_basic_set_fix_si(
2284 __isl_take isl_basic_set *bset,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_basic_set *isl_basic_set_fix_val(
2287 __isl_take isl_basic_set *bset,
2288 enum isl_dim_type type, unsigned pos,
2289 __isl_take isl_val *v);
2290 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2291 enum isl_dim_type type, unsigned pos,
2293 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2294 enum isl_dim_type type, unsigned pos, int value);
2295 __isl_give isl_set *isl_set_fix_val(
2296 __isl_take isl_set *set,
2297 enum isl_dim_type type, unsigned pos,
2298 __isl_take isl_val *v);
2299 __isl_give isl_basic_map *isl_basic_map_fix_si(
2300 __isl_take isl_basic_map *bmap,
2301 enum isl_dim_type type, unsigned pos, int value);
2302 __isl_give isl_basic_map *isl_basic_map_fix_val(
2303 __isl_take isl_basic_map *bmap,
2304 enum isl_dim_type type, unsigned pos,
2305 __isl_take isl_val *v);
2306 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2307 enum isl_dim_type type, unsigned pos,
2309 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2310 enum isl_dim_type type, unsigned pos, int value);
2311 __isl_give isl_map *isl_map_fix_val(
2312 __isl_take isl_map *map,
2313 enum isl_dim_type type, unsigned pos,
2314 __isl_take isl_val *v);
2316 Intersect the set or relation with the hyperplane where the given
2317 dimension has the fixed given value.
2319 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2320 __isl_take isl_basic_map *bmap,
2321 enum isl_dim_type type, unsigned pos, int value);
2322 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2323 __isl_take isl_basic_map *bmap,
2324 enum isl_dim_type type, unsigned pos, int value);
2325 __isl_give isl_set *isl_set_lower_bound(
2326 __isl_take isl_set *set,
2327 enum isl_dim_type type, unsigned pos,
2329 __isl_give isl_set *isl_set_lower_bound_si(
2330 __isl_take isl_set *set,
2331 enum isl_dim_type type, unsigned pos, int value);
2332 __isl_give isl_map *isl_map_lower_bound_si(
2333 __isl_take isl_map *map,
2334 enum isl_dim_type type, unsigned pos, int value);
2335 __isl_give isl_set *isl_set_upper_bound(
2336 __isl_take isl_set *set,
2337 enum isl_dim_type type, unsigned pos,
2339 __isl_give isl_set *isl_set_upper_bound_si(
2340 __isl_take isl_set *set,
2341 enum isl_dim_type type, unsigned pos, int value);
2342 __isl_give isl_map *isl_map_upper_bound_si(
2343 __isl_take isl_map *map,
2344 enum isl_dim_type type, unsigned pos, int value);
2346 Intersect the set or relation with the half-space where the given
2347 dimension has a value bounded by the fixed given value.
2349 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2350 enum isl_dim_type type1, int pos1,
2351 enum isl_dim_type type2, int pos2);
2352 __isl_give isl_basic_map *isl_basic_map_equate(
2353 __isl_take isl_basic_map *bmap,
2354 enum isl_dim_type type1, int pos1,
2355 enum isl_dim_type type2, int pos2);
2356 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2357 enum isl_dim_type type1, int pos1,
2358 enum isl_dim_type type2, int pos2);
2360 Intersect the set or relation with the hyperplane where the given
2361 dimensions are equal to each other.
2363 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2364 enum isl_dim_type type1, int pos1,
2365 enum isl_dim_type type2, int pos2);
2367 Intersect the relation with the hyperplane where the given
2368 dimensions have opposite values.
2370 __isl_give isl_basic_map *isl_basic_map_order_ge(
2371 __isl_take isl_basic_map *bmap,
2372 enum isl_dim_type type1, int pos1,
2373 enum isl_dim_type type2, int pos2);
2374 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2375 enum isl_dim_type type1, int pos1,
2376 enum isl_dim_type type2, int pos2);
2377 __isl_give isl_basic_map *isl_basic_map_order_gt(
2378 __isl_take isl_basic_map *bmap,
2379 enum isl_dim_type type1, int pos1,
2380 enum isl_dim_type type2, int pos2);
2381 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2382 enum isl_dim_type type1, int pos1,
2383 enum isl_dim_type type2, int pos2);
2385 Intersect the relation with the half-space where the given
2386 dimensions satisfy the given ordering.
2390 __isl_give isl_map *isl_set_identity(
2391 __isl_take isl_set *set);
2392 __isl_give isl_union_map *isl_union_set_identity(
2393 __isl_take isl_union_set *uset);
2395 Construct an identity relation on the given (union) set.
2399 __isl_give isl_basic_set *isl_basic_map_deltas(
2400 __isl_take isl_basic_map *bmap);
2401 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2402 __isl_give isl_union_set *isl_union_map_deltas(
2403 __isl_take isl_union_map *umap);
2405 These functions return a (basic) set containing the differences
2406 between image elements and corresponding domain elements in the input.
2408 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2409 __isl_take isl_basic_map *bmap);
2410 __isl_give isl_map *isl_map_deltas_map(
2411 __isl_take isl_map *map);
2412 __isl_give isl_union_map *isl_union_map_deltas_map(
2413 __isl_take isl_union_map *umap);
2415 The functions above construct a (basic, regular or union) relation
2416 that maps (a wrapped version of) the input relation to its delta set.
2420 Simplify the representation of a set or relation by trying
2421 to combine pairs of basic sets or relations into a single
2422 basic set or relation.
2424 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2425 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2426 __isl_give isl_union_set *isl_union_set_coalesce(
2427 __isl_take isl_union_set *uset);
2428 __isl_give isl_union_map *isl_union_map_coalesce(
2429 __isl_take isl_union_map *umap);
2431 One of the methods for combining pairs of basic sets or relations
2432 can result in coefficients that are much larger than those that appear
2433 in the constraints of the input. By default, the coefficients are
2434 not allowed to grow larger, but this can be changed by unsetting
2435 the following option.
2437 int isl_options_set_coalesce_bounded_wrapping(
2438 isl_ctx *ctx, int val);
2439 int isl_options_get_coalesce_bounded_wrapping(
2442 =item * Detecting equalities
2444 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2445 __isl_take isl_basic_set *bset);
2446 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2447 __isl_take isl_basic_map *bmap);
2448 __isl_give isl_set *isl_set_detect_equalities(
2449 __isl_take isl_set *set);
2450 __isl_give isl_map *isl_map_detect_equalities(
2451 __isl_take isl_map *map);
2452 __isl_give isl_union_set *isl_union_set_detect_equalities(
2453 __isl_take isl_union_set *uset);
2454 __isl_give isl_union_map *isl_union_map_detect_equalities(
2455 __isl_take isl_union_map *umap);
2457 Simplify the representation of a set or relation by detecting implicit
2460 =item * Removing redundant constraints
2462 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2463 __isl_take isl_basic_set *bset);
2464 __isl_give isl_set *isl_set_remove_redundancies(
2465 __isl_take isl_set *set);
2466 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2467 __isl_take isl_basic_map *bmap);
2468 __isl_give isl_map *isl_map_remove_redundancies(
2469 __isl_take isl_map *map);
2473 __isl_give isl_basic_set *isl_set_convex_hull(
2474 __isl_take isl_set *set);
2475 __isl_give isl_basic_map *isl_map_convex_hull(
2476 __isl_take isl_map *map);
2478 If the input set or relation has any existentially quantified
2479 variables, then the result of these operations is currently undefined.
2483 __isl_give isl_basic_set *
2484 isl_set_unshifted_simple_hull(
2485 __isl_take isl_set *set);
2486 __isl_give isl_basic_map *
2487 isl_map_unshifted_simple_hull(
2488 __isl_take isl_map *map);
2489 __isl_give isl_basic_set *isl_set_simple_hull(
2490 __isl_take isl_set *set);
2491 __isl_give isl_basic_map *isl_map_simple_hull(
2492 __isl_take isl_map *map);
2493 __isl_give isl_union_map *isl_union_map_simple_hull(
2494 __isl_take isl_union_map *umap);
2496 These functions compute a single basic set or relation
2497 that contains the whole input set or relation.
2498 In particular, the output is described by translates
2499 of the constraints describing the basic sets or relations in the input.
2500 In case of C<isl_set_unshifted_simple_hull>, only the original
2501 constraints are used, without any translation.
2505 (See \autoref{s:simple hull}.)
2511 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2512 __isl_take isl_basic_set *bset);
2513 __isl_give isl_basic_set *isl_set_affine_hull(
2514 __isl_take isl_set *set);
2515 __isl_give isl_union_set *isl_union_set_affine_hull(
2516 __isl_take isl_union_set *uset);
2517 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2518 __isl_take isl_basic_map *bmap);
2519 __isl_give isl_basic_map *isl_map_affine_hull(
2520 __isl_take isl_map *map);
2521 __isl_give isl_union_map *isl_union_map_affine_hull(
2522 __isl_take isl_union_map *umap);
2524 In case of union sets and relations, the affine hull is computed
2527 =item * Polyhedral hull
2529 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2530 __isl_take isl_set *set);
2531 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2532 __isl_take isl_map *map);
2533 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2534 __isl_take isl_union_set *uset);
2535 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2536 __isl_take isl_union_map *umap);
2538 These functions compute a single basic set or relation
2539 not involving any existentially quantified variables
2540 that contains the whole input set or relation.
2541 In case of union sets and relations, the polyhedral hull is computed
2544 =item * Other approximations
2546 __isl_give isl_basic_set *
2547 isl_basic_set_drop_constraints_involving_dims(
2548 __isl_take isl_basic_set *bset,
2549 enum isl_dim_type type,
2550 unsigned first, unsigned n);
2551 __isl_give isl_basic_map *
2552 isl_basic_map_drop_constraints_involving_dims(
2553 __isl_take isl_basic_map *bmap,
2554 enum isl_dim_type type,
2555 unsigned first, unsigned n);
2556 __isl_give isl_basic_set *
2557 isl_basic_set_drop_constraints_not_involving_dims(
2558 __isl_take isl_basic_set *bset,
2559 enum isl_dim_type type,
2560 unsigned first, unsigned n);
2561 __isl_give isl_set *
2562 isl_set_drop_constraints_involving_dims(
2563 __isl_take isl_set *set,
2564 enum isl_dim_type type,
2565 unsigned first, unsigned n);
2566 __isl_give isl_map *
2567 isl_map_drop_constraints_involving_dims(
2568 __isl_take isl_map *map,
2569 enum isl_dim_type type,
2570 unsigned first, unsigned n);
2572 These functions drop any constraints (not) involving the specified dimensions.
2573 Note that the result depends on the representation of the input.
2577 __isl_give isl_basic_set *isl_basic_set_sample(
2578 __isl_take isl_basic_set *bset);
2579 __isl_give isl_basic_set *isl_set_sample(
2580 __isl_take isl_set *set);
2581 __isl_give isl_basic_map *isl_basic_map_sample(
2582 __isl_take isl_basic_map *bmap);
2583 __isl_give isl_basic_map *isl_map_sample(
2584 __isl_take isl_map *map);
2586 If the input (basic) set or relation is non-empty, then return
2587 a singleton subset of the input. Otherwise, return an empty set.
2589 =item * Optimization
2591 #include <isl/ilp.h>
2592 enum isl_lp_result isl_basic_set_max(
2593 __isl_keep isl_basic_set *bset,
2594 __isl_keep isl_aff *obj, isl_int *opt)
2595 __isl_give isl_val *isl_basic_set_max_val(
2596 __isl_keep isl_basic_set *bset,
2597 __isl_keep isl_aff *obj);
2598 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2599 __isl_keep isl_aff *obj, isl_int *opt);
2600 __isl_give isl_val *isl_set_min_val(
2601 __isl_keep isl_set *set,
2602 __isl_keep isl_aff *obj);
2603 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2604 __isl_keep isl_aff *obj, isl_int *opt);
2605 __isl_give isl_val *isl_set_max_val(
2606 __isl_keep isl_set *set,
2607 __isl_keep isl_aff *obj);
2609 Compute the minimum or maximum of the integer affine expression C<obj>
2610 over the points in C<set>, returning the result in C<opt>.
2611 The return value may be one of C<isl_lp_error>,
2612 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2613 an C<isl_lp_result>. If the result is an C<isl_val> then
2614 the result is C<NULL> in case of an error, the optimal value in case
2615 there is one, negative infinity or infinity if the problem is unbounded and
2616 NaN if the problem is empty.
2618 =item * Parametric optimization
2620 __isl_give isl_pw_aff *isl_set_dim_min(
2621 __isl_take isl_set *set, int pos);
2622 __isl_give isl_pw_aff *isl_set_dim_max(
2623 __isl_take isl_set *set, int pos);
2624 __isl_give isl_pw_aff *isl_map_dim_max(
2625 __isl_take isl_map *map, int pos);
2627 Compute the minimum or maximum of the given set or output dimension
2628 as a function of the parameters (and input dimensions), but independently
2629 of the other set or output dimensions.
2630 For lexicographic optimization, see L<"Lexicographic Optimization">.
2634 The following functions compute either the set of (rational) coefficient
2635 values of valid constraints for the given set or the set of (rational)
2636 values satisfying the constraints with coefficients from the given set.
2637 Internally, these two sets of functions perform essentially the
2638 same operations, except that the set of coefficients is assumed to
2639 be a cone, while the set of values may be any polyhedron.
2640 The current implementation is based on the Farkas lemma and
2641 Fourier-Motzkin elimination, but this may change or be made optional
2642 in future. In particular, future implementations may use different
2643 dualization algorithms or skip the elimination step.
2645 __isl_give isl_basic_set *isl_basic_set_coefficients(
2646 __isl_take isl_basic_set *bset);
2647 __isl_give isl_basic_set *isl_set_coefficients(
2648 __isl_take isl_set *set);
2649 __isl_give isl_union_set *isl_union_set_coefficients(
2650 __isl_take isl_union_set *bset);
2651 __isl_give isl_basic_set *isl_basic_set_solutions(
2652 __isl_take isl_basic_set *bset);
2653 __isl_give isl_basic_set *isl_set_solutions(
2654 __isl_take isl_set *set);
2655 __isl_give isl_union_set *isl_union_set_solutions(
2656 __isl_take isl_union_set *bset);
2660 __isl_give isl_map *isl_map_fixed_power(
2661 __isl_take isl_map *map, isl_int exp);
2662 __isl_give isl_union_map *isl_union_map_fixed_power(
2663 __isl_take isl_union_map *umap, isl_int exp);
2665 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2666 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2667 of C<map> is computed.
2669 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2671 __isl_give isl_union_map *isl_union_map_power(
2672 __isl_take isl_union_map *umap, int *exact);
2674 Compute a parametric representation for all positive powers I<k> of C<map>.
2675 The result maps I<k> to a nested relation corresponding to the
2676 I<k>th power of C<map>.
2677 The result may be an overapproximation. If the result is known to be exact,
2678 then C<*exact> is set to C<1>.
2680 =item * Transitive closure
2682 __isl_give isl_map *isl_map_transitive_closure(
2683 __isl_take isl_map *map, int *exact);
2684 __isl_give isl_union_map *isl_union_map_transitive_closure(
2685 __isl_take isl_union_map *umap, int *exact);
2687 Compute the transitive closure of C<map>.
2688 The result may be an overapproximation. If the result is known to be exact,
2689 then C<*exact> is set to C<1>.
2691 =item * Reaching path lengths
2693 __isl_give isl_map *isl_map_reaching_path_lengths(
2694 __isl_take isl_map *map, int *exact);
2696 Compute a relation that maps each element in the range of C<map>
2697 to the lengths of all paths composed of edges in C<map> that
2698 end up in the given element.
2699 The result may be an overapproximation. If the result is known to be exact,
2700 then C<*exact> is set to C<1>.
2701 To compute the I<maximal> path length, the resulting relation
2702 should be postprocessed by C<isl_map_lexmax>.
2703 In particular, if the input relation is a dependence relation
2704 (mapping sources to sinks), then the maximal path length corresponds
2705 to the free schedule.
2706 Note, however, that C<isl_map_lexmax> expects the maximum to be
2707 finite, so if the path lengths are unbounded (possibly due to
2708 the overapproximation), then you will get an error message.
2712 __isl_give isl_basic_set *isl_basic_map_wrap(
2713 __isl_take isl_basic_map *bmap);
2714 __isl_give isl_set *isl_map_wrap(
2715 __isl_take isl_map *map);
2716 __isl_give isl_union_set *isl_union_map_wrap(
2717 __isl_take isl_union_map *umap);
2718 __isl_give isl_basic_map *isl_basic_set_unwrap(
2719 __isl_take isl_basic_set *bset);
2720 __isl_give isl_map *isl_set_unwrap(
2721 __isl_take isl_set *set);
2722 __isl_give isl_union_map *isl_union_set_unwrap(
2723 __isl_take isl_union_set *uset);
2727 Remove any internal structure of domain (and range) of the given
2728 set or relation. If there is any such internal structure in the input,
2729 then the name of the space is also removed.
2731 __isl_give isl_basic_set *isl_basic_set_flatten(
2732 __isl_take isl_basic_set *bset);
2733 __isl_give isl_set *isl_set_flatten(
2734 __isl_take isl_set *set);
2735 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2736 __isl_take isl_basic_map *bmap);
2737 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2738 __isl_take isl_basic_map *bmap);
2739 __isl_give isl_map *isl_map_flatten_range(
2740 __isl_take isl_map *map);
2741 __isl_give isl_map *isl_map_flatten_domain(
2742 __isl_take isl_map *map);
2743 __isl_give isl_basic_map *isl_basic_map_flatten(
2744 __isl_take isl_basic_map *bmap);
2745 __isl_give isl_map *isl_map_flatten(
2746 __isl_take isl_map *map);
2748 __isl_give isl_map *isl_set_flatten_map(
2749 __isl_take isl_set *set);
2751 The function above constructs a relation
2752 that maps the input set to a flattened version of the set.
2756 Lift the input set to a space with extra dimensions corresponding
2757 to the existentially quantified variables in the input.
2758 In particular, the result lives in a wrapped map where the domain
2759 is the original space and the range corresponds to the original
2760 existentially quantified variables.
2762 __isl_give isl_basic_set *isl_basic_set_lift(
2763 __isl_take isl_basic_set *bset);
2764 __isl_give isl_set *isl_set_lift(
2765 __isl_take isl_set *set);
2766 __isl_give isl_union_set *isl_union_set_lift(
2767 __isl_take isl_union_set *uset);
2769 Given a local space that contains the existentially quantified
2770 variables of a set, a basic relation that, when applied to
2771 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2772 can be constructed using the following function.
2774 #include <isl/local_space.h>
2775 __isl_give isl_basic_map *isl_local_space_lifting(
2776 __isl_take isl_local_space *ls);
2778 =item * Internal Product
2780 __isl_give isl_basic_map *isl_basic_map_zip(
2781 __isl_take isl_basic_map *bmap);
2782 __isl_give isl_map *isl_map_zip(
2783 __isl_take isl_map *map);
2784 __isl_give isl_union_map *isl_union_map_zip(
2785 __isl_take isl_union_map *umap);
2787 Given a relation with nested relations for domain and range,
2788 interchange the range of the domain with the domain of the range.
2792 __isl_give isl_basic_map *isl_basic_map_curry(
2793 __isl_take isl_basic_map *bmap);
2794 __isl_give isl_basic_map *isl_basic_map_uncurry(
2795 __isl_take isl_basic_map *bmap);
2796 __isl_give isl_map *isl_map_curry(
2797 __isl_take isl_map *map);
2798 __isl_give isl_map *isl_map_uncurry(
2799 __isl_take isl_map *map);
2800 __isl_give isl_union_map *isl_union_map_curry(
2801 __isl_take isl_union_map *umap);
2802 __isl_give isl_union_map *isl_union_map_uncurry(
2803 __isl_take isl_union_map *umap);
2805 Given a relation with a nested relation for domain,
2806 the C<curry> functions
2807 move the range of the nested relation out of the domain
2808 and use it as the domain of a nested relation in the range,
2809 with the original range as range of this nested relation.
2810 The C<uncurry> functions perform the inverse operation.
2812 =item * Aligning parameters
2814 __isl_give isl_basic_set *isl_basic_set_align_params(
2815 __isl_take isl_basic_set *bset,
2816 __isl_take isl_space *model);
2817 __isl_give isl_set *isl_set_align_params(
2818 __isl_take isl_set *set,
2819 __isl_take isl_space *model);
2820 __isl_give isl_basic_map *isl_basic_map_align_params(
2821 __isl_take isl_basic_map *bmap,
2822 __isl_take isl_space *model);
2823 __isl_give isl_map *isl_map_align_params(
2824 __isl_take isl_map *map,
2825 __isl_take isl_space *model);
2827 Change the order of the parameters of the given set or relation
2828 such that the first parameters match those of C<model>.
2829 This may involve the introduction of extra parameters.
2830 All parameters need to be named.
2832 =item * Dimension manipulation
2834 __isl_give isl_basic_set *isl_basic_set_add_dims(
2835 __isl_take isl_basic_set *bset,
2836 enum isl_dim_type type, unsigned n);
2837 __isl_give isl_set *isl_set_add_dims(
2838 __isl_take isl_set *set,
2839 enum isl_dim_type type, unsigned n);
2840 __isl_give isl_map *isl_map_add_dims(
2841 __isl_take isl_map *map,
2842 enum isl_dim_type type, unsigned n);
2843 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2844 __isl_take isl_basic_set *bset,
2845 enum isl_dim_type type, unsigned pos,
2847 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2848 __isl_take isl_basic_map *bmap,
2849 enum isl_dim_type type, unsigned pos,
2851 __isl_give isl_set *isl_set_insert_dims(
2852 __isl_take isl_set *set,
2853 enum isl_dim_type type, unsigned pos, unsigned n);
2854 __isl_give isl_map *isl_map_insert_dims(
2855 __isl_take isl_map *map,
2856 enum isl_dim_type type, unsigned pos, unsigned n);
2857 __isl_give isl_basic_set *isl_basic_set_move_dims(
2858 __isl_take isl_basic_set *bset,
2859 enum isl_dim_type dst_type, unsigned dst_pos,
2860 enum isl_dim_type src_type, unsigned src_pos,
2862 __isl_give isl_basic_map *isl_basic_map_move_dims(
2863 __isl_take isl_basic_map *bmap,
2864 enum isl_dim_type dst_type, unsigned dst_pos,
2865 enum isl_dim_type src_type, unsigned src_pos,
2867 __isl_give isl_set *isl_set_move_dims(
2868 __isl_take isl_set *set,
2869 enum isl_dim_type dst_type, unsigned dst_pos,
2870 enum isl_dim_type src_type, unsigned src_pos,
2872 __isl_give isl_map *isl_map_move_dims(
2873 __isl_take isl_map *map,
2874 enum isl_dim_type dst_type, unsigned dst_pos,
2875 enum isl_dim_type src_type, unsigned src_pos,
2878 It is usually not advisable to directly change the (input or output)
2879 space of a set or a relation as this removes the name and the internal
2880 structure of the space. However, the above functions can be useful
2881 to add new parameters, assuming
2882 C<isl_set_align_params> and C<isl_map_align_params>
2887 =head2 Binary Operations
2889 The two arguments of a binary operation not only need to live
2890 in the same C<isl_ctx>, they currently also need to have
2891 the same (number of) parameters.
2893 =head3 Basic Operations
2897 =item * Intersection
2899 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2900 __isl_take isl_basic_set *bset1,
2901 __isl_take isl_basic_set *bset2);
2902 __isl_give isl_basic_set *isl_basic_set_intersect(
2903 __isl_take isl_basic_set *bset1,
2904 __isl_take isl_basic_set *bset2);
2905 __isl_give isl_set *isl_set_intersect_params(
2906 __isl_take isl_set *set,
2907 __isl_take isl_set *params);
2908 __isl_give isl_set *isl_set_intersect(
2909 __isl_take isl_set *set1,
2910 __isl_take isl_set *set2);
2911 __isl_give isl_union_set *isl_union_set_intersect_params(
2912 __isl_take isl_union_set *uset,
2913 __isl_take isl_set *set);
2914 __isl_give isl_union_map *isl_union_map_intersect_params(
2915 __isl_take isl_union_map *umap,
2916 __isl_take isl_set *set);
2917 __isl_give isl_union_set *isl_union_set_intersect(
2918 __isl_take isl_union_set *uset1,
2919 __isl_take isl_union_set *uset2);
2920 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2921 __isl_take isl_basic_map *bmap,
2922 __isl_take isl_basic_set *bset);
2923 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2924 __isl_take isl_basic_map *bmap,
2925 __isl_take isl_basic_set *bset);
2926 __isl_give isl_basic_map *isl_basic_map_intersect(
2927 __isl_take isl_basic_map *bmap1,
2928 __isl_take isl_basic_map *bmap2);
2929 __isl_give isl_map *isl_map_intersect_params(
2930 __isl_take isl_map *map,
2931 __isl_take isl_set *params);
2932 __isl_give isl_map *isl_map_intersect_domain(
2933 __isl_take isl_map *map,
2934 __isl_take isl_set *set);
2935 __isl_give isl_map *isl_map_intersect_range(
2936 __isl_take isl_map *map,
2937 __isl_take isl_set *set);
2938 __isl_give isl_map *isl_map_intersect(
2939 __isl_take isl_map *map1,
2940 __isl_take isl_map *map2);
2941 __isl_give isl_union_map *isl_union_map_intersect_domain(
2942 __isl_take isl_union_map *umap,
2943 __isl_take isl_union_set *uset);
2944 __isl_give isl_union_map *isl_union_map_intersect_range(
2945 __isl_take isl_union_map *umap,
2946 __isl_take isl_union_set *uset);
2947 __isl_give isl_union_map *isl_union_map_intersect(
2948 __isl_take isl_union_map *umap1,
2949 __isl_take isl_union_map *umap2);
2951 The second argument to the C<_params> functions needs to be
2952 a parametric (basic) set. For the other functions, a parametric set
2953 for either argument is only allowed if the other argument is
2954 a parametric set as well.
2958 __isl_give isl_set *isl_basic_set_union(
2959 __isl_take isl_basic_set *bset1,
2960 __isl_take isl_basic_set *bset2);
2961 __isl_give isl_map *isl_basic_map_union(
2962 __isl_take isl_basic_map *bmap1,
2963 __isl_take isl_basic_map *bmap2);
2964 __isl_give isl_set *isl_set_union(
2965 __isl_take isl_set *set1,
2966 __isl_take isl_set *set2);
2967 __isl_give isl_map *isl_map_union(
2968 __isl_take isl_map *map1,
2969 __isl_take isl_map *map2);
2970 __isl_give isl_union_set *isl_union_set_union(
2971 __isl_take isl_union_set *uset1,
2972 __isl_take isl_union_set *uset2);
2973 __isl_give isl_union_map *isl_union_map_union(
2974 __isl_take isl_union_map *umap1,
2975 __isl_take isl_union_map *umap2);
2977 =item * Set difference
2979 __isl_give isl_set *isl_set_subtract(
2980 __isl_take isl_set *set1,
2981 __isl_take isl_set *set2);
2982 __isl_give isl_map *isl_map_subtract(
2983 __isl_take isl_map *map1,
2984 __isl_take isl_map *map2);
2985 __isl_give isl_map *isl_map_subtract_domain(
2986 __isl_take isl_map *map,
2987 __isl_take isl_set *dom);
2988 __isl_give isl_map *isl_map_subtract_range(
2989 __isl_take isl_map *map,
2990 __isl_take isl_set *dom);
2991 __isl_give isl_union_set *isl_union_set_subtract(
2992 __isl_take isl_union_set *uset1,
2993 __isl_take isl_union_set *uset2);
2994 __isl_give isl_union_map *isl_union_map_subtract(
2995 __isl_take isl_union_map *umap1,
2996 __isl_take isl_union_map *umap2);
2997 __isl_give isl_union_map *isl_union_map_subtract_domain(
2998 __isl_take isl_union_map *umap,
2999 __isl_take isl_union_set *dom);
3000 __isl_give isl_union_map *isl_union_map_subtract_range(
3001 __isl_take isl_union_map *umap,
3002 __isl_take isl_union_set *dom);
3006 __isl_give isl_basic_set *isl_basic_set_apply(
3007 __isl_take isl_basic_set *bset,
3008 __isl_take isl_basic_map *bmap);
3009 __isl_give isl_set *isl_set_apply(
3010 __isl_take isl_set *set,
3011 __isl_take isl_map *map);
3012 __isl_give isl_union_set *isl_union_set_apply(
3013 __isl_take isl_union_set *uset,
3014 __isl_take isl_union_map *umap);
3015 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3016 __isl_take isl_basic_map *bmap1,
3017 __isl_take isl_basic_map *bmap2);
3018 __isl_give isl_basic_map *isl_basic_map_apply_range(
3019 __isl_take isl_basic_map *bmap1,
3020 __isl_take isl_basic_map *bmap2);
3021 __isl_give isl_map *isl_map_apply_domain(
3022 __isl_take isl_map *map1,
3023 __isl_take isl_map *map2);
3024 __isl_give isl_union_map *isl_union_map_apply_domain(
3025 __isl_take isl_union_map *umap1,
3026 __isl_take isl_union_map *umap2);
3027 __isl_give isl_map *isl_map_apply_range(
3028 __isl_take isl_map *map1,
3029 __isl_take isl_map *map2);
3030 __isl_give isl_union_map *isl_union_map_apply_range(
3031 __isl_take isl_union_map *umap1,
3032 __isl_take isl_union_map *umap2);
3036 __isl_give isl_basic_set *
3037 isl_basic_set_preimage_multi_aff(
3038 __isl_take isl_basic_set *bset,
3039 __isl_take isl_multi_aff *ma);
3040 __isl_give isl_set *isl_set_preimage_multi_aff(
3041 __isl_take isl_set *set,
3042 __isl_take isl_multi_aff *ma);
3043 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3044 __isl_take isl_set *set,
3045 __isl_take isl_pw_multi_aff *pma);
3046 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3047 __isl_take isl_map *map,
3048 __isl_take isl_multi_aff *ma);
3049 __isl_give isl_union_map *
3050 isl_union_map_preimage_domain_multi_aff(
3051 __isl_take isl_union_map *umap,
3052 __isl_take isl_multi_aff *ma);
3054 These functions compute the preimage of the given set or map domain under
3055 the given function. In other words, the expression is plugged
3056 into the set description or into the domain of the map.
3057 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3058 L</"Piecewise Multiple Quasi Affine Expressions">.
3060 =item * Cartesian Product
3062 __isl_give isl_set *isl_set_product(
3063 __isl_take isl_set *set1,
3064 __isl_take isl_set *set2);
3065 __isl_give isl_union_set *isl_union_set_product(
3066 __isl_take isl_union_set *uset1,
3067 __isl_take isl_union_set *uset2);
3068 __isl_give isl_basic_map *isl_basic_map_domain_product(
3069 __isl_take isl_basic_map *bmap1,
3070 __isl_take isl_basic_map *bmap2);
3071 __isl_give isl_basic_map *isl_basic_map_range_product(
3072 __isl_take isl_basic_map *bmap1,
3073 __isl_take isl_basic_map *bmap2);
3074 __isl_give isl_basic_map *isl_basic_map_product(
3075 __isl_take isl_basic_map *bmap1,
3076 __isl_take isl_basic_map *bmap2);
3077 __isl_give isl_map *isl_map_domain_product(
3078 __isl_take isl_map *map1,
3079 __isl_take isl_map *map2);
3080 __isl_give isl_map *isl_map_range_product(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3083 __isl_give isl_union_map *isl_union_map_domain_product(
3084 __isl_take isl_union_map *umap1,
3085 __isl_take isl_union_map *umap2);
3086 __isl_give isl_union_map *isl_union_map_range_product(
3087 __isl_take isl_union_map *umap1,
3088 __isl_take isl_union_map *umap2);
3089 __isl_give isl_map *isl_map_product(
3090 __isl_take isl_map *map1,
3091 __isl_take isl_map *map2);
3092 __isl_give isl_union_map *isl_union_map_product(
3093 __isl_take isl_union_map *umap1,
3094 __isl_take isl_union_map *umap2);
3096 The above functions compute the cross product of the given
3097 sets or relations. The domains and ranges of the results
3098 are wrapped maps between domains and ranges of the inputs.
3099 To obtain a ``flat'' product, use the following functions
3102 __isl_give isl_basic_set *isl_basic_set_flat_product(
3103 __isl_take isl_basic_set *bset1,
3104 __isl_take isl_basic_set *bset2);
3105 __isl_give isl_set *isl_set_flat_product(
3106 __isl_take isl_set *set1,
3107 __isl_take isl_set *set2);
3108 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3109 __isl_take isl_basic_map *bmap1,
3110 __isl_take isl_basic_map *bmap2);
3111 __isl_give isl_map *isl_map_flat_domain_product(
3112 __isl_take isl_map *map1,
3113 __isl_take isl_map *map2);
3114 __isl_give isl_map *isl_map_flat_range_product(
3115 __isl_take isl_map *map1,
3116 __isl_take isl_map *map2);
3117 __isl_give isl_union_map *isl_union_map_flat_range_product(
3118 __isl_take isl_union_map *umap1,
3119 __isl_take isl_union_map *umap2);
3120 __isl_give isl_basic_map *isl_basic_map_flat_product(
3121 __isl_take isl_basic_map *bmap1,
3122 __isl_take isl_basic_map *bmap2);
3123 __isl_give isl_map *isl_map_flat_product(
3124 __isl_take isl_map *map1,
3125 __isl_take isl_map *map2);
3127 =item * Simplification
3129 __isl_give isl_basic_set *isl_basic_set_gist(
3130 __isl_take isl_basic_set *bset,
3131 __isl_take isl_basic_set *context);
3132 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3133 __isl_take isl_set *context);
3134 __isl_give isl_set *isl_set_gist_params(
3135 __isl_take isl_set *set,
3136 __isl_take isl_set *context);
3137 __isl_give isl_union_set *isl_union_set_gist(
3138 __isl_take isl_union_set *uset,
3139 __isl_take isl_union_set *context);
3140 __isl_give isl_union_set *isl_union_set_gist_params(
3141 __isl_take isl_union_set *uset,
3142 __isl_take isl_set *set);
3143 __isl_give isl_basic_map *isl_basic_map_gist(
3144 __isl_take isl_basic_map *bmap,
3145 __isl_take isl_basic_map *context);
3146 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3147 __isl_take isl_map *context);
3148 __isl_give isl_map *isl_map_gist_params(
3149 __isl_take isl_map *map,
3150 __isl_take isl_set *context);
3151 __isl_give isl_map *isl_map_gist_domain(
3152 __isl_take isl_map *map,
3153 __isl_take isl_set *context);
3154 __isl_give isl_map *isl_map_gist_range(
3155 __isl_take isl_map *map,
3156 __isl_take isl_set *context);
3157 __isl_give isl_union_map *isl_union_map_gist(
3158 __isl_take isl_union_map *umap,
3159 __isl_take isl_union_map *context);
3160 __isl_give isl_union_map *isl_union_map_gist_params(
3161 __isl_take isl_union_map *umap,
3162 __isl_take isl_set *set);
3163 __isl_give isl_union_map *isl_union_map_gist_domain(
3164 __isl_take isl_union_map *umap,
3165 __isl_take isl_union_set *uset);
3166 __isl_give isl_union_map *isl_union_map_gist_range(
3167 __isl_take isl_union_map *umap,
3168 __isl_take isl_union_set *uset);
3170 The gist operation returns a set or relation that has the
3171 same intersection with the context as the input set or relation.
3172 Any implicit equality in the intersection is made explicit in the result,
3173 while all inequalities that are redundant with respect to the intersection
3175 In case of union sets and relations, the gist operation is performed
3180 =head3 Lexicographic Optimization
3182 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3183 the following functions
3184 compute a set that contains the lexicographic minimum or maximum
3185 of the elements in C<set> (or C<bset>) for those values of the parameters
3186 that satisfy C<dom>.
3187 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3188 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3190 In other words, the union of the parameter values
3191 for which the result is non-empty and of C<*empty>
3194 __isl_give isl_set *isl_basic_set_partial_lexmin(
3195 __isl_take isl_basic_set *bset,
3196 __isl_take isl_basic_set *dom,
3197 __isl_give isl_set **empty);
3198 __isl_give isl_set *isl_basic_set_partial_lexmax(
3199 __isl_take isl_basic_set *bset,
3200 __isl_take isl_basic_set *dom,
3201 __isl_give isl_set **empty);
3202 __isl_give isl_set *isl_set_partial_lexmin(
3203 __isl_take isl_set *set, __isl_take isl_set *dom,
3204 __isl_give isl_set **empty);
3205 __isl_give isl_set *isl_set_partial_lexmax(
3206 __isl_take isl_set *set, __isl_take isl_set *dom,
3207 __isl_give isl_set **empty);
3209 Given a (basic) set C<set> (or C<bset>), the following functions simply
3210 return a set containing the lexicographic minimum or maximum
3211 of the elements in C<set> (or C<bset>).
3212 In case of union sets, the optimum is computed per space.
3214 __isl_give isl_set *isl_basic_set_lexmin(
3215 __isl_take isl_basic_set *bset);
3216 __isl_give isl_set *isl_basic_set_lexmax(
3217 __isl_take isl_basic_set *bset);
3218 __isl_give isl_set *isl_set_lexmin(
3219 __isl_take isl_set *set);
3220 __isl_give isl_set *isl_set_lexmax(
3221 __isl_take isl_set *set);
3222 __isl_give isl_union_set *isl_union_set_lexmin(
3223 __isl_take isl_union_set *uset);
3224 __isl_give isl_union_set *isl_union_set_lexmax(
3225 __isl_take isl_union_set *uset);
3227 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3228 the following functions
3229 compute a relation that maps each element of C<dom>
3230 to the single lexicographic minimum or maximum
3231 of the elements that are associated to that same
3232 element in C<map> (or C<bmap>).
3233 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3234 that contains the elements in C<dom> that do not map
3235 to any elements in C<map> (or C<bmap>).
3236 In other words, the union of the domain of the result and of C<*empty>
3239 __isl_give isl_map *isl_basic_map_partial_lexmax(
3240 __isl_take isl_basic_map *bmap,
3241 __isl_take isl_basic_set *dom,
3242 __isl_give isl_set **empty);
3243 __isl_give isl_map *isl_basic_map_partial_lexmin(
3244 __isl_take isl_basic_map *bmap,
3245 __isl_take isl_basic_set *dom,
3246 __isl_give isl_set **empty);
3247 __isl_give isl_map *isl_map_partial_lexmax(
3248 __isl_take isl_map *map, __isl_take isl_set *dom,
3249 __isl_give isl_set **empty);
3250 __isl_give isl_map *isl_map_partial_lexmin(
3251 __isl_take isl_map *map, __isl_take isl_set *dom,
3252 __isl_give isl_set **empty);
3254 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3255 return a map mapping each element in the domain of
3256 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3257 of all elements associated to that element.
3258 In case of union relations, the optimum is computed per space.
3260 __isl_give isl_map *isl_basic_map_lexmin(
3261 __isl_take isl_basic_map *bmap);
3262 __isl_give isl_map *isl_basic_map_lexmax(
3263 __isl_take isl_basic_map *bmap);
3264 __isl_give isl_map *isl_map_lexmin(
3265 __isl_take isl_map *map);
3266 __isl_give isl_map *isl_map_lexmax(
3267 __isl_take isl_map *map);
3268 __isl_give isl_union_map *isl_union_map_lexmin(
3269 __isl_take isl_union_map *umap);
3270 __isl_give isl_union_map *isl_union_map_lexmax(
3271 __isl_take isl_union_map *umap);
3273 The following functions return their result in the form of
3274 a piecewise multi-affine expression
3275 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3276 but are otherwise equivalent to the corresponding functions
3277 returning a basic set or relation.
3279 __isl_give isl_pw_multi_aff *
3280 isl_basic_map_lexmin_pw_multi_aff(
3281 __isl_take isl_basic_map *bmap);
3282 __isl_give isl_pw_multi_aff *
3283 isl_basic_set_partial_lexmin_pw_multi_aff(
3284 __isl_take isl_basic_set *bset,
3285 __isl_take isl_basic_set *dom,
3286 __isl_give isl_set **empty);
3287 __isl_give isl_pw_multi_aff *
3288 isl_basic_set_partial_lexmax_pw_multi_aff(
3289 __isl_take isl_basic_set *bset,
3290 __isl_take isl_basic_set *dom,
3291 __isl_give isl_set **empty);
3292 __isl_give isl_pw_multi_aff *
3293 isl_basic_map_partial_lexmin_pw_multi_aff(
3294 __isl_take isl_basic_map *bmap,
3295 __isl_take isl_basic_set *dom,
3296 __isl_give isl_set **empty);
3297 __isl_give isl_pw_multi_aff *
3298 isl_basic_map_partial_lexmax_pw_multi_aff(
3299 __isl_take isl_basic_map *bmap,
3300 __isl_take isl_basic_set *dom,
3301 __isl_give isl_set **empty);
3302 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3303 __isl_take isl_set *set);
3304 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3305 __isl_take isl_set *set);
3306 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3307 __isl_take isl_map *map);
3308 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3309 __isl_take isl_map *map);
3313 Lists are defined over several element types, including
3314 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3315 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3316 Here we take lists of C<isl_set>s as an example.
3317 Lists can be created, copied, modified and freed using the following functions.
3319 #include <isl/list.h>
3320 __isl_give isl_set_list *isl_set_list_from_set(
3321 __isl_take isl_set *el);
3322 __isl_give isl_set_list *isl_set_list_alloc(
3323 isl_ctx *ctx, int n);
3324 __isl_give isl_set_list *isl_set_list_copy(
3325 __isl_keep isl_set_list *list);
3326 __isl_give isl_set_list *isl_set_list_insert(
3327 __isl_take isl_set_list *list, unsigned pos,
3328 __isl_take isl_set *el);
3329 __isl_give isl_set_list *isl_set_list_add(
3330 __isl_take isl_set_list *list,
3331 __isl_take isl_set *el);
3332 __isl_give isl_set_list *isl_set_list_drop(
3333 __isl_take isl_set_list *list,
3334 unsigned first, unsigned n);
3335 __isl_give isl_set_list *isl_set_list_set_set(
3336 __isl_take isl_set_list *list, int index,
3337 __isl_take isl_set *set);
3338 __isl_give isl_set_list *isl_set_list_concat(
3339 __isl_take isl_set_list *list1,
3340 __isl_take isl_set_list *list2);
3341 __isl_give isl_set_list *isl_set_list_sort(
3342 __isl_take isl_set_list *list,
3343 int (*cmp)(__isl_keep isl_set *a,
3344 __isl_keep isl_set *b, void *user),
3346 void *isl_set_list_free(__isl_take isl_set_list *list);
3348 C<isl_set_list_alloc> creates an empty list with a capacity for
3349 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3352 Lists can be inspected using the following functions.
3354 #include <isl/list.h>
3355 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3356 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3357 __isl_give isl_set *isl_set_list_get_set(
3358 __isl_keep isl_set_list *list, int index);
3359 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3360 int (*fn)(__isl_take isl_set *el, void *user),
3362 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3363 int (*follows)(__isl_keep isl_set *a,
3364 __isl_keep isl_set *b, void *user),
3366 int (*fn)(__isl_take isl_set *el, void *user),
3369 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3370 strongly connected components of the graph with as vertices the elements
3371 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3372 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3373 should return C<-1> on error.
3375 Lists can be printed using
3377 #include <isl/list.h>
3378 __isl_give isl_printer *isl_printer_print_set_list(
3379 __isl_take isl_printer *p,
3380 __isl_keep isl_set_list *list);
3382 =head2 Multiple Values
3384 An C<isl_multi_val> object represents a sequence of zero or more values,
3385 living in a set space.
3387 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3388 using the following function
3390 #include <isl/val.h>
3391 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3392 __isl_take isl_space *space,
3393 __isl_take isl_val_list *list);
3395 The zero multiple value (with value zero for each set dimension)
3396 can be created using the following function.
3398 #include <isl/val.h>
3399 __isl_give isl_multi_val *isl_multi_val_zero(
3400 __isl_take isl_space *space);
3402 Multiple values can be copied and freed using
3404 #include <isl/val.h>
3405 __isl_give isl_multi_val *isl_multi_val_copy(
3406 __isl_keep isl_multi_val *mv);
3407 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3409 They can be inspected using
3411 #include <isl/val.h>
3412 isl_ctx *isl_multi_val_get_ctx(
3413 __isl_keep isl_multi_val *mv);
3414 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3415 enum isl_dim_type type);
3416 __isl_give isl_val *isl_multi_val_get_val(
3417 __isl_keep isl_multi_val *mv, int pos);
3418 const char *isl_multi_val_get_tuple_name(
3419 __isl_keep isl_multi_val *mv,
3420 enum isl_dim_type type);
3422 They can be modified using
3424 #include <isl/val.h>
3425 __isl_give isl_multi_val *isl_multi_val_set_val(
3426 __isl_take isl_multi_val *mv, int pos,
3427 __isl_take isl_val *val);
3428 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3429 __isl_take isl_multi_val *mv,
3430 enum isl_dim_type type, unsigned pos, const char *s);
3431 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3432 __isl_take isl_multi_val *mv,
3433 enum isl_dim_type type, const char *s);
3434 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3435 __isl_take isl_multi_val *mv,
3436 enum isl_dim_type type, __isl_take isl_id *id);
3438 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3439 __isl_take isl_multi_val *mv,
3440 enum isl_dim_type type, unsigned first, unsigned n);
3441 __isl_give isl_multi_val *isl_multi_val_add_dims(
3442 __isl_take isl_multi_val *mv,
3443 enum isl_dim_type type, unsigned n);
3444 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3445 __isl_take isl_multi_val *mv,
3446 enum isl_dim_type type, unsigned first, unsigned n);
3450 #include <isl/val.h>
3451 __isl_give isl_multi_val *isl_multi_val_align_params(
3452 __isl_take isl_multi_val *mv,
3453 __isl_take isl_space *model);
3454 __isl_give isl_multi_val *isl_multi_val_range_splice(
3455 __isl_take isl_multi_val *mv1, unsigned pos,
3456 __isl_take isl_multi_val *mv2);
3457 __isl_give isl_multi_val *isl_multi_val_range_product(
3458 __isl_take isl_multi_val *mv1,
3459 __isl_take isl_multi_val *mv2);
3460 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3461 __isl_take isl_multi_val *mv1,
3462 __isl_take isl_multi_aff *mv2);
3463 __isl_give isl_multi_val *isl_multi_val_add_val(
3464 __isl_take isl_multi_val *mv,
3465 __isl_take isl_val *v);
3466 __isl_give isl_multi_val *isl_multi_val_mod_val(
3467 __isl_take isl_multi_val *mv,
3468 __isl_take isl_val *v);
3469 __isl_give isl_multi_val *isl_multi_val_scale_val(
3470 __isl_take isl_multi_val *mv,
3471 __isl_take isl_val *v);
3475 Vectors can be created, copied and freed using the following functions.
3477 #include <isl/vec.h>
3478 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3480 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3481 void *isl_vec_free(__isl_take isl_vec *vec);
3483 Note that the elements of a newly created vector may have arbitrary values.
3484 The elements can be changed and inspected using the following functions.
3486 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3487 int isl_vec_size(__isl_keep isl_vec *vec);
3488 int isl_vec_get_element(__isl_keep isl_vec *vec,
3489 int pos, isl_int *v);
3490 __isl_give isl_val *isl_vec_get_element_val(
3491 __isl_keep isl_vec *vec, int pos);
3492 __isl_give isl_vec *isl_vec_set_element(
3493 __isl_take isl_vec *vec, int pos, isl_int v);
3494 __isl_give isl_vec *isl_vec_set_element_si(
3495 __isl_take isl_vec *vec, int pos, int v);
3496 __isl_give isl_vec *isl_vec_set_element_val(
3497 __isl_take isl_vec *vec, int pos,
3498 __isl_take isl_val *v);
3499 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3501 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3503 __isl_give isl_vec *isl_vec_set_val(
3504 __isl_take isl_vec *vec, __isl_take isl_val *v);
3505 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3508 C<isl_vec_get_element> will return a negative value if anything went wrong.
3509 In that case, the value of C<*v> is undefined.
3511 The following function can be used to concatenate two vectors.
3513 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3514 __isl_take isl_vec *vec2);
3518 Matrices can be created, copied and freed using the following functions.
3520 #include <isl/mat.h>
3521 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3522 unsigned n_row, unsigned n_col);
3523 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3524 void *isl_mat_free(__isl_take isl_mat *mat);
3526 Note that the elements of a newly created matrix may have arbitrary values.
3527 The elements can be changed and inspected using the following functions.
3529 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3530 int isl_mat_rows(__isl_keep isl_mat *mat);
3531 int isl_mat_cols(__isl_keep isl_mat *mat);
3532 int isl_mat_get_element(__isl_keep isl_mat *mat,
3533 int row, int col, isl_int *v);
3534 __isl_give isl_val *isl_mat_get_element_val(
3535 __isl_keep isl_mat *mat, int row, int col);
3536 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3537 int row, int col, isl_int v);
3538 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3539 int row, int col, int v);
3540 __isl_give isl_mat *isl_mat_set_element_val(
3541 __isl_take isl_mat *mat, int row, int col,
3542 __isl_take isl_val *v);
3544 C<isl_mat_get_element> will return a negative value if anything went wrong.
3545 In that case, the value of C<*v> is undefined.
3547 The following function can be used to compute the (right) inverse
3548 of a matrix, i.e., a matrix such that the product of the original
3549 and the inverse (in that order) is a multiple of the identity matrix.
3550 The input matrix is assumed to be of full row-rank.
3552 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3554 The following function can be used to compute the (right) kernel
3555 (or null space) of a matrix, i.e., a matrix such that the product of
3556 the original and the kernel (in that order) is the zero matrix.
3558 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3560 =head2 Piecewise Quasi Affine Expressions
3562 The zero quasi affine expression or the quasi affine expression
3563 that is equal to a specified dimension on a given domain can be created using
3565 __isl_give isl_aff *isl_aff_zero_on_domain(
3566 __isl_take isl_local_space *ls);
3567 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3568 __isl_take isl_local_space *ls);
3569 __isl_give isl_aff *isl_aff_var_on_domain(
3570 __isl_take isl_local_space *ls,
3571 enum isl_dim_type type, unsigned pos);
3572 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3573 __isl_take isl_local_space *ls,
3574 enum isl_dim_type type, unsigned pos);
3576 Note that the space in which the resulting objects live is a map space
3577 with the given space as domain and a one-dimensional range.
3579 An empty piecewise quasi affine expression (one with no cells)
3580 or a piecewise quasi affine expression with a single cell can
3581 be created using the following functions.
3583 #include <isl/aff.h>
3584 __isl_give isl_pw_aff *isl_pw_aff_empty(
3585 __isl_take isl_space *space);
3586 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3587 __isl_take isl_set *set, __isl_take isl_aff *aff);
3588 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3589 __isl_take isl_aff *aff);
3591 A piecewise quasi affine expression that is equal to 1 on a set
3592 and 0 outside the set can be created using the following function.
3594 #include <isl/aff.h>
3595 __isl_give isl_pw_aff *isl_set_indicator_function(
3596 __isl_take isl_set *set);
3598 Quasi affine expressions can be copied and freed using
3600 #include <isl/aff.h>
3601 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3602 void *isl_aff_free(__isl_take isl_aff *aff);
3604 __isl_give isl_pw_aff *isl_pw_aff_copy(
3605 __isl_keep isl_pw_aff *pwaff);
3606 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3608 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3609 using the following function. The constraint is required to have
3610 a non-zero coefficient for the specified dimension.
3612 #include <isl/constraint.h>
3613 __isl_give isl_aff *isl_constraint_get_bound(
3614 __isl_keep isl_constraint *constraint,
3615 enum isl_dim_type type, int pos);
3617 The entire affine expression of the constraint can also be extracted
3618 using the following function.
3620 #include <isl/constraint.h>
3621 __isl_give isl_aff *isl_constraint_get_aff(
3622 __isl_keep isl_constraint *constraint);
3624 Conversely, an equality constraint equating
3625 the affine expression to zero or an inequality constraint enforcing
3626 the affine expression to be non-negative, can be constructed using
3628 __isl_give isl_constraint *isl_equality_from_aff(
3629 __isl_take isl_aff *aff);
3630 __isl_give isl_constraint *isl_inequality_from_aff(
3631 __isl_take isl_aff *aff);
3633 The expression can be inspected using
3635 #include <isl/aff.h>
3636 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3637 int isl_aff_dim(__isl_keep isl_aff *aff,
3638 enum isl_dim_type type);
3639 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3640 __isl_keep isl_aff *aff);
3641 __isl_give isl_local_space *isl_aff_get_local_space(
3642 __isl_keep isl_aff *aff);
3643 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3644 enum isl_dim_type type, unsigned pos);
3645 const char *isl_pw_aff_get_dim_name(
3646 __isl_keep isl_pw_aff *pa,
3647 enum isl_dim_type type, unsigned pos);
3648 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3649 enum isl_dim_type type, unsigned pos);
3650 __isl_give isl_id *isl_pw_aff_get_dim_id(
3651 __isl_keep isl_pw_aff *pa,
3652 enum isl_dim_type type, unsigned pos);
3653 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3654 __isl_keep isl_pw_aff *pa,
3655 enum isl_dim_type type);
3656 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3658 __isl_give isl_val *isl_aff_get_constant_val(
3659 __isl_keep isl_aff *aff);
3660 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3661 enum isl_dim_type type, int pos, isl_int *v);
3662 __isl_give isl_val *isl_aff_get_coefficient_val(
3663 __isl_keep isl_aff *aff,
3664 enum isl_dim_type type, int pos);
3665 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3667 __isl_give isl_val *isl_aff_get_denominator_val(
3668 __isl_keep isl_aff *aff);
3669 __isl_give isl_aff *isl_aff_get_div(
3670 __isl_keep isl_aff *aff, int pos);
3672 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3673 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3674 int (*fn)(__isl_take isl_set *set,
3675 __isl_take isl_aff *aff,
3676 void *user), void *user);
3678 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3679 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3681 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3682 enum isl_dim_type type, unsigned first, unsigned n);
3683 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3684 enum isl_dim_type type, unsigned first, unsigned n);
3686 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3687 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3688 enum isl_dim_type type);
3689 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3691 It can be modified using
3693 #include <isl/aff.h>
3694 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3695 __isl_take isl_pw_aff *pwaff,
3696 enum isl_dim_type type, __isl_take isl_id *id);
3697 __isl_give isl_aff *isl_aff_set_dim_name(
3698 __isl_take isl_aff *aff, enum isl_dim_type type,
3699 unsigned pos, const char *s);
3700 __isl_give isl_aff *isl_aff_set_dim_id(
3701 __isl_take isl_aff *aff, enum isl_dim_type type,
3702 unsigned pos, __isl_take isl_id *id);
3703 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3704 __isl_take isl_pw_aff *pma,
3705 enum isl_dim_type type, unsigned pos,
3706 __isl_take isl_id *id);
3707 __isl_give isl_aff *isl_aff_set_constant(
3708 __isl_take isl_aff *aff, isl_int v);
3709 __isl_give isl_aff *isl_aff_set_constant_si(
3710 __isl_take isl_aff *aff, int v);
3711 __isl_give isl_aff *isl_aff_set_constant_val(
3712 __isl_take isl_aff *aff, __isl_take isl_val *v);
3713 __isl_give isl_aff *isl_aff_set_coefficient(
3714 __isl_take isl_aff *aff,
3715 enum isl_dim_type type, int pos, isl_int v);
3716 __isl_give isl_aff *isl_aff_set_coefficient_si(
3717 __isl_take isl_aff *aff,
3718 enum isl_dim_type type, int pos, int v);
3719 __isl_give isl_aff *isl_aff_set_coefficient_val(
3720 __isl_take isl_aff *aff,
3721 enum isl_dim_type type, int pos,
3722 __isl_take isl_val *v);
3723 __isl_give isl_aff *isl_aff_set_denominator(
3724 __isl_take isl_aff *aff, isl_int v);
3726 __isl_give isl_aff *isl_aff_add_constant(
3727 __isl_take isl_aff *aff, isl_int v);
3728 __isl_give isl_aff *isl_aff_add_constant_si(
3729 __isl_take isl_aff *aff, int v);
3730 __isl_give isl_aff *isl_aff_add_constant_val(
3731 __isl_take isl_aff *aff, __isl_take isl_val *v);
3732 __isl_give isl_aff *isl_aff_add_constant_num(
3733 __isl_take isl_aff *aff, isl_int v);
3734 __isl_give isl_aff *isl_aff_add_constant_num_si(
3735 __isl_take isl_aff *aff, int v);
3736 __isl_give isl_aff *isl_aff_add_coefficient(
3737 __isl_take isl_aff *aff,
3738 enum isl_dim_type type, int pos, isl_int v);
3739 __isl_give isl_aff *isl_aff_add_coefficient_si(
3740 __isl_take isl_aff *aff,
3741 enum isl_dim_type type, int pos, int v);
3742 __isl_give isl_aff *isl_aff_add_coefficient_val(
3743 __isl_take isl_aff *aff,
3744 enum isl_dim_type type, int pos,
3745 __isl_take isl_val *v);
3747 __isl_give isl_aff *isl_aff_insert_dims(
3748 __isl_take isl_aff *aff,
3749 enum isl_dim_type type, unsigned first, unsigned n);
3750 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3751 __isl_take isl_pw_aff *pwaff,
3752 enum isl_dim_type type, unsigned first, unsigned n);
3753 __isl_give isl_aff *isl_aff_add_dims(
3754 __isl_take isl_aff *aff,
3755 enum isl_dim_type type, unsigned n);
3756 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3757 __isl_take isl_pw_aff *pwaff,
3758 enum isl_dim_type type, unsigned n);
3759 __isl_give isl_aff *isl_aff_drop_dims(
3760 __isl_take isl_aff *aff,
3761 enum isl_dim_type type, unsigned first, unsigned n);
3762 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3763 __isl_take isl_pw_aff *pwaff,
3764 enum isl_dim_type type, unsigned first, unsigned n);
3766 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3767 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3768 set the I<numerator> of the constant or coefficient, while
3769 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3770 the constant or coefficient as a whole.
3771 The C<add_constant> and C<add_coefficient> functions add an integer
3772 or rational value to
3773 the possibly rational constant or coefficient.
3774 The C<add_constant_num> functions add an integer value to
3777 To check whether an affine expressions is obviously zero
3778 or obviously equal to some other affine expression, use
3780 #include <isl/aff.h>
3781 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3782 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3783 __isl_keep isl_aff *aff2);
3784 int isl_pw_aff_plain_is_equal(
3785 __isl_keep isl_pw_aff *pwaff1,
3786 __isl_keep isl_pw_aff *pwaff2);
3790 #include <isl/aff.h>
3791 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3792 __isl_take isl_aff *aff2);
3793 __isl_give isl_pw_aff *isl_pw_aff_add(
3794 __isl_take isl_pw_aff *pwaff1,
3795 __isl_take isl_pw_aff *pwaff2);
3796 __isl_give isl_pw_aff *isl_pw_aff_min(
3797 __isl_take isl_pw_aff *pwaff1,
3798 __isl_take isl_pw_aff *pwaff2);
3799 __isl_give isl_pw_aff *isl_pw_aff_max(
3800 __isl_take isl_pw_aff *pwaff1,
3801 __isl_take isl_pw_aff *pwaff2);
3802 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3803 __isl_take isl_aff *aff2);
3804 __isl_give isl_pw_aff *isl_pw_aff_sub(
3805 __isl_take isl_pw_aff *pwaff1,
3806 __isl_take isl_pw_aff *pwaff2);
3807 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3808 __isl_give isl_pw_aff *isl_pw_aff_neg(
3809 __isl_take isl_pw_aff *pwaff);
3810 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3811 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3812 __isl_take isl_pw_aff *pwaff);
3813 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3814 __isl_give isl_pw_aff *isl_pw_aff_floor(
3815 __isl_take isl_pw_aff *pwaff);
3816 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3818 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3819 __isl_take isl_val *mod);
3820 __isl_give isl_pw_aff *isl_pw_aff_mod(
3821 __isl_take isl_pw_aff *pwaff, isl_int mod);
3822 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3823 __isl_take isl_pw_aff *pa,
3824 __isl_take isl_val *mod);
3825 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3827 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3828 __isl_take isl_val *v);
3829 __isl_give isl_pw_aff *isl_pw_aff_scale(
3830 __isl_take isl_pw_aff *pwaff, isl_int f);
3831 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3832 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3833 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3835 __isl_give isl_aff *isl_aff_scale_down_ui(
3836 __isl_take isl_aff *aff, unsigned f);
3837 __isl_give isl_aff *isl_aff_scale_down_val(
3838 __isl_take isl_aff *aff, __isl_take isl_val *v);
3839 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3840 __isl_take isl_pw_aff *pwaff, isl_int f);
3841 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3842 __isl_take isl_pw_aff *pa,
3843 __isl_take isl_val *f);
3845 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3846 __isl_take isl_pw_aff_list *list);
3847 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3848 __isl_take isl_pw_aff_list *list);
3850 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3851 __isl_take isl_pw_aff *pwqp);
3853 __isl_give isl_aff *isl_aff_align_params(
3854 __isl_take isl_aff *aff,
3855 __isl_take isl_space *model);
3856 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3857 __isl_take isl_pw_aff *pwaff,
3858 __isl_take isl_space *model);
3860 __isl_give isl_aff *isl_aff_project_domain_on_params(
3861 __isl_take isl_aff *aff);
3863 __isl_give isl_aff *isl_aff_gist_params(
3864 __isl_take isl_aff *aff,
3865 __isl_take isl_set *context);
3866 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3867 __isl_take isl_set *context);
3868 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3869 __isl_take isl_pw_aff *pwaff,
3870 __isl_take isl_set *context);
3871 __isl_give isl_pw_aff *isl_pw_aff_gist(
3872 __isl_take isl_pw_aff *pwaff,
3873 __isl_take isl_set *context);
3875 __isl_give isl_set *isl_pw_aff_domain(
3876 __isl_take isl_pw_aff *pwaff);
3877 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3878 __isl_take isl_pw_aff *pa,
3879 __isl_take isl_set *set);
3880 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3881 __isl_take isl_pw_aff *pa,
3882 __isl_take isl_set *set);
3884 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3885 __isl_take isl_aff *aff2);
3886 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3887 __isl_take isl_aff *aff2);
3888 __isl_give isl_pw_aff *isl_pw_aff_mul(
3889 __isl_take isl_pw_aff *pwaff1,
3890 __isl_take isl_pw_aff *pwaff2);
3891 __isl_give isl_pw_aff *isl_pw_aff_div(
3892 __isl_take isl_pw_aff *pa1,
3893 __isl_take isl_pw_aff *pa2);
3894 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3895 __isl_take isl_pw_aff *pa1,
3896 __isl_take isl_pw_aff *pa2);
3897 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3898 __isl_take isl_pw_aff *pa1,
3899 __isl_take isl_pw_aff *pa2);
3901 When multiplying two affine expressions, at least one of the two needs
3902 to be a constant. Similarly, when dividing an affine expression by another,
3903 the second expression needs to be a constant.
3904 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3905 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3908 #include <isl/aff.h>
3909 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3910 __isl_take isl_aff *aff,
3911 __isl_take isl_multi_aff *ma);
3912 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3913 __isl_take isl_pw_aff *pa,
3914 __isl_take isl_multi_aff *ma);
3915 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3916 __isl_take isl_pw_aff *pa,
3917 __isl_take isl_pw_multi_aff *pma);
3919 These functions precompose the input expression by the given
3920 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3921 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3922 into the (piecewise) affine expression.
3923 Objects of type C<isl_multi_aff> are described in
3924 L</"Piecewise Multiple Quasi Affine Expressions">.
3926 #include <isl/aff.h>
3927 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3928 __isl_take isl_aff *aff);
3929 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3930 __isl_take isl_aff *aff);
3931 __isl_give isl_basic_set *isl_aff_le_basic_set(
3932 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3933 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3934 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3935 __isl_give isl_set *isl_pw_aff_eq_set(
3936 __isl_take isl_pw_aff *pwaff1,
3937 __isl_take isl_pw_aff *pwaff2);
3938 __isl_give isl_set *isl_pw_aff_ne_set(
3939 __isl_take isl_pw_aff *pwaff1,
3940 __isl_take isl_pw_aff *pwaff2);
3941 __isl_give isl_set *isl_pw_aff_le_set(
3942 __isl_take isl_pw_aff *pwaff1,
3943 __isl_take isl_pw_aff *pwaff2);
3944 __isl_give isl_set *isl_pw_aff_lt_set(
3945 __isl_take isl_pw_aff *pwaff1,
3946 __isl_take isl_pw_aff *pwaff2);
3947 __isl_give isl_set *isl_pw_aff_ge_set(
3948 __isl_take isl_pw_aff *pwaff1,
3949 __isl_take isl_pw_aff *pwaff2);
3950 __isl_give isl_set *isl_pw_aff_gt_set(
3951 __isl_take isl_pw_aff *pwaff1,
3952 __isl_take isl_pw_aff *pwaff2);
3954 __isl_give isl_set *isl_pw_aff_list_eq_set(
3955 __isl_take isl_pw_aff_list *list1,
3956 __isl_take isl_pw_aff_list *list2);
3957 __isl_give isl_set *isl_pw_aff_list_ne_set(
3958 __isl_take isl_pw_aff_list *list1,
3959 __isl_take isl_pw_aff_list *list2);
3960 __isl_give isl_set *isl_pw_aff_list_le_set(
3961 __isl_take isl_pw_aff_list *list1,
3962 __isl_take isl_pw_aff_list *list2);
3963 __isl_give isl_set *isl_pw_aff_list_lt_set(
3964 __isl_take isl_pw_aff_list *list1,
3965 __isl_take isl_pw_aff_list *list2);
3966 __isl_give isl_set *isl_pw_aff_list_ge_set(
3967 __isl_take isl_pw_aff_list *list1,
3968 __isl_take isl_pw_aff_list *list2);
3969 __isl_give isl_set *isl_pw_aff_list_gt_set(
3970 __isl_take isl_pw_aff_list *list1,
3971 __isl_take isl_pw_aff_list *list2);
3973 The function C<isl_aff_neg_basic_set> returns a basic set
3974 containing those elements in the domain space
3975 of C<aff> where C<aff> is negative.
3976 The function C<isl_aff_ge_basic_set> returns a basic set
3977 containing those elements in the shared space
3978 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3979 The function C<isl_pw_aff_ge_set> returns a set
3980 containing those elements in the shared domain
3981 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3982 The functions operating on C<isl_pw_aff_list> apply the corresponding
3983 C<isl_pw_aff> function to each pair of elements in the two lists.
3985 #include <isl/aff.h>
3986 __isl_give isl_set *isl_pw_aff_nonneg_set(
3987 __isl_take isl_pw_aff *pwaff);
3988 __isl_give isl_set *isl_pw_aff_zero_set(
3989 __isl_take isl_pw_aff *pwaff);
3990 __isl_give isl_set *isl_pw_aff_non_zero_set(
3991 __isl_take isl_pw_aff *pwaff);
3993 The function C<isl_pw_aff_nonneg_set> returns a set
3994 containing those elements in the domain
3995 of C<pwaff> where C<pwaff> is non-negative.
3997 #include <isl/aff.h>
3998 __isl_give isl_pw_aff *isl_pw_aff_cond(
3999 __isl_take isl_pw_aff *cond,
4000 __isl_take isl_pw_aff *pwaff_true,
4001 __isl_take isl_pw_aff *pwaff_false);
4003 The function C<isl_pw_aff_cond> performs a conditional operator
4004 and returns an expression that is equal to C<pwaff_true>
4005 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4006 where C<cond> is zero.
4008 #include <isl/aff.h>
4009 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4010 __isl_take isl_pw_aff *pwaff1,
4011 __isl_take isl_pw_aff *pwaff2);
4012 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4013 __isl_take isl_pw_aff *pwaff1,
4014 __isl_take isl_pw_aff *pwaff2);
4015 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4016 __isl_take isl_pw_aff *pwaff1,
4017 __isl_take isl_pw_aff *pwaff2);
4019 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4020 expression with a domain that is the union of those of C<pwaff1> and
4021 C<pwaff2> and such that on each cell, the quasi-affine expression is
4022 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4023 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4024 associated expression is the defined one.
4026 An expression can be read from input using
4028 #include <isl/aff.h>
4029 __isl_give isl_aff *isl_aff_read_from_str(
4030 isl_ctx *ctx, const char *str);
4031 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4032 isl_ctx *ctx, const char *str);
4034 An expression can be printed using
4036 #include <isl/aff.h>
4037 __isl_give isl_printer *isl_printer_print_aff(
4038 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4040 __isl_give isl_printer *isl_printer_print_pw_aff(
4041 __isl_take isl_printer *p,
4042 __isl_keep isl_pw_aff *pwaff);
4044 =head2 Piecewise Multiple Quasi Affine Expressions
4046 An C<isl_multi_aff> object represents a sequence of
4047 zero or more affine expressions, all defined on the same domain space.
4048 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4049 zero or more piecewise affine expressions.
4051 An C<isl_multi_aff> can be constructed from a single
4052 C<isl_aff> or an C<isl_aff_list> using the
4053 following functions. Similarly for C<isl_multi_pw_aff>.
4055 #include <isl/aff.h>
4056 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4057 __isl_take isl_aff *aff);
4058 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4059 __isl_take isl_pw_aff *pa);
4060 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4061 __isl_take isl_space *space,
4062 __isl_take isl_aff_list *list);
4064 An empty piecewise multiple quasi affine expression (one with no cells),
4065 the zero piecewise multiple quasi affine expression (with value zero
4066 for each output dimension),
4067 a piecewise multiple quasi affine expression with a single cell (with
4068 either a universe or a specified domain) or
4069 a zero-dimensional piecewise multiple quasi affine expression
4071 can be created using the following functions.
4073 #include <isl/aff.h>
4074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4075 __isl_take isl_space *space);
4076 __isl_give isl_multi_aff *isl_multi_aff_zero(
4077 __isl_take isl_space *space);
4078 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4079 __isl_take isl_space *space);
4080 __isl_give isl_multi_aff *isl_multi_aff_identity(
4081 __isl_take isl_space *space);
4082 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4083 __isl_take isl_space *space);
4084 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4085 __isl_take isl_space *space);
4086 __isl_give isl_pw_multi_aff *
4087 isl_pw_multi_aff_from_multi_aff(
4088 __isl_take isl_multi_aff *ma);
4089 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4090 __isl_take isl_set *set,
4091 __isl_take isl_multi_aff *maff);
4092 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4093 __isl_take isl_set *set);
4095 __isl_give isl_union_pw_multi_aff *
4096 isl_union_pw_multi_aff_empty(
4097 __isl_take isl_space *space);
4098 __isl_give isl_union_pw_multi_aff *
4099 isl_union_pw_multi_aff_add_pw_multi_aff(
4100 __isl_take isl_union_pw_multi_aff *upma,
4101 __isl_take isl_pw_multi_aff *pma);
4102 __isl_give isl_union_pw_multi_aff *
4103 isl_union_pw_multi_aff_from_domain(
4104 __isl_take isl_union_set *uset);
4106 A piecewise multiple quasi affine expression can also be initialized
4107 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4108 and the C<isl_map> is single-valued.
4109 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4110 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4112 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4113 __isl_take isl_set *set);
4114 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4115 __isl_take isl_map *map);
4117 __isl_give isl_union_pw_multi_aff *
4118 isl_union_pw_multi_aff_from_union_set(
4119 __isl_take isl_union_set *uset);
4120 __isl_give isl_union_pw_multi_aff *
4121 isl_union_pw_multi_aff_from_union_map(
4122 __isl_take isl_union_map *umap);
4124 Multiple quasi affine expressions can be copied and freed using
4126 #include <isl/aff.h>
4127 __isl_give isl_multi_aff *isl_multi_aff_copy(
4128 __isl_keep isl_multi_aff *maff);
4129 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4131 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4132 __isl_keep isl_pw_multi_aff *pma);
4133 void *isl_pw_multi_aff_free(
4134 __isl_take isl_pw_multi_aff *pma);
4136 __isl_give isl_union_pw_multi_aff *
4137 isl_union_pw_multi_aff_copy(
4138 __isl_keep isl_union_pw_multi_aff *upma);
4139 void *isl_union_pw_multi_aff_free(
4140 __isl_take isl_union_pw_multi_aff *upma);
4142 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4143 __isl_keep isl_multi_pw_aff *mpa);
4144 void *isl_multi_pw_aff_free(
4145 __isl_take isl_multi_pw_aff *mpa);
4147 The expression can be inspected using
4149 #include <isl/aff.h>
4150 isl_ctx *isl_multi_aff_get_ctx(
4151 __isl_keep isl_multi_aff *maff);
4152 isl_ctx *isl_pw_multi_aff_get_ctx(
4153 __isl_keep isl_pw_multi_aff *pma);
4154 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4155 __isl_keep isl_union_pw_multi_aff *upma);
4156 isl_ctx *isl_multi_pw_aff_get_ctx(
4157 __isl_keep isl_multi_pw_aff *mpa);
4158 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4159 enum isl_dim_type type);
4160 unsigned isl_pw_multi_aff_dim(
4161 __isl_keep isl_pw_multi_aff *pma,
4162 enum isl_dim_type type);
4163 unsigned isl_multi_pw_aff_dim(
4164 __isl_keep isl_multi_pw_aff *mpa,
4165 enum isl_dim_type type);
4166 __isl_give isl_aff *isl_multi_aff_get_aff(
4167 __isl_keep isl_multi_aff *multi, int pos);
4168 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4169 __isl_keep isl_pw_multi_aff *pma, int pos);
4170 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4171 __isl_keep isl_multi_pw_aff *mpa, int pos);
4172 const char *isl_pw_multi_aff_get_dim_name(
4173 __isl_keep isl_pw_multi_aff *pma,
4174 enum isl_dim_type type, unsigned pos);
4175 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4176 __isl_keep isl_pw_multi_aff *pma,
4177 enum isl_dim_type type, unsigned pos);
4178 const char *isl_multi_aff_get_tuple_name(
4179 __isl_keep isl_multi_aff *multi,
4180 enum isl_dim_type type);
4181 int isl_pw_multi_aff_has_tuple_name(
4182 __isl_keep isl_pw_multi_aff *pma,
4183 enum isl_dim_type type);
4184 const char *isl_pw_multi_aff_get_tuple_name(
4185 __isl_keep isl_pw_multi_aff *pma,
4186 enum isl_dim_type type);
4187 int isl_pw_multi_aff_has_tuple_id(
4188 __isl_keep isl_pw_multi_aff *pma,
4189 enum isl_dim_type type);
4190 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4191 __isl_keep isl_pw_multi_aff *pma,
4192 enum isl_dim_type type);
4194 int isl_pw_multi_aff_foreach_piece(
4195 __isl_keep isl_pw_multi_aff *pma,
4196 int (*fn)(__isl_take isl_set *set,
4197 __isl_take isl_multi_aff *maff,
4198 void *user), void *user);
4200 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4201 __isl_keep isl_union_pw_multi_aff *upma,
4202 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4203 void *user), void *user);
4205 It can be modified using
4207 #include <isl/aff.h>
4208 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4209 __isl_take isl_multi_aff *multi, int pos,
4210 __isl_take isl_aff *aff);
4211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4212 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4213 __isl_take isl_pw_aff *pa);
4214 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4215 __isl_take isl_multi_aff *maff,
4216 enum isl_dim_type type, unsigned pos, const char *s);
4217 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4218 __isl_take isl_multi_aff *maff,
4219 enum isl_dim_type type, const char *s);
4220 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4221 __isl_take isl_multi_aff *maff,
4222 enum isl_dim_type type, __isl_take isl_id *id);
4223 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4224 __isl_take isl_pw_multi_aff *pma,
4225 enum isl_dim_type type, __isl_take isl_id *id);
4227 __isl_give isl_multi_pw_aff *
4228 isl_multi_pw_aff_set_dim_name(
4229 __isl_take isl_multi_pw_aff *mpa,
4230 enum isl_dim_type type, unsigned pos, const char *s);
4231 __isl_give isl_multi_pw_aff *
4232 isl_multi_pw_aff_set_tuple_name(
4233 __isl_take isl_multi_pw_aff *mpa,
4234 enum isl_dim_type type, const char *s);
4236 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4237 __isl_take isl_multi_aff *ma,
4238 enum isl_dim_type type, unsigned first, unsigned n);
4239 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4240 __isl_take isl_multi_aff *ma,
4241 enum isl_dim_type type, unsigned n);
4242 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4243 __isl_take isl_multi_aff *maff,
4244 enum isl_dim_type type, unsigned first, unsigned n);
4245 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4246 __isl_take isl_pw_multi_aff *pma,
4247 enum isl_dim_type type, unsigned first, unsigned n);
4249 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4250 __isl_take isl_multi_pw_aff *mpa,
4251 enum isl_dim_type type, unsigned first, unsigned n);
4252 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4253 __isl_take isl_multi_pw_aff *mpa,
4254 enum isl_dim_type type, unsigned n);
4256 To check whether two multiple affine expressions are
4257 obviously equal to each other, use
4259 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4260 __isl_keep isl_multi_aff *maff2);
4261 int isl_pw_multi_aff_plain_is_equal(
4262 __isl_keep isl_pw_multi_aff *pma1,
4263 __isl_keep isl_pw_multi_aff *pma2);
4267 #include <isl/aff.h>
4268 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4269 __isl_take isl_pw_multi_aff *pma1,
4270 __isl_take isl_pw_multi_aff *pma2);
4271 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4272 __isl_take isl_pw_multi_aff *pma1,
4273 __isl_take isl_pw_multi_aff *pma2);
4274 __isl_give isl_multi_aff *isl_multi_aff_add(
4275 __isl_take isl_multi_aff *maff1,
4276 __isl_take isl_multi_aff *maff2);
4277 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4278 __isl_take isl_pw_multi_aff *pma1,
4279 __isl_take isl_pw_multi_aff *pma2);
4280 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4281 __isl_take isl_union_pw_multi_aff *upma1,
4282 __isl_take isl_union_pw_multi_aff *upma2);
4283 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4284 __isl_take isl_pw_multi_aff *pma1,
4285 __isl_take isl_pw_multi_aff *pma2);
4286 __isl_give isl_multi_aff *isl_multi_aff_sub(
4287 __isl_take isl_multi_aff *ma1,
4288 __isl_take isl_multi_aff *ma2);
4289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4290 __isl_take isl_pw_multi_aff *pma1,
4291 __isl_take isl_pw_multi_aff *pma2);
4292 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4293 __isl_take isl_union_pw_multi_aff *upma1,
4294 __isl_take isl_union_pw_multi_aff *upma2);
4296 C<isl_multi_aff_sub> subtracts the second argument from the first.
4298 __isl_give isl_multi_aff *isl_multi_aff_scale(
4299 __isl_take isl_multi_aff *maff,
4301 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4302 __isl_take isl_multi_aff *ma,
4303 __isl_take isl_val *v);
4304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4305 __isl_take isl_pw_multi_aff *pma,
4306 __isl_take isl_val *v);
4307 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4308 __isl_take isl_multi_pw_aff *mpa,
4309 __isl_take isl_val *v);
4310 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4311 __isl_take isl_multi_aff *ma,
4312 __isl_take isl_vec *v);
4313 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4314 __isl_take isl_pw_multi_aff *pma,
4315 __isl_take isl_vec *v);
4316 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4317 __isl_take isl_union_pw_multi_aff *upma,
4318 __isl_take isl_vec *v);
4320 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4321 by the corresponding elements of C<v>.
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4324 __isl_take isl_pw_multi_aff *pma,
4325 __isl_take isl_set *set);
4326 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4327 __isl_take isl_pw_multi_aff *pma,
4328 __isl_take isl_set *set);
4329 __isl_give isl_union_pw_multi_aff *
4330 isl_union_pw_multi_aff_intersect_domain(
4331 __isl_take isl_union_pw_multi_aff *upma,
4332 __isl_take isl_union_set *uset);
4333 __isl_give isl_multi_aff *isl_multi_aff_lift(
4334 __isl_take isl_multi_aff *maff,
4335 __isl_give isl_local_space **ls);
4336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4337 __isl_take isl_pw_multi_aff *pma);
4338 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4339 __isl_take isl_multi_aff *multi,
4340 __isl_take isl_space *model);
4341 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4342 __isl_take isl_pw_multi_aff *pma,
4343 __isl_take isl_space *model);
4344 __isl_give isl_pw_multi_aff *
4345 isl_pw_multi_aff_project_domain_on_params(
4346 __isl_take isl_pw_multi_aff *pma);
4347 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4348 __isl_take isl_multi_aff *maff,
4349 __isl_take isl_set *context);
4350 __isl_give isl_multi_aff *isl_multi_aff_gist(
4351 __isl_take isl_multi_aff *maff,
4352 __isl_take isl_set *context);
4353 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4354 __isl_take isl_pw_multi_aff *pma,
4355 __isl_take isl_set *set);
4356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4357 __isl_take isl_pw_multi_aff *pma,
4358 __isl_take isl_set *set);
4359 __isl_give isl_set *isl_pw_multi_aff_domain(
4360 __isl_take isl_pw_multi_aff *pma);
4361 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4362 __isl_take isl_union_pw_multi_aff *upma);
4363 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4364 __isl_take isl_multi_aff *ma1, unsigned pos,
4365 __isl_take isl_multi_aff *ma2);
4366 __isl_give isl_multi_aff *isl_multi_aff_splice(
4367 __isl_take isl_multi_aff *ma1,
4368 unsigned in_pos, unsigned out_pos,
4369 __isl_take isl_multi_aff *ma2);
4370 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4371 __isl_take isl_multi_aff *ma1,
4372 __isl_take isl_multi_aff *ma2);
4373 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4374 __isl_take isl_multi_aff *ma1,
4375 __isl_take isl_multi_aff *ma2);
4376 __isl_give isl_multi_aff *isl_multi_aff_product(
4377 __isl_take isl_multi_aff *ma1,
4378 __isl_take isl_multi_aff *ma2);
4379 __isl_give isl_pw_multi_aff *
4380 isl_pw_multi_aff_range_product(
4381 __isl_take isl_pw_multi_aff *pma1,
4382 __isl_take isl_pw_multi_aff *pma2);
4383 __isl_give isl_pw_multi_aff *
4384 isl_pw_multi_aff_flat_range_product(
4385 __isl_take isl_pw_multi_aff *pma1,
4386 __isl_take isl_pw_multi_aff *pma2);
4387 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4388 __isl_take isl_pw_multi_aff *pma1,
4389 __isl_take isl_pw_multi_aff *pma2);
4390 __isl_give isl_union_pw_multi_aff *
4391 isl_union_pw_multi_aff_flat_range_product(
4392 __isl_take isl_union_pw_multi_aff *upma1,
4393 __isl_take isl_union_pw_multi_aff *upma2);
4394 __isl_give isl_multi_pw_aff *
4395 isl_multi_pw_aff_range_splice(
4396 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4397 __isl_take isl_multi_pw_aff *mpa2);
4398 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4399 __isl_take isl_multi_pw_aff *mpa1,
4400 unsigned in_pos, unsigned out_pos,
4401 __isl_take isl_multi_pw_aff *mpa2);
4402 __isl_give isl_multi_pw_aff *
4403 isl_multi_pw_aff_range_product(
4404 __isl_take isl_multi_pw_aff *mpa1,
4405 __isl_take isl_multi_pw_aff *mpa2);
4406 __isl_give isl_multi_pw_aff *
4407 isl_multi_pw_aff_flat_range_product(
4408 __isl_take isl_multi_pw_aff *mpa1,
4409 __isl_take isl_multi_pw_aff *mpa2);
4411 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4412 then it is assigned the local space that lies at the basis of
4413 the lifting applied.
4415 #include <isl/aff.h>
4416 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4417 __isl_take isl_multi_aff *ma1,
4418 __isl_take isl_multi_aff *ma2);
4419 __isl_give isl_pw_multi_aff *
4420 isl_pw_multi_aff_pullback_multi_aff(
4421 __isl_take isl_pw_multi_aff *pma,
4422 __isl_take isl_multi_aff *ma);
4423 __isl_give isl_pw_multi_aff *
4424 isl_pw_multi_aff_pullback_pw_multi_aff(
4425 __isl_take isl_pw_multi_aff *pma1,
4426 __isl_take isl_pw_multi_aff *pma2);
4428 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4429 In other words, C<ma2> is plugged
4432 __isl_give isl_set *isl_multi_aff_lex_le_set(
4433 __isl_take isl_multi_aff *ma1,
4434 __isl_take isl_multi_aff *ma2);
4435 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4436 __isl_take isl_multi_aff *ma1,
4437 __isl_take isl_multi_aff *ma2);
4439 The function C<isl_multi_aff_lex_le_set> returns a set
4440 containing those elements in the shared domain space
4441 where C<ma1> is lexicographically smaller than or
4444 An expression can be read from input using
4446 #include <isl/aff.h>
4447 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4448 isl_ctx *ctx, const char *str);
4449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4450 isl_ctx *ctx, const char *str);
4451 __isl_give isl_union_pw_multi_aff *
4452 isl_union_pw_multi_aff_read_from_str(
4453 isl_ctx *ctx, const char *str);
4455 An expression can be printed using
4457 #include <isl/aff.h>
4458 __isl_give isl_printer *isl_printer_print_multi_aff(
4459 __isl_take isl_printer *p,
4460 __isl_keep isl_multi_aff *maff);
4461 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4462 __isl_take isl_printer *p,
4463 __isl_keep isl_pw_multi_aff *pma);
4464 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4465 __isl_take isl_printer *p,
4466 __isl_keep isl_union_pw_multi_aff *upma);
4467 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4468 __isl_take isl_printer *p,
4469 __isl_keep isl_multi_pw_aff *mpa);
4473 Points are elements of a set. They can be used to construct
4474 simple sets (boxes) or they can be used to represent the
4475 individual elements of a set.
4476 The zero point (the origin) can be created using
4478 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4480 The coordinates of a point can be inspected, set and changed
4483 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4484 enum isl_dim_type type, int pos, isl_int *v);
4485 __isl_give isl_val *isl_point_get_coordinate_val(
4486 __isl_keep isl_point *pnt,
4487 enum isl_dim_type type, int pos);
4488 __isl_give isl_point *isl_point_set_coordinate(
4489 __isl_take isl_point *pnt,
4490 enum isl_dim_type type, int pos, isl_int v);
4491 __isl_give isl_point *isl_point_set_coordinate_val(
4492 __isl_take isl_point *pnt,
4493 enum isl_dim_type type, int pos,
4494 __isl_take isl_val *v);
4496 __isl_give isl_point *isl_point_add_ui(
4497 __isl_take isl_point *pnt,
4498 enum isl_dim_type type, int pos, unsigned val);
4499 __isl_give isl_point *isl_point_sub_ui(
4500 __isl_take isl_point *pnt,
4501 enum isl_dim_type type, int pos, unsigned val);
4503 Other properties can be obtained using
4505 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4507 Points can be copied or freed using
4509 __isl_give isl_point *isl_point_copy(
4510 __isl_keep isl_point *pnt);
4511 void isl_point_free(__isl_take isl_point *pnt);
4513 A singleton set can be created from a point using
4515 __isl_give isl_basic_set *isl_basic_set_from_point(
4516 __isl_take isl_point *pnt);
4517 __isl_give isl_set *isl_set_from_point(
4518 __isl_take isl_point *pnt);
4520 and a box can be created from two opposite extremal points using
4522 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4523 __isl_take isl_point *pnt1,
4524 __isl_take isl_point *pnt2);
4525 __isl_give isl_set *isl_set_box_from_points(
4526 __isl_take isl_point *pnt1,
4527 __isl_take isl_point *pnt2);
4529 All elements of a B<bounded> (union) set can be enumerated using
4530 the following functions.
4532 int isl_set_foreach_point(__isl_keep isl_set *set,
4533 int (*fn)(__isl_take isl_point *pnt, void *user),
4535 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4536 int (*fn)(__isl_take isl_point *pnt, void *user),
4539 The function C<fn> is called for each integer point in
4540 C<set> with as second argument the last argument of
4541 the C<isl_set_foreach_point> call. The function C<fn>
4542 should return C<0> on success and C<-1> on failure.
4543 In the latter case, C<isl_set_foreach_point> will stop
4544 enumerating and return C<-1> as well.
4545 If the enumeration is performed successfully and to completion,
4546 then C<isl_set_foreach_point> returns C<0>.
4548 To obtain a single point of a (basic) set, use
4550 __isl_give isl_point *isl_basic_set_sample_point(
4551 __isl_take isl_basic_set *bset);
4552 __isl_give isl_point *isl_set_sample_point(
4553 __isl_take isl_set *set);
4555 If C<set> does not contain any (integer) points, then the
4556 resulting point will be ``void'', a property that can be
4559 int isl_point_is_void(__isl_keep isl_point *pnt);
4561 =head2 Piecewise Quasipolynomials
4563 A piecewise quasipolynomial is a particular kind of function that maps
4564 a parametric point to a rational value.
4565 More specifically, a quasipolynomial is a polynomial expression in greatest
4566 integer parts of affine expressions of parameters and variables.
4567 A piecewise quasipolynomial is a subdivision of a given parametric
4568 domain into disjoint cells with a quasipolynomial associated to
4569 each cell. The value of the piecewise quasipolynomial at a given
4570 point is the value of the quasipolynomial associated to the cell
4571 that contains the point. Outside of the union of cells,
4572 the value is assumed to be zero.
4573 For example, the piecewise quasipolynomial
4575 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4577 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4578 A given piecewise quasipolynomial has a fixed domain dimension.
4579 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4580 defined over different domains.
4581 Piecewise quasipolynomials are mainly used by the C<barvinok>
4582 library for representing the number of elements in a parametric set or map.
4583 For example, the piecewise quasipolynomial above represents
4584 the number of points in the map
4586 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4588 =head3 Input and Output
4590 Piecewise quasipolynomials can be read from input using
4592 __isl_give isl_union_pw_qpolynomial *
4593 isl_union_pw_qpolynomial_read_from_str(
4594 isl_ctx *ctx, const char *str);
4596 Quasipolynomials and piecewise quasipolynomials can be printed
4597 using the following functions.
4599 __isl_give isl_printer *isl_printer_print_qpolynomial(
4600 __isl_take isl_printer *p,
4601 __isl_keep isl_qpolynomial *qp);
4603 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4604 __isl_take isl_printer *p,
4605 __isl_keep isl_pw_qpolynomial *pwqp);
4607 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4608 __isl_take isl_printer *p,
4609 __isl_keep isl_union_pw_qpolynomial *upwqp);
4611 The output format of the printer
4612 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4613 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4615 In case of printing in C<ISL_FORMAT_C>, the user may want
4616 to set the names of all dimensions
4618 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4619 __isl_take isl_qpolynomial *qp,
4620 enum isl_dim_type type, unsigned pos,
4622 __isl_give isl_pw_qpolynomial *
4623 isl_pw_qpolynomial_set_dim_name(
4624 __isl_take isl_pw_qpolynomial *pwqp,
4625 enum isl_dim_type type, unsigned pos,
4628 =head3 Creating New (Piecewise) Quasipolynomials
4630 Some simple quasipolynomials can be created using the following functions.
4631 More complicated quasipolynomials can be created by applying
4632 operations such as addition and multiplication
4633 on the resulting quasipolynomials
4635 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4636 __isl_take isl_space *domain);
4637 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4638 __isl_take isl_space *domain);
4639 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4640 __isl_take isl_space *domain);
4641 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4642 __isl_take isl_space *domain);
4643 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4644 __isl_take isl_space *domain);
4645 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4646 __isl_take isl_space *domain,
4647 const isl_int n, const isl_int d);
4648 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4649 __isl_take isl_space *domain,
4650 __isl_take isl_val *val);
4651 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4652 __isl_take isl_space *domain,
4653 enum isl_dim_type type, unsigned pos);
4654 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4655 __isl_take isl_aff *aff);
4657 Note that the space in which a quasipolynomial lives is a map space
4658 with a one-dimensional range. The C<domain> argument in some of
4659 the functions above corresponds to the domain of this map space.
4661 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4662 with a single cell can be created using the following functions.
4663 Multiple of these single cell piecewise quasipolynomials can
4664 be combined to create more complicated piecewise quasipolynomials.
4666 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4667 __isl_take isl_space *space);
4668 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4669 __isl_take isl_set *set,
4670 __isl_take isl_qpolynomial *qp);
4671 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4672 __isl_take isl_qpolynomial *qp);
4673 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4674 __isl_take isl_pw_aff *pwaff);
4676 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4677 __isl_take isl_space *space);
4678 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4679 __isl_take isl_pw_qpolynomial *pwqp);
4680 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4681 __isl_take isl_union_pw_qpolynomial *upwqp,
4682 __isl_take isl_pw_qpolynomial *pwqp);
4684 Quasipolynomials can be copied and freed again using the following
4687 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4688 __isl_keep isl_qpolynomial *qp);
4689 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4691 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4692 __isl_keep isl_pw_qpolynomial *pwqp);
4693 void *isl_pw_qpolynomial_free(
4694 __isl_take isl_pw_qpolynomial *pwqp);
4696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4697 __isl_keep isl_union_pw_qpolynomial *upwqp);
4698 void *isl_union_pw_qpolynomial_free(
4699 __isl_take isl_union_pw_qpolynomial *upwqp);
4701 =head3 Inspecting (Piecewise) Quasipolynomials
4703 To iterate over all piecewise quasipolynomials in a union
4704 piecewise quasipolynomial, use the following function
4706 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4707 __isl_keep isl_union_pw_qpolynomial *upwqp,
4708 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4711 To extract the piecewise quasipolynomial in a given space from a union, use
4713 __isl_give isl_pw_qpolynomial *
4714 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4715 __isl_keep isl_union_pw_qpolynomial *upwqp,
4716 __isl_take isl_space *space);
4718 To iterate over the cells in a piecewise quasipolynomial,
4719 use either of the following two functions
4721 int isl_pw_qpolynomial_foreach_piece(
4722 __isl_keep isl_pw_qpolynomial *pwqp,
4723 int (*fn)(__isl_take isl_set *set,
4724 __isl_take isl_qpolynomial *qp,
4725 void *user), void *user);
4726 int isl_pw_qpolynomial_foreach_lifted_piece(
4727 __isl_keep isl_pw_qpolynomial *pwqp,
4728 int (*fn)(__isl_take isl_set *set,
4729 __isl_take isl_qpolynomial *qp,
4730 void *user), void *user);
4732 As usual, the function C<fn> should return C<0> on success
4733 and C<-1> on failure. The difference between
4734 C<isl_pw_qpolynomial_foreach_piece> and
4735 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4736 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4737 compute unique representations for all existentially quantified
4738 variables and then turn these existentially quantified variables
4739 into extra set variables, adapting the associated quasipolynomial
4740 accordingly. This means that the C<set> passed to C<fn>
4741 will not have any existentially quantified variables, but that
4742 the dimensions of the sets may be different for different
4743 invocations of C<fn>.
4745 The constant term of a quasipolynomial can be extracted using
4747 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4748 __isl_keep isl_qpolynomial *qp);
4750 To iterate over all terms in a quasipolynomial,
4753 int isl_qpolynomial_foreach_term(
4754 __isl_keep isl_qpolynomial *qp,
4755 int (*fn)(__isl_take isl_term *term,
4756 void *user), void *user);
4758 The terms themselves can be inspected and freed using
4761 unsigned isl_term_dim(__isl_keep isl_term *term,
4762 enum isl_dim_type type);
4763 void isl_term_get_num(__isl_keep isl_term *term,
4765 void isl_term_get_den(__isl_keep isl_term *term,
4767 __isl_give isl_val *isl_term_get_coefficient_val(
4768 __isl_keep isl_term *term);
4769 int isl_term_get_exp(__isl_keep isl_term *term,
4770 enum isl_dim_type type, unsigned pos);
4771 __isl_give isl_aff *isl_term_get_div(
4772 __isl_keep isl_term *term, unsigned pos);
4773 void isl_term_free(__isl_take isl_term *term);
4775 Each term is a product of parameters, set variables and
4776 integer divisions. The function C<isl_term_get_exp>
4777 returns the exponent of a given dimensions in the given term.
4778 The C<isl_int>s in the arguments of C<isl_term_get_num>
4779 and C<isl_term_get_den> need to have been initialized
4780 using C<isl_int_init> before calling these functions.
4782 =head3 Properties of (Piecewise) Quasipolynomials
4784 To check whether a quasipolynomial is actually a constant,
4785 use the following function.
4787 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4788 isl_int *n, isl_int *d);
4790 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4791 then the numerator and denominator of the constant
4792 are returned in C<*n> and C<*d>, respectively.
4794 To check whether two union piecewise quasipolynomials are
4795 obviously equal, use
4797 int isl_union_pw_qpolynomial_plain_is_equal(
4798 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4799 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4801 =head3 Operations on (Piecewise) Quasipolynomials
4803 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4804 __isl_take isl_qpolynomial *qp, isl_int v);
4805 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4806 __isl_take isl_qpolynomial *qp,
4807 __isl_take isl_val *v);
4808 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4809 __isl_take isl_qpolynomial *qp);
4810 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4811 __isl_take isl_qpolynomial *qp1,
4812 __isl_take isl_qpolynomial *qp2);
4813 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4814 __isl_take isl_qpolynomial *qp1,
4815 __isl_take isl_qpolynomial *qp2);
4816 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4817 __isl_take isl_qpolynomial *qp1,
4818 __isl_take isl_qpolynomial *qp2);
4819 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4820 __isl_take isl_qpolynomial *qp, unsigned exponent);
4822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4823 __isl_take isl_pw_qpolynomial *pwqp,
4824 enum isl_dim_type type, unsigned n,
4825 __isl_take isl_val *v);
4826 __isl_give isl_pw_qpolynomial *
4827 isl_pw_qpolynomial_scale_val(
4828 __isl_take isl_pw_qpolynomial *pwqp,
4829 __isl_take isl_val *v);
4830 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4831 __isl_take isl_pw_qpolynomial *pwqp1,
4832 __isl_take isl_pw_qpolynomial *pwqp2);
4833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4834 __isl_take isl_pw_qpolynomial *pwqp1,
4835 __isl_take isl_pw_qpolynomial *pwqp2);
4836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4837 __isl_take isl_pw_qpolynomial *pwqp1,
4838 __isl_take isl_pw_qpolynomial *pwqp2);
4839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4840 __isl_take isl_pw_qpolynomial *pwqp);
4841 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4842 __isl_take isl_pw_qpolynomial *pwqp1,
4843 __isl_take isl_pw_qpolynomial *pwqp2);
4844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4845 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4847 __isl_give isl_union_pw_qpolynomial *
4848 isl_union_pw_qpolynomial_scale_val(
4849 __isl_take isl_union_pw_qpolynomial *upwqp,
4850 __isl_take isl_val *v);
4851 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4852 __isl_take isl_union_pw_qpolynomial *upwqp1,
4853 __isl_take isl_union_pw_qpolynomial *upwqp2);
4854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4855 __isl_take isl_union_pw_qpolynomial *upwqp1,
4856 __isl_take isl_union_pw_qpolynomial *upwqp2);
4857 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4858 __isl_take isl_union_pw_qpolynomial *upwqp1,
4859 __isl_take isl_union_pw_qpolynomial *upwqp2);
4861 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4862 __isl_take isl_pw_qpolynomial *pwqp,
4863 __isl_take isl_point *pnt);
4865 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4866 __isl_take isl_union_pw_qpolynomial *upwqp,
4867 __isl_take isl_point *pnt);
4869 __isl_give isl_set *isl_pw_qpolynomial_domain(
4870 __isl_take isl_pw_qpolynomial *pwqp);
4871 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4872 __isl_take isl_pw_qpolynomial *pwpq,
4873 __isl_take isl_set *set);
4874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4875 __isl_take isl_pw_qpolynomial *pwpq,
4876 __isl_take isl_set *set);
4878 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4879 __isl_take isl_union_pw_qpolynomial *upwqp);
4880 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4881 __isl_take isl_union_pw_qpolynomial *upwpq,
4882 __isl_take isl_union_set *uset);
4883 __isl_give isl_union_pw_qpolynomial *
4884 isl_union_pw_qpolynomial_intersect_params(
4885 __isl_take isl_union_pw_qpolynomial *upwpq,
4886 __isl_take isl_set *set);
4888 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4889 __isl_take isl_qpolynomial *qp,
4890 __isl_take isl_space *model);
4892 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4893 __isl_take isl_qpolynomial *qp);
4894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4895 __isl_take isl_pw_qpolynomial *pwqp);
4897 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4898 __isl_take isl_union_pw_qpolynomial *upwqp);
4900 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4901 __isl_take isl_qpolynomial *qp,
4902 __isl_take isl_set *context);
4903 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4904 __isl_take isl_qpolynomial *qp,
4905 __isl_take isl_set *context);
4907 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4908 __isl_take isl_pw_qpolynomial *pwqp,
4909 __isl_take isl_set *context);
4910 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4911 __isl_take isl_pw_qpolynomial *pwqp,
4912 __isl_take isl_set *context);
4914 __isl_give isl_union_pw_qpolynomial *
4915 isl_union_pw_qpolynomial_gist_params(
4916 __isl_take isl_union_pw_qpolynomial *upwqp,
4917 __isl_take isl_set *context);
4918 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4919 __isl_take isl_union_pw_qpolynomial *upwqp,
4920 __isl_take isl_union_set *context);
4922 The gist operation applies the gist operation to each of
4923 the cells in the domain of the input piecewise quasipolynomial.
4924 The context is also exploited
4925 to simplify the quasipolynomials associated to each cell.
4927 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4928 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4929 __isl_give isl_union_pw_qpolynomial *
4930 isl_union_pw_qpolynomial_to_polynomial(
4931 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4933 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4934 the polynomial will be an overapproximation. If C<sign> is negative,
4935 it will be an underapproximation. If C<sign> is zero, the approximation
4936 will lie somewhere in between.
4938 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4940 A piecewise quasipolynomial reduction is a piecewise
4941 reduction (or fold) of quasipolynomials.
4942 In particular, the reduction can be maximum or a minimum.
4943 The objects are mainly used to represent the result of
4944 an upper or lower bound on a quasipolynomial over its domain,
4945 i.e., as the result of the following function.
4947 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4948 __isl_take isl_pw_qpolynomial *pwqp,
4949 enum isl_fold type, int *tight);
4951 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4952 __isl_take isl_union_pw_qpolynomial *upwqp,
4953 enum isl_fold type, int *tight);
4955 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4956 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4957 is the returned bound is known be tight, i.e., for each value
4958 of the parameters there is at least
4959 one element in the domain that reaches the bound.
4960 If the domain of C<pwqp> is not wrapping, then the bound is computed
4961 over all elements in that domain and the result has a purely parametric
4962 domain. If the domain of C<pwqp> is wrapping, then the bound is
4963 computed over the range of the wrapped relation. The domain of the
4964 wrapped relation becomes the domain of the result.
4966 A (piecewise) quasipolynomial reduction can be copied or freed using the
4967 following functions.
4969 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4970 __isl_keep isl_qpolynomial_fold *fold);
4971 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4972 __isl_keep isl_pw_qpolynomial_fold *pwf);
4973 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4974 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4975 void isl_qpolynomial_fold_free(
4976 __isl_take isl_qpolynomial_fold *fold);
4977 void *isl_pw_qpolynomial_fold_free(
4978 __isl_take isl_pw_qpolynomial_fold *pwf);
4979 void *isl_union_pw_qpolynomial_fold_free(
4980 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4982 =head3 Printing Piecewise Quasipolynomial Reductions
4984 Piecewise quasipolynomial reductions can be printed
4985 using the following function.
4987 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4988 __isl_take isl_printer *p,
4989 __isl_keep isl_pw_qpolynomial_fold *pwf);
4990 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4991 __isl_take isl_printer *p,
4992 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4994 For C<isl_printer_print_pw_qpolynomial_fold>,
4995 output format of the printer
4996 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4997 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4998 output format of the printer
4999 needs to be set to C<ISL_FORMAT_ISL>.
5000 In case of printing in C<ISL_FORMAT_C>, the user may want
5001 to set the names of all dimensions
5003 __isl_give isl_pw_qpolynomial_fold *
5004 isl_pw_qpolynomial_fold_set_dim_name(
5005 __isl_take isl_pw_qpolynomial_fold *pwf,
5006 enum isl_dim_type type, unsigned pos,
5009 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5011 To iterate over all piecewise quasipolynomial reductions in a union
5012 piecewise quasipolynomial reduction, use the following function
5014 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5015 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5016 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5017 void *user), void *user);
5019 To iterate over the cells in a piecewise quasipolynomial reduction,
5020 use either of the following two functions
5022 int isl_pw_qpolynomial_fold_foreach_piece(
5023 __isl_keep isl_pw_qpolynomial_fold *pwf,
5024 int (*fn)(__isl_take isl_set *set,
5025 __isl_take isl_qpolynomial_fold *fold,
5026 void *user), void *user);
5027 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5028 __isl_keep isl_pw_qpolynomial_fold *pwf,
5029 int (*fn)(__isl_take isl_set *set,
5030 __isl_take isl_qpolynomial_fold *fold,
5031 void *user), void *user);
5033 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5034 of the difference between these two functions.
5036 To iterate over all quasipolynomials in a reduction, use
5038 int isl_qpolynomial_fold_foreach_qpolynomial(
5039 __isl_keep isl_qpolynomial_fold *fold,
5040 int (*fn)(__isl_take isl_qpolynomial *qp,
5041 void *user), void *user);
5043 =head3 Properties of Piecewise Quasipolynomial Reductions
5045 To check whether two union piecewise quasipolynomial reductions are
5046 obviously equal, use
5048 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5049 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5050 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5052 =head3 Operations on Piecewise Quasipolynomial Reductions
5054 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5055 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5056 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5057 __isl_take isl_qpolynomial_fold *fold,
5058 __isl_take isl_val *v);
5059 __isl_give isl_pw_qpolynomial_fold *
5060 isl_pw_qpolynomial_fold_scale_val(
5061 __isl_take isl_pw_qpolynomial_fold *pwf,
5062 __isl_take isl_val *v);
5063 __isl_give isl_union_pw_qpolynomial_fold *
5064 isl_union_pw_qpolynomial_fold_scale_val(
5065 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5066 __isl_take isl_val *v);
5068 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5069 __isl_take isl_pw_qpolynomial_fold *pwf1,
5070 __isl_take isl_pw_qpolynomial_fold *pwf2);
5072 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5073 __isl_take isl_pw_qpolynomial_fold *pwf1,
5074 __isl_take isl_pw_qpolynomial_fold *pwf2);
5076 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5077 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5078 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5080 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5081 __isl_take isl_pw_qpolynomial_fold *pwf,
5082 __isl_take isl_point *pnt);
5084 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5085 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5086 __isl_take isl_point *pnt);
5088 __isl_give isl_pw_qpolynomial_fold *
5089 isl_pw_qpolynomial_fold_intersect_params(
5090 __isl_take isl_pw_qpolynomial_fold *pwf,
5091 __isl_take isl_set *set);
5093 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5094 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5095 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5096 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5097 __isl_take isl_union_set *uset);
5098 __isl_give isl_union_pw_qpolynomial_fold *
5099 isl_union_pw_qpolynomial_fold_intersect_params(
5100 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5101 __isl_take isl_set *set);
5103 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5104 __isl_take isl_pw_qpolynomial_fold *pwf);
5106 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5107 __isl_take isl_pw_qpolynomial_fold *pwf);
5109 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5110 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5112 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5113 __isl_take isl_qpolynomial_fold *fold,
5114 __isl_take isl_set *context);
5115 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5116 __isl_take isl_qpolynomial_fold *fold,
5117 __isl_take isl_set *context);
5119 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5120 __isl_take isl_pw_qpolynomial_fold *pwf,
5121 __isl_take isl_set *context);
5122 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5123 __isl_take isl_pw_qpolynomial_fold *pwf,
5124 __isl_take isl_set *context);
5126 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5127 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5128 __isl_take isl_union_set *context);
5129 __isl_give isl_union_pw_qpolynomial_fold *
5130 isl_union_pw_qpolynomial_fold_gist_params(
5131 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5132 __isl_take isl_set *context);
5134 The gist operation applies the gist operation to each of
5135 the cells in the domain of the input piecewise quasipolynomial reduction.
5136 In future, the operation will also exploit the context
5137 to simplify the quasipolynomial reductions associated to each cell.
5139 __isl_give isl_pw_qpolynomial_fold *
5140 isl_set_apply_pw_qpolynomial_fold(
5141 __isl_take isl_set *set,
5142 __isl_take isl_pw_qpolynomial_fold *pwf,
5144 __isl_give isl_pw_qpolynomial_fold *
5145 isl_map_apply_pw_qpolynomial_fold(
5146 __isl_take isl_map *map,
5147 __isl_take isl_pw_qpolynomial_fold *pwf,
5149 __isl_give isl_union_pw_qpolynomial_fold *
5150 isl_union_set_apply_union_pw_qpolynomial_fold(
5151 __isl_take isl_union_set *uset,
5152 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5154 __isl_give isl_union_pw_qpolynomial_fold *
5155 isl_union_map_apply_union_pw_qpolynomial_fold(
5156 __isl_take isl_union_map *umap,
5157 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5160 The functions taking a map
5161 compose the given map with the given piecewise quasipolynomial reduction.
5162 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5163 over all elements in the intersection of the range of the map
5164 and the domain of the piecewise quasipolynomial reduction
5165 as a function of an element in the domain of the map.
5166 The functions taking a set compute a bound over all elements in the
5167 intersection of the set and the domain of the
5168 piecewise quasipolynomial reduction.
5170 =head2 Parametric Vertex Enumeration
5172 The parametric vertex enumeration described in this section
5173 is mainly intended to be used internally and by the C<barvinok>
5176 #include <isl/vertices.h>
5177 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5178 __isl_keep isl_basic_set *bset);
5180 The function C<isl_basic_set_compute_vertices> performs the
5181 actual computation of the parametric vertices and the chamber
5182 decomposition and store the result in an C<isl_vertices> object.
5183 This information can be queried by either iterating over all
5184 the vertices or iterating over all the chambers or cells
5185 and then iterating over all vertices that are active on the chamber.
5187 int isl_vertices_foreach_vertex(
5188 __isl_keep isl_vertices *vertices,
5189 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5192 int isl_vertices_foreach_cell(
5193 __isl_keep isl_vertices *vertices,
5194 int (*fn)(__isl_take isl_cell *cell, void *user),
5196 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5197 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5200 Other operations that can be performed on an C<isl_vertices> object are
5203 isl_ctx *isl_vertices_get_ctx(
5204 __isl_keep isl_vertices *vertices);
5205 int isl_vertices_get_n_vertices(
5206 __isl_keep isl_vertices *vertices);
5207 void isl_vertices_free(__isl_take isl_vertices *vertices);
5209 Vertices can be inspected and destroyed using the following functions.
5211 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5212 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5213 __isl_give isl_basic_set *isl_vertex_get_domain(
5214 __isl_keep isl_vertex *vertex);
5215 __isl_give isl_basic_set *isl_vertex_get_expr(
5216 __isl_keep isl_vertex *vertex);
5217 void isl_vertex_free(__isl_take isl_vertex *vertex);
5219 C<isl_vertex_get_expr> returns a singleton parametric set describing
5220 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5222 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5223 B<rational> basic sets, so they should mainly be used for inspection
5224 and should not be mixed with integer sets.
5226 Chambers can be inspected and destroyed using the following functions.
5228 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5229 __isl_give isl_basic_set *isl_cell_get_domain(
5230 __isl_keep isl_cell *cell);
5231 void isl_cell_free(__isl_take isl_cell *cell);
5233 =head1 Polyhedral Compilation Library
5235 This section collects functionality in C<isl> that has been specifically
5236 designed for use during polyhedral compilation.
5238 =head2 Dependence Analysis
5240 C<isl> contains specialized functionality for performing
5241 array dataflow analysis. That is, given a I<sink> access relation
5242 and a collection of possible I<source> access relations,
5243 C<isl> can compute relations that describe
5244 for each iteration of the sink access, which iteration
5245 of which of the source access relations was the last
5246 to access the same data element before the given iteration
5248 The resulting dependence relations map source iterations
5249 to the corresponding sink iterations.
5250 To compute standard flow dependences, the sink should be
5251 a read, while the sources should be writes.
5252 If any of the source accesses are marked as being I<may>
5253 accesses, then there will be a dependence from the last
5254 I<must> access B<and> from any I<may> access that follows
5255 this last I<must> access.
5256 In particular, if I<all> sources are I<may> accesses,
5257 then memory based dependence analysis is performed.
5258 If, on the other hand, all sources are I<must> accesses,
5259 then value based dependence analysis is performed.
5261 #include <isl/flow.h>
5263 typedef int (*isl_access_level_before)(void *first, void *second);
5265 __isl_give isl_access_info *isl_access_info_alloc(
5266 __isl_take isl_map *sink,
5267 void *sink_user, isl_access_level_before fn,
5269 __isl_give isl_access_info *isl_access_info_add_source(
5270 __isl_take isl_access_info *acc,
5271 __isl_take isl_map *source, int must,
5273 void *isl_access_info_free(__isl_take isl_access_info *acc);
5275 __isl_give isl_flow *isl_access_info_compute_flow(
5276 __isl_take isl_access_info *acc);
5278 int isl_flow_foreach(__isl_keep isl_flow *deps,
5279 int (*fn)(__isl_take isl_map *dep, int must,
5280 void *dep_user, void *user),
5282 __isl_give isl_map *isl_flow_get_no_source(
5283 __isl_keep isl_flow *deps, int must);
5284 void isl_flow_free(__isl_take isl_flow *deps);
5286 The function C<isl_access_info_compute_flow> performs the actual
5287 dependence analysis. The other functions are used to construct
5288 the input for this function or to read off the output.
5290 The input is collected in an C<isl_access_info>, which can
5291 be created through a call to C<isl_access_info_alloc>.
5292 The arguments to this functions are the sink access relation
5293 C<sink>, a token C<sink_user> used to identify the sink
5294 access to the user, a callback function for specifying the
5295 relative order of source and sink accesses, and the number
5296 of source access relations that will be added.
5297 The callback function has type C<int (*)(void *first, void *second)>.
5298 The function is called with two user supplied tokens identifying
5299 either a source or the sink and it should return the shared nesting
5300 level and the relative order of the two accesses.
5301 In particular, let I<n> be the number of loops shared by
5302 the two accesses. If C<first> precedes C<second> textually,
5303 then the function should return I<2 * n + 1>; otherwise,
5304 it should return I<2 * n>.
5305 The sources can be added to the C<isl_access_info> by performing
5306 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5307 C<must> indicates whether the source is a I<must> access
5308 or a I<may> access. Note that a multi-valued access relation
5309 should only be marked I<must> if every iteration in the domain
5310 of the relation accesses I<all> elements in its image.
5311 The C<source_user> token is again used to identify
5312 the source access. The range of the source access relation
5313 C<source> should have the same dimension as the range
5314 of the sink access relation.
5315 The C<isl_access_info_free> function should usually not be
5316 called explicitly, because it is called implicitly by
5317 C<isl_access_info_compute_flow>.
5319 The result of the dependence analysis is collected in an
5320 C<isl_flow>. There may be elements of
5321 the sink access for which no preceding source access could be
5322 found or for which all preceding sources are I<may> accesses.
5323 The relations containing these elements can be obtained through
5324 calls to C<isl_flow_get_no_source>, the first with C<must> set
5325 and the second with C<must> unset.
5326 In the case of standard flow dependence analysis,
5327 with the sink a read and the sources I<must> writes,
5328 the first relation corresponds to the reads from uninitialized
5329 array elements and the second relation is empty.
5330 The actual flow dependences can be extracted using
5331 C<isl_flow_foreach>. This function will call the user-specified
5332 callback function C<fn> for each B<non-empty> dependence between
5333 a source and the sink. The callback function is called
5334 with four arguments, the actual flow dependence relation
5335 mapping source iterations to sink iterations, a boolean that
5336 indicates whether it is a I<must> or I<may> dependence, a token
5337 identifying the source and an additional C<void *> with value
5338 equal to the third argument of the C<isl_flow_foreach> call.
5339 A dependence is marked I<must> if it originates from a I<must>
5340 source and if it is not followed by any I<may> sources.
5342 After finishing with an C<isl_flow>, the user should call
5343 C<isl_flow_free> to free all associated memory.
5345 A higher-level interface to dependence analysis is provided
5346 by the following function.
5348 #include <isl/flow.h>
5350 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5351 __isl_take isl_union_map *must_source,
5352 __isl_take isl_union_map *may_source,
5353 __isl_take isl_union_map *schedule,
5354 __isl_give isl_union_map **must_dep,
5355 __isl_give isl_union_map **may_dep,
5356 __isl_give isl_union_map **must_no_source,
5357 __isl_give isl_union_map **may_no_source);
5359 The arrays are identified by the tuple names of the ranges
5360 of the accesses. The iteration domains by the tuple names
5361 of the domains of the accesses and of the schedule.
5362 The relative order of the iteration domains is given by the
5363 schedule. The relations returned through C<must_no_source>
5364 and C<may_no_source> are subsets of C<sink>.
5365 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5366 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5367 any of the other arguments is treated as an error.
5369 =head3 Interaction with Dependence Analysis
5371 During the dependence analysis, we frequently need to perform
5372 the following operation. Given a relation between sink iterations
5373 and potential source iterations from a particular source domain,
5374 what is the last potential source iteration corresponding to each
5375 sink iteration. It can sometimes be convenient to adjust
5376 the set of potential source iterations before or after each such operation.
5377 The prototypical example is fuzzy array dataflow analysis,
5378 where we need to analyze if, based on data-dependent constraints,
5379 the sink iteration can ever be executed without one or more of
5380 the corresponding potential source iterations being executed.
5381 If so, we can introduce extra parameters and select an unknown
5382 but fixed source iteration from the potential source iterations.
5383 To be able to perform such manipulations, C<isl> provides the following
5386 #include <isl/flow.h>
5388 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5389 __isl_keep isl_map *source_map,
5390 __isl_keep isl_set *sink, void *source_user,
5392 __isl_give isl_access_info *isl_access_info_set_restrict(
5393 __isl_take isl_access_info *acc,
5394 isl_access_restrict fn, void *user);
5396 The function C<isl_access_info_set_restrict> should be called
5397 before calling C<isl_access_info_compute_flow> and registers a callback function
5398 that will be called any time C<isl> is about to compute the last
5399 potential source. The first argument is the (reverse) proto-dependence,
5400 mapping sink iterations to potential source iterations.
5401 The second argument represents the sink iterations for which
5402 we want to compute the last source iteration.
5403 The third argument is the token corresponding to the source
5404 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5405 The callback is expected to return a restriction on either the input or
5406 the output of the operation computing the last potential source.
5407 If the input needs to be restricted then restrictions are needed
5408 for both the source and the sink iterations. The sink iterations
5409 and the potential source iterations will be intersected with these sets.
5410 If the output needs to be restricted then only a restriction on the source
5411 iterations is required.
5412 If any error occurs, the callback should return C<NULL>.
5413 An C<isl_restriction> object can be created, freed and inspected
5414 using the following functions.
5416 #include <isl/flow.h>
5418 __isl_give isl_restriction *isl_restriction_input(
5419 __isl_take isl_set *source_restr,
5420 __isl_take isl_set *sink_restr);
5421 __isl_give isl_restriction *isl_restriction_output(
5422 __isl_take isl_set *source_restr);
5423 __isl_give isl_restriction *isl_restriction_none(
5424 __isl_take isl_map *source_map);
5425 __isl_give isl_restriction *isl_restriction_empty(
5426 __isl_take isl_map *source_map);
5427 void *isl_restriction_free(
5428 __isl_take isl_restriction *restr);
5429 isl_ctx *isl_restriction_get_ctx(
5430 __isl_keep isl_restriction *restr);
5432 C<isl_restriction_none> and C<isl_restriction_empty> are special
5433 cases of C<isl_restriction_input>. C<isl_restriction_none>
5434 is essentially equivalent to
5436 isl_restriction_input(isl_set_universe(
5437 isl_space_range(isl_map_get_space(source_map))),
5439 isl_space_domain(isl_map_get_space(source_map))));
5441 whereas C<isl_restriction_empty> is essentially equivalent to
5443 isl_restriction_input(isl_set_empty(
5444 isl_space_range(isl_map_get_space(source_map))),
5446 isl_space_domain(isl_map_get_space(source_map))));
5450 B<The functionality described in this section is fairly new
5451 and may be subject to change.>
5453 The following function can be used to compute a schedule
5454 for a union of domains.
5455 By default, the algorithm used to construct the schedule is similar
5456 to that of C<Pluto>.
5457 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5459 The generated schedule respects all C<validity> dependences.
5460 That is, all dependence distances over these dependences in the
5461 scheduled space are lexicographically positive.
5462 The default algorithm tries to minimize the dependence distances over
5463 C<proximity> dependences.
5464 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5465 for groups of domains where the dependence distances have only
5466 non-negative values.
5467 When using Feautrier's algorithm, the C<proximity> dependence
5468 distances are only minimized during the extension to a
5469 full-dimensional schedule.
5471 #include <isl/schedule.h>
5472 __isl_give isl_schedule *isl_union_set_compute_schedule(
5473 __isl_take isl_union_set *domain,
5474 __isl_take isl_union_map *validity,
5475 __isl_take isl_union_map *proximity);
5476 void *isl_schedule_free(__isl_take isl_schedule *sched);
5478 A mapping from the domains to the scheduled space can be obtained
5479 from an C<isl_schedule> using the following function.
5481 __isl_give isl_union_map *isl_schedule_get_map(
5482 __isl_keep isl_schedule *sched);
5484 A representation of the schedule can be printed using
5486 __isl_give isl_printer *isl_printer_print_schedule(
5487 __isl_take isl_printer *p,
5488 __isl_keep isl_schedule *schedule);
5490 A representation of the schedule as a forest of bands can be obtained
5491 using the following function.
5493 __isl_give isl_band_list *isl_schedule_get_band_forest(
5494 __isl_keep isl_schedule *schedule);
5496 The individual bands can be visited in depth-first post-order
5497 using the following function.
5499 #include <isl/schedule.h>
5500 int isl_schedule_foreach_band(
5501 __isl_keep isl_schedule *sched,
5502 int (*fn)(__isl_keep isl_band *band, void *user),
5505 The list can be manipulated as explained in L<"Lists">.
5506 The bands inside the list can be copied and freed using the following
5509 #include <isl/band.h>
5510 __isl_give isl_band *isl_band_copy(
5511 __isl_keep isl_band *band);
5512 void *isl_band_free(__isl_take isl_band *band);
5514 Each band contains zero or more scheduling dimensions.
5515 These are referred to as the members of the band.
5516 The section of the schedule that corresponds to the band is
5517 referred to as the partial schedule of the band.
5518 For those nodes that participate in a band, the outer scheduling
5519 dimensions form the prefix schedule, while the inner scheduling
5520 dimensions form the suffix schedule.
5521 That is, if we take a cut of the band forest, then the union of
5522 the concatenations of the prefix, partial and suffix schedules of
5523 each band in the cut is equal to the entire schedule (modulo
5524 some possible padding at the end with zero scheduling dimensions).
5525 The properties of a band can be inspected using the following functions.
5527 #include <isl/band.h>
5528 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5530 int isl_band_has_children(__isl_keep isl_band *band);
5531 __isl_give isl_band_list *isl_band_get_children(
5532 __isl_keep isl_band *band);
5534 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5535 __isl_keep isl_band *band);
5536 __isl_give isl_union_map *isl_band_get_partial_schedule(
5537 __isl_keep isl_band *band);
5538 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5539 __isl_keep isl_band *band);
5541 int isl_band_n_member(__isl_keep isl_band *band);
5542 int isl_band_member_is_zero_distance(
5543 __isl_keep isl_band *band, int pos);
5545 int isl_band_list_foreach_band(
5546 __isl_keep isl_band_list *list,
5547 int (*fn)(__isl_keep isl_band *band, void *user),
5550 Note that a scheduling dimension is considered to be ``zero
5551 distance'' if it does not carry any proximity dependences
5553 That is, if the dependence distances of the proximity
5554 dependences are all zero in that direction (for fixed
5555 iterations of outer bands).
5556 Like C<isl_schedule_foreach_band>,
5557 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5558 in depth-first post-order.
5560 A band can be tiled using the following function.
5562 #include <isl/band.h>
5563 int isl_band_tile(__isl_keep isl_band *band,
5564 __isl_take isl_vec *sizes);
5566 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5568 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5569 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5571 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5573 The C<isl_band_tile> function tiles the band using the given tile sizes
5574 inside its schedule.
5575 A new child band is created to represent the point loops and it is
5576 inserted between the modified band and its children.
5577 The C<tile_scale_tile_loops> option specifies whether the tile
5578 loops iterators should be scaled by the tile sizes.
5579 If the C<tile_shift_point_loops> option is set, then the point loops
5580 are shifted to start at zero.
5582 A band can be split into two nested bands using the following function.
5584 int isl_band_split(__isl_keep isl_band *band, int pos);
5586 The resulting outer band contains the first C<pos> dimensions of C<band>
5587 while the inner band contains the remaining dimensions.
5589 A representation of the band can be printed using
5591 #include <isl/band.h>
5592 __isl_give isl_printer *isl_printer_print_band(
5593 __isl_take isl_printer *p,
5594 __isl_keep isl_band *band);
5598 #include <isl/schedule.h>
5599 int isl_options_set_schedule_max_coefficient(
5600 isl_ctx *ctx, int val);
5601 int isl_options_get_schedule_max_coefficient(
5603 int isl_options_set_schedule_max_constant_term(
5604 isl_ctx *ctx, int val);
5605 int isl_options_get_schedule_max_constant_term(
5607 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5608 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5609 int isl_options_set_schedule_maximize_band_depth(
5610 isl_ctx *ctx, int val);
5611 int isl_options_get_schedule_maximize_band_depth(
5613 int isl_options_set_schedule_outer_zero_distance(
5614 isl_ctx *ctx, int val);
5615 int isl_options_get_schedule_outer_zero_distance(
5617 int isl_options_set_schedule_split_scaled(
5618 isl_ctx *ctx, int val);
5619 int isl_options_get_schedule_split_scaled(
5621 int isl_options_set_schedule_algorithm(
5622 isl_ctx *ctx, int val);
5623 int isl_options_get_schedule_algorithm(
5625 int isl_options_set_schedule_separate_components(
5626 isl_ctx *ctx, int val);
5627 int isl_options_get_schedule_separate_components(
5632 =item * schedule_max_coefficient
5634 This option enforces that the coefficients for variable and parameter
5635 dimensions in the calculated schedule are not larger than the specified value.
5636 This option can significantly increase the speed of the scheduling calculation
5637 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5638 this option does not introduce bounds on the variable or parameter
5641 =item * schedule_max_constant_term
5643 This option enforces that the constant coefficients in the calculated schedule
5644 are not larger than the maximal constant term. This option can significantly
5645 increase the speed of the scheduling calculation and may also prevent fusing of
5646 unrelated dimensions. A value of -1 means that this option does not introduce
5647 bounds on the constant coefficients.
5649 =item * schedule_fuse
5651 This option controls the level of fusion.
5652 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5653 resulting schedule will be distributed as much as possible.
5654 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5655 try to fuse loops in the resulting schedule.
5657 =item * schedule_maximize_band_depth
5659 If this option is set, we do not split bands at the point
5660 where we detect splitting is necessary. Instead, we
5661 backtrack and split bands as early as possible. This
5662 reduces the number of splits and maximizes the width of
5663 the bands. Wider bands give more possibilities for tiling.
5664 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5665 then bands will be split as early as possible, even if there is no need.
5666 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5668 =item * schedule_outer_zero_distance
5670 If this option is set, then we try to construct schedules
5671 where the outermost scheduling dimension in each band
5672 results in a zero dependence distance over the proximity
5675 =item * schedule_split_scaled
5677 If this option is set, then we try to construct schedules in which the
5678 constant term is split off from the linear part if the linear parts of
5679 the scheduling rows for all nodes in the graphs have a common non-trivial
5681 The constant term is then placed in a separate band and the linear
5684 =item * schedule_algorithm
5686 Selects the scheduling algorithm to be used.
5687 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5688 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5690 =item * schedule_separate_components
5692 If at any point the dependence graph contains any (weakly connected) components,
5693 then these components are scheduled separately.
5694 If this option is not set, then some iterations of the domains
5695 in these components may be scheduled together.
5696 If this option is set, then the components are given consecutive
5701 =head2 AST Generation
5703 This section describes the C<isl> functionality for generating
5704 ASTs that visit all the elements
5705 in a domain in an order specified by a schedule.
5706 In particular, given a C<isl_union_map>, an AST is generated
5707 that visits all the elements in the domain of the C<isl_union_map>
5708 according to the lexicographic order of the corresponding image
5709 element(s). If the range of the C<isl_union_map> consists of
5710 elements in more than one space, then each of these spaces is handled
5711 separately in an arbitrary order.
5712 It should be noted that the image elements only specify the I<order>
5713 in which the corresponding domain elements should be visited.
5714 No direct relation between the image elements and the loop iterators
5715 in the generated AST should be assumed.
5717 Each AST is generated within a build. The initial build
5718 simply specifies the constraints on the parameters (if any)
5719 and can be created, inspected, copied and freed using the following functions.
5721 #include <isl/ast_build.h>
5722 __isl_give isl_ast_build *isl_ast_build_from_context(
5723 __isl_take isl_set *set);
5724 isl_ctx *isl_ast_build_get_ctx(
5725 __isl_keep isl_ast_build *build);
5726 __isl_give isl_ast_build *isl_ast_build_copy(
5727 __isl_keep isl_ast_build *build);
5728 void *isl_ast_build_free(
5729 __isl_take isl_ast_build *build);
5731 The C<set> argument is usually a parameter set with zero or more parameters.
5732 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5733 and L</"Fine-grained Control over AST Generation">.
5734 Finally, the AST itself can be constructed using the following
5737 #include <isl/ast_build.h>
5738 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5739 __isl_keep isl_ast_build *build,
5740 __isl_take isl_union_map *schedule);
5742 =head3 Inspecting the AST
5744 The basic properties of an AST node can be obtained as follows.
5746 #include <isl/ast.h>
5747 isl_ctx *isl_ast_node_get_ctx(
5748 __isl_keep isl_ast_node *node);
5749 enum isl_ast_node_type isl_ast_node_get_type(
5750 __isl_keep isl_ast_node *node);
5752 The type of an AST node is one of
5753 C<isl_ast_node_for>,
5755 C<isl_ast_node_block> or
5756 C<isl_ast_node_user>.
5757 An C<isl_ast_node_for> represents a for node.
5758 An C<isl_ast_node_if> represents an if node.
5759 An C<isl_ast_node_block> represents a compound node.
5760 An C<isl_ast_node_user> represents an expression statement.
5761 An expression statement typically corresponds to a domain element, i.e.,
5762 one of the elements that is visited by the AST.
5764 Each type of node has its own additional properties.
5766 #include <isl/ast.h>
5767 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5768 __isl_keep isl_ast_node *node);
5769 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5770 __isl_keep isl_ast_node *node);
5771 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5772 __isl_keep isl_ast_node *node);
5773 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5774 __isl_keep isl_ast_node *node);
5775 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5776 __isl_keep isl_ast_node *node);
5777 int isl_ast_node_for_is_degenerate(
5778 __isl_keep isl_ast_node *node);
5780 An C<isl_ast_for> is considered degenerate if it is known to execute
5783 #include <isl/ast.h>
5784 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5785 __isl_keep isl_ast_node *node);
5786 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5787 __isl_keep isl_ast_node *node);
5788 int isl_ast_node_if_has_else(
5789 __isl_keep isl_ast_node *node);
5790 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5791 __isl_keep isl_ast_node *node);
5793 __isl_give isl_ast_node_list *
5794 isl_ast_node_block_get_children(
5795 __isl_keep isl_ast_node *node);
5797 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5798 __isl_keep isl_ast_node *node);
5800 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5801 the following functions.
5803 #include <isl/ast.h>
5804 isl_ctx *isl_ast_expr_get_ctx(
5805 __isl_keep isl_ast_expr *expr);
5806 enum isl_ast_expr_type isl_ast_expr_get_type(
5807 __isl_keep isl_ast_expr *expr);
5809 The type of an AST expression is one of
5811 C<isl_ast_expr_id> or
5812 C<isl_ast_expr_int>.
5813 An C<isl_ast_expr_op> represents the result of an operation.
5814 An C<isl_ast_expr_id> represents an identifier.
5815 An C<isl_ast_expr_int> represents an integer value.
5817 Each type of expression has its own additional properties.
5819 #include <isl/ast.h>
5820 enum isl_ast_op_type isl_ast_expr_get_op_type(
5821 __isl_keep isl_ast_expr *expr);
5822 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5823 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5824 __isl_keep isl_ast_expr *expr, int pos);
5825 int isl_ast_node_foreach_ast_op_type(
5826 __isl_keep isl_ast_node *node,
5827 int (*fn)(enum isl_ast_op_type type, void *user),
5830 C<isl_ast_expr_get_op_type> returns the type of the operation
5831 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5832 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5834 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5835 C<isl_ast_op_type> that appears in C<node>.
5836 The operation type is one of the following.
5840 =item C<isl_ast_op_and>
5842 Logical I<and> of two arguments.
5843 Both arguments can be evaluated.
5845 =item C<isl_ast_op_and_then>
5847 Logical I<and> of two arguments.
5848 The second argument can only be evaluated if the first evaluates to true.
5850 =item C<isl_ast_op_or>
5852 Logical I<or> of two arguments.
5853 Both arguments can be evaluated.
5855 =item C<isl_ast_op_or_else>
5857 Logical I<or> of two arguments.
5858 The second argument can only be evaluated if the first evaluates to false.
5860 =item C<isl_ast_op_max>
5862 Maximum of two or more arguments.
5864 =item C<isl_ast_op_min>
5866 Minimum of two or more arguments.
5868 =item C<isl_ast_op_minus>
5872 =item C<isl_ast_op_add>
5874 Sum of two arguments.
5876 =item C<isl_ast_op_sub>
5878 Difference of two arguments.
5880 =item C<isl_ast_op_mul>
5882 Product of two arguments.
5884 =item C<isl_ast_op_div>
5886 Exact division. That is, the result is known to be an integer.
5888 =item C<isl_ast_op_fdiv_q>
5890 Result of integer division, rounded towards negative
5893 =item C<isl_ast_op_pdiv_q>
5895 Result of integer division, where dividend is known to be non-negative.
5897 =item C<isl_ast_op_pdiv_r>
5899 Remainder of integer division, where dividend is known to be non-negative.
5901 =item C<isl_ast_op_cond>
5903 Conditional operator defined on three arguments.
5904 If the first argument evaluates to true, then the result
5905 is equal to the second argument. Otherwise, the result
5906 is equal to the third argument.
5907 The second and third argument may only be evaluated if
5908 the first argument evaluates to true and false, respectively.
5909 Corresponds to C<a ? b : c> in C.
5911 =item C<isl_ast_op_select>
5913 Conditional operator defined on three arguments.
5914 If the first argument evaluates to true, then the result
5915 is equal to the second argument. Otherwise, the result
5916 is equal to the third argument.
5917 The second and third argument may be evaluated independently
5918 of the value of the first argument.
5919 Corresponds to C<a * b + (1 - a) * c> in C.
5921 =item C<isl_ast_op_eq>
5925 =item C<isl_ast_op_le>
5927 Less than or equal relation.
5929 =item C<isl_ast_op_lt>
5933 =item C<isl_ast_op_ge>
5935 Greater than or equal relation.
5937 =item C<isl_ast_op_gt>
5939 Greater than relation.
5941 =item C<isl_ast_op_call>
5944 The number of arguments of the C<isl_ast_expr> is one more than
5945 the number of arguments in the function call, the first argument
5946 representing the function being called.
5950 #include <isl/ast.h>
5951 __isl_give isl_id *isl_ast_expr_get_id(
5952 __isl_keep isl_ast_expr *expr);
5954 Return the identifier represented by the AST expression.
5956 #include <isl/ast.h>
5957 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5960 Return the integer represented by the AST expression.
5961 Note that the integer is returned through the C<v> argument.
5962 The return value of the function itself indicates whether the
5963 operation was performed successfully.
5965 =head3 Manipulating and printing the AST
5967 AST nodes can be copied and freed using the following functions.
5969 #include <isl/ast.h>
5970 __isl_give isl_ast_node *isl_ast_node_copy(
5971 __isl_keep isl_ast_node *node);
5972 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5974 AST expressions can be copied and freed using the following functions.
5976 #include <isl/ast.h>
5977 __isl_give isl_ast_expr *isl_ast_expr_copy(
5978 __isl_keep isl_ast_expr *expr);
5979 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5981 New AST expressions can be created either directly or within
5982 the context of an C<isl_ast_build>.
5984 #include <isl/ast.h>
5985 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5986 __isl_take isl_id *id);
5987 __isl_give isl_ast_expr *isl_ast_expr_neg(
5988 __isl_take isl_ast_expr *expr);
5989 __isl_give isl_ast_expr *isl_ast_expr_add(
5990 __isl_take isl_ast_expr *expr1,
5991 __isl_take isl_ast_expr *expr2);
5992 __isl_give isl_ast_expr *isl_ast_expr_sub(
5993 __isl_take isl_ast_expr *expr1,
5994 __isl_take isl_ast_expr *expr2);
5995 __isl_give isl_ast_expr *isl_ast_expr_mul(
5996 __isl_take isl_ast_expr *expr1,
5997 __isl_take isl_ast_expr *expr2);
5998 __isl_give isl_ast_expr *isl_ast_expr_div(
5999 __isl_take isl_ast_expr *expr1,
6000 __isl_take isl_ast_expr *expr2);
6001 __isl_give isl_ast_expr *isl_ast_expr_and(
6002 __isl_take isl_ast_expr *expr1,
6003 __isl_take isl_ast_expr *expr2)
6004 __isl_give isl_ast_expr *isl_ast_expr_or(
6005 __isl_take isl_ast_expr *expr1,
6006 __isl_take isl_ast_expr *expr2)
6008 #include <isl/ast_build.h>
6009 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6010 __isl_keep isl_ast_build *build,
6011 __isl_take isl_pw_aff *pa);
6012 __isl_give isl_ast_expr *
6013 isl_ast_build_call_from_pw_multi_aff(
6014 __isl_keep isl_ast_build *build,
6015 __isl_take isl_pw_multi_aff *pma);
6017 The domains of C<pa> and C<pma> should correspond
6018 to the schedule space of C<build>.
6019 The tuple id of C<pma> is used as the function being called.
6021 User specified data can be attached to an C<isl_ast_node> and obtained
6022 from the same C<isl_ast_node> using the following functions.
6024 #include <isl/ast.h>
6025 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6026 __isl_take isl_ast_node *node,
6027 __isl_take isl_id *annotation);
6028 __isl_give isl_id *isl_ast_node_get_annotation(
6029 __isl_keep isl_ast_node *node);
6031 Basic printing can be performed using the following functions.
6033 #include <isl/ast.h>
6034 __isl_give isl_printer *isl_printer_print_ast_expr(
6035 __isl_take isl_printer *p,
6036 __isl_keep isl_ast_expr *expr);
6037 __isl_give isl_printer *isl_printer_print_ast_node(
6038 __isl_take isl_printer *p,
6039 __isl_keep isl_ast_node *node);
6041 More advanced printing can be performed using the following functions.
6043 #include <isl/ast.h>
6044 __isl_give isl_printer *isl_ast_op_type_print_macro(
6045 enum isl_ast_op_type type,
6046 __isl_take isl_printer *p);
6047 __isl_give isl_printer *isl_ast_node_print_macros(
6048 __isl_keep isl_ast_node *node,
6049 __isl_take isl_printer *p);
6050 __isl_give isl_printer *isl_ast_node_print(
6051 __isl_keep isl_ast_node *node,
6052 __isl_take isl_printer *p,
6053 __isl_take isl_ast_print_options *options);
6054 __isl_give isl_printer *isl_ast_node_for_print(
6055 __isl_keep isl_ast_node *node,
6056 __isl_take isl_printer *p,
6057 __isl_take isl_ast_print_options *options);
6058 __isl_give isl_printer *isl_ast_node_if_print(
6059 __isl_keep isl_ast_node *node,
6060 __isl_take isl_printer *p,
6061 __isl_take isl_ast_print_options *options);
6063 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6064 C<isl> may print out an AST that makes use of macros such
6065 as C<floord>, C<min> and C<max>.
6066 C<isl_ast_op_type_print_macro> prints out the macro
6067 corresponding to a specific C<isl_ast_op_type>.
6068 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6069 for expressions where these macros would be used and prints
6070 out the required macro definitions.
6071 Essentially, C<isl_ast_node_print_macros> calls
6072 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6073 as function argument.
6074 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6075 C<isl_ast_node_if_print> print an C<isl_ast_node>
6076 in C<ISL_FORMAT_C>, but allow for some extra control
6077 through an C<isl_ast_print_options> object.
6078 This object can be created using the following functions.
6080 #include <isl/ast.h>
6081 __isl_give isl_ast_print_options *
6082 isl_ast_print_options_alloc(isl_ctx *ctx);
6083 __isl_give isl_ast_print_options *
6084 isl_ast_print_options_copy(
6085 __isl_keep isl_ast_print_options *options);
6086 void *isl_ast_print_options_free(
6087 __isl_take isl_ast_print_options *options);
6089 __isl_give isl_ast_print_options *
6090 isl_ast_print_options_set_print_user(
6091 __isl_take isl_ast_print_options *options,
6092 __isl_give isl_printer *(*print_user)(
6093 __isl_take isl_printer *p,
6094 __isl_take isl_ast_print_options *options,
6095 __isl_keep isl_ast_node *node, void *user),
6097 __isl_give isl_ast_print_options *
6098 isl_ast_print_options_set_print_for(
6099 __isl_take isl_ast_print_options *options,
6100 __isl_give isl_printer *(*print_for)(
6101 __isl_take isl_printer *p,
6102 __isl_take isl_ast_print_options *options,
6103 __isl_keep isl_ast_node *node, void *user),
6106 The callback set by C<isl_ast_print_options_set_print_user>
6107 is called whenever a node of type C<isl_ast_node_user> needs to
6109 The callback set by C<isl_ast_print_options_set_print_for>
6110 is called whenever a node of type C<isl_ast_node_for> needs to
6112 Note that C<isl_ast_node_for_print> will I<not> call the
6113 callback set by C<isl_ast_print_options_set_print_for> on the node
6114 on which C<isl_ast_node_for_print> is called, but only on nested
6115 nodes of type C<isl_ast_node_for>. It is therefore safe to
6116 call C<isl_ast_node_for_print> from within the callback set by
6117 C<isl_ast_print_options_set_print_for>.
6119 The following option determines the type to be used for iterators
6120 while printing the AST.
6122 int isl_options_set_ast_iterator_type(
6123 isl_ctx *ctx, const char *val);
6124 const char *isl_options_get_ast_iterator_type(
6129 #include <isl/ast_build.h>
6130 int isl_options_set_ast_build_atomic_upper_bound(
6131 isl_ctx *ctx, int val);
6132 int isl_options_get_ast_build_atomic_upper_bound(
6134 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6136 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6137 int isl_options_set_ast_build_exploit_nested_bounds(
6138 isl_ctx *ctx, int val);
6139 int isl_options_get_ast_build_exploit_nested_bounds(
6141 int isl_options_set_ast_build_group_coscheduled(
6142 isl_ctx *ctx, int val);
6143 int isl_options_get_ast_build_group_coscheduled(
6145 int isl_options_set_ast_build_scale_strides(
6146 isl_ctx *ctx, int val);
6147 int isl_options_get_ast_build_scale_strides(
6149 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6151 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6152 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6154 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6158 =item * ast_build_atomic_upper_bound
6160 Generate loop upper bounds that consist of the current loop iterator,
6161 an operator and an expression not involving the iterator.
6162 If this option is not set, then the current loop iterator may appear
6163 several times in the upper bound.
6164 For example, when this option is turned off, AST generation
6167 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6171 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6174 When the option is turned on, the following AST is generated
6176 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6179 =item * ast_build_prefer_pdiv
6181 If this option is turned off, then the AST generation will
6182 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6183 operators, but no C<isl_ast_op_pdiv_q> or
6184 C<isl_ast_op_pdiv_r> operators.
6185 If this options is turned on, then C<isl> will try to convert
6186 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6187 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6189 =item * ast_build_exploit_nested_bounds
6191 Simplify conditions based on bounds of nested for loops.
6192 In particular, remove conditions that are implied by the fact
6193 that one or more nested loops have at least one iteration,
6194 meaning that the upper bound is at least as large as the lower bound.
6195 For example, when this option is turned off, AST generation
6198 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6204 for (int c0 = 0; c0 <= N; c0 += 1)
6205 for (int c1 = 0; c1 <= M; c1 += 1)
6208 When the option is turned on, the following AST is generated
6210 for (int c0 = 0; c0 <= N; c0 += 1)
6211 for (int c1 = 0; c1 <= M; c1 += 1)
6214 =item * ast_build_group_coscheduled
6216 If two domain elements are assigned the same schedule point, then
6217 they may be executed in any order and they may even appear in different
6218 loops. If this options is set, then the AST generator will make
6219 sure that coscheduled domain elements do not appear in separate parts
6220 of the AST. This is useful in case of nested AST generation
6221 if the outer AST generation is given only part of a schedule
6222 and the inner AST generation should handle the domains that are
6223 coscheduled by this initial part of the schedule together.
6224 For example if an AST is generated for a schedule
6226 { A[i] -> [0]; B[i] -> [0] }
6228 then the C<isl_ast_build_set_create_leaf> callback described
6229 below may get called twice, once for each domain.
6230 Setting this option ensures that the callback is only called once
6231 on both domains together.
6233 =item * ast_build_separation_bounds
6235 This option specifies which bounds to use during separation.
6236 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6237 then all (possibly implicit) bounds on the current dimension will
6238 be used during separation.
6239 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6240 then only those bounds that are explicitly available will
6241 be used during separation.
6243 =item * ast_build_scale_strides
6245 This option specifies whether the AST generator is allowed
6246 to scale down iterators of strided loops.
6248 =item * ast_build_allow_else
6250 This option specifies whether the AST generator is allowed
6251 to construct if statements with else branches.
6253 =item * ast_build_allow_or
6255 This option specifies whether the AST generator is allowed
6256 to construct if conditions with disjunctions.
6260 =head3 Fine-grained Control over AST Generation
6262 Besides specifying the constraints on the parameters,
6263 an C<isl_ast_build> object can be used to control
6264 various aspects of the AST generation process.
6265 The most prominent way of control is through ``options'',
6266 which can be set using the following function.
6268 #include <isl/ast_build.h>
6269 __isl_give isl_ast_build *
6270 isl_ast_build_set_options(
6271 __isl_take isl_ast_build *control,
6272 __isl_take isl_union_map *options);
6274 The options are encoded in an <isl_union_map>.
6275 The domain of this union relation refers to the schedule domain,
6276 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6277 In the case of nested AST generation (see L</"Nested AST Generation">),
6278 the domain of C<options> should refer to the extra piece of the schedule.
6279 That is, it should be equal to the range of the wrapped relation in the
6280 range of the schedule.
6281 The range of the options can consist of elements in one or more spaces,
6282 the names of which determine the effect of the option.
6283 The values of the range typically also refer to the schedule dimension
6284 to which the option applies. In case of nested AST generation
6285 (see L</"Nested AST Generation">), these values refer to the position
6286 of the schedule dimension within the innermost AST generation.
6287 The constraints on the domain elements of
6288 the option should only refer to this dimension and earlier dimensions.
6289 We consider the following spaces.
6293 =item C<separation_class>
6295 This space is a wrapped relation between two one dimensional spaces.
6296 The input space represents the schedule dimension to which the option
6297 applies and the output space represents the separation class.
6298 While constructing a loop corresponding to the specified schedule
6299 dimension(s), the AST generator will try to generate separate loops
6300 for domain elements that are assigned different classes.
6301 If only some of the elements are assigned a class, then those elements
6302 that are not assigned any class will be treated as belonging to a class
6303 that is separate from the explicitly assigned classes.
6304 The typical use case for this option is to separate full tiles from
6306 The other options, described below, are applied after the separation
6309 As an example, consider the separation into full and partial tiles
6310 of a tiling of a triangular domain.
6311 Take, for example, the domain
6313 { A[i,j] : 0 <= i,j and i + j <= 100 }
6315 and a tiling into tiles of 10 by 10. The input to the AST generator
6316 is then the schedule
6318 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6321 Without any options, the following AST is generated
6323 for (int c0 = 0; c0 <= 10; c0 += 1)
6324 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6325 for (int c2 = 10 * c0;
6326 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6328 for (int c3 = 10 * c1;
6329 c3 <= min(10 * c1 + 9, -c2 + 100);
6333 Separation into full and partial tiles can be obtained by assigning
6334 a class, say C<0>, to the full tiles. The full tiles are represented by those
6335 values of the first and second schedule dimensions for which there are
6336 values of the third and fourth dimensions to cover an entire tile.
6337 That is, we need to specify the following option
6339 { [a,b,c,d] -> separation_class[[0]->[0]] :
6340 exists b': 0 <= 10a,10b' and
6341 10a+9+10b'+9 <= 100;
6342 [a,b,c,d] -> separation_class[[1]->[0]] :
6343 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6347 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6348 a >= 0 and b >= 0 and b <= 8 - a;
6349 [a, b, c, d] -> separation_class[[0] -> [0]] :
6352 With this option, the generated AST is as follows
6355 for (int c0 = 0; c0 <= 8; c0 += 1) {
6356 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6357 for (int c2 = 10 * c0;
6358 c2 <= 10 * c0 + 9; c2 += 1)
6359 for (int c3 = 10 * c1;
6360 c3 <= 10 * c1 + 9; c3 += 1)
6362 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6363 for (int c2 = 10 * c0;
6364 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6366 for (int c3 = 10 * c1;
6367 c3 <= min(-c2 + 100, 10 * c1 + 9);
6371 for (int c0 = 9; c0 <= 10; c0 += 1)
6372 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6373 for (int c2 = 10 * c0;
6374 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6376 for (int c3 = 10 * c1;
6377 c3 <= min(10 * c1 + 9, -c2 + 100);
6384 This is a single-dimensional space representing the schedule dimension(s)
6385 to which ``separation'' should be applied. Separation tries to split
6386 a loop into several pieces if this can avoid the generation of guards
6388 See also the C<atomic> option.
6392 This is a single-dimensional space representing the schedule dimension(s)
6393 for which the domains should be considered ``atomic''. That is, the
6394 AST generator will make sure that any given domain space will only appear
6395 in a single loop at the specified level.
6397 Consider the following schedule
6399 { a[i] -> [i] : 0 <= i < 10;
6400 b[i] -> [i+1] : 0 <= i < 10 }
6402 If the following option is specified
6404 { [i] -> separate[x] }
6406 then the following AST will be generated
6410 for (int c0 = 1; c0 <= 9; c0 += 1) {
6417 If, on the other hand, the following option is specified
6419 { [i] -> atomic[x] }
6421 then the following AST will be generated
6423 for (int c0 = 0; c0 <= 10; c0 += 1) {
6430 If neither C<atomic> nor C<separate> is specified, then the AST generator
6431 may produce either of these two results or some intermediate form.
6435 This is a single-dimensional space representing the schedule dimension(s)
6436 that should be I<completely> unrolled.
6437 To obtain a partial unrolling, the user should apply an additional
6438 strip-mining to the schedule and fully unroll the inner loop.
6442 Additional control is available through the following functions.
6444 #include <isl/ast_build.h>
6445 __isl_give isl_ast_build *
6446 isl_ast_build_set_iterators(
6447 __isl_take isl_ast_build *control,
6448 __isl_take isl_id_list *iterators);
6450 The function C<isl_ast_build_set_iterators> allows the user to
6451 specify a list of iterator C<isl_id>s to be used as iterators.
6452 If the input schedule is injective, then
6453 the number of elements in this list should be as large as the dimension
6454 of the schedule space, but no direct correspondence should be assumed
6455 between dimensions and elements.
6456 If the input schedule is not injective, then an additional number
6457 of C<isl_id>s equal to the largest dimension of the input domains
6459 If the number of provided C<isl_id>s is insufficient, then additional
6460 names are automatically generated.
6462 #include <isl/ast_build.h>
6463 __isl_give isl_ast_build *
6464 isl_ast_build_set_create_leaf(
6465 __isl_take isl_ast_build *control,
6466 __isl_give isl_ast_node *(*fn)(
6467 __isl_take isl_ast_build *build,
6468 void *user), void *user);
6471 C<isl_ast_build_set_create_leaf> function allows for the
6472 specification of a callback that should be called whenever the AST
6473 generator arrives at an element of the schedule domain.
6474 The callback should return an AST node that should be inserted
6475 at the corresponding position of the AST. The default action (when
6476 the callback is not set) is to continue generating parts of the AST to scan
6477 all the domain elements associated to the schedule domain element
6478 and to insert user nodes, ``calling'' the domain element, for each of them.
6479 The C<build> argument contains the current state of the C<isl_ast_build>.
6480 To ease nested AST generation (see L</"Nested AST Generation">),
6481 all control information that is
6482 specific to the current AST generation such as the options and
6483 the callbacks has been removed from this C<isl_ast_build>.
6484 The callback would typically return the result of a nested
6486 user defined node created using the following function.
6488 #include <isl/ast.h>
6489 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6490 __isl_take isl_ast_expr *expr);
6492 #include <isl/ast_build.h>
6493 __isl_give isl_ast_build *
6494 isl_ast_build_set_at_each_domain(
6495 __isl_take isl_ast_build *build,
6496 __isl_give isl_ast_node *(*fn)(
6497 __isl_take isl_ast_node *node,
6498 __isl_keep isl_ast_build *build,
6499 void *user), void *user);
6500 __isl_give isl_ast_build *
6501 isl_ast_build_set_before_each_for(
6502 __isl_take isl_ast_build *build,
6503 __isl_give isl_id *(*fn)(
6504 __isl_keep isl_ast_build *build,
6505 void *user), void *user);
6506 __isl_give isl_ast_build *
6507 isl_ast_build_set_after_each_for(
6508 __isl_take isl_ast_build *build,
6509 __isl_give isl_ast_node *(*fn)(
6510 __isl_take isl_ast_node *node,
6511 __isl_keep isl_ast_build *build,
6512 void *user), void *user);
6514 The callback set by C<isl_ast_build_set_at_each_domain> will
6515 be called for each domain AST node.
6516 The callbacks set by C<isl_ast_build_set_before_each_for>
6517 and C<isl_ast_build_set_after_each_for> will be called
6518 for each for AST node. The first will be called in depth-first
6519 pre-order, while the second will be called in depth-first post-order.
6520 Since C<isl_ast_build_set_before_each_for> is called before the for
6521 node is actually constructed, it is only passed an C<isl_ast_build>.
6522 The returned C<isl_id> will be added as an annotation (using
6523 C<isl_ast_node_set_annotation>) to the constructed for node.
6524 In particular, if the user has also specified an C<after_each_for>
6525 callback, then the annotation can be retrieved from the node passed to
6526 that callback using C<isl_ast_node_get_annotation>.
6527 All callbacks should C<NULL> on failure.
6528 The given C<isl_ast_build> can be used to create new
6529 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6530 or C<isl_ast_build_call_from_pw_multi_aff>.
6532 =head3 Nested AST Generation
6534 C<isl> allows the user to create an AST within the context
6535 of another AST. These nested ASTs are created using the
6536 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6537 outer AST. The C<build> argument should be an C<isl_ast_build>
6538 passed to a callback set by
6539 C<isl_ast_build_set_create_leaf>.
6540 The space of the range of the C<schedule> argument should refer
6541 to this build. In particular, the space should be a wrapped
6542 relation and the domain of this wrapped relation should be the
6543 same as that of the range of the schedule returned by
6544 C<isl_ast_build_get_schedule> below.
6545 In practice, the new schedule is typically
6546 created by calling C<isl_union_map_range_product> on the old schedule
6547 and some extra piece of the schedule.
6548 The space of the schedule domain is also available from
6549 the C<isl_ast_build>.
6551 #include <isl/ast_build.h>
6552 __isl_give isl_union_map *isl_ast_build_get_schedule(
6553 __isl_keep isl_ast_build *build);
6554 __isl_give isl_space *isl_ast_build_get_schedule_space(
6555 __isl_keep isl_ast_build *build);
6556 __isl_give isl_ast_build *isl_ast_build_restrict(
6557 __isl_take isl_ast_build *build,
6558 __isl_take isl_set *set);
6560 The C<isl_ast_build_get_schedule> function returns a (partial)
6561 schedule for the domains elements for which part of the AST still needs to
6562 be generated in the current build.
6563 In particular, the domain elements are mapped to those iterations of the loops
6564 enclosing the current point of the AST generation inside which
6565 the domain elements are executed.
6566 No direct correspondence between
6567 the input schedule and this schedule should be assumed.
6568 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6569 to create a set for C<isl_ast_build_restrict> to intersect
6570 with the current build. In particular, the set passed to
6571 C<isl_ast_build_restrict> can have additional parameters.
6572 The ids of the set dimensions in the space returned by
6573 C<isl_ast_build_get_schedule_space> correspond to the
6574 iterators of the already generated loops.
6575 The user should not rely on the ids of the output dimensions
6576 of the relations in the union relation returned by
6577 C<isl_ast_build_get_schedule> having any particular value.
6581 Although C<isl> is mainly meant to be used as a library,
6582 it also contains some basic applications that use some
6583 of the functionality of C<isl>.
6584 The input may be specified in either the L<isl format>
6585 or the L<PolyLib format>.
6587 =head2 C<isl_polyhedron_sample>
6589 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6590 an integer element of the polyhedron, if there is any.
6591 The first column in the output is the denominator and is always
6592 equal to 1. If the polyhedron contains no integer points,
6593 then a vector of length zero is printed.
6597 C<isl_pip> takes the same input as the C<example> program
6598 from the C<piplib> distribution, i.e., a set of constraints
6599 on the parameters, a line containing only -1 and finally a set
6600 of constraints on a parametric polyhedron.
6601 The coefficients of the parameters appear in the last columns
6602 (but before the final constant column).
6603 The output is the lexicographic minimum of the parametric polyhedron.
6604 As C<isl> currently does not have its own output format, the output
6605 is just a dump of the internal state.
6607 =head2 C<isl_polyhedron_minimize>
6609 C<isl_polyhedron_minimize> computes the minimum of some linear
6610 or affine objective function over the integer points in a polyhedron.
6611 If an affine objective function
6612 is given, then the constant should appear in the last column.
6614 =head2 C<isl_polytope_scan>
6616 Given a polytope, C<isl_polytope_scan> prints
6617 all integer points in the polytope.
6619 =head2 C<isl_codegen>
6621 Given a schedule, a context set and an options relation,
6622 C<isl_codegen> prints out an AST that scans the domain elements
6623 of the schedule in the order of their image(s) taking into account
6624 the constraints in the context set.