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>.
2063 __isl_give isl_val *
2064 isl_basic_map_plain_get_val_if_fixed(
2065 __isl_keep isl_basic_map *bmap,
2066 enum isl_dim_type type, unsigned pos);
2067 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2068 __isl_keep isl_set *set,
2069 enum isl_dim_type type, unsigned pos);
2070 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2071 __isl_keep isl_map *map,
2072 enum isl_dim_type type, unsigned pos);
2074 If the set or relation obviously lies on a hyperplane where the given dimension
2075 has a fixed value, then return that value.
2076 Otherwise return NaN.
2080 To check whether a set is a parameter domain, use this function:
2082 int isl_set_is_params(__isl_keep isl_set *set);
2083 int isl_union_set_is_params(
2084 __isl_keep isl_union_set *uset);
2088 The following functions check whether the domain of the given
2089 (basic) set is a wrapped relation.
2091 int isl_basic_set_is_wrapping(
2092 __isl_keep isl_basic_set *bset);
2093 int isl_set_is_wrapping(__isl_keep isl_set *set);
2095 =item * Internal Product
2097 int isl_basic_map_can_zip(
2098 __isl_keep isl_basic_map *bmap);
2099 int isl_map_can_zip(__isl_keep isl_map *map);
2101 Check whether the product of domain and range of the given relation
2103 i.e., whether both domain and range are nested relations.
2107 int isl_basic_map_can_curry(
2108 __isl_keep isl_basic_map *bmap);
2109 int isl_map_can_curry(__isl_keep isl_map *map);
2111 Check whether the domain of the (basic) relation is a wrapped relation.
2113 int isl_basic_map_can_uncurry(
2114 __isl_keep isl_basic_map *bmap);
2115 int isl_map_can_uncurry(__isl_keep isl_map *map);
2117 Check whether the range of the (basic) relation is a wrapped relation.
2121 =head3 Binary Properties
2127 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2128 __isl_keep isl_set *set2);
2129 int isl_set_is_equal(__isl_keep isl_set *set1,
2130 __isl_keep isl_set *set2);
2131 int isl_union_set_is_equal(
2132 __isl_keep isl_union_set *uset1,
2133 __isl_keep isl_union_set *uset2);
2134 int isl_basic_map_is_equal(
2135 __isl_keep isl_basic_map *bmap1,
2136 __isl_keep isl_basic_map *bmap2);
2137 int isl_map_is_equal(__isl_keep isl_map *map1,
2138 __isl_keep isl_map *map2);
2139 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2140 __isl_keep isl_map *map2);
2141 int isl_union_map_is_equal(
2142 __isl_keep isl_union_map *umap1,
2143 __isl_keep isl_union_map *umap2);
2145 =item * Disjointness
2147 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2148 __isl_keep isl_set *set2);
2149 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2150 __isl_keep isl_set *set2);
2151 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2152 __isl_keep isl_map *map2);
2156 int isl_basic_set_is_subset(
2157 __isl_keep isl_basic_set *bset1,
2158 __isl_keep isl_basic_set *bset2);
2159 int isl_set_is_subset(__isl_keep isl_set *set1,
2160 __isl_keep isl_set *set2);
2161 int isl_set_is_strict_subset(
2162 __isl_keep isl_set *set1,
2163 __isl_keep isl_set *set2);
2164 int isl_union_set_is_subset(
2165 __isl_keep isl_union_set *uset1,
2166 __isl_keep isl_union_set *uset2);
2167 int isl_union_set_is_strict_subset(
2168 __isl_keep isl_union_set *uset1,
2169 __isl_keep isl_union_set *uset2);
2170 int isl_basic_map_is_subset(
2171 __isl_keep isl_basic_map *bmap1,
2172 __isl_keep isl_basic_map *bmap2);
2173 int isl_basic_map_is_strict_subset(
2174 __isl_keep isl_basic_map *bmap1,
2175 __isl_keep isl_basic_map *bmap2);
2176 int isl_map_is_subset(
2177 __isl_keep isl_map *map1,
2178 __isl_keep isl_map *map2);
2179 int isl_map_is_strict_subset(
2180 __isl_keep isl_map *map1,
2181 __isl_keep isl_map *map2);
2182 int isl_union_map_is_subset(
2183 __isl_keep isl_union_map *umap1,
2184 __isl_keep isl_union_map *umap2);
2185 int isl_union_map_is_strict_subset(
2186 __isl_keep isl_union_map *umap1,
2187 __isl_keep isl_union_map *umap2);
2189 Check whether the first argument is a (strict) subset of the
2194 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2195 __isl_keep isl_set *set2);
2197 This function is useful for sorting C<isl_set>s.
2198 The order depends on the internal representation of the inputs.
2199 The order is fixed over different calls to the function (assuming
2200 the internal representation of the inputs has not changed), but may
2201 change over different versions of C<isl>.
2205 =head2 Unary Operations
2211 __isl_give isl_set *isl_set_complement(
2212 __isl_take isl_set *set);
2213 __isl_give isl_map *isl_map_complement(
2214 __isl_take isl_map *map);
2218 __isl_give isl_basic_map *isl_basic_map_reverse(
2219 __isl_take isl_basic_map *bmap);
2220 __isl_give isl_map *isl_map_reverse(
2221 __isl_take isl_map *map);
2222 __isl_give isl_union_map *isl_union_map_reverse(
2223 __isl_take isl_union_map *umap);
2227 __isl_give isl_basic_set *isl_basic_set_project_out(
2228 __isl_take isl_basic_set *bset,
2229 enum isl_dim_type type, unsigned first, unsigned n);
2230 __isl_give isl_basic_map *isl_basic_map_project_out(
2231 __isl_take isl_basic_map *bmap,
2232 enum isl_dim_type type, unsigned first, unsigned n);
2233 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2234 enum isl_dim_type type, unsigned first, unsigned n);
2235 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2236 enum isl_dim_type type, unsigned first, unsigned n);
2237 __isl_give isl_basic_set *isl_basic_set_params(
2238 __isl_take isl_basic_set *bset);
2239 __isl_give isl_basic_set *isl_basic_map_domain(
2240 __isl_take isl_basic_map *bmap);
2241 __isl_give isl_basic_set *isl_basic_map_range(
2242 __isl_take isl_basic_map *bmap);
2243 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2244 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2245 __isl_give isl_set *isl_map_domain(
2246 __isl_take isl_map *bmap);
2247 __isl_give isl_set *isl_map_range(
2248 __isl_take isl_map *map);
2249 __isl_give isl_set *isl_union_set_params(
2250 __isl_take isl_union_set *uset);
2251 __isl_give isl_set *isl_union_map_params(
2252 __isl_take isl_union_map *umap);
2253 __isl_give isl_union_set *isl_union_map_domain(
2254 __isl_take isl_union_map *umap);
2255 __isl_give isl_union_set *isl_union_map_range(
2256 __isl_take isl_union_map *umap);
2258 __isl_give isl_basic_map *isl_basic_map_domain_map(
2259 __isl_take isl_basic_map *bmap);
2260 __isl_give isl_basic_map *isl_basic_map_range_map(
2261 __isl_take isl_basic_map *bmap);
2262 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2263 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2264 __isl_give isl_union_map *isl_union_map_domain_map(
2265 __isl_take isl_union_map *umap);
2266 __isl_give isl_union_map *isl_union_map_range_map(
2267 __isl_take isl_union_map *umap);
2269 The functions above construct a (basic, regular or union) relation
2270 that maps (a wrapped version of) the input relation to its domain or range.
2274 __isl_give isl_basic_set *isl_basic_set_eliminate(
2275 __isl_take isl_basic_set *bset,
2276 enum isl_dim_type type,
2277 unsigned first, unsigned n);
2278 __isl_give isl_set *isl_set_eliminate(
2279 __isl_take isl_set *set, enum isl_dim_type type,
2280 unsigned first, unsigned n);
2281 __isl_give isl_basic_map *isl_basic_map_eliminate(
2282 __isl_take isl_basic_map *bmap,
2283 enum isl_dim_type type,
2284 unsigned first, unsigned n);
2285 __isl_give isl_map *isl_map_eliminate(
2286 __isl_take isl_map *map, enum isl_dim_type type,
2287 unsigned first, unsigned n);
2289 Eliminate the coefficients for the given dimensions from the constraints,
2290 without removing the dimensions.
2294 __isl_give isl_basic_set *isl_basic_set_fix(
2295 __isl_take isl_basic_set *bset,
2296 enum isl_dim_type type, unsigned pos,
2298 __isl_give isl_basic_set *isl_basic_set_fix_si(
2299 __isl_take isl_basic_set *bset,
2300 enum isl_dim_type type, unsigned pos, int value);
2301 __isl_give isl_basic_set *isl_basic_set_fix_val(
2302 __isl_take isl_basic_set *bset,
2303 enum isl_dim_type type, unsigned pos,
2304 __isl_take isl_val *v);
2305 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos,
2308 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2309 enum isl_dim_type type, unsigned pos, int value);
2310 __isl_give isl_set *isl_set_fix_val(
2311 __isl_take isl_set *set,
2312 enum isl_dim_type type, unsigned pos,
2313 __isl_take isl_val *v);
2314 __isl_give isl_basic_map *isl_basic_map_fix_si(
2315 __isl_take isl_basic_map *bmap,
2316 enum isl_dim_type type, unsigned pos, int value);
2317 __isl_give isl_basic_map *isl_basic_map_fix_val(
2318 __isl_take isl_basic_map *bmap,
2319 enum isl_dim_type type, unsigned pos,
2320 __isl_take isl_val *v);
2321 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2322 enum isl_dim_type type, unsigned pos,
2324 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2325 enum isl_dim_type type, unsigned pos, int value);
2326 __isl_give isl_map *isl_map_fix_val(
2327 __isl_take isl_map *map,
2328 enum isl_dim_type type, unsigned pos,
2329 __isl_take isl_val *v);
2331 Intersect the set or relation with the hyperplane where the given
2332 dimension has the fixed given value.
2334 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2335 __isl_take isl_basic_map *bmap,
2336 enum isl_dim_type type, unsigned pos, int value);
2337 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2338 __isl_take isl_basic_map *bmap,
2339 enum isl_dim_type type, unsigned pos, int value);
2340 __isl_give isl_set *isl_set_lower_bound(
2341 __isl_take isl_set *set,
2342 enum isl_dim_type type, unsigned pos,
2344 __isl_give isl_set *isl_set_lower_bound_si(
2345 __isl_take isl_set *set,
2346 enum isl_dim_type type, unsigned pos, int value);
2347 __isl_give isl_set *isl_set_lower_bound_val(
2348 __isl_take isl_set *set,
2349 enum isl_dim_type type, unsigned pos,
2350 __isl_take isl_val *value);
2351 __isl_give isl_map *isl_map_lower_bound_si(
2352 __isl_take isl_map *map,
2353 enum isl_dim_type type, unsigned pos, int value);
2354 __isl_give isl_set *isl_set_upper_bound(
2355 __isl_take isl_set *set,
2356 enum isl_dim_type type, unsigned pos,
2358 __isl_give isl_set *isl_set_upper_bound_si(
2359 __isl_take isl_set *set,
2360 enum isl_dim_type type, unsigned pos, int value);
2361 __isl_give isl_set *isl_set_upper_bound_val(
2362 __isl_take isl_set *set,
2363 enum isl_dim_type type, unsigned pos,
2364 __isl_take isl_val *value);
2365 __isl_give isl_map *isl_map_upper_bound_si(
2366 __isl_take isl_map *map,
2367 enum isl_dim_type type, unsigned pos, int value);
2369 Intersect the set or relation with the half-space where the given
2370 dimension has a value bounded by the fixed given integer value.
2372 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2373 enum isl_dim_type type1, int pos1,
2374 enum isl_dim_type type2, int pos2);
2375 __isl_give isl_basic_map *isl_basic_map_equate(
2376 __isl_take isl_basic_map *bmap,
2377 enum isl_dim_type type1, int pos1,
2378 enum isl_dim_type type2, int pos2);
2379 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2380 enum isl_dim_type type1, int pos1,
2381 enum isl_dim_type type2, int pos2);
2383 Intersect the set or relation with the hyperplane where the given
2384 dimensions are equal to each other.
2386 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2387 enum isl_dim_type type1, int pos1,
2388 enum isl_dim_type type2, int pos2);
2390 Intersect the relation with the hyperplane where the given
2391 dimensions have opposite values.
2393 __isl_give isl_basic_map *isl_basic_map_order_ge(
2394 __isl_take isl_basic_map *bmap,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2397 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2398 enum isl_dim_type type1, int pos1,
2399 enum isl_dim_type type2, int pos2);
2400 __isl_give isl_basic_map *isl_basic_map_order_gt(
2401 __isl_take isl_basic_map *bmap,
2402 enum isl_dim_type type1, int pos1,
2403 enum isl_dim_type type2, int pos2);
2404 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2405 enum isl_dim_type type1, int pos1,
2406 enum isl_dim_type type2, int pos2);
2408 Intersect the relation with the half-space where the given
2409 dimensions satisfy the given ordering.
2413 __isl_give isl_map *isl_set_identity(
2414 __isl_take isl_set *set);
2415 __isl_give isl_union_map *isl_union_set_identity(
2416 __isl_take isl_union_set *uset);
2418 Construct an identity relation on the given (union) set.
2422 __isl_give isl_basic_set *isl_basic_map_deltas(
2423 __isl_take isl_basic_map *bmap);
2424 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2425 __isl_give isl_union_set *isl_union_map_deltas(
2426 __isl_take isl_union_map *umap);
2428 These functions return a (basic) set containing the differences
2429 between image elements and corresponding domain elements in the input.
2431 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2432 __isl_take isl_basic_map *bmap);
2433 __isl_give isl_map *isl_map_deltas_map(
2434 __isl_take isl_map *map);
2435 __isl_give isl_union_map *isl_union_map_deltas_map(
2436 __isl_take isl_union_map *umap);
2438 The functions above construct a (basic, regular or union) relation
2439 that maps (a wrapped version of) the input relation to its delta set.
2443 Simplify the representation of a set or relation by trying
2444 to combine pairs of basic sets or relations into a single
2445 basic set or relation.
2447 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2448 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2449 __isl_give isl_union_set *isl_union_set_coalesce(
2450 __isl_take isl_union_set *uset);
2451 __isl_give isl_union_map *isl_union_map_coalesce(
2452 __isl_take isl_union_map *umap);
2454 One of the methods for combining pairs of basic sets or relations
2455 can result in coefficients that are much larger than those that appear
2456 in the constraints of the input. By default, the coefficients are
2457 not allowed to grow larger, but this can be changed by unsetting
2458 the following option.
2460 int isl_options_set_coalesce_bounded_wrapping(
2461 isl_ctx *ctx, int val);
2462 int isl_options_get_coalesce_bounded_wrapping(
2465 =item * Detecting equalities
2467 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2468 __isl_take isl_basic_set *bset);
2469 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2470 __isl_take isl_basic_map *bmap);
2471 __isl_give isl_set *isl_set_detect_equalities(
2472 __isl_take isl_set *set);
2473 __isl_give isl_map *isl_map_detect_equalities(
2474 __isl_take isl_map *map);
2475 __isl_give isl_union_set *isl_union_set_detect_equalities(
2476 __isl_take isl_union_set *uset);
2477 __isl_give isl_union_map *isl_union_map_detect_equalities(
2478 __isl_take isl_union_map *umap);
2480 Simplify the representation of a set or relation by detecting implicit
2483 =item * Removing redundant constraints
2485 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2486 __isl_take isl_basic_set *bset);
2487 __isl_give isl_set *isl_set_remove_redundancies(
2488 __isl_take isl_set *set);
2489 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2490 __isl_take isl_basic_map *bmap);
2491 __isl_give isl_map *isl_map_remove_redundancies(
2492 __isl_take isl_map *map);
2496 __isl_give isl_basic_set *isl_set_convex_hull(
2497 __isl_take isl_set *set);
2498 __isl_give isl_basic_map *isl_map_convex_hull(
2499 __isl_take isl_map *map);
2501 If the input set or relation has any existentially quantified
2502 variables, then the result of these operations is currently undefined.
2506 __isl_give isl_basic_set *
2507 isl_set_unshifted_simple_hull(
2508 __isl_take isl_set *set);
2509 __isl_give isl_basic_map *
2510 isl_map_unshifted_simple_hull(
2511 __isl_take isl_map *map);
2512 __isl_give isl_basic_set *isl_set_simple_hull(
2513 __isl_take isl_set *set);
2514 __isl_give isl_basic_map *isl_map_simple_hull(
2515 __isl_take isl_map *map);
2516 __isl_give isl_union_map *isl_union_map_simple_hull(
2517 __isl_take isl_union_map *umap);
2519 These functions compute a single basic set or relation
2520 that contains the whole input set or relation.
2521 In particular, the output is described by translates
2522 of the constraints describing the basic sets or relations in the input.
2523 In case of C<isl_set_unshifted_simple_hull>, only the original
2524 constraints are used, without any translation.
2528 (See \autoref{s:simple hull}.)
2534 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2535 __isl_take isl_basic_set *bset);
2536 __isl_give isl_basic_set *isl_set_affine_hull(
2537 __isl_take isl_set *set);
2538 __isl_give isl_union_set *isl_union_set_affine_hull(
2539 __isl_take isl_union_set *uset);
2540 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2541 __isl_take isl_basic_map *bmap);
2542 __isl_give isl_basic_map *isl_map_affine_hull(
2543 __isl_take isl_map *map);
2544 __isl_give isl_union_map *isl_union_map_affine_hull(
2545 __isl_take isl_union_map *umap);
2547 In case of union sets and relations, the affine hull is computed
2550 =item * Polyhedral hull
2552 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2553 __isl_take isl_set *set);
2554 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2555 __isl_take isl_map *map);
2556 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2557 __isl_take isl_union_set *uset);
2558 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2559 __isl_take isl_union_map *umap);
2561 These functions compute a single basic set or relation
2562 not involving any existentially quantified variables
2563 that contains the whole input set or relation.
2564 In case of union sets and relations, the polyhedral hull is computed
2567 =item * Other approximations
2569 __isl_give isl_basic_set *
2570 isl_basic_set_drop_constraints_involving_dims(
2571 __isl_take isl_basic_set *bset,
2572 enum isl_dim_type type,
2573 unsigned first, unsigned n);
2574 __isl_give isl_basic_map *
2575 isl_basic_map_drop_constraints_involving_dims(
2576 __isl_take isl_basic_map *bmap,
2577 enum isl_dim_type type,
2578 unsigned first, unsigned n);
2579 __isl_give isl_basic_set *
2580 isl_basic_set_drop_constraints_not_involving_dims(
2581 __isl_take isl_basic_set *bset,
2582 enum isl_dim_type type,
2583 unsigned first, unsigned n);
2584 __isl_give isl_set *
2585 isl_set_drop_constraints_involving_dims(
2586 __isl_take isl_set *set,
2587 enum isl_dim_type type,
2588 unsigned first, unsigned n);
2589 __isl_give isl_map *
2590 isl_map_drop_constraints_involving_dims(
2591 __isl_take isl_map *map,
2592 enum isl_dim_type type,
2593 unsigned first, unsigned n);
2595 These functions drop any constraints (not) involving the specified dimensions.
2596 Note that the result depends on the representation of the input.
2600 __isl_give isl_basic_set *isl_basic_set_sample(
2601 __isl_take isl_basic_set *bset);
2602 __isl_give isl_basic_set *isl_set_sample(
2603 __isl_take isl_set *set);
2604 __isl_give isl_basic_map *isl_basic_map_sample(
2605 __isl_take isl_basic_map *bmap);
2606 __isl_give isl_basic_map *isl_map_sample(
2607 __isl_take isl_map *map);
2609 If the input (basic) set or relation is non-empty, then return
2610 a singleton subset of the input. Otherwise, return an empty set.
2612 =item * Optimization
2614 #include <isl/ilp.h>
2615 enum isl_lp_result isl_basic_set_max(
2616 __isl_keep isl_basic_set *bset,
2617 __isl_keep isl_aff *obj, isl_int *opt)
2618 __isl_give isl_val *isl_basic_set_max_val(
2619 __isl_keep isl_basic_set *bset,
2620 __isl_keep isl_aff *obj);
2621 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2622 __isl_keep isl_aff *obj, isl_int *opt);
2623 __isl_give isl_val *isl_set_min_val(
2624 __isl_keep isl_set *set,
2625 __isl_keep isl_aff *obj);
2626 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2627 __isl_keep isl_aff *obj, isl_int *opt);
2628 __isl_give isl_val *isl_set_max_val(
2629 __isl_keep isl_set *set,
2630 __isl_keep isl_aff *obj);
2632 Compute the minimum or maximum of the integer affine expression C<obj>
2633 over the points in C<set>, returning the result in C<opt>.
2634 The return value may be one of C<isl_lp_error>,
2635 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2636 an C<isl_lp_result>. If the result is an C<isl_val> then
2637 the result is C<NULL> in case of an error, the optimal value in case
2638 there is one, negative infinity or infinity if the problem is unbounded and
2639 NaN if the problem is empty.
2641 =item * Parametric optimization
2643 __isl_give isl_pw_aff *isl_set_dim_min(
2644 __isl_take isl_set *set, int pos);
2645 __isl_give isl_pw_aff *isl_set_dim_max(
2646 __isl_take isl_set *set, int pos);
2647 __isl_give isl_pw_aff *isl_map_dim_max(
2648 __isl_take isl_map *map, int pos);
2650 Compute the minimum or maximum of the given set or output dimension
2651 as a function of the parameters (and input dimensions), but independently
2652 of the other set or output dimensions.
2653 For lexicographic optimization, see L<"Lexicographic Optimization">.
2657 The following functions compute either the set of (rational) coefficient
2658 values of valid constraints for the given set or the set of (rational)
2659 values satisfying the constraints with coefficients from the given set.
2660 Internally, these two sets of functions perform essentially the
2661 same operations, except that the set of coefficients is assumed to
2662 be a cone, while the set of values may be any polyhedron.
2663 The current implementation is based on the Farkas lemma and
2664 Fourier-Motzkin elimination, but this may change or be made optional
2665 in future. In particular, future implementations may use different
2666 dualization algorithms or skip the elimination step.
2668 __isl_give isl_basic_set *isl_basic_set_coefficients(
2669 __isl_take isl_basic_set *bset);
2670 __isl_give isl_basic_set *isl_set_coefficients(
2671 __isl_take isl_set *set);
2672 __isl_give isl_union_set *isl_union_set_coefficients(
2673 __isl_take isl_union_set *bset);
2674 __isl_give isl_basic_set *isl_basic_set_solutions(
2675 __isl_take isl_basic_set *bset);
2676 __isl_give isl_basic_set *isl_set_solutions(
2677 __isl_take isl_set *set);
2678 __isl_give isl_union_set *isl_union_set_solutions(
2679 __isl_take isl_union_set *bset);
2683 __isl_give isl_map *isl_map_fixed_power(
2684 __isl_take isl_map *map, isl_int exp);
2685 __isl_give isl_union_map *isl_union_map_fixed_power(
2686 __isl_take isl_union_map *umap, isl_int exp);
2688 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2689 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2690 of C<map> is computed.
2692 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2694 __isl_give isl_union_map *isl_union_map_power(
2695 __isl_take isl_union_map *umap, int *exact);
2697 Compute a parametric representation for all positive powers I<k> of C<map>.
2698 The result maps I<k> to a nested relation corresponding to the
2699 I<k>th power of C<map>.
2700 The result may be an overapproximation. If the result is known to be exact,
2701 then C<*exact> is set to C<1>.
2703 =item * Transitive closure
2705 __isl_give isl_map *isl_map_transitive_closure(
2706 __isl_take isl_map *map, int *exact);
2707 __isl_give isl_union_map *isl_union_map_transitive_closure(
2708 __isl_take isl_union_map *umap, int *exact);
2710 Compute the transitive closure of C<map>.
2711 The result may be an overapproximation. If the result is known to be exact,
2712 then C<*exact> is set to C<1>.
2714 =item * Reaching path lengths
2716 __isl_give isl_map *isl_map_reaching_path_lengths(
2717 __isl_take isl_map *map, int *exact);
2719 Compute a relation that maps each element in the range of C<map>
2720 to the lengths of all paths composed of edges in C<map> that
2721 end up in the given element.
2722 The result may be an overapproximation. If the result is known to be exact,
2723 then C<*exact> is set to C<1>.
2724 To compute the I<maximal> path length, the resulting relation
2725 should be postprocessed by C<isl_map_lexmax>.
2726 In particular, if the input relation is a dependence relation
2727 (mapping sources to sinks), then the maximal path length corresponds
2728 to the free schedule.
2729 Note, however, that C<isl_map_lexmax> expects the maximum to be
2730 finite, so if the path lengths are unbounded (possibly due to
2731 the overapproximation), then you will get an error message.
2735 __isl_give isl_basic_set *isl_basic_map_wrap(
2736 __isl_take isl_basic_map *bmap);
2737 __isl_give isl_set *isl_map_wrap(
2738 __isl_take isl_map *map);
2739 __isl_give isl_union_set *isl_union_map_wrap(
2740 __isl_take isl_union_map *umap);
2741 __isl_give isl_basic_map *isl_basic_set_unwrap(
2742 __isl_take isl_basic_set *bset);
2743 __isl_give isl_map *isl_set_unwrap(
2744 __isl_take isl_set *set);
2745 __isl_give isl_union_map *isl_union_set_unwrap(
2746 __isl_take isl_union_set *uset);
2750 Remove any internal structure of domain (and range) of the given
2751 set or relation. If there is any such internal structure in the input,
2752 then the name of the space is also removed.
2754 __isl_give isl_basic_set *isl_basic_set_flatten(
2755 __isl_take isl_basic_set *bset);
2756 __isl_give isl_set *isl_set_flatten(
2757 __isl_take isl_set *set);
2758 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2759 __isl_take isl_basic_map *bmap);
2760 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2761 __isl_take isl_basic_map *bmap);
2762 __isl_give isl_map *isl_map_flatten_range(
2763 __isl_take isl_map *map);
2764 __isl_give isl_map *isl_map_flatten_domain(
2765 __isl_take isl_map *map);
2766 __isl_give isl_basic_map *isl_basic_map_flatten(
2767 __isl_take isl_basic_map *bmap);
2768 __isl_give isl_map *isl_map_flatten(
2769 __isl_take isl_map *map);
2771 __isl_give isl_map *isl_set_flatten_map(
2772 __isl_take isl_set *set);
2774 The function above constructs a relation
2775 that maps the input set to a flattened version of the set.
2779 Lift the input set to a space with extra dimensions corresponding
2780 to the existentially quantified variables in the input.
2781 In particular, the result lives in a wrapped map where the domain
2782 is the original space and the range corresponds to the original
2783 existentially quantified variables.
2785 __isl_give isl_basic_set *isl_basic_set_lift(
2786 __isl_take isl_basic_set *bset);
2787 __isl_give isl_set *isl_set_lift(
2788 __isl_take isl_set *set);
2789 __isl_give isl_union_set *isl_union_set_lift(
2790 __isl_take isl_union_set *uset);
2792 Given a local space that contains the existentially quantified
2793 variables of a set, a basic relation that, when applied to
2794 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2795 can be constructed using the following function.
2797 #include <isl/local_space.h>
2798 __isl_give isl_basic_map *isl_local_space_lifting(
2799 __isl_take isl_local_space *ls);
2801 =item * Internal Product
2803 __isl_give isl_basic_map *isl_basic_map_zip(
2804 __isl_take isl_basic_map *bmap);
2805 __isl_give isl_map *isl_map_zip(
2806 __isl_take isl_map *map);
2807 __isl_give isl_union_map *isl_union_map_zip(
2808 __isl_take isl_union_map *umap);
2810 Given a relation with nested relations for domain and range,
2811 interchange the range of the domain with the domain of the range.
2815 __isl_give isl_basic_map *isl_basic_map_curry(
2816 __isl_take isl_basic_map *bmap);
2817 __isl_give isl_basic_map *isl_basic_map_uncurry(
2818 __isl_take isl_basic_map *bmap);
2819 __isl_give isl_map *isl_map_curry(
2820 __isl_take isl_map *map);
2821 __isl_give isl_map *isl_map_uncurry(
2822 __isl_take isl_map *map);
2823 __isl_give isl_union_map *isl_union_map_curry(
2824 __isl_take isl_union_map *umap);
2825 __isl_give isl_union_map *isl_union_map_uncurry(
2826 __isl_take isl_union_map *umap);
2828 Given a relation with a nested relation for domain,
2829 the C<curry> functions
2830 move the range of the nested relation out of the domain
2831 and use it as the domain of a nested relation in the range,
2832 with the original range as range of this nested relation.
2833 The C<uncurry> functions perform the inverse operation.
2835 =item * Aligning parameters
2837 __isl_give isl_basic_set *isl_basic_set_align_params(
2838 __isl_take isl_basic_set *bset,
2839 __isl_take isl_space *model);
2840 __isl_give isl_set *isl_set_align_params(
2841 __isl_take isl_set *set,
2842 __isl_take isl_space *model);
2843 __isl_give isl_basic_map *isl_basic_map_align_params(
2844 __isl_take isl_basic_map *bmap,
2845 __isl_take isl_space *model);
2846 __isl_give isl_map *isl_map_align_params(
2847 __isl_take isl_map *map,
2848 __isl_take isl_space *model);
2850 Change the order of the parameters of the given set or relation
2851 such that the first parameters match those of C<model>.
2852 This may involve the introduction of extra parameters.
2853 All parameters need to be named.
2855 =item * Dimension manipulation
2857 __isl_give isl_basic_set *isl_basic_set_add_dims(
2858 __isl_take isl_basic_set *bset,
2859 enum isl_dim_type type, unsigned n);
2860 __isl_give isl_set *isl_set_add_dims(
2861 __isl_take isl_set *set,
2862 enum isl_dim_type type, unsigned n);
2863 __isl_give isl_map *isl_map_add_dims(
2864 __isl_take isl_map *map,
2865 enum isl_dim_type type, unsigned n);
2866 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2867 __isl_take isl_basic_set *bset,
2868 enum isl_dim_type type, unsigned pos,
2870 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2871 __isl_take isl_basic_map *bmap,
2872 enum isl_dim_type type, unsigned pos,
2874 __isl_give isl_set *isl_set_insert_dims(
2875 __isl_take isl_set *set,
2876 enum isl_dim_type type, unsigned pos, unsigned n);
2877 __isl_give isl_map *isl_map_insert_dims(
2878 __isl_take isl_map *map,
2879 enum isl_dim_type type, unsigned pos, unsigned n);
2880 __isl_give isl_basic_set *isl_basic_set_move_dims(
2881 __isl_take isl_basic_set *bset,
2882 enum isl_dim_type dst_type, unsigned dst_pos,
2883 enum isl_dim_type src_type, unsigned src_pos,
2885 __isl_give isl_basic_map *isl_basic_map_move_dims(
2886 __isl_take isl_basic_map *bmap,
2887 enum isl_dim_type dst_type, unsigned dst_pos,
2888 enum isl_dim_type src_type, unsigned src_pos,
2890 __isl_give isl_set *isl_set_move_dims(
2891 __isl_take isl_set *set,
2892 enum isl_dim_type dst_type, unsigned dst_pos,
2893 enum isl_dim_type src_type, unsigned src_pos,
2895 __isl_give isl_map *isl_map_move_dims(
2896 __isl_take isl_map *map,
2897 enum isl_dim_type dst_type, unsigned dst_pos,
2898 enum isl_dim_type src_type, unsigned src_pos,
2901 It is usually not advisable to directly change the (input or output)
2902 space of a set or a relation as this removes the name and the internal
2903 structure of the space. However, the above functions can be useful
2904 to add new parameters, assuming
2905 C<isl_set_align_params> and C<isl_map_align_params>
2910 =head2 Binary Operations
2912 The two arguments of a binary operation not only need to live
2913 in the same C<isl_ctx>, they currently also need to have
2914 the same (number of) parameters.
2916 =head3 Basic Operations
2920 =item * Intersection
2922 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2923 __isl_take isl_basic_set *bset1,
2924 __isl_take isl_basic_set *bset2);
2925 __isl_give isl_basic_set *isl_basic_set_intersect(
2926 __isl_take isl_basic_set *bset1,
2927 __isl_take isl_basic_set *bset2);
2928 __isl_give isl_set *isl_set_intersect_params(
2929 __isl_take isl_set *set,
2930 __isl_take isl_set *params);
2931 __isl_give isl_set *isl_set_intersect(
2932 __isl_take isl_set *set1,
2933 __isl_take isl_set *set2);
2934 __isl_give isl_union_set *isl_union_set_intersect_params(
2935 __isl_take isl_union_set *uset,
2936 __isl_take isl_set *set);
2937 __isl_give isl_union_map *isl_union_map_intersect_params(
2938 __isl_take isl_union_map *umap,
2939 __isl_take isl_set *set);
2940 __isl_give isl_union_set *isl_union_set_intersect(
2941 __isl_take isl_union_set *uset1,
2942 __isl_take isl_union_set *uset2);
2943 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2944 __isl_take isl_basic_map *bmap,
2945 __isl_take isl_basic_set *bset);
2946 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2947 __isl_take isl_basic_map *bmap,
2948 __isl_take isl_basic_set *bset);
2949 __isl_give isl_basic_map *isl_basic_map_intersect(
2950 __isl_take isl_basic_map *bmap1,
2951 __isl_take isl_basic_map *bmap2);
2952 __isl_give isl_map *isl_map_intersect_params(
2953 __isl_take isl_map *map,
2954 __isl_take isl_set *params);
2955 __isl_give isl_map *isl_map_intersect_domain(
2956 __isl_take isl_map *map,
2957 __isl_take isl_set *set);
2958 __isl_give isl_map *isl_map_intersect_range(
2959 __isl_take isl_map *map,
2960 __isl_take isl_set *set);
2961 __isl_give isl_map *isl_map_intersect(
2962 __isl_take isl_map *map1,
2963 __isl_take isl_map *map2);
2964 __isl_give isl_union_map *isl_union_map_intersect_domain(
2965 __isl_take isl_union_map *umap,
2966 __isl_take isl_union_set *uset);
2967 __isl_give isl_union_map *isl_union_map_intersect_range(
2968 __isl_take isl_union_map *umap,
2969 __isl_take isl_union_set *uset);
2970 __isl_give isl_union_map *isl_union_map_intersect(
2971 __isl_take isl_union_map *umap1,
2972 __isl_take isl_union_map *umap2);
2974 The second argument to the C<_params> functions needs to be
2975 a parametric (basic) set. For the other functions, a parametric set
2976 for either argument is only allowed if the other argument is
2977 a parametric set as well.
2981 __isl_give isl_set *isl_basic_set_union(
2982 __isl_take isl_basic_set *bset1,
2983 __isl_take isl_basic_set *bset2);
2984 __isl_give isl_map *isl_basic_map_union(
2985 __isl_take isl_basic_map *bmap1,
2986 __isl_take isl_basic_map *bmap2);
2987 __isl_give isl_set *isl_set_union(
2988 __isl_take isl_set *set1,
2989 __isl_take isl_set *set2);
2990 __isl_give isl_map *isl_map_union(
2991 __isl_take isl_map *map1,
2992 __isl_take isl_map *map2);
2993 __isl_give isl_union_set *isl_union_set_union(
2994 __isl_take isl_union_set *uset1,
2995 __isl_take isl_union_set *uset2);
2996 __isl_give isl_union_map *isl_union_map_union(
2997 __isl_take isl_union_map *umap1,
2998 __isl_take isl_union_map *umap2);
3000 =item * Set difference
3002 __isl_give isl_set *isl_set_subtract(
3003 __isl_take isl_set *set1,
3004 __isl_take isl_set *set2);
3005 __isl_give isl_map *isl_map_subtract(
3006 __isl_take isl_map *map1,
3007 __isl_take isl_map *map2);
3008 __isl_give isl_map *isl_map_subtract_domain(
3009 __isl_take isl_map *map,
3010 __isl_take isl_set *dom);
3011 __isl_give isl_map *isl_map_subtract_range(
3012 __isl_take isl_map *map,
3013 __isl_take isl_set *dom);
3014 __isl_give isl_union_set *isl_union_set_subtract(
3015 __isl_take isl_union_set *uset1,
3016 __isl_take isl_union_set *uset2);
3017 __isl_give isl_union_map *isl_union_map_subtract(
3018 __isl_take isl_union_map *umap1,
3019 __isl_take isl_union_map *umap2);
3020 __isl_give isl_union_map *isl_union_map_subtract_domain(
3021 __isl_take isl_union_map *umap,
3022 __isl_take isl_union_set *dom);
3023 __isl_give isl_union_map *isl_union_map_subtract_range(
3024 __isl_take isl_union_map *umap,
3025 __isl_take isl_union_set *dom);
3029 __isl_give isl_basic_set *isl_basic_set_apply(
3030 __isl_take isl_basic_set *bset,
3031 __isl_take isl_basic_map *bmap);
3032 __isl_give isl_set *isl_set_apply(
3033 __isl_take isl_set *set,
3034 __isl_take isl_map *map);
3035 __isl_give isl_union_set *isl_union_set_apply(
3036 __isl_take isl_union_set *uset,
3037 __isl_take isl_union_map *umap);
3038 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3039 __isl_take isl_basic_map *bmap1,
3040 __isl_take isl_basic_map *bmap2);
3041 __isl_give isl_basic_map *isl_basic_map_apply_range(
3042 __isl_take isl_basic_map *bmap1,
3043 __isl_take isl_basic_map *bmap2);
3044 __isl_give isl_map *isl_map_apply_domain(
3045 __isl_take isl_map *map1,
3046 __isl_take isl_map *map2);
3047 __isl_give isl_union_map *isl_union_map_apply_domain(
3048 __isl_take isl_union_map *umap1,
3049 __isl_take isl_union_map *umap2);
3050 __isl_give isl_map *isl_map_apply_range(
3051 __isl_take isl_map *map1,
3052 __isl_take isl_map *map2);
3053 __isl_give isl_union_map *isl_union_map_apply_range(
3054 __isl_take isl_union_map *umap1,
3055 __isl_take isl_union_map *umap2);
3059 __isl_give isl_basic_set *
3060 isl_basic_set_preimage_multi_aff(
3061 __isl_take isl_basic_set *bset,
3062 __isl_take isl_multi_aff *ma);
3063 __isl_give isl_set *isl_set_preimage_multi_aff(
3064 __isl_take isl_set *set,
3065 __isl_take isl_multi_aff *ma);
3066 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3067 __isl_take isl_set *set,
3068 __isl_take isl_pw_multi_aff *pma);
3069 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3070 __isl_take isl_map *map,
3071 __isl_take isl_multi_aff *ma);
3072 __isl_give isl_union_map *
3073 isl_union_map_preimage_domain_multi_aff(
3074 __isl_take isl_union_map *umap,
3075 __isl_take isl_multi_aff *ma);
3077 These functions compute the preimage of the given set or map domain under
3078 the given function. In other words, the expression is plugged
3079 into the set description or into the domain of the map.
3080 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3081 L</"Piecewise Multiple Quasi Affine Expressions">.
3083 =item * Cartesian Product
3085 __isl_give isl_set *isl_set_product(
3086 __isl_take isl_set *set1,
3087 __isl_take isl_set *set2);
3088 __isl_give isl_union_set *isl_union_set_product(
3089 __isl_take isl_union_set *uset1,
3090 __isl_take isl_union_set *uset2);
3091 __isl_give isl_basic_map *isl_basic_map_domain_product(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_basic_map *isl_basic_map_range_product(
3095 __isl_take isl_basic_map *bmap1,
3096 __isl_take isl_basic_map *bmap2);
3097 __isl_give isl_basic_map *isl_basic_map_product(
3098 __isl_take isl_basic_map *bmap1,
3099 __isl_take isl_basic_map *bmap2);
3100 __isl_give isl_map *isl_map_domain_product(
3101 __isl_take isl_map *map1,
3102 __isl_take isl_map *map2);
3103 __isl_give isl_map *isl_map_range_product(
3104 __isl_take isl_map *map1,
3105 __isl_take isl_map *map2);
3106 __isl_give isl_union_map *isl_union_map_domain_product(
3107 __isl_take isl_union_map *umap1,
3108 __isl_take isl_union_map *umap2);
3109 __isl_give isl_union_map *isl_union_map_range_product(
3110 __isl_take isl_union_map *umap1,
3111 __isl_take isl_union_map *umap2);
3112 __isl_give isl_map *isl_map_product(
3113 __isl_take isl_map *map1,
3114 __isl_take isl_map *map2);
3115 __isl_give isl_union_map *isl_union_map_product(
3116 __isl_take isl_union_map *umap1,
3117 __isl_take isl_union_map *umap2);
3119 The above functions compute the cross product of the given
3120 sets or relations. The domains and ranges of the results
3121 are wrapped maps between domains and ranges of the inputs.
3122 To obtain a ``flat'' product, use the following functions
3125 __isl_give isl_basic_set *isl_basic_set_flat_product(
3126 __isl_take isl_basic_set *bset1,
3127 __isl_take isl_basic_set *bset2);
3128 __isl_give isl_set *isl_set_flat_product(
3129 __isl_take isl_set *set1,
3130 __isl_take isl_set *set2);
3131 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3132 __isl_take isl_basic_map *bmap1,
3133 __isl_take isl_basic_map *bmap2);
3134 __isl_give isl_map *isl_map_flat_domain_product(
3135 __isl_take isl_map *map1,
3136 __isl_take isl_map *map2);
3137 __isl_give isl_map *isl_map_flat_range_product(
3138 __isl_take isl_map *map1,
3139 __isl_take isl_map *map2);
3140 __isl_give isl_union_map *isl_union_map_flat_range_product(
3141 __isl_take isl_union_map *umap1,
3142 __isl_take isl_union_map *umap2);
3143 __isl_give isl_basic_map *isl_basic_map_flat_product(
3144 __isl_take isl_basic_map *bmap1,
3145 __isl_take isl_basic_map *bmap2);
3146 __isl_give isl_map *isl_map_flat_product(
3147 __isl_take isl_map *map1,
3148 __isl_take isl_map *map2);
3150 =item * Simplification
3152 __isl_give isl_basic_set *isl_basic_set_gist(
3153 __isl_take isl_basic_set *bset,
3154 __isl_take isl_basic_set *context);
3155 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3156 __isl_take isl_set *context);
3157 __isl_give isl_set *isl_set_gist_params(
3158 __isl_take isl_set *set,
3159 __isl_take isl_set *context);
3160 __isl_give isl_union_set *isl_union_set_gist(
3161 __isl_take isl_union_set *uset,
3162 __isl_take isl_union_set *context);
3163 __isl_give isl_union_set *isl_union_set_gist_params(
3164 __isl_take isl_union_set *uset,
3165 __isl_take isl_set *set);
3166 __isl_give isl_basic_map *isl_basic_map_gist(
3167 __isl_take isl_basic_map *bmap,
3168 __isl_take isl_basic_map *context);
3169 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3170 __isl_take isl_map *context);
3171 __isl_give isl_map *isl_map_gist_params(
3172 __isl_take isl_map *map,
3173 __isl_take isl_set *context);
3174 __isl_give isl_map *isl_map_gist_domain(
3175 __isl_take isl_map *map,
3176 __isl_take isl_set *context);
3177 __isl_give isl_map *isl_map_gist_range(
3178 __isl_take isl_map *map,
3179 __isl_take isl_set *context);
3180 __isl_give isl_union_map *isl_union_map_gist(
3181 __isl_take isl_union_map *umap,
3182 __isl_take isl_union_map *context);
3183 __isl_give isl_union_map *isl_union_map_gist_params(
3184 __isl_take isl_union_map *umap,
3185 __isl_take isl_set *set);
3186 __isl_give isl_union_map *isl_union_map_gist_domain(
3187 __isl_take isl_union_map *umap,
3188 __isl_take isl_union_set *uset);
3189 __isl_give isl_union_map *isl_union_map_gist_range(
3190 __isl_take isl_union_map *umap,
3191 __isl_take isl_union_set *uset);
3193 The gist operation returns a set or relation that has the
3194 same intersection with the context as the input set or relation.
3195 Any implicit equality in the intersection is made explicit in the result,
3196 while all inequalities that are redundant with respect to the intersection
3198 In case of union sets and relations, the gist operation is performed
3203 =head3 Lexicographic Optimization
3205 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3206 the following functions
3207 compute a set that contains the lexicographic minimum or maximum
3208 of the elements in C<set> (or C<bset>) for those values of the parameters
3209 that satisfy C<dom>.
3210 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3211 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3213 In other words, the union of the parameter values
3214 for which the result is non-empty and of C<*empty>
3217 __isl_give isl_set *isl_basic_set_partial_lexmin(
3218 __isl_take isl_basic_set *bset,
3219 __isl_take isl_basic_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_set *isl_basic_set_partial_lexmax(
3222 __isl_take isl_basic_set *bset,
3223 __isl_take isl_basic_set *dom,
3224 __isl_give isl_set **empty);
3225 __isl_give isl_set *isl_set_partial_lexmin(
3226 __isl_take isl_set *set, __isl_take isl_set *dom,
3227 __isl_give isl_set **empty);
3228 __isl_give isl_set *isl_set_partial_lexmax(
3229 __isl_take isl_set *set, __isl_take isl_set *dom,
3230 __isl_give isl_set **empty);
3232 Given a (basic) set C<set> (or C<bset>), the following functions simply
3233 return a set containing the lexicographic minimum or maximum
3234 of the elements in C<set> (or C<bset>).
3235 In case of union sets, the optimum is computed per space.
3237 __isl_give isl_set *isl_basic_set_lexmin(
3238 __isl_take isl_basic_set *bset);
3239 __isl_give isl_set *isl_basic_set_lexmax(
3240 __isl_take isl_basic_set *bset);
3241 __isl_give isl_set *isl_set_lexmin(
3242 __isl_take isl_set *set);
3243 __isl_give isl_set *isl_set_lexmax(
3244 __isl_take isl_set *set);
3245 __isl_give isl_union_set *isl_union_set_lexmin(
3246 __isl_take isl_union_set *uset);
3247 __isl_give isl_union_set *isl_union_set_lexmax(
3248 __isl_take isl_union_set *uset);
3250 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3251 the following functions
3252 compute a relation that maps each element of C<dom>
3253 to the single lexicographic minimum or maximum
3254 of the elements that are associated to that same
3255 element in C<map> (or C<bmap>).
3256 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3257 that contains the elements in C<dom> that do not map
3258 to any elements in C<map> (or C<bmap>).
3259 In other words, the union of the domain of the result and of C<*empty>
3262 __isl_give isl_map *isl_basic_map_partial_lexmax(
3263 __isl_take isl_basic_map *bmap,
3264 __isl_take isl_basic_set *dom,
3265 __isl_give isl_set **empty);
3266 __isl_give isl_map *isl_basic_map_partial_lexmin(
3267 __isl_take isl_basic_map *bmap,
3268 __isl_take isl_basic_set *dom,
3269 __isl_give isl_set **empty);
3270 __isl_give isl_map *isl_map_partial_lexmax(
3271 __isl_take isl_map *map, __isl_take isl_set *dom,
3272 __isl_give isl_set **empty);
3273 __isl_give isl_map *isl_map_partial_lexmin(
3274 __isl_take isl_map *map, __isl_take isl_set *dom,
3275 __isl_give isl_set **empty);
3277 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3278 return a map mapping each element in the domain of
3279 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3280 of all elements associated to that element.
3281 In case of union relations, the optimum is computed per space.
3283 __isl_give isl_map *isl_basic_map_lexmin(
3284 __isl_take isl_basic_map *bmap);
3285 __isl_give isl_map *isl_basic_map_lexmax(
3286 __isl_take isl_basic_map *bmap);
3287 __isl_give isl_map *isl_map_lexmin(
3288 __isl_take isl_map *map);
3289 __isl_give isl_map *isl_map_lexmax(
3290 __isl_take isl_map *map);
3291 __isl_give isl_union_map *isl_union_map_lexmin(
3292 __isl_take isl_union_map *umap);
3293 __isl_give isl_union_map *isl_union_map_lexmax(
3294 __isl_take isl_union_map *umap);
3296 The following functions return their result in the form of
3297 a piecewise multi-affine expression
3298 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3299 but are otherwise equivalent to the corresponding functions
3300 returning a basic set or relation.
3302 __isl_give isl_pw_multi_aff *
3303 isl_basic_map_lexmin_pw_multi_aff(
3304 __isl_take isl_basic_map *bmap);
3305 __isl_give isl_pw_multi_aff *
3306 isl_basic_set_partial_lexmin_pw_multi_aff(
3307 __isl_take isl_basic_set *bset,
3308 __isl_take isl_basic_set *dom,
3309 __isl_give isl_set **empty);
3310 __isl_give isl_pw_multi_aff *
3311 isl_basic_set_partial_lexmax_pw_multi_aff(
3312 __isl_take isl_basic_set *bset,
3313 __isl_take isl_basic_set *dom,
3314 __isl_give isl_set **empty);
3315 __isl_give isl_pw_multi_aff *
3316 isl_basic_map_partial_lexmin_pw_multi_aff(
3317 __isl_take isl_basic_map *bmap,
3318 __isl_take isl_basic_set *dom,
3319 __isl_give isl_set **empty);
3320 __isl_give isl_pw_multi_aff *
3321 isl_basic_map_partial_lexmax_pw_multi_aff(
3322 __isl_take isl_basic_map *bmap,
3323 __isl_take isl_basic_set *dom,
3324 __isl_give isl_set **empty);
3325 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3326 __isl_take isl_set *set);
3327 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3328 __isl_take isl_set *set);
3329 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3330 __isl_take isl_map *map);
3331 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3332 __isl_take isl_map *map);
3336 Lists are defined over several element types, including
3337 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3338 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3339 Here we take lists of C<isl_set>s as an example.
3340 Lists can be created, copied, modified and freed using the following functions.
3342 #include <isl/list.h>
3343 __isl_give isl_set_list *isl_set_list_from_set(
3344 __isl_take isl_set *el);
3345 __isl_give isl_set_list *isl_set_list_alloc(
3346 isl_ctx *ctx, int n);
3347 __isl_give isl_set_list *isl_set_list_copy(
3348 __isl_keep isl_set_list *list);
3349 __isl_give isl_set_list *isl_set_list_insert(
3350 __isl_take isl_set_list *list, unsigned pos,
3351 __isl_take isl_set *el);
3352 __isl_give isl_set_list *isl_set_list_add(
3353 __isl_take isl_set_list *list,
3354 __isl_take isl_set *el);
3355 __isl_give isl_set_list *isl_set_list_drop(
3356 __isl_take isl_set_list *list,
3357 unsigned first, unsigned n);
3358 __isl_give isl_set_list *isl_set_list_set_set(
3359 __isl_take isl_set_list *list, int index,
3360 __isl_take isl_set *set);
3361 __isl_give isl_set_list *isl_set_list_concat(
3362 __isl_take isl_set_list *list1,
3363 __isl_take isl_set_list *list2);
3364 __isl_give isl_set_list *isl_set_list_sort(
3365 __isl_take isl_set_list *list,
3366 int (*cmp)(__isl_keep isl_set *a,
3367 __isl_keep isl_set *b, void *user),
3369 void *isl_set_list_free(__isl_take isl_set_list *list);
3371 C<isl_set_list_alloc> creates an empty list with a capacity for
3372 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3375 Lists can be inspected using the following functions.
3377 #include <isl/list.h>
3378 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3379 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3380 __isl_give isl_set *isl_set_list_get_set(
3381 __isl_keep isl_set_list *list, int index);
3382 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3383 int (*fn)(__isl_take isl_set *el, void *user),
3385 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3386 int (*follows)(__isl_keep isl_set *a,
3387 __isl_keep isl_set *b, void *user),
3389 int (*fn)(__isl_take isl_set *el, void *user),
3392 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3393 strongly connected components of the graph with as vertices the elements
3394 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3395 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3396 should return C<-1> on error.
3398 Lists can be printed using
3400 #include <isl/list.h>
3401 __isl_give isl_printer *isl_printer_print_set_list(
3402 __isl_take isl_printer *p,
3403 __isl_keep isl_set_list *list);
3405 =head2 Multiple Values
3407 An C<isl_multi_val> object represents a sequence of zero or more values,
3408 living in a set space.
3410 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3411 using the following function
3413 #include <isl/val.h>
3414 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3415 __isl_take isl_space *space,
3416 __isl_take isl_val_list *list);
3418 The zero multiple value (with value zero for each set dimension)
3419 can be created using the following function.
3421 #include <isl/val.h>
3422 __isl_give isl_multi_val *isl_multi_val_zero(
3423 __isl_take isl_space *space);
3425 Multiple values can be copied and freed using
3427 #include <isl/val.h>
3428 __isl_give isl_multi_val *isl_multi_val_copy(
3429 __isl_keep isl_multi_val *mv);
3430 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3432 They can be inspected using
3434 #include <isl/val.h>
3435 isl_ctx *isl_multi_val_get_ctx(
3436 __isl_keep isl_multi_val *mv);
3437 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3438 enum isl_dim_type type);
3439 __isl_give isl_val *isl_multi_val_get_val(
3440 __isl_keep isl_multi_val *mv, int pos);
3441 const char *isl_multi_val_get_tuple_name(
3442 __isl_keep isl_multi_val *mv,
3443 enum isl_dim_type type);
3445 They can be modified using
3447 #include <isl/val.h>
3448 __isl_give isl_multi_val *isl_multi_val_set_val(
3449 __isl_take isl_multi_val *mv, int pos,
3450 __isl_take isl_val *val);
3451 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3452 __isl_take isl_multi_val *mv,
3453 enum isl_dim_type type, unsigned pos, const char *s);
3454 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3455 __isl_take isl_multi_val *mv,
3456 enum isl_dim_type type, const char *s);
3457 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3458 __isl_take isl_multi_val *mv,
3459 enum isl_dim_type type, __isl_take isl_id *id);
3461 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3462 __isl_take isl_multi_val *mv,
3463 enum isl_dim_type type, unsigned first, unsigned n);
3464 __isl_give isl_multi_val *isl_multi_val_add_dims(
3465 __isl_take isl_multi_val *mv,
3466 enum isl_dim_type type, unsigned n);
3467 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3468 __isl_take isl_multi_val *mv,
3469 enum isl_dim_type type, unsigned first, unsigned n);
3473 #include <isl/val.h>
3474 __isl_give isl_multi_val *isl_multi_val_align_params(
3475 __isl_take isl_multi_val *mv,
3476 __isl_take isl_space *model);
3477 __isl_give isl_multi_val *isl_multi_val_range_splice(
3478 __isl_take isl_multi_val *mv1, unsigned pos,
3479 __isl_take isl_multi_val *mv2);
3480 __isl_give isl_multi_val *isl_multi_val_range_product(
3481 __isl_take isl_multi_val *mv1,
3482 __isl_take isl_multi_val *mv2);
3483 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3484 __isl_take isl_multi_val *mv1,
3485 __isl_take isl_multi_aff *mv2);
3486 __isl_give isl_multi_val *isl_multi_val_add_val(
3487 __isl_take isl_multi_val *mv,
3488 __isl_take isl_val *v);
3489 __isl_give isl_multi_val *isl_multi_val_mod_val(
3490 __isl_take isl_multi_val *mv,
3491 __isl_take isl_val *v);
3492 __isl_give isl_multi_val *isl_multi_val_scale_val(
3493 __isl_take isl_multi_val *mv,
3494 __isl_take isl_val *v);
3498 Vectors can be created, copied and freed using the following functions.
3500 #include <isl/vec.h>
3501 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3503 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3504 void *isl_vec_free(__isl_take isl_vec *vec);
3506 Note that the elements of a newly created vector may have arbitrary values.
3507 The elements can be changed and inspected using the following functions.
3509 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3510 int isl_vec_size(__isl_keep isl_vec *vec);
3511 int isl_vec_get_element(__isl_keep isl_vec *vec,
3512 int pos, isl_int *v);
3513 __isl_give isl_val *isl_vec_get_element_val(
3514 __isl_keep isl_vec *vec, int pos);
3515 __isl_give isl_vec *isl_vec_set_element(
3516 __isl_take isl_vec *vec, int pos, isl_int v);
3517 __isl_give isl_vec *isl_vec_set_element_si(
3518 __isl_take isl_vec *vec, int pos, int v);
3519 __isl_give isl_vec *isl_vec_set_element_val(
3520 __isl_take isl_vec *vec, int pos,
3521 __isl_take isl_val *v);
3522 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3524 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3526 __isl_give isl_vec *isl_vec_set_val(
3527 __isl_take isl_vec *vec, __isl_take isl_val *v);
3528 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3531 C<isl_vec_get_element> will return a negative value if anything went wrong.
3532 In that case, the value of C<*v> is undefined.
3534 The following function can be used to concatenate two vectors.
3536 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3537 __isl_take isl_vec *vec2);
3541 Matrices can be created, copied and freed using the following functions.
3543 #include <isl/mat.h>
3544 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3545 unsigned n_row, unsigned n_col);
3546 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3547 void *isl_mat_free(__isl_take isl_mat *mat);
3549 Note that the elements of a newly created matrix may have arbitrary values.
3550 The elements can be changed and inspected using the following functions.
3552 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3553 int isl_mat_rows(__isl_keep isl_mat *mat);
3554 int isl_mat_cols(__isl_keep isl_mat *mat);
3555 int isl_mat_get_element(__isl_keep isl_mat *mat,
3556 int row, int col, isl_int *v);
3557 __isl_give isl_val *isl_mat_get_element_val(
3558 __isl_keep isl_mat *mat, int row, int col);
3559 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3560 int row, int col, isl_int v);
3561 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3562 int row, int col, int v);
3563 __isl_give isl_mat *isl_mat_set_element_val(
3564 __isl_take isl_mat *mat, int row, int col,
3565 __isl_take isl_val *v);
3567 C<isl_mat_get_element> will return a negative value if anything went wrong.
3568 In that case, the value of C<*v> is undefined.
3570 The following function can be used to compute the (right) inverse
3571 of a matrix, i.e., a matrix such that the product of the original
3572 and the inverse (in that order) is a multiple of the identity matrix.
3573 The input matrix is assumed to be of full row-rank.
3575 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3577 The following function can be used to compute the (right) kernel
3578 (or null space) of a matrix, i.e., a matrix such that the product of
3579 the original and the kernel (in that order) is the zero matrix.
3581 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3583 =head2 Piecewise Quasi Affine Expressions
3585 The zero quasi affine expression or the quasi affine expression
3586 that is equal to a specified dimension on a given domain can be created using
3588 __isl_give isl_aff *isl_aff_zero_on_domain(
3589 __isl_take isl_local_space *ls);
3590 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3591 __isl_take isl_local_space *ls);
3592 __isl_give isl_aff *isl_aff_var_on_domain(
3593 __isl_take isl_local_space *ls,
3594 enum isl_dim_type type, unsigned pos);
3595 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3596 __isl_take isl_local_space *ls,
3597 enum isl_dim_type type, unsigned pos);
3599 Note that the space in which the resulting objects live is a map space
3600 with the given space as domain and a one-dimensional range.
3602 An empty piecewise quasi affine expression (one with no cells)
3603 or a piecewise quasi affine expression with a single cell can
3604 be created using the following functions.
3606 #include <isl/aff.h>
3607 __isl_give isl_pw_aff *isl_pw_aff_empty(
3608 __isl_take isl_space *space);
3609 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3610 __isl_take isl_set *set, __isl_take isl_aff *aff);
3611 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3612 __isl_take isl_aff *aff);
3614 A piecewise quasi affine expression that is equal to 1 on a set
3615 and 0 outside the set can be created using the following function.
3617 #include <isl/aff.h>
3618 __isl_give isl_pw_aff *isl_set_indicator_function(
3619 __isl_take isl_set *set);
3621 Quasi affine expressions can be copied and freed using
3623 #include <isl/aff.h>
3624 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3625 void *isl_aff_free(__isl_take isl_aff *aff);
3627 __isl_give isl_pw_aff *isl_pw_aff_copy(
3628 __isl_keep isl_pw_aff *pwaff);
3629 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3631 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3632 using the following function. The constraint is required to have
3633 a non-zero coefficient for the specified dimension.
3635 #include <isl/constraint.h>
3636 __isl_give isl_aff *isl_constraint_get_bound(
3637 __isl_keep isl_constraint *constraint,
3638 enum isl_dim_type type, int pos);
3640 The entire affine expression of the constraint can also be extracted
3641 using the following function.
3643 #include <isl/constraint.h>
3644 __isl_give isl_aff *isl_constraint_get_aff(
3645 __isl_keep isl_constraint *constraint);
3647 Conversely, an equality constraint equating
3648 the affine expression to zero or an inequality constraint enforcing
3649 the affine expression to be non-negative, can be constructed using
3651 __isl_give isl_constraint *isl_equality_from_aff(
3652 __isl_take isl_aff *aff);
3653 __isl_give isl_constraint *isl_inequality_from_aff(
3654 __isl_take isl_aff *aff);
3656 The expression can be inspected using
3658 #include <isl/aff.h>
3659 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3660 int isl_aff_dim(__isl_keep isl_aff *aff,
3661 enum isl_dim_type type);
3662 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3663 __isl_keep isl_aff *aff);
3664 __isl_give isl_local_space *isl_aff_get_local_space(
3665 __isl_keep isl_aff *aff);
3666 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3667 enum isl_dim_type type, unsigned pos);
3668 const char *isl_pw_aff_get_dim_name(
3669 __isl_keep isl_pw_aff *pa,
3670 enum isl_dim_type type, unsigned pos);
3671 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3672 enum isl_dim_type type, unsigned pos);
3673 __isl_give isl_id *isl_pw_aff_get_dim_id(
3674 __isl_keep isl_pw_aff *pa,
3675 enum isl_dim_type type, unsigned pos);
3676 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3677 __isl_keep isl_pw_aff *pa,
3678 enum isl_dim_type type);
3679 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3681 __isl_give isl_val *isl_aff_get_constant_val(
3682 __isl_keep isl_aff *aff);
3683 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3684 enum isl_dim_type type, int pos, isl_int *v);
3685 __isl_give isl_val *isl_aff_get_coefficient_val(
3686 __isl_keep isl_aff *aff,
3687 enum isl_dim_type type, int pos);
3688 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3690 __isl_give isl_val *isl_aff_get_denominator_val(
3691 __isl_keep isl_aff *aff);
3692 __isl_give isl_aff *isl_aff_get_div(
3693 __isl_keep isl_aff *aff, int pos);
3695 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3696 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3697 int (*fn)(__isl_take isl_set *set,
3698 __isl_take isl_aff *aff,
3699 void *user), void *user);
3701 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3702 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3704 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3705 enum isl_dim_type type, unsigned first, unsigned n);
3706 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3707 enum isl_dim_type type, unsigned first, unsigned n);
3709 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3710 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3711 enum isl_dim_type type);
3712 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3714 It can be modified using
3716 #include <isl/aff.h>
3717 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3718 __isl_take isl_pw_aff *pwaff,
3719 enum isl_dim_type type, __isl_take isl_id *id);
3720 __isl_give isl_aff *isl_aff_set_dim_name(
3721 __isl_take isl_aff *aff, enum isl_dim_type type,
3722 unsigned pos, const char *s);
3723 __isl_give isl_aff *isl_aff_set_dim_id(
3724 __isl_take isl_aff *aff, enum isl_dim_type type,
3725 unsigned pos, __isl_take isl_id *id);
3726 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3727 __isl_take isl_pw_aff *pma,
3728 enum isl_dim_type type, unsigned pos,
3729 __isl_take isl_id *id);
3730 __isl_give isl_aff *isl_aff_set_constant(
3731 __isl_take isl_aff *aff, isl_int v);
3732 __isl_give isl_aff *isl_aff_set_constant_si(
3733 __isl_take isl_aff *aff, int v);
3734 __isl_give isl_aff *isl_aff_set_constant_val(
3735 __isl_take isl_aff *aff, __isl_take isl_val *v);
3736 __isl_give isl_aff *isl_aff_set_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_set_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_set_coefficient_val(
3743 __isl_take isl_aff *aff,
3744 enum isl_dim_type type, int pos,
3745 __isl_take isl_val *v);
3746 __isl_give isl_aff *isl_aff_set_denominator(
3747 __isl_take isl_aff *aff, isl_int v);
3749 __isl_give isl_aff *isl_aff_add_constant(
3750 __isl_take isl_aff *aff, isl_int v);
3751 __isl_give isl_aff *isl_aff_add_constant_si(
3752 __isl_take isl_aff *aff, int v);
3753 __isl_give isl_aff *isl_aff_add_constant_val(
3754 __isl_take isl_aff *aff, __isl_take isl_val *v);
3755 __isl_give isl_aff *isl_aff_add_constant_num(
3756 __isl_take isl_aff *aff, isl_int v);
3757 __isl_give isl_aff *isl_aff_add_constant_num_si(
3758 __isl_take isl_aff *aff, int v);
3759 __isl_give isl_aff *isl_aff_add_coefficient(
3760 __isl_take isl_aff *aff,
3761 enum isl_dim_type type, int pos, isl_int v);
3762 __isl_give isl_aff *isl_aff_add_coefficient_si(
3763 __isl_take isl_aff *aff,
3764 enum isl_dim_type type, int pos, int v);
3765 __isl_give isl_aff *isl_aff_add_coefficient_val(
3766 __isl_take isl_aff *aff,
3767 enum isl_dim_type type, int pos,
3768 __isl_take isl_val *v);
3770 __isl_give isl_aff *isl_aff_insert_dims(
3771 __isl_take isl_aff *aff,
3772 enum isl_dim_type type, unsigned first, unsigned n);
3773 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3774 __isl_take isl_pw_aff *pwaff,
3775 enum isl_dim_type type, unsigned first, unsigned n);
3776 __isl_give isl_aff *isl_aff_add_dims(
3777 __isl_take isl_aff *aff,
3778 enum isl_dim_type type, unsigned n);
3779 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3780 __isl_take isl_pw_aff *pwaff,
3781 enum isl_dim_type type, unsigned n);
3782 __isl_give isl_aff *isl_aff_drop_dims(
3783 __isl_take isl_aff *aff,
3784 enum isl_dim_type type, unsigned first, unsigned n);
3785 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3786 __isl_take isl_pw_aff *pwaff,
3787 enum isl_dim_type type, unsigned first, unsigned n);
3789 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3790 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3791 set the I<numerator> of the constant or coefficient, while
3792 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3793 the constant or coefficient as a whole.
3794 The C<add_constant> and C<add_coefficient> functions add an integer
3795 or rational value to
3796 the possibly rational constant or coefficient.
3797 The C<add_constant_num> functions add an integer value to
3800 To check whether an affine expressions is obviously zero
3801 or obviously equal to some other affine expression, use
3803 #include <isl/aff.h>
3804 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3805 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3806 __isl_keep isl_aff *aff2);
3807 int isl_pw_aff_plain_is_equal(
3808 __isl_keep isl_pw_aff *pwaff1,
3809 __isl_keep isl_pw_aff *pwaff2);
3813 #include <isl/aff.h>
3814 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3815 __isl_take isl_aff *aff2);
3816 __isl_give isl_pw_aff *isl_pw_aff_add(
3817 __isl_take isl_pw_aff *pwaff1,
3818 __isl_take isl_pw_aff *pwaff2);
3819 __isl_give isl_pw_aff *isl_pw_aff_min(
3820 __isl_take isl_pw_aff *pwaff1,
3821 __isl_take isl_pw_aff *pwaff2);
3822 __isl_give isl_pw_aff *isl_pw_aff_max(
3823 __isl_take isl_pw_aff *pwaff1,
3824 __isl_take isl_pw_aff *pwaff2);
3825 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3826 __isl_take isl_aff *aff2);
3827 __isl_give isl_pw_aff *isl_pw_aff_sub(
3828 __isl_take isl_pw_aff *pwaff1,
3829 __isl_take isl_pw_aff *pwaff2);
3830 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3831 __isl_give isl_pw_aff *isl_pw_aff_neg(
3832 __isl_take isl_pw_aff *pwaff);
3833 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3834 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3835 __isl_take isl_pw_aff *pwaff);
3836 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3837 __isl_give isl_pw_aff *isl_pw_aff_floor(
3838 __isl_take isl_pw_aff *pwaff);
3839 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3841 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3842 __isl_take isl_val *mod);
3843 __isl_give isl_pw_aff *isl_pw_aff_mod(
3844 __isl_take isl_pw_aff *pwaff, isl_int mod);
3845 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3846 __isl_take isl_pw_aff *pa,
3847 __isl_take isl_val *mod);
3848 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3850 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3851 __isl_take isl_val *v);
3852 __isl_give isl_pw_aff *isl_pw_aff_scale(
3853 __isl_take isl_pw_aff *pwaff, isl_int f);
3854 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3855 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3856 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3858 __isl_give isl_aff *isl_aff_scale_down_ui(
3859 __isl_take isl_aff *aff, unsigned f);
3860 __isl_give isl_aff *isl_aff_scale_down_val(
3861 __isl_take isl_aff *aff, __isl_take isl_val *v);
3862 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3863 __isl_take isl_pw_aff *pwaff, isl_int f);
3864 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3865 __isl_take isl_pw_aff *pa,
3866 __isl_take isl_val *f);
3868 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3869 __isl_take isl_pw_aff_list *list);
3870 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3871 __isl_take isl_pw_aff_list *list);
3873 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3874 __isl_take isl_pw_aff *pwqp);
3876 __isl_give isl_aff *isl_aff_align_params(
3877 __isl_take isl_aff *aff,
3878 __isl_take isl_space *model);
3879 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3880 __isl_take isl_pw_aff *pwaff,
3881 __isl_take isl_space *model);
3883 __isl_give isl_aff *isl_aff_project_domain_on_params(
3884 __isl_take isl_aff *aff);
3886 __isl_give isl_aff *isl_aff_gist_params(
3887 __isl_take isl_aff *aff,
3888 __isl_take isl_set *context);
3889 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3890 __isl_take isl_set *context);
3891 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3892 __isl_take isl_pw_aff *pwaff,
3893 __isl_take isl_set *context);
3894 __isl_give isl_pw_aff *isl_pw_aff_gist(
3895 __isl_take isl_pw_aff *pwaff,
3896 __isl_take isl_set *context);
3898 __isl_give isl_set *isl_pw_aff_domain(
3899 __isl_take isl_pw_aff *pwaff);
3900 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3901 __isl_take isl_pw_aff *pa,
3902 __isl_take isl_set *set);
3903 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3904 __isl_take isl_pw_aff *pa,
3905 __isl_take isl_set *set);
3907 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3908 __isl_take isl_aff *aff2);
3909 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3910 __isl_take isl_aff *aff2);
3911 __isl_give isl_pw_aff *isl_pw_aff_mul(
3912 __isl_take isl_pw_aff *pwaff1,
3913 __isl_take isl_pw_aff *pwaff2);
3914 __isl_give isl_pw_aff *isl_pw_aff_div(
3915 __isl_take isl_pw_aff *pa1,
3916 __isl_take isl_pw_aff *pa2);
3917 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3918 __isl_take isl_pw_aff *pa1,
3919 __isl_take isl_pw_aff *pa2);
3920 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3921 __isl_take isl_pw_aff *pa1,
3922 __isl_take isl_pw_aff *pa2);
3924 When multiplying two affine expressions, at least one of the two needs
3925 to be a constant. Similarly, when dividing an affine expression by another,
3926 the second expression needs to be a constant.
3927 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3928 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3931 #include <isl/aff.h>
3932 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3933 __isl_take isl_aff *aff,
3934 __isl_take isl_multi_aff *ma);
3935 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3936 __isl_take isl_pw_aff *pa,
3937 __isl_take isl_multi_aff *ma);
3938 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3939 __isl_take isl_pw_aff *pa,
3940 __isl_take isl_pw_multi_aff *pma);
3942 These functions precompose the input expression by the given
3943 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3944 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3945 into the (piecewise) affine expression.
3946 Objects of type C<isl_multi_aff> are described in
3947 L</"Piecewise Multiple Quasi Affine Expressions">.
3949 #include <isl/aff.h>
3950 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3951 __isl_take isl_aff *aff);
3952 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3953 __isl_take isl_aff *aff);
3954 __isl_give isl_basic_set *isl_aff_le_basic_set(
3955 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3956 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3957 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3958 __isl_give isl_set *isl_pw_aff_eq_set(
3959 __isl_take isl_pw_aff *pwaff1,
3960 __isl_take isl_pw_aff *pwaff2);
3961 __isl_give isl_set *isl_pw_aff_ne_set(
3962 __isl_take isl_pw_aff *pwaff1,
3963 __isl_take isl_pw_aff *pwaff2);
3964 __isl_give isl_set *isl_pw_aff_le_set(
3965 __isl_take isl_pw_aff *pwaff1,
3966 __isl_take isl_pw_aff *pwaff2);
3967 __isl_give isl_set *isl_pw_aff_lt_set(
3968 __isl_take isl_pw_aff *pwaff1,
3969 __isl_take isl_pw_aff *pwaff2);
3970 __isl_give isl_set *isl_pw_aff_ge_set(
3971 __isl_take isl_pw_aff *pwaff1,
3972 __isl_take isl_pw_aff *pwaff2);
3973 __isl_give isl_set *isl_pw_aff_gt_set(
3974 __isl_take isl_pw_aff *pwaff1,
3975 __isl_take isl_pw_aff *pwaff2);
3977 __isl_give isl_set *isl_pw_aff_list_eq_set(
3978 __isl_take isl_pw_aff_list *list1,
3979 __isl_take isl_pw_aff_list *list2);
3980 __isl_give isl_set *isl_pw_aff_list_ne_set(
3981 __isl_take isl_pw_aff_list *list1,
3982 __isl_take isl_pw_aff_list *list2);
3983 __isl_give isl_set *isl_pw_aff_list_le_set(
3984 __isl_take isl_pw_aff_list *list1,
3985 __isl_take isl_pw_aff_list *list2);
3986 __isl_give isl_set *isl_pw_aff_list_lt_set(
3987 __isl_take isl_pw_aff_list *list1,
3988 __isl_take isl_pw_aff_list *list2);
3989 __isl_give isl_set *isl_pw_aff_list_ge_set(
3990 __isl_take isl_pw_aff_list *list1,
3991 __isl_take isl_pw_aff_list *list2);
3992 __isl_give isl_set *isl_pw_aff_list_gt_set(
3993 __isl_take isl_pw_aff_list *list1,
3994 __isl_take isl_pw_aff_list *list2);
3996 The function C<isl_aff_neg_basic_set> returns a basic set
3997 containing those elements in the domain space
3998 of C<aff> where C<aff> is negative.
3999 The function C<isl_aff_ge_basic_set> returns a basic set
4000 containing those elements in the shared space
4001 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4002 The function C<isl_pw_aff_ge_set> returns a set
4003 containing those elements in the shared domain
4004 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4005 The functions operating on C<isl_pw_aff_list> apply the corresponding
4006 C<isl_pw_aff> function to each pair of elements in the two lists.
4008 #include <isl/aff.h>
4009 __isl_give isl_set *isl_pw_aff_nonneg_set(
4010 __isl_take isl_pw_aff *pwaff);
4011 __isl_give isl_set *isl_pw_aff_zero_set(
4012 __isl_take isl_pw_aff *pwaff);
4013 __isl_give isl_set *isl_pw_aff_non_zero_set(
4014 __isl_take isl_pw_aff *pwaff);
4016 The function C<isl_pw_aff_nonneg_set> returns a set
4017 containing those elements in the domain
4018 of C<pwaff> where C<pwaff> is non-negative.
4020 #include <isl/aff.h>
4021 __isl_give isl_pw_aff *isl_pw_aff_cond(
4022 __isl_take isl_pw_aff *cond,
4023 __isl_take isl_pw_aff *pwaff_true,
4024 __isl_take isl_pw_aff *pwaff_false);
4026 The function C<isl_pw_aff_cond> performs a conditional operator
4027 and returns an expression that is equal to C<pwaff_true>
4028 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4029 where C<cond> is zero.
4031 #include <isl/aff.h>
4032 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4033 __isl_take isl_pw_aff *pwaff1,
4034 __isl_take isl_pw_aff *pwaff2);
4035 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4036 __isl_take isl_pw_aff *pwaff1,
4037 __isl_take isl_pw_aff *pwaff2);
4038 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4039 __isl_take isl_pw_aff *pwaff1,
4040 __isl_take isl_pw_aff *pwaff2);
4042 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4043 expression with a domain that is the union of those of C<pwaff1> and
4044 C<pwaff2> and such that on each cell, the quasi-affine expression is
4045 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4046 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4047 associated expression is the defined one.
4049 An expression can be read from input using
4051 #include <isl/aff.h>
4052 __isl_give isl_aff *isl_aff_read_from_str(
4053 isl_ctx *ctx, const char *str);
4054 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4055 isl_ctx *ctx, const char *str);
4057 An expression can be printed using
4059 #include <isl/aff.h>
4060 __isl_give isl_printer *isl_printer_print_aff(
4061 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4063 __isl_give isl_printer *isl_printer_print_pw_aff(
4064 __isl_take isl_printer *p,
4065 __isl_keep isl_pw_aff *pwaff);
4067 =head2 Piecewise Multiple Quasi Affine Expressions
4069 An C<isl_multi_aff> object represents a sequence of
4070 zero or more affine expressions, all defined on the same domain space.
4071 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4072 zero or more piecewise affine expressions.
4074 An C<isl_multi_aff> can be constructed from a single
4075 C<isl_aff> or an C<isl_aff_list> using the
4076 following functions. Similarly for C<isl_multi_pw_aff>.
4078 #include <isl/aff.h>
4079 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4080 __isl_take isl_aff *aff);
4081 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4082 __isl_take isl_pw_aff *pa);
4083 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4084 __isl_take isl_space *space,
4085 __isl_take isl_aff_list *list);
4087 An empty piecewise multiple quasi affine expression (one with no cells),
4088 the zero piecewise multiple quasi affine expression (with value zero
4089 for each output dimension),
4090 a piecewise multiple quasi affine expression with a single cell (with
4091 either a universe or a specified domain) or
4092 a zero-dimensional piecewise multiple quasi affine expression
4094 can be created using the following functions.
4096 #include <isl/aff.h>
4097 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4098 __isl_take isl_space *space);
4099 __isl_give isl_multi_aff *isl_multi_aff_zero(
4100 __isl_take isl_space *space);
4101 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4102 __isl_take isl_space *space);
4103 __isl_give isl_multi_aff *isl_multi_aff_identity(
4104 __isl_take isl_space *space);
4105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4106 __isl_take isl_space *space);
4107 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4108 __isl_take isl_space *space);
4109 __isl_give isl_pw_multi_aff *
4110 isl_pw_multi_aff_from_multi_aff(
4111 __isl_take isl_multi_aff *ma);
4112 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4113 __isl_take isl_set *set,
4114 __isl_take isl_multi_aff *maff);
4115 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4116 __isl_take isl_set *set);
4118 __isl_give isl_union_pw_multi_aff *
4119 isl_union_pw_multi_aff_empty(
4120 __isl_take isl_space *space);
4121 __isl_give isl_union_pw_multi_aff *
4122 isl_union_pw_multi_aff_add_pw_multi_aff(
4123 __isl_take isl_union_pw_multi_aff *upma,
4124 __isl_take isl_pw_multi_aff *pma);
4125 __isl_give isl_union_pw_multi_aff *
4126 isl_union_pw_multi_aff_from_domain(
4127 __isl_take isl_union_set *uset);
4129 A piecewise multiple quasi affine expression can also be initialized
4130 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4131 and the C<isl_map> is single-valued.
4132 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4133 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4135 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4136 __isl_take isl_set *set);
4137 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4138 __isl_take isl_map *map);
4140 __isl_give isl_union_pw_multi_aff *
4141 isl_union_pw_multi_aff_from_union_set(
4142 __isl_take isl_union_set *uset);
4143 __isl_give isl_union_pw_multi_aff *
4144 isl_union_pw_multi_aff_from_union_map(
4145 __isl_take isl_union_map *umap);
4147 Multiple quasi affine expressions can be copied and freed using
4149 #include <isl/aff.h>
4150 __isl_give isl_multi_aff *isl_multi_aff_copy(
4151 __isl_keep isl_multi_aff *maff);
4152 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4155 __isl_keep isl_pw_multi_aff *pma);
4156 void *isl_pw_multi_aff_free(
4157 __isl_take isl_pw_multi_aff *pma);
4159 __isl_give isl_union_pw_multi_aff *
4160 isl_union_pw_multi_aff_copy(
4161 __isl_keep isl_union_pw_multi_aff *upma);
4162 void *isl_union_pw_multi_aff_free(
4163 __isl_take isl_union_pw_multi_aff *upma);
4165 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4166 __isl_keep isl_multi_pw_aff *mpa);
4167 void *isl_multi_pw_aff_free(
4168 __isl_take isl_multi_pw_aff *mpa);
4170 The expression can be inspected using
4172 #include <isl/aff.h>
4173 isl_ctx *isl_multi_aff_get_ctx(
4174 __isl_keep isl_multi_aff *maff);
4175 isl_ctx *isl_pw_multi_aff_get_ctx(
4176 __isl_keep isl_pw_multi_aff *pma);
4177 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4178 __isl_keep isl_union_pw_multi_aff *upma);
4179 isl_ctx *isl_multi_pw_aff_get_ctx(
4180 __isl_keep isl_multi_pw_aff *mpa);
4181 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4182 enum isl_dim_type type);
4183 unsigned isl_pw_multi_aff_dim(
4184 __isl_keep isl_pw_multi_aff *pma,
4185 enum isl_dim_type type);
4186 unsigned isl_multi_pw_aff_dim(
4187 __isl_keep isl_multi_pw_aff *mpa,
4188 enum isl_dim_type type);
4189 __isl_give isl_aff *isl_multi_aff_get_aff(
4190 __isl_keep isl_multi_aff *multi, int pos);
4191 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4192 __isl_keep isl_pw_multi_aff *pma, int pos);
4193 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4194 __isl_keep isl_multi_pw_aff *mpa, int pos);
4195 const char *isl_pw_multi_aff_get_dim_name(
4196 __isl_keep isl_pw_multi_aff *pma,
4197 enum isl_dim_type type, unsigned pos);
4198 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4199 __isl_keep isl_pw_multi_aff *pma,
4200 enum isl_dim_type type, unsigned pos);
4201 const char *isl_multi_aff_get_tuple_name(
4202 __isl_keep isl_multi_aff *multi,
4203 enum isl_dim_type type);
4204 int isl_pw_multi_aff_has_tuple_name(
4205 __isl_keep isl_pw_multi_aff *pma,
4206 enum isl_dim_type type);
4207 const char *isl_pw_multi_aff_get_tuple_name(
4208 __isl_keep isl_pw_multi_aff *pma,
4209 enum isl_dim_type type);
4210 int isl_pw_multi_aff_has_tuple_id(
4211 __isl_keep isl_pw_multi_aff *pma,
4212 enum isl_dim_type type);
4213 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4214 __isl_keep isl_pw_multi_aff *pma,
4215 enum isl_dim_type type);
4217 int isl_pw_multi_aff_foreach_piece(
4218 __isl_keep isl_pw_multi_aff *pma,
4219 int (*fn)(__isl_take isl_set *set,
4220 __isl_take isl_multi_aff *maff,
4221 void *user), void *user);
4223 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4224 __isl_keep isl_union_pw_multi_aff *upma,
4225 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4226 void *user), void *user);
4228 It can be modified using
4230 #include <isl/aff.h>
4231 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4232 __isl_take isl_multi_aff *multi, int pos,
4233 __isl_take isl_aff *aff);
4234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4235 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4236 __isl_take isl_pw_aff *pa);
4237 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4238 __isl_take isl_multi_aff *maff,
4239 enum isl_dim_type type, unsigned pos, const char *s);
4240 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4241 __isl_take isl_multi_aff *maff,
4242 enum isl_dim_type type, const char *s);
4243 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4244 __isl_take isl_multi_aff *maff,
4245 enum isl_dim_type type, __isl_take isl_id *id);
4246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4247 __isl_take isl_pw_multi_aff *pma,
4248 enum isl_dim_type type, __isl_take isl_id *id);
4250 __isl_give isl_multi_pw_aff *
4251 isl_multi_pw_aff_set_dim_name(
4252 __isl_take isl_multi_pw_aff *mpa,
4253 enum isl_dim_type type, unsigned pos, const char *s);
4254 __isl_give isl_multi_pw_aff *
4255 isl_multi_pw_aff_set_tuple_name(
4256 __isl_take isl_multi_pw_aff *mpa,
4257 enum isl_dim_type type, const char *s);
4259 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4260 __isl_take isl_multi_aff *ma,
4261 enum isl_dim_type type, unsigned first, unsigned n);
4262 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4263 __isl_take isl_multi_aff *ma,
4264 enum isl_dim_type type, unsigned n);
4265 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4266 __isl_take isl_multi_aff *maff,
4267 enum isl_dim_type type, unsigned first, unsigned n);
4268 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4269 __isl_take isl_pw_multi_aff *pma,
4270 enum isl_dim_type type, unsigned first, unsigned n);
4272 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4273 __isl_take isl_multi_pw_aff *mpa,
4274 enum isl_dim_type type, unsigned first, unsigned n);
4275 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4276 __isl_take isl_multi_pw_aff *mpa,
4277 enum isl_dim_type type, unsigned n);
4279 To check whether two multiple affine expressions are
4280 obviously equal to each other, use
4282 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4283 __isl_keep isl_multi_aff *maff2);
4284 int isl_pw_multi_aff_plain_is_equal(
4285 __isl_keep isl_pw_multi_aff *pma1,
4286 __isl_keep isl_pw_multi_aff *pma2);
4290 #include <isl/aff.h>
4291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4292 __isl_take isl_pw_multi_aff *pma1,
4293 __isl_take isl_pw_multi_aff *pma2);
4294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4295 __isl_take isl_pw_multi_aff *pma1,
4296 __isl_take isl_pw_multi_aff *pma2);
4297 __isl_give isl_multi_aff *isl_multi_aff_add(
4298 __isl_take isl_multi_aff *maff1,
4299 __isl_take isl_multi_aff *maff2);
4300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4301 __isl_take isl_pw_multi_aff *pma1,
4302 __isl_take isl_pw_multi_aff *pma2);
4303 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4304 __isl_take isl_union_pw_multi_aff *upma1,
4305 __isl_take isl_union_pw_multi_aff *upma2);
4306 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4307 __isl_take isl_pw_multi_aff *pma1,
4308 __isl_take isl_pw_multi_aff *pma2);
4309 __isl_give isl_multi_aff *isl_multi_aff_sub(
4310 __isl_take isl_multi_aff *ma1,
4311 __isl_take isl_multi_aff *ma2);
4312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4313 __isl_take isl_pw_multi_aff *pma1,
4314 __isl_take isl_pw_multi_aff *pma2);
4315 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4316 __isl_take isl_union_pw_multi_aff *upma1,
4317 __isl_take isl_union_pw_multi_aff *upma2);
4319 C<isl_multi_aff_sub> subtracts the second argument from the first.
4321 __isl_give isl_multi_aff *isl_multi_aff_scale(
4322 __isl_take isl_multi_aff *maff,
4324 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4325 __isl_take isl_multi_aff *ma,
4326 __isl_take isl_val *v);
4327 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4328 __isl_take isl_pw_multi_aff *pma,
4329 __isl_take isl_val *v);
4330 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4331 __isl_take isl_multi_pw_aff *mpa,
4332 __isl_take isl_val *v);
4333 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4334 __isl_take isl_multi_aff *ma,
4335 __isl_take isl_vec *v);
4336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4337 __isl_take isl_pw_multi_aff *pma,
4338 __isl_take isl_vec *v);
4339 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4340 __isl_take isl_union_pw_multi_aff *upma,
4341 __isl_take isl_vec *v);
4343 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4344 by the corresponding elements of C<v>.
4346 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4347 __isl_take isl_pw_multi_aff *pma,
4348 __isl_take isl_set *set);
4349 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4350 __isl_take isl_pw_multi_aff *pma,
4351 __isl_take isl_set *set);
4352 __isl_give isl_union_pw_multi_aff *
4353 isl_union_pw_multi_aff_intersect_domain(
4354 __isl_take isl_union_pw_multi_aff *upma,
4355 __isl_take isl_union_set *uset);
4356 __isl_give isl_multi_aff *isl_multi_aff_lift(
4357 __isl_take isl_multi_aff *maff,
4358 __isl_give isl_local_space **ls);
4359 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4360 __isl_take isl_pw_multi_aff *pma);
4361 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4362 __isl_take isl_multi_aff *multi,
4363 __isl_take isl_space *model);
4364 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4365 __isl_take isl_pw_multi_aff *pma,
4366 __isl_take isl_space *model);
4367 __isl_give isl_pw_multi_aff *
4368 isl_pw_multi_aff_project_domain_on_params(
4369 __isl_take isl_pw_multi_aff *pma);
4370 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4371 __isl_take isl_multi_aff *maff,
4372 __isl_take isl_set *context);
4373 __isl_give isl_multi_aff *isl_multi_aff_gist(
4374 __isl_take isl_multi_aff *maff,
4375 __isl_take isl_set *context);
4376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4377 __isl_take isl_pw_multi_aff *pma,
4378 __isl_take isl_set *set);
4379 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4380 __isl_take isl_pw_multi_aff *pma,
4381 __isl_take isl_set *set);
4382 __isl_give isl_set *isl_pw_multi_aff_domain(
4383 __isl_take isl_pw_multi_aff *pma);
4384 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4385 __isl_take isl_union_pw_multi_aff *upma);
4386 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4387 __isl_take isl_multi_aff *ma1, unsigned pos,
4388 __isl_take isl_multi_aff *ma2);
4389 __isl_give isl_multi_aff *isl_multi_aff_splice(
4390 __isl_take isl_multi_aff *ma1,
4391 unsigned in_pos, unsigned out_pos,
4392 __isl_take isl_multi_aff *ma2);
4393 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4394 __isl_take isl_multi_aff *ma1,
4395 __isl_take isl_multi_aff *ma2);
4396 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4397 __isl_take isl_multi_aff *ma1,
4398 __isl_take isl_multi_aff *ma2);
4399 __isl_give isl_multi_aff *isl_multi_aff_product(
4400 __isl_take isl_multi_aff *ma1,
4401 __isl_take isl_multi_aff *ma2);
4402 __isl_give isl_pw_multi_aff *
4403 isl_pw_multi_aff_range_product(
4404 __isl_take isl_pw_multi_aff *pma1,
4405 __isl_take isl_pw_multi_aff *pma2);
4406 __isl_give isl_pw_multi_aff *
4407 isl_pw_multi_aff_flat_range_product(
4408 __isl_take isl_pw_multi_aff *pma1,
4409 __isl_take isl_pw_multi_aff *pma2);
4410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4411 __isl_take isl_pw_multi_aff *pma1,
4412 __isl_take isl_pw_multi_aff *pma2);
4413 __isl_give isl_union_pw_multi_aff *
4414 isl_union_pw_multi_aff_flat_range_product(
4415 __isl_take isl_union_pw_multi_aff *upma1,
4416 __isl_take isl_union_pw_multi_aff *upma2);
4417 __isl_give isl_multi_pw_aff *
4418 isl_multi_pw_aff_range_splice(
4419 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4420 __isl_take isl_multi_pw_aff *mpa2);
4421 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4422 __isl_take isl_multi_pw_aff *mpa1,
4423 unsigned in_pos, unsigned out_pos,
4424 __isl_take isl_multi_pw_aff *mpa2);
4425 __isl_give isl_multi_pw_aff *
4426 isl_multi_pw_aff_range_product(
4427 __isl_take isl_multi_pw_aff *mpa1,
4428 __isl_take isl_multi_pw_aff *mpa2);
4429 __isl_give isl_multi_pw_aff *
4430 isl_multi_pw_aff_flat_range_product(
4431 __isl_take isl_multi_pw_aff *mpa1,
4432 __isl_take isl_multi_pw_aff *mpa2);
4434 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4435 then it is assigned the local space that lies at the basis of
4436 the lifting applied.
4438 #include <isl/aff.h>
4439 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4440 __isl_take isl_multi_aff *ma1,
4441 __isl_take isl_multi_aff *ma2);
4442 __isl_give isl_pw_multi_aff *
4443 isl_pw_multi_aff_pullback_multi_aff(
4444 __isl_take isl_pw_multi_aff *pma,
4445 __isl_take isl_multi_aff *ma);
4446 __isl_give isl_pw_multi_aff *
4447 isl_pw_multi_aff_pullback_pw_multi_aff(
4448 __isl_take isl_pw_multi_aff *pma1,
4449 __isl_take isl_pw_multi_aff *pma2);
4451 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4452 In other words, C<ma2> is plugged
4455 __isl_give isl_set *isl_multi_aff_lex_le_set(
4456 __isl_take isl_multi_aff *ma1,
4457 __isl_take isl_multi_aff *ma2);
4458 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4459 __isl_take isl_multi_aff *ma1,
4460 __isl_take isl_multi_aff *ma2);
4462 The function C<isl_multi_aff_lex_le_set> returns a set
4463 containing those elements in the shared domain space
4464 where C<ma1> is lexicographically smaller than or
4467 An expression can be read from input using
4469 #include <isl/aff.h>
4470 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4471 isl_ctx *ctx, const char *str);
4472 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4473 isl_ctx *ctx, const char *str);
4474 __isl_give isl_union_pw_multi_aff *
4475 isl_union_pw_multi_aff_read_from_str(
4476 isl_ctx *ctx, const char *str);
4478 An expression can be printed using
4480 #include <isl/aff.h>
4481 __isl_give isl_printer *isl_printer_print_multi_aff(
4482 __isl_take isl_printer *p,
4483 __isl_keep isl_multi_aff *maff);
4484 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4485 __isl_take isl_printer *p,
4486 __isl_keep isl_pw_multi_aff *pma);
4487 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4488 __isl_take isl_printer *p,
4489 __isl_keep isl_union_pw_multi_aff *upma);
4490 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4491 __isl_take isl_printer *p,
4492 __isl_keep isl_multi_pw_aff *mpa);
4496 Points are elements of a set. They can be used to construct
4497 simple sets (boxes) or they can be used to represent the
4498 individual elements of a set.
4499 The zero point (the origin) can be created using
4501 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4503 The coordinates of a point can be inspected, set and changed
4506 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4507 enum isl_dim_type type, int pos, isl_int *v);
4508 __isl_give isl_val *isl_point_get_coordinate_val(
4509 __isl_keep isl_point *pnt,
4510 enum isl_dim_type type, int pos);
4511 __isl_give isl_point *isl_point_set_coordinate(
4512 __isl_take isl_point *pnt,
4513 enum isl_dim_type type, int pos, isl_int v);
4514 __isl_give isl_point *isl_point_set_coordinate_val(
4515 __isl_take isl_point *pnt,
4516 enum isl_dim_type type, int pos,
4517 __isl_take isl_val *v);
4519 __isl_give isl_point *isl_point_add_ui(
4520 __isl_take isl_point *pnt,
4521 enum isl_dim_type type, int pos, unsigned val);
4522 __isl_give isl_point *isl_point_sub_ui(
4523 __isl_take isl_point *pnt,
4524 enum isl_dim_type type, int pos, unsigned val);
4526 Other properties can be obtained using
4528 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4530 Points can be copied or freed using
4532 __isl_give isl_point *isl_point_copy(
4533 __isl_keep isl_point *pnt);
4534 void isl_point_free(__isl_take isl_point *pnt);
4536 A singleton set can be created from a point using
4538 __isl_give isl_basic_set *isl_basic_set_from_point(
4539 __isl_take isl_point *pnt);
4540 __isl_give isl_set *isl_set_from_point(
4541 __isl_take isl_point *pnt);
4543 and a box can be created from two opposite extremal points using
4545 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4546 __isl_take isl_point *pnt1,
4547 __isl_take isl_point *pnt2);
4548 __isl_give isl_set *isl_set_box_from_points(
4549 __isl_take isl_point *pnt1,
4550 __isl_take isl_point *pnt2);
4552 All elements of a B<bounded> (union) set can be enumerated using
4553 the following functions.
4555 int isl_set_foreach_point(__isl_keep isl_set *set,
4556 int (*fn)(__isl_take isl_point *pnt, void *user),
4558 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4559 int (*fn)(__isl_take isl_point *pnt, void *user),
4562 The function C<fn> is called for each integer point in
4563 C<set> with as second argument the last argument of
4564 the C<isl_set_foreach_point> call. The function C<fn>
4565 should return C<0> on success and C<-1> on failure.
4566 In the latter case, C<isl_set_foreach_point> will stop
4567 enumerating and return C<-1> as well.
4568 If the enumeration is performed successfully and to completion,
4569 then C<isl_set_foreach_point> returns C<0>.
4571 To obtain a single point of a (basic) set, use
4573 __isl_give isl_point *isl_basic_set_sample_point(
4574 __isl_take isl_basic_set *bset);
4575 __isl_give isl_point *isl_set_sample_point(
4576 __isl_take isl_set *set);
4578 If C<set> does not contain any (integer) points, then the
4579 resulting point will be ``void'', a property that can be
4582 int isl_point_is_void(__isl_keep isl_point *pnt);
4584 =head2 Piecewise Quasipolynomials
4586 A piecewise quasipolynomial is a particular kind of function that maps
4587 a parametric point to a rational value.
4588 More specifically, a quasipolynomial is a polynomial expression in greatest
4589 integer parts of affine expressions of parameters and variables.
4590 A piecewise quasipolynomial is a subdivision of a given parametric
4591 domain into disjoint cells with a quasipolynomial associated to
4592 each cell. The value of the piecewise quasipolynomial at a given
4593 point is the value of the quasipolynomial associated to the cell
4594 that contains the point. Outside of the union of cells,
4595 the value is assumed to be zero.
4596 For example, the piecewise quasipolynomial
4598 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4600 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4601 A given piecewise quasipolynomial has a fixed domain dimension.
4602 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4603 defined over different domains.
4604 Piecewise quasipolynomials are mainly used by the C<barvinok>
4605 library for representing the number of elements in a parametric set or map.
4606 For example, the piecewise quasipolynomial above represents
4607 the number of points in the map
4609 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4611 =head3 Input and Output
4613 Piecewise quasipolynomials can be read from input using
4615 __isl_give isl_union_pw_qpolynomial *
4616 isl_union_pw_qpolynomial_read_from_str(
4617 isl_ctx *ctx, const char *str);
4619 Quasipolynomials and piecewise quasipolynomials can be printed
4620 using the following functions.
4622 __isl_give isl_printer *isl_printer_print_qpolynomial(
4623 __isl_take isl_printer *p,
4624 __isl_keep isl_qpolynomial *qp);
4626 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4627 __isl_take isl_printer *p,
4628 __isl_keep isl_pw_qpolynomial *pwqp);
4630 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4631 __isl_take isl_printer *p,
4632 __isl_keep isl_union_pw_qpolynomial *upwqp);
4634 The output format of the printer
4635 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4636 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4638 In case of printing in C<ISL_FORMAT_C>, the user may want
4639 to set the names of all dimensions
4641 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4642 __isl_take isl_qpolynomial *qp,
4643 enum isl_dim_type type, unsigned pos,
4645 __isl_give isl_pw_qpolynomial *
4646 isl_pw_qpolynomial_set_dim_name(
4647 __isl_take isl_pw_qpolynomial *pwqp,
4648 enum isl_dim_type type, unsigned pos,
4651 =head3 Creating New (Piecewise) Quasipolynomials
4653 Some simple quasipolynomials can be created using the following functions.
4654 More complicated quasipolynomials can be created by applying
4655 operations such as addition and multiplication
4656 on the resulting quasipolynomials
4658 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4659 __isl_take isl_space *domain);
4660 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4661 __isl_take isl_space *domain);
4662 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4663 __isl_take isl_space *domain);
4664 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4665 __isl_take isl_space *domain);
4666 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4667 __isl_take isl_space *domain);
4668 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4669 __isl_take isl_space *domain,
4670 const isl_int n, const isl_int d);
4671 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4672 __isl_take isl_space *domain,
4673 __isl_take isl_val *val);
4674 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4675 __isl_take isl_space *domain,
4676 enum isl_dim_type type, unsigned pos);
4677 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4678 __isl_take isl_aff *aff);
4680 Note that the space in which a quasipolynomial lives is a map space
4681 with a one-dimensional range. The C<domain> argument in some of
4682 the functions above corresponds to the domain of this map space.
4684 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4685 with a single cell can be created using the following functions.
4686 Multiple of these single cell piecewise quasipolynomials can
4687 be combined to create more complicated piecewise quasipolynomials.
4689 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4690 __isl_take isl_space *space);
4691 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4692 __isl_take isl_set *set,
4693 __isl_take isl_qpolynomial *qp);
4694 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4695 __isl_take isl_qpolynomial *qp);
4696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4697 __isl_take isl_pw_aff *pwaff);
4699 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4700 __isl_take isl_space *space);
4701 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4702 __isl_take isl_pw_qpolynomial *pwqp);
4703 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4704 __isl_take isl_union_pw_qpolynomial *upwqp,
4705 __isl_take isl_pw_qpolynomial *pwqp);
4707 Quasipolynomials can be copied and freed again using the following
4710 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4711 __isl_keep isl_qpolynomial *qp);
4712 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4714 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4715 __isl_keep isl_pw_qpolynomial *pwqp);
4716 void *isl_pw_qpolynomial_free(
4717 __isl_take isl_pw_qpolynomial *pwqp);
4719 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4720 __isl_keep isl_union_pw_qpolynomial *upwqp);
4721 void *isl_union_pw_qpolynomial_free(
4722 __isl_take isl_union_pw_qpolynomial *upwqp);
4724 =head3 Inspecting (Piecewise) Quasipolynomials
4726 To iterate over all piecewise quasipolynomials in a union
4727 piecewise quasipolynomial, use the following function
4729 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4730 __isl_keep isl_union_pw_qpolynomial *upwqp,
4731 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4734 To extract the piecewise quasipolynomial in a given space from a union, use
4736 __isl_give isl_pw_qpolynomial *
4737 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4738 __isl_keep isl_union_pw_qpolynomial *upwqp,
4739 __isl_take isl_space *space);
4741 To iterate over the cells in a piecewise quasipolynomial,
4742 use either of the following two functions
4744 int isl_pw_qpolynomial_foreach_piece(
4745 __isl_keep isl_pw_qpolynomial *pwqp,
4746 int (*fn)(__isl_take isl_set *set,
4747 __isl_take isl_qpolynomial *qp,
4748 void *user), void *user);
4749 int isl_pw_qpolynomial_foreach_lifted_piece(
4750 __isl_keep isl_pw_qpolynomial *pwqp,
4751 int (*fn)(__isl_take isl_set *set,
4752 __isl_take isl_qpolynomial *qp,
4753 void *user), void *user);
4755 As usual, the function C<fn> should return C<0> on success
4756 and C<-1> on failure. The difference between
4757 C<isl_pw_qpolynomial_foreach_piece> and
4758 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4759 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4760 compute unique representations for all existentially quantified
4761 variables and then turn these existentially quantified variables
4762 into extra set variables, adapting the associated quasipolynomial
4763 accordingly. This means that the C<set> passed to C<fn>
4764 will not have any existentially quantified variables, but that
4765 the dimensions of the sets may be different for different
4766 invocations of C<fn>.
4768 The constant term of a quasipolynomial can be extracted using
4770 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4771 __isl_keep isl_qpolynomial *qp);
4773 To iterate over all terms in a quasipolynomial,
4776 int isl_qpolynomial_foreach_term(
4777 __isl_keep isl_qpolynomial *qp,
4778 int (*fn)(__isl_take isl_term *term,
4779 void *user), void *user);
4781 The terms themselves can be inspected and freed using
4784 unsigned isl_term_dim(__isl_keep isl_term *term,
4785 enum isl_dim_type type);
4786 void isl_term_get_num(__isl_keep isl_term *term,
4788 void isl_term_get_den(__isl_keep isl_term *term,
4790 __isl_give isl_val *isl_term_get_coefficient_val(
4791 __isl_keep isl_term *term);
4792 int isl_term_get_exp(__isl_keep isl_term *term,
4793 enum isl_dim_type type, unsigned pos);
4794 __isl_give isl_aff *isl_term_get_div(
4795 __isl_keep isl_term *term, unsigned pos);
4796 void isl_term_free(__isl_take isl_term *term);
4798 Each term is a product of parameters, set variables and
4799 integer divisions. The function C<isl_term_get_exp>
4800 returns the exponent of a given dimensions in the given term.
4801 The C<isl_int>s in the arguments of C<isl_term_get_num>
4802 and C<isl_term_get_den> need to have been initialized
4803 using C<isl_int_init> before calling these functions.
4805 =head3 Properties of (Piecewise) Quasipolynomials
4807 To check whether a quasipolynomial is actually a constant,
4808 use the following function.
4810 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4811 isl_int *n, isl_int *d);
4813 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4814 then the numerator and denominator of the constant
4815 are returned in C<*n> and C<*d>, respectively.
4817 To check whether two union piecewise quasipolynomials are
4818 obviously equal, use
4820 int isl_union_pw_qpolynomial_plain_is_equal(
4821 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4822 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4824 =head3 Operations on (Piecewise) Quasipolynomials
4826 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4827 __isl_take isl_qpolynomial *qp, isl_int v);
4828 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4829 __isl_take isl_qpolynomial *qp,
4830 __isl_take isl_val *v);
4831 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4832 __isl_take isl_qpolynomial *qp);
4833 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4834 __isl_take isl_qpolynomial *qp1,
4835 __isl_take isl_qpolynomial *qp2);
4836 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4837 __isl_take isl_qpolynomial *qp1,
4838 __isl_take isl_qpolynomial *qp2);
4839 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4840 __isl_take isl_qpolynomial *qp1,
4841 __isl_take isl_qpolynomial *qp2);
4842 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4843 __isl_take isl_qpolynomial *qp, unsigned exponent);
4845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4846 __isl_take isl_pw_qpolynomial *pwqp,
4847 enum isl_dim_type type, unsigned n,
4848 __isl_take isl_val *v);
4849 __isl_give isl_pw_qpolynomial *
4850 isl_pw_qpolynomial_scale_val(
4851 __isl_take isl_pw_qpolynomial *pwqp,
4852 __isl_take isl_val *v);
4853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4854 __isl_take isl_pw_qpolynomial *pwqp1,
4855 __isl_take isl_pw_qpolynomial *pwqp2);
4856 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4857 __isl_take isl_pw_qpolynomial *pwqp1,
4858 __isl_take isl_pw_qpolynomial *pwqp2);
4859 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4860 __isl_take isl_pw_qpolynomial *pwqp1,
4861 __isl_take isl_pw_qpolynomial *pwqp2);
4862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4863 __isl_take isl_pw_qpolynomial *pwqp);
4864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4865 __isl_take isl_pw_qpolynomial *pwqp1,
4866 __isl_take isl_pw_qpolynomial *pwqp2);
4867 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4868 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4870 __isl_give isl_union_pw_qpolynomial *
4871 isl_union_pw_qpolynomial_scale_val(
4872 __isl_take isl_union_pw_qpolynomial *upwqp,
4873 __isl_take isl_val *v);
4874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4875 __isl_take isl_union_pw_qpolynomial *upwqp1,
4876 __isl_take isl_union_pw_qpolynomial *upwqp2);
4877 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4878 __isl_take isl_union_pw_qpolynomial *upwqp1,
4879 __isl_take isl_union_pw_qpolynomial *upwqp2);
4880 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4881 __isl_take isl_union_pw_qpolynomial *upwqp1,
4882 __isl_take isl_union_pw_qpolynomial *upwqp2);
4884 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4885 __isl_take isl_pw_qpolynomial *pwqp,
4886 __isl_take isl_point *pnt);
4888 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4889 __isl_take isl_union_pw_qpolynomial *upwqp,
4890 __isl_take isl_point *pnt);
4892 __isl_give isl_set *isl_pw_qpolynomial_domain(
4893 __isl_take isl_pw_qpolynomial *pwqp);
4894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4895 __isl_take isl_pw_qpolynomial *pwpq,
4896 __isl_take isl_set *set);
4897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4898 __isl_take isl_pw_qpolynomial *pwpq,
4899 __isl_take isl_set *set);
4901 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4902 __isl_take isl_union_pw_qpolynomial *upwqp);
4903 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4904 __isl_take isl_union_pw_qpolynomial *upwpq,
4905 __isl_take isl_union_set *uset);
4906 __isl_give isl_union_pw_qpolynomial *
4907 isl_union_pw_qpolynomial_intersect_params(
4908 __isl_take isl_union_pw_qpolynomial *upwpq,
4909 __isl_take isl_set *set);
4911 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4912 __isl_take isl_qpolynomial *qp,
4913 __isl_take isl_space *model);
4915 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4916 __isl_take isl_qpolynomial *qp);
4917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4918 __isl_take isl_pw_qpolynomial *pwqp);
4920 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4921 __isl_take isl_union_pw_qpolynomial *upwqp);
4923 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4924 __isl_take isl_qpolynomial *qp,
4925 __isl_take isl_set *context);
4926 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4927 __isl_take isl_qpolynomial *qp,
4928 __isl_take isl_set *context);
4930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4931 __isl_take isl_pw_qpolynomial *pwqp,
4932 __isl_take isl_set *context);
4933 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4934 __isl_take isl_pw_qpolynomial *pwqp,
4935 __isl_take isl_set *context);
4937 __isl_give isl_union_pw_qpolynomial *
4938 isl_union_pw_qpolynomial_gist_params(
4939 __isl_take isl_union_pw_qpolynomial *upwqp,
4940 __isl_take isl_set *context);
4941 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4942 __isl_take isl_union_pw_qpolynomial *upwqp,
4943 __isl_take isl_union_set *context);
4945 The gist operation applies the gist operation to each of
4946 the cells in the domain of the input piecewise quasipolynomial.
4947 The context is also exploited
4948 to simplify the quasipolynomials associated to each cell.
4950 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4951 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4952 __isl_give isl_union_pw_qpolynomial *
4953 isl_union_pw_qpolynomial_to_polynomial(
4954 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4956 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4957 the polynomial will be an overapproximation. If C<sign> is negative,
4958 it will be an underapproximation. If C<sign> is zero, the approximation
4959 will lie somewhere in between.
4961 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4963 A piecewise quasipolynomial reduction is a piecewise
4964 reduction (or fold) of quasipolynomials.
4965 In particular, the reduction can be maximum or a minimum.
4966 The objects are mainly used to represent the result of
4967 an upper or lower bound on a quasipolynomial over its domain,
4968 i.e., as the result of the following function.
4970 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4971 __isl_take isl_pw_qpolynomial *pwqp,
4972 enum isl_fold type, int *tight);
4974 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4975 __isl_take isl_union_pw_qpolynomial *upwqp,
4976 enum isl_fold type, int *tight);
4978 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4979 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4980 is the returned bound is known be tight, i.e., for each value
4981 of the parameters there is at least
4982 one element in the domain that reaches the bound.
4983 If the domain of C<pwqp> is not wrapping, then the bound is computed
4984 over all elements in that domain and the result has a purely parametric
4985 domain. If the domain of C<pwqp> is wrapping, then the bound is
4986 computed over the range of the wrapped relation. The domain of the
4987 wrapped relation becomes the domain of the result.
4989 A (piecewise) quasipolynomial reduction can be copied or freed using the
4990 following functions.
4992 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4993 __isl_keep isl_qpolynomial_fold *fold);
4994 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4995 __isl_keep isl_pw_qpolynomial_fold *pwf);
4996 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4997 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4998 void isl_qpolynomial_fold_free(
4999 __isl_take isl_qpolynomial_fold *fold);
5000 void *isl_pw_qpolynomial_fold_free(
5001 __isl_take isl_pw_qpolynomial_fold *pwf);
5002 void *isl_union_pw_qpolynomial_fold_free(
5003 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5005 =head3 Printing Piecewise Quasipolynomial Reductions
5007 Piecewise quasipolynomial reductions can be printed
5008 using the following function.
5010 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5011 __isl_take isl_printer *p,
5012 __isl_keep isl_pw_qpolynomial_fold *pwf);
5013 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5014 __isl_take isl_printer *p,
5015 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5017 For C<isl_printer_print_pw_qpolynomial_fold>,
5018 output format of the printer
5019 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5020 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5021 output format of the printer
5022 needs to be set to C<ISL_FORMAT_ISL>.
5023 In case of printing in C<ISL_FORMAT_C>, the user may want
5024 to set the names of all dimensions
5026 __isl_give isl_pw_qpolynomial_fold *
5027 isl_pw_qpolynomial_fold_set_dim_name(
5028 __isl_take isl_pw_qpolynomial_fold *pwf,
5029 enum isl_dim_type type, unsigned pos,
5032 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5034 To iterate over all piecewise quasipolynomial reductions in a union
5035 piecewise quasipolynomial reduction, use the following function
5037 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5038 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5039 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5040 void *user), void *user);
5042 To iterate over the cells in a piecewise quasipolynomial reduction,
5043 use either of the following two functions
5045 int isl_pw_qpolynomial_fold_foreach_piece(
5046 __isl_keep isl_pw_qpolynomial_fold *pwf,
5047 int (*fn)(__isl_take isl_set *set,
5048 __isl_take isl_qpolynomial_fold *fold,
5049 void *user), void *user);
5050 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5051 __isl_keep isl_pw_qpolynomial_fold *pwf,
5052 int (*fn)(__isl_take isl_set *set,
5053 __isl_take isl_qpolynomial_fold *fold,
5054 void *user), void *user);
5056 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5057 of the difference between these two functions.
5059 To iterate over all quasipolynomials in a reduction, use
5061 int isl_qpolynomial_fold_foreach_qpolynomial(
5062 __isl_keep isl_qpolynomial_fold *fold,
5063 int (*fn)(__isl_take isl_qpolynomial *qp,
5064 void *user), void *user);
5066 =head3 Properties of Piecewise Quasipolynomial Reductions
5068 To check whether two union piecewise quasipolynomial reductions are
5069 obviously equal, use
5071 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5072 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5073 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5075 =head3 Operations on Piecewise Quasipolynomial Reductions
5077 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5078 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5079 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5080 __isl_take isl_qpolynomial_fold *fold,
5081 __isl_take isl_val *v);
5082 __isl_give isl_pw_qpolynomial_fold *
5083 isl_pw_qpolynomial_fold_scale_val(
5084 __isl_take isl_pw_qpolynomial_fold *pwf,
5085 __isl_take isl_val *v);
5086 __isl_give isl_union_pw_qpolynomial_fold *
5087 isl_union_pw_qpolynomial_fold_scale_val(
5088 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5089 __isl_take isl_val *v);
5091 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5092 __isl_take isl_pw_qpolynomial_fold *pwf1,
5093 __isl_take isl_pw_qpolynomial_fold *pwf2);
5095 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5096 __isl_take isl_pw_qpolynomial_fold *pwf1,
5097 __isl_take isl_pw_qpolynomial_fold *pwf2);
5099 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5100 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5101 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5103 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5104 __isl_take isl_pw_qpolynomial_fold *pwf,
5105 __isl_take isl_point *pnt);
5107 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5108 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5109 __isl_take isl_point *pnt);
5111 __isl_give isl_pw_qpolynomial_fold *
5112 isl_pw_qpolynomial_fold_intersect_params(
5113 __isl_take isl_pw_qpolynomial_fold *pwf,
5114 __isl_take isl_set *set);
5116 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5117 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5118 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5119 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5120 __isl_take isl_union_set *uset);
5121 __isl_give isl_union_pw_qpolynomial_fold *
5122 isl_union_pw_qpolynomial_fold_intersect_params(
5123 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5124 __isl_take isl_set *set);
5126 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5127 __isl_take isl_pw_qpolynomial_fold *pwf);
5129 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5130 __isl_take isl_pw_qpolynomial_fold *pwf);
5132 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5133 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5135 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5136 __isl_take isl_qpolynomial_fold *fold,
5137 __isl_take isl_set *context);
5138 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5139 __isl_take isl_qpolynomial_fold *fold,
5140 __isl_take isl_set *context);
5142 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5143 __isl_take isl_pw_qpolynomial_fold *pwf,
5144 __isl_take isl_set *context);
5145 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5146 __isl_take isl_pw_qpolynomial_fold *pwf,
5147 __isl_take isl_set *context);
5149 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5150 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5151 __isl_take isl_union_set *context);
5152 __isl_give isl_union_pw_qpolynomial_fold *
5153 isl_union_pw_qpolynomial_fold_gist_params(
5154 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5155 __isl_take isl_set *context);
5157 The gist operation applies the gist operation to each of
5158 the cells in the domain of the input piecewise quasipolynomial reduction.
5159 In future, the operation will also exploit the context
5160 to simplify the quasipolynomial reductions associated to each cell.
5162 __isl_give isl_pw_qpolynomial_fold *
5163 isl_set_apply_pw_qpolynomial_fold(
5164 __isl_take isl_set *set,
5165 __isl_take isl_pw_qpolynomial_fold *pwf,
5167 __isl_give isl_pw_qpolynomial_fold *
5168 isl_map_apply_pw_qpolynomial_fold(
5169 __isl_take isl_map *map,
5170 __isl_take isl_pw_qpolynomial_fold *pwf,
5172 __isl_give isl_union_pw_qpolynomial_fold *
5173 isl_union_set_apply_union_pw_qpolynomial_fold(
5174 __isl_take isl_union_set *uset,
5175 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5177 __isl_give isl_union_pw_qpolynomial_fold *
5178 isl_union_map_apply_union_pw_qpolynomial_fold(
5179 __isl_take isl_union_map *umap,
5180 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5183 The functions taking a map
5184 compose the given map with the given piecewise quasipolynomial reduction.
5185 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5186 over all elements in the intersection of the range of the map
5187 and the domain of the piecewise quasipolynomial reduction
5188 as a function of an element in the domain of the map.
5189 The functions taking a set compute a bound over all elements in the
5190 intersection of the set and the domain of the
5191 piecewise quasipolynomial reduction.
5193 =head2 Parametric Vertex Enumeration
5195 The parametric vertex enumeration described in this section
5196 is mainly intended to be used internally and by the C<barvinok>
5199 #include <isl/vertices.h>
5200 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5201 __isl_keep isl_basic_set *bset);
5203 The function C<isl_basic_set_compute_vertices> performs the
5204 actual computation of the parametric vertices and the chamber
5205 decomposition and store the result in an C<isl_vertices> object.
5206 This information can be queried by either iterating over all
5207 the vertices or iterating over all the chambers or cells
5208 and then iterating over all vertices that are active on the chamber.
5210 int isl_vertices_foreach_vertex(
5211 __isl_keep isl_vertices *vertices,
5212 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5215 int isl_vertices_foreach_cell(
5216 __isl_keep isl_vertices *vertices,
5217 int (*fn)(__isl_take isl_cell *cell, void *user),
5219 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5220 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5223 Other operations that can be performed on an C<isl_vertices> object are
5226 isl_ctx *isl_vertices_get_ctx(
5227 __isl_keep isl_vertices *vertices);
5228 int isl_vertices_get_n_vertices(
5229 __isl_keep isl_vertices *vertices);
5230 void isl_vertices_free(__isl_take isl_vertices *vertices);
5232 Vertices can be inspected and destroyed using the following functions.
5234 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5235 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5236 __isl_give isl_basic_set *isl_vertex_get_domain(
5237 __isl_keep isl_vertex *vertex);
5238 __isl_give isl_basic_set *isl_vertex_get_expr(
5239 __isl_keep isl_vertex *vertex);
5240 void isl_vertex_free(__isl_take isl_vertex *vertex);
5242 C<isl_vertex_get_expr> returns a singleton parametric set describing
5243 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5245 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5246 B<rational> basic sets, so they should mainly be used for inspection
5247 and should not be mixed with integer sets.
5249 Chambers can be inspected and destroyed using the following functions.
5251 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5252 __isl_give isl_basic_set *isl_cell_get_domain(
5253 __isl_keep isl_cell *cell);
5254 void isl_cell_free(__isl_take isl_cell *cell);
5256 =head1 Polyhedral Compilation Library
5258 This section collects functionality in C<isl> that has been specifically
5259 designed for use during polyhedral compilation.
5261 =head2 Dependence Analysis
5263 C<isl> contains specialized functionality for performing
5264 array dataflow analysis. That is, given a I<sink> access relation
5265 and a collection of possible I<source> access relations,
5266 C<isl> can compute relations that describe
5267 for each iteration of the sink access, which iteration
5268 of which of the source access relations was the last
5269 to access the same data element before the given iteration
5271 The resulting dependence relations map source iterations
5272 to the corresponding sink iterations.
5273 To compute standard flow dependences, the sink should be
5274 a read, while the sources should be writes.
5275 If any of the source accesses are marked as being I<may>
5276 accesses, then there will be a dependence from the last
5277 I<must> access B<and> from any I<may> access that follows
5278 this last I<must> access.
5279 In particular, if I<all> sources are I<may> accesses,
5280 then memory based dependence analysis is performed.
5281 If, on the other hand, all sources are I<must> accesses,
5282 then value based dependence analysis is performed.
5284 #include <isl/flow.h>
5286 typedef int (*isl_access_level_before)(void *first, void *second);
5288 __isl_give isl_access_info *isl_access_info_alloc(
5289 __isl_take isl_map *sink,
5290 void *sink_user, isl_access_level_before fn,
5292 __isl_give isl_access_info *isl_access_info_add_source(
5293 __isl_take isl_access_info *acc,
5294 __isl_take isl_map *source, int must,
5296 void *isl_access_info_free(__isl_take isl_access_info *acc);
5298 __isl_give isl_flow *isl_access_info_compute_flow(
5299 __isl_take isl_access_info *acc);
5301 int isl_flow_foreach(__isl_keep isl_flow *deps,
5302 int (*fn)(__isl_take isl_map *dep, int must,
5303 void *dep_user, void *user),
5305 __isl_give isl_map *isl_flow_get_no_source(
5306 __isl_keep isl_flow *deps, int must);
5307 void isl_flow_free(__isl_take isl_flow *deps);
5309 The function C<isl_access_info_compute_flow> performs the actual
5310 dependence analysis. The other functions are used to construct
5311 the input for this function or to read off the output.
5313 The input is collected in an C<isl_access_info>, which can
5314 be created through a call to C<isl_access_info_alloc>.
5315 The arguments to this functions are the sink access relation
5316 C<sink>, a token C<sink_user> used to identify the sink
5317 access to the user, a callback function for specifying the
5318 relative order of source and sink accesses, and the number
5319 of source access relations that will be added.
5320 The callback function has type C<int (*)(void *first, void *second)>.
5321 The function is called with two user supplied tokens identifying
5322 either a source or the sink and it should return the shared nesting
5323 level and the relative order of the two accesses.
5324 In particular, let I<n> be the number of loops shared by
5325 the two accesses. If C<first> precedes C<second> textually,
5326 then the function should return I<2 * n + 1>; otherwise,
5327 it should return I<2 * n>.
5328 The sources can be added to the C<isl_access_info> by performing
5329 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5330 C<must> indicates whether the source is a I<must> access
5331 or a I<may> access. Note that a multi-valued access relation
5332 should only be marked I<must> if every iteration in the domain
5333 of the relation accesses I<all> elements in its image.
5334 The C<source_user> token is again used to identify
5335 the source access. The range of the source access relation
5336 C<source> should have the same dimension as the range
5337 of the sink access relation.
5338 The C<isl_access_info_free> function should usually not be
5339 called explicitly, because it is called implicitly by
5340 C<isl_access_info_compute_flow>.
5342 The result of the dependence analysis is collected in an
5343 C<isl_flow>. There may be elements of
5344 the sink access for which no preceding source access could be
5345 found or for which all preceding sources are I<may> accesses.
5346 The relations containing these elements can be obtained through
5347 calls to C<isl_flow_get_no_source>, the first with C<must> set
5348 and the second with C<must> unset.
5349 In the case of standard flow dependence analysis,
5350 with the sink a read and the sources I<must> writes,
5351 the first relation corresponds to the reads from uninitialized
5352 array elements and the second relation is empty.
5353 The actual flow dependences can be extracted using
5354 C<isl_flow_foreach>. This function will call the user-specified
5355 callback function C<fn> for each B<non-empty> dependence between
5356 a source and the sink. The callback function is called
5357 with four arguments, the actual flow dependence relation
5358 mapping source iterations to sink iterations, a boolean that
5359 indicates whether it is a I<must> or I<may> dependence, a token
5360 identifying the source and an additional C<void *> with value
5361 equal to the third argument of the C<isl_flow_foreach> call.
5362 A dependence is marked I<must> if it originates from a I<must>
5363 source and if it is not followed by any I<may> sources.
5365 After finishing with an C<isl_flow>, the user should call
5366 C<isl_flow_free> to free all associated memory.
5368 A higher-level interface to dependence analysis is provided
5369 by the following function.
5371 #include <isl/flow.h>
5373 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5374 __isl_take isl_union_map *must_source,
5375 __isl_take isl_union_map *may_source,
5376 __isl_take isl_union_map *schedule,
5377 __isl_give isl_union_map **must_dep,
5378 __isl_give isl_union_map **may_dep,
5379 __isl_give isl_union_map **must_no_source,
5380 __isl_give isl_union_map **may_no_source);
5382 The arrays are identified by the tuple names of the ranges
5383 of the accesses. The iteration domains by the tuple names
5384 of the domains of the accesses and of the schedule.
5385 The relative order of the iteration domains is given by the
5386 schedule. The relations returned through C<must_no_source>
5387 and C<may_no_source> are subsets of C<sink>.
5388 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5389 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5390 any of the other arguments is treated as an error.
5392 =head3 Interaction with Dependence Analysis
5394 During the dependence analysis, we frequently need to perform
5395 the following operation. Given a relation between sink iterations
5396 and potential source iterations from a particular source domain,
5397 what is the last potential source iteration corresponding to each
5398 sink iteration. It can sometimes be convenient to adjust
5399 the set of potential source iterations before or after each such operation.
5400 The prototypical example is fuzzy array dataflow analysis,
5401 where we need to analyze if, based on data-dependent constraints,
5402 the sink iteration can ever be executed without one or more of
5403 the corresponding potential source iterations being executed.
5404 If so, we can introduce extra parameters and select an unknown
5405 but fixed source iteration from the potential source iterations.
5406 To be able to perform such manipulations, C<isl> provides the following
5409 #include <isl/flow.h>
5411 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5412 __isl_keep isl_map *source_map,
5413 __isl_keep isl_set *sink, void *source_user,
5415 __isl_give isl_access_info *isl_access_info_set_restrict(
5416 __isl_take isl_access_info *acc,
5417 isl_access_restrict fn, void *user);
5419 The function C<isl_access_info_set_restrict> should be called
5420 before calling C<isl_access_info_compute_flow> and registers a callback function
5421 that will be called any time C<isl> is about to compute the last
5422 potential source. The first argument is the (reverse) proto-dependence,
5423 mapping sink iterations to potential source iterations.
5424 The second argument represents the sink iterations for which
5425 we want to compute the last source iteration.
5426 The third argument is the token corresponding to the source
5427 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5428 The callback is expected to return a restriction on either the input or
5429 the output of the operation computing the last potential source.
5430 If the input needs to be restricted then restrictions are needed
5431 for both the source and the sink iterations. The sink iterations
5432 and the potential source iterations will be intersected with these sets.
5433 If the output needs to be restricted then only a restriction on the source
5434 iterations is required.
5435 If any error occurs, the callback should return C<NULL>.
5436 An C<isl_restriction> object can be created, freed and inspected
5437 using the following functions.
5439 #include <isl/flow.h>
5441 __isl_give isl_restriction *isl_restriction_input(
5442 __isl_take isl_set *source_restr,
5443 __isl_take isl_set *sink_restr);
5444 __isl_give isl_restriction *isl_restriction_output(
5445 __isl_take isl_set *source_restr);
5446 __isl_give isl_restriction *isl_restriction_none(
5447 __isl_take isl_map *source_map);
5448 __isl_give isl_restriction *isl_restriction_empty(
5449 __isl_take isl_map *source_map);
5450 void *isl_restriction_free(
5451 __isl_take isl_restriction *restr);
5452 isl_ctx *isl_restriction_get_ctx(
5453 __isl_keep isl_restriction *restr);
5455 C<isl_restriction_none> and C<isl_restriction_empty> are special
5456 cases of C<isl_restriction_input>. C<isl_restriction_none>
5457 is essentially equivalent to
5459 isl_restriction_input(isl_set_universe(
5460 isl_space_range(isl_map_get_space(source_map))),
5462 isl_space_domain(isl_map_get_space(source_map))));
5464 whereas C<isl_restriction_empty> is essentially equivalent to
5466 isl_restriction_input(isl_set_empty(
5467 isl_space_range(isl_map_get_space(source_map))),
5469 isl_space_domain(isl_map_get_space(source_map))));
5473 B<The functionality described in this section is fairly new
5474 and may be subject to change.>
5476 The following function can be used to compute a schedule
5477 for a union of domains.
5478 By default, the algorithm used to construct the schedule is similar
5479 to that of C<Pluto>.
5480 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5482 The generated schedule respects all C<validity> dependences.
5483 That is, all dependence distances over these dependences in the
5484 scheduled space are lexicographically positive.
5485 The default algorithm tries to minimize the dependence distances over
5486 C<proximity> dependences.
5487 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5488 for groups of domains where the dependence distances have only
5489 non-negative values.
5490 When using Feautrier's algorithm, the C<proximity> dependence
5491 distances are only minimized during the extension to a
5492 full-dimensional schedule.
5494 #include <isl/schedule.h>
5495 __isl_give isl_schedule *isl_union_set_compute_schedule(
5496 __isl_take isl_union_set *domain,
5497 __isl_take isl_union_map *validity,
5498 __isl_take isl_union_map *proximity);
5499 void *isl_schedule_free(__isl_take isl_schedule *sched);
5501 A mapping from the domains to the scheduled space can be obtained
5502 from an C<isl_schedule> using the following function.
5504 __isl_give isl_union_map *isl_schedule_get_map(
5505 __isl_keep isl_schedule *sched);
5507 A representation of the schedule can be printed using
5509 __isl_give isl_printer *isl_printer_print_schedule(
5510 __isl_take isl_printer *p,
5511 __isl_keep isl_schedule *schedule);
5513 A representation of the schedule as a forest of bands can be obtained
5514 using the following function.
5516 __isl_give isl_band_list *isl_schedule_get_band_forest(
5517 __isl_keep isl_schedule *schedule);
5519 The individual bands can be visited in depth-first post-order
5520 using the following function.
5522 #include <isl/schedule.h>
5523 int isl_schedule_foreach_band(
5524 __isl_keep isl_schedule *sched,
5525 int (*fn)(__isl_keep isl_band *band, void *user),
5528 The list can be manipulated as explained in L<"Lists">.
5529 The bands inside the list can be copied and freed using the following
5532 #include <isl/band.h>
5533 __isl_give isl_band *isl_band_copy(
5534 __isl_keep isl_band *band);
5535 void *isl_band_free(__isl_take isl_band *band);
5537 Each band contains zero or more scheduling dimensions.
5538 These are referred to as the members of the band.
5539 The section of the schedule that corresponds to the band is
5540 referred to as the partial schedule of the band.
5541 For those nodes that participate in a band, the outer scheduling
5542 dimensions form the prefix schedule, while the inner scheduling
5543 dimensions form the suffix schedule.
5544 That is, if we take a cut of the band forest, then the union of
5545 the concatenations of the prefix, partial and suffix schedules of
5546 each band in the cut is equal to the entire schedule (modulo
5547 some possible padding at the end with zero scheduling dimensions).
5548 The properties of a band can be inspected using the following functions.
5550 #include <isl/band.h>
5551 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5553 int isl_band_has_children(__isl_keep isl_band *band);
5554 __isl_give isl_band_list *isl_band_get_children(
5555 __isl_keep isl_band *band);
5557 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5558 __isl_keep isl_band *band);
5559 __isl_give isl_union_map *isl_band_get_partial_schedule(
5560 __isl_keep isl_band *band);
5561 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5562 __isl_keep isl_band *band);
5564 int isl_band_n_member(__isl_keep isl_band *band);
5565 int isl_band_member_is_zero_distance(
5566 __isl_keep isl_band *band, int pos);
5568 int isl_band_list_foreach_band(
5569 __isl_keep isl_band_list *list,
5570 int (*fn)(__isl_keep isl_band *band, void *user),
5573 Note that a scheduling dimension is considered to be ``zero
5574 distance'' if it does not carry any proximity dependences
5576 That is, if the dependence distances of the proximity
5577 dependences are all zero in that direction (for fixed
5578 iterations of outer bands).
5579 Like C<isl_schedule_foreach_band>,
5580 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5581 in depth-first post-order.
5583 A band can be tiled using the following function.
5585 #include <isl/band.h>
5586 int isl_band_tile(__isl_keep isl_band *band,
5587 __isl_take isl_vec *sizes);
5589 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5591 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5592 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5594 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5596 The C<isl_band_tile> function tiles the band using the given tile sizes
5597 inside its schedule.
5598 A new child band is created to represent the point loops and it is
5599 inserted between the modified band and its children.
5600 The C<tile_scale_tile_loops> option specifies whether the tile
5601 loops iterators should be scaled by the tile sizes.
5602 If the C<tile_shift_point_loops> option is set, then the point loops
5603 are shifted to start at zero.
5605 A band can be split into two nested bands using the following function.
5607 int isl_band_split(__isl_keep isl_band *band, int pos);
5609 The resulting outer band contains the first C<pos> dimensions of C<band>
5610 while the inner band contains the remaining dimensions.
5612 A representation of the band can be printed using
5614 #include <isl/band.h>
5615 __isl_give isl_printer *isl_printer_print_band(
5616 __isl_take isl_printer *p,
5617 __isl_keep isl_band *band);
5621 #include <isl/schedule.h>
5622 int isl_options_set_schedule_max_coefficient(
5623 isl_ctx *ctx, int val);
5624 int isl_options_get_schedule_max_coefficient(
5626 int isl_options_set_schedule_max_constant_term(
5627 isl_ctx *ctx, int val);
5628 int isl_options_get_schedule_max_constant_term(
5630 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5631 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5632 int isl_options_set_schedule_maximize_band_depth(
5633 isl_ctx *ctx, int val);
5634 int isl_options_get_schedule_maximize_band_depth(
5636 int isl_options_set_schedule_outer_zero_distance(
5637 isl_ctx *ctx, int val);
5638 int isl_options_get_schedule_outer_zero_distance(
5640 int isl_options_set_schedule_split_scaled(
5641 isl_ctx *ctx, int val);
5642 int isl_options_get_schedule_split_scaled(
5644 int isl_options_set_schedule_algorithm(
5645 isl_ctx *ctx, int val);
5646 int isl_options_get_schedule_algorithm(
5648 int isl_options_set_schedule_separate_components(
5649 isl_ctx *ctx, int val);
5650 int isl_options_get_schedule_separate_components(
5655 =item * schedule_max_coefficient
5657 This option enforces that the coefficients for variable and parameter
5658 dimensions in the calculated schedule are not larger than the specified value.
5659 This option can significantly increase the speed of the scheduling calculation
5660 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5661 this option does not introduce bounds on the variable or parameter
5664 =item * schedule_max_constant_term
5666 This option enforces that the constant coefficients in the calculated schedule
5667 are not larger than the maximal constant term. This option can significantly
5668 increase the speed of the scheduling calculation and may also prevent fusing of
5669 unrelated dimensions. A value of -1 means that this option does not introduce
5670 bounds on the constant coefficients.
5672 =item * schedule_fuse
5674 This option controls the level of fusion.
5675 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5676 resulting schedule will be distributed as much as possible.
5677 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5678 try to fuse loops in the resulting schedule.
5680 =item * schedule_maximize_band_depth
5682 If this option is set, we do not split bands at the point
5683 where we detect splitting is necessary. Instead, we
5684 backtrack and split bands as early as possible. This
5685 reduces the number of splits and maximizes the width of
5686 the bands. Wider bands give more possibilities for tiling.
5687 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5688 then bands will be split as early as possible, even if there is no need.
5689 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5691 =item * schedule_outer_zero_distance
5693 If this option is set, then we try to construct schedules
5694 where the outermost scheduling dimension in each band
5695 results in a zero dependence distance over the proximity
5698 =item * schedule_split_scaled
5700 If this option is set, then we try to construct schedules in which the
5701 constant term is split off from the linear part if the linear parts of
5702 the scheduling rows for all nodes in the graphs have a common non-trivial
5704 The constant term is then placed in a separate band and the linear
5707 =item * schedule_algorithm
5709 Selects the scheduling algorithm to be used.
5710 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5711 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5713 =item * schedule_separate_components
5715 If at any point the dependence graph contains any (weakly connected) components,
5716 then these components are scheduled separately.
5717 If this option is not set, then some iterations of the domains
5718 in these components may be scheduled together.
5719 If this option is set, then the components are given consecutive
5724 =head2 AST Generation
5726 This section describes the C<isl> functionality for generating
5727 ASTs that visit all the elements
5728 in a domain in an order specified by a schedule.
5729 In particular, given a C<isl_union_map>, an AST is generated
5730 that visits all the elements in the domain of the C<isl_union_map>
5731 according to the lexicographic order of the corresponding image
5732 element(s). If the range of the C<isl_union_map> consists of
5733 elements in more than one space, then each of these spaces is handled
5734 separately in an arbitrary order.
5735 It should be noted that the image elements only specify the I<order>
5736 in which the corresponding domain elements should be visited.
5737 No direct relation between the image elements and the loop iterators
5738 in the generated AST should be assumed.
5740 Each AST is generated within a build. The initial build
5741 simply specifies the constraints on the parameters (if any)
5742 and can be created, inspected, copied and freed using the following functions.
5744 #include <isl/ast_build.h>
5745 __isl_give isl_ast_build *isl_ast_build_from_context(
5746 __isl_take isl_set *set);
5747 isl_ctx *isl_ast_build_get_ctx(
5748 __isl_keep isl_ast_build *build);
5749 __isl_give isl_ast_build *isl_ast_build_copy(
5750 __isl_keep isl_ast_build *build);
5751 void *isl_ast_build_free(
5752 __isl_take isl_ast_build *build);
5754 The C<set> argument is usually a parameter set with zero or more parameters.
5755 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5756 and L</"Fine-grained Control over AST Generation">.
5757 Finally, the AST itself can be constructed using the following
5760 #include <isl/ast_build.h>
5761 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5762 __isl_keep isl_ast_build *build,
5763 __isl_take isl_union_map *schedule);
5765 =head3 Inspecting the AST
5767 The basic properties of an AST node can be obtained as follows.
5769 #include <isl/ast.h>
5770 isl_ctx *isl_ast_node_get_ctx(
5771 __isl_keep isl_ast_node *node);
5772 enum isl_ast_node_type isl_ast_node_get_type(
5773 __isl_keep isl_ast_node *node);
5775 The type of an AST node is one of
5776 C<isl_ast_node_for>,
5778 C<isl_ast_node_block> or
5779 C<isl_ast_node_user>.
5780 An C<isl_ast_node_for> represents a for node.
5781 An C<isl_ast_node_if> represents an if node.
5782 An C<isl_ast_node_block> represents a compound node.
5783 An C<isl_ast_node_user> represents an expression statement.
5784 An expression statement typically corresponds to a domain element, i.e.,
5785 one of the elements that is visited by the AST.
5787 Each type of node has its own additional properties.
5789 #include <isl/ast.h>
5790 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5791 __isl_keep isl_ast_node *node);
5792 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5793 __isl_keep isl_ast_node *node);
5794 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5795 __isl_keep isl_ast_node *node);
5796 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5797 __isl_keep isl_ast_node *node);
5798 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5799 __isl_keep isl_ast_node *node);
5800 int isl_ast_node_for_is_degenerate(
5801 __isl_keep isl_ast_node *node);
5803 An C<isl_ast_for> is considered degenerate if it is known to execute
5806 #include <isl/ast.h>
5807 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5808 __isl_keep isl_ast_node *node);
5809 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5810 __isl_keep isl_ast_node *node);
5811 int isl_ast_node_if_has_else(
5812 __isl_keep isl_ast_node *node);
5813 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5814 __isl_keep isl_ast_node *node);
5816 __isl_give isl_ast_node_list *
5817 isl_ast_node_block_get_children(
5818 __isl_keep isl_ast_node *node);
5820 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5821 __isl_keep isl_ast_node *node);
5823 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5824 the following functions.
5826 #include <isl/ast.h>
5827 isl_ctx *isl_ast_expr_get_ctx(
5828 __isl_keep isl_ast_expr *expr);
5829 enum isl_ast_expr_type isl_ast_expr_get_type(
5830 __isl_keep isl_ast_expr *expr);
5832 The type of an AST expression is one of
5834 C<isl_ast_expr_id> or
5835 C<isl_ast_expr_int>.
5836 An C<isl_ast_expr_op> represents the result of an operation.
5837 An C<isl_ast_expr_id> represents an identifier.
5838 An C<isl_ast_expr_int> represents an integer value.
5840 Each type of expression has its own additional properties.
5842 #include <isl/ast.h>
5843 enum isl_ast_op_type isl_ast_expr_get_op_type(
5844 __isl_keep isl_ast_expr *expr);
5845 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5846 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5847 __isl_keep isl_ast_expr *expr, int pos);
5848 int isl_ast_node_foreach_ast_op_type(
5849 __isl_keep isl_ast_node *node,
5850 int (*fn)(enum isl_ast_op_type type, void *user),
5853 C<isl_ast_expr_get_op_type> returns the type of the operation
5854 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5855 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5857 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5858 C<isl_ast_op_type> that appears in C<node>.
5859 The operation type is one of the following.
5863 =item C<isl_ast_op_and>
5865 Logical I<and> of two arguments.
5866 Both arguments can be evaluated.
5868 =item C<isl_ast_op_and_then>
5870 Logical I<and> of two arguments.
5871 The second argument can only be evaluated if the first evaluates to true.
5873 =item C<isl_ast_op_or>
5875 Logical I<or> of two arguments.
5876 Both arguments can be evaluated.
5878 =item C<isl_ast_op_or_else>
5880 Logical I<or> of two arguments.
5881 The second argument can only be evaluated if the first evaluates to false.
5883 =item C<isl_ast_op_max>
5885 Maximum of two or more arguments.
5887 =item C<isl_ast_op_min>
5889 Minimum of two or more arguments.
5891 =item C<isl_ast_op_minus>
5895 =item C<isl_ast_op_add>
5897 Sum of two arguments.
5899 =item C<isl_ast_op_sub>
5901 Difference of two arguments.
5903 =item C<isl_ast_op_mul>
5905 Product of two arguments.
5907 =item C<isl_ast_op_div>
5909 Exact division. That is, the result is known to be an integer.
5911 =item C<isl_ast_op_fdiv_q>
5913 Result of integer division, rounded towards negative
5916 =item C<isl_ast_op_pdiv_q>
5918 Result of integer division, where dividend is known to be non-negative.
5920 =item C<isl_ast_op_pdiv_r>
5922 Remainder of integer division, where dividend is known to be non-negative.
5924 =item C<isl_ast_op_cond>
5926 Conditional operator defined on three arguments.
5927 If the first argument evaluates to true, then the result
5928 is equal to the second argument. Otherwise, the result
5929 is equal to the third argument.
5930 The second and third argument may only be evaluated if
5931 the first argument evaluates to true and false, respectively.
5932 Corresponds to C<a ? b : c> in C.
5934 =item C<isl_ast_op_select>
5936 Conditional operator defined on three arguments.
5937 If the first argument evaluates to true, then the result
5938 is equal to the second argument. Otherwise, the result
5939 is equal to the third argument.
5940 The second and third argument may be evaluated independently
5941 of the value of the first argument.
5942 Corresponds to C<a * b + (1 - a) * c> in C.
5944 =item C<isl_ast_op_eq>
5948 =item C<isl_ast_op_le>
5950 Less than or equal relation.
5952 =item C<isl_ast_op_lt>
5956 =item C<isl_ast_op_ge>
5958 Greater than or equal relation.
5960 =item C<isl_ast_op_gt>
5962 Greater than relation.
5964 =item C<isl_ast_op_call>
5967 The number of arguments of the C<isl_ast_expr> is one more than
5968 the number of arguments in the function call, the first argument
5969 representing the function being called.
5973 #include <isl/ast.h>
5974 __isl_give isl_id *isl_ast_expr_get_id(
5975 __isl_keep isl_ast_expr *expr);
5977 Return the identifier represented by the AST expression.
5979 #include <isl/ast.h>
5980 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5983 Return the integer represented by the AST expression.
5984 Note that the integer is returned through the C<v> argument.
5985 The return value of the function itself indicates whether the
5986 operation was performed successfully.
5988 =head3 Manipulating and printing the AST
5990 AST nodes can be copied and freed using the following functions.
5992 #include <isl/ast.h>
5993 __isl_give isl_ast_node *isl_ast_node_copy(
5994 __isl_keep isl_ast_node *node);
5995 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5997 AST expressions can be copied and freed using the following functions.
5999 #include <isl/ast.h>
6000 __isl_give isl_ast_expr *isl_ast_expr_copy(
6001 __isl_keep isl_ast_expr *expr);
6002 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6004 New AST expressions can be created either directly or within
6005 the context of an C<isl_ast_build>.
6007 #include <isl/ast.h>
6008 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6009 __isl_take isl_id *id);
6010 __isl_give isl_ast_expr *isl_ast_expr_neg(
6011 __isl_take isl_ast_expr *expr);
6012 __isl_give isl_ast_expr *isl_ast_expr_add(
6013 __isl_take isl_ast_expr *expr1,
6014 __isl_take isl_ast_expr *expr2);
6015 __isl_give isl_ast_expr *isl_ast_expr_sub(
6016 __isl_take isl_ast_expr *expr1,
6017 __isl_take isl_ast_expr *expr2);
6018 __isl_give isl_ast_expr *isl_ast_expr_mul(
6019 __isl_take isl_ast_expr *expr1,
6020 __isl_take isl_ast_expr *expr2);
6021 __isl_give isl_ast_expr *isl_ast_expr_div(
6022 __isl_take isl_ast_expr *expr1,
6023 __isl_take isl_ast_expr *expr2);
6024 __isl_give isl_ast_expr *isl_ast_expr_and(
6025 __isl_take isl_ast_expr *expr1,
6026 __isl_take isl_ast_expr *expr2)
6027 __isl_give isl_ast_expr *isl_ast_expr_or(
6028 __isl_take isl_ast_expr *expr1,
6029 __isl_take isl_ast_expr *expr2)
6031 #include <isl/ast_build.h>
6032 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6033 __isl_keep isl_ast_build *build,
6034 __isl_take isl_pw_aff *pa);
6035 __isl_give isl_ast_expr *
6036 isl_ast_build_call_from_pw_multi_aff(
6037 __isl_keep isl_ast_build *build,
6038 __isl_take isl_pw_multi_aff *pma);
6040 The domains of C<pa> and C<pma> should correspond
6041 to the schedule space of C<build>.
6042 The tuple id of C<pma> is used as the function being called.
6044 User specified data can be attached to an C<isl_ast_node> and obtained
6045 from the same C<isl_ast_node> using the following functions.
6047 #include <isl/ast.h>
6048 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6049 __isl_take isl_ast_node *node,
6050 __isl_take isl_id *annotation);
6051 __isl_give isl_id *isl_ast_node_get_annotation(
6052 __isl_keep isl_ast_node *node);
6054 Basic printing can be performed using the following functions.
6056 #include <isl/ast.h>
6057 __isl_give isl_printer *isl_printer_print_ast_expr(
6058 __isl_take isl_printer *p,
6059 __isl_keep isl_ast_expr *expr);
6060 __isl_give isl_printer *isl_printer_print_ast_node(
6061 __isl_take isl_printer *p,
6062 __isl_keep isl_ast_node *node);
6064 More advanced printing can be performed using the following functions.
6066 #include <isl/ast.h>
6067 __isl_give isl_printer *isl_ast_op_type_print_macro(
6068 enum isl_ast_op_type type,
6069 __isl_take isl_printer *p);
6070 __isl_give isl_printer *isl_ast_node_print_macros(
6071 __isl_keep isl_ast_node *node,
6072 __isl_take isl_printer *p);
6073 __isl_give isl_printer *isl_ast_node_print(
6074 __isl_keep isl_ast_node *node,
6075 __isl_take isl_printer *p,
6076 __isl_take isl_ast_print_options *options);
6077 __isl_give isl_printer *isl_ast_node_for_print(
6078 __isl_keep isl_ast_node *node,
6079 __isl_take isl_printer *p,
6080 __isl_take isl_ast_print_options *options);
6081 __isl_give isl_printer *isl_ast_node_if_print(
6082 __isl_keep isl_ast_node *node,
6083 __isl_take isl_printer *p,
6084 __isl_take isl_ast_print_options *options);
6086 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6087 C<isl> may print out an AST that makes use of macros such
6088 as C<floord>, C<min> and C<max>.
6089 C<isl_ast_op_type_print_macro> prints out the macro
6090 corresponding to a specific C<isl_ast_op_type>.
6091 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6092 for expressions where these macros would be used and prints
6093 out the required macro definitions.
6094 Essentially, C<isl_ast_node_print_macros> calls
6095 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6096 as function argument.
6097 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6098 C<isl_ast_node_if_print> print an C<isl_ast_node>
6099 in C<ISL_FORMAT_C>, but allow for some extra control
6100 through an C<isl_ast_print_options> object.
6101 This object can be created using the following functions.
6103 #include <isl/ast.h>
6104 __isl_give isl_ast_print_options *
6105 isl_ast_print_options_alloc(isl_ctx *ctx);
6106 __isl_give isl_ast_print_options *
6107 isl_ast_print_options_copy(
6108 __isl_keep isl_ast_print_options *options);
6109 void *isl_ast_print_options_free(
6110 __isl_take isl_ast_print_options *options);
6112 __isl_give isl_ast_print_options *
6113 isl_ast_print_options_set_print_user(
6114 __isl_take isl_ast_print_options *options,
6115 __isl_give isl_printer *(*print_user)(
6116 __isl_take isl_printer *p,
6117 __isl_take isl_ast_print_options *options,
6118 __isl_keep isl_ast_node *node, void *user),
6120 __isl_give isl_ast_print_options *
6121 isl_ast_print_options_set_print_for(
6122 __isl_take isl_ast_print_options *options,
6123 __isl_give isl_printer *(*print_for)(
6124 __isl_take isl_printer *p,
6125 __isl_take isl_ast_print_options *options,
6126 __isl_keep isl_ast_node *node, void *user),
6129 The callback set by C<isl_ast_print_options_set_print_user>
6130 is called whenever a node of type C<isl_ast_node_user> needs to
6132 The callback set by C<isl_ast_print_options_set_print_for>
6133 is called whenever a node of type C<isl_ast_node_for> needs to
6135 Note that C<isl_ast_node_for_print> will I<not> call the
6136 callback set by C<isl_ast_print_options_set_print_for> on the node
6137 on which C<isl_ast_node_for_print> is called, but only on nested
6138 nodes of type C<isl_ast_node_for>. It is therefore safe to
6139 call C<isl_ast_node_for_print> from within the callback set by
6140 C<isl_ast_print_options_set_print_for>.
6142 The following option determines the type to be used for iterators
6143 while printing the AST.
6145 int isl_options_set_ast_iterator_type(
6146 isl_ctx *ctx, const char *val);
6147 const char *isl_options_get_ast_iterator_type(
6152 #include <isl/ast_build.h>
6153 int isl_options_set_ast_build_atomic_upper_bound(
6154 isl_ctx *ctx, int val);
6155 int isl_options_get_ast_build_atomic_upper_bound(
6157 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6159 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6160 int isl_options_set_ast_build_exploit_nested_bounds(
6161 isl_ctx *ctx, int val);
6162 int isl_options_get_ast_build_exploit_nested_bounds(
6164 int isl_options_set_ast_build_group_coscheduled(
6165 isl_ctx *ctx, int val);
6166 int isl_options_get_ast_build_group_coscheduled(
6168 int isl_options_set_ast_build_scale_strides(
6169 isl_ctx *ctx, int val);
6170 int isl_options_get_ast_build_scale_strides(
6172 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6174 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6175 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6177 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6181 =item * ast_build_atomic_upper_bound
6183 Generate loop upper bounds that consist of the current loop iterator,
6184 an operator and an expression not involving the iterator.
6185 If this option is not set, then the current loop iterator may appear
6186 several times in the upper bound.
6187 For example, when this option is turned off, AST generation
6190 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6194 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6197 When the option is turned on, the following AST is generated
6199 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6202 =item * ast_build_prefer_pdiv
6204 If this option is turned off, then the AST generation will
6205 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6206 operators, but no C<isl_ast_op_pdiv_q> or
6207 C<isl_ast_op_pdiv_r> operators.
6208 If this options is turned on, then C<isl> will try to convert
6209 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6210 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6212 =item * ast_build_exploit_nested_bounds
6214 Simplify conditions based on bounds of nested for loops.
6215 In particular, remove conditions that are implied by the fact
6216 that one or more nested loops have at least one iteration,
6217 meaning that the upper bound is at least as large as the lower bound.
6218 For example, when this option is turned off, AST generation
6221 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6227 for (int c0 = 0; c0 <= N; c0 += 1)
6228 for (int c1 = 0; c1 <= M; c1 += 1)
6231 When the option is turned on, the following AST is generated
6233 for (int c0 = 0; c0 <= N; c0 += 1)
6234 for (int c1 = 0; c1 <= M; c1 += 1)
6237 =item * ast_build_group_coscheduled
6239 If two domain elements are assigned the same schedule point, then
6240 they may be executed in any order and they may even appear in different
6241 loops. If this options is set, then the AST generator will make
6242 sure that coscheduled domain elements do not appear in separate parts
6243 of the AST. This is useful in case of nested AST generation
6244 if the outer AST generation is given only part of a schedule
6245 and the inner AST generation should handle the domains that are
6246 coscheduled by this initial part of the schedule together.
6247 For example if an AST is generated for a schedule
6249 { A[i] -> [0]; B[i] -> [0] }
6251 then the C<isl_ast_build_set_create_leaf> callback described
6252 below may get called twice, once for each domain.
6253 Setting this option ensures that the callback is only called once
6254 on both domains together.
6256 =item * ast_build_separation_bounds
6258 This option specifies which bounds to use during separation.
6259 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6260 then all (possibly implicit) bounds on the current dimension will
6261 be used during separation.
6262 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6263 then only those bounds that are explicitly available will
6264 be used during separation.
6266 =item * ast_build_scale_strides
6268 This option specifies whether the AST generator is allowed
6269 to scale down iterators of strided loops.
6271 =item * ast_build_allow_else
6273 This option specifies whether the AST generator is allowed
6274 to construct if statements with else branches.
6276 =item * ast_build_allow_or
6278 This option specifies whether the AST generator is allowed
6279 to construct if conditions with disjunctions.
6283 =head3 Fine-grained Control over AST Generation
6285 Besides specifying the constraints on the parameters,
6286 an C<isl_ast_build> object can be used to control
6287 various aspects of the AST generation process.
6288 The most prominent way of control is through ``options'',
6289 which can be set using the following function.
6291 #include <isl/ast_build.h>
6292 __isl_give isl_ast_build *
6293 isl_ast_build_set_options(
6294 __isl_take isl_ast_build *control,
6295 __isl_take isl_union_map *options);
6297 The options are encoded in an <isl_union_map>.
6298 The domain of this union relation refers to the schedule domain,
6299 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6300 In the case of nested AST generation (see L</"Nested AST Generation">),
6301 the domain of C<options> should refer to the extra piece of the schedule.
6302 That is, it should be equal to the range of the wrapped relation in the
6303 range of the schedule.
6304 The range of the options can consist of elements in one or more spaces,
6305 the names of which determine the effect of the option.
6306 The values of the range typically also refer to the schedule dimension
6307 to which the option applies. In case of nested AST generation
6308 (see L</"Nested AST Generation">), these values refer to the position
6309 of the schedule dimension within the innermost AST generation.
6310 The constraints on the domain elements of
6311 the option should only refer to this dimension and earlier dimensions.
6312 We consider the following spaces.
6316 =item C<separation_class>
6318 This space is a wrapped relation between two one dimensional spaces.
6319 The input space represents the schedule dimension to which the option
6320 applies and the output space represents the separation class.
6321 While constructing a loop corresponding to the specified schedule
6322 dimension(s), the AST generator will try to generate separate loops
6323 for domain elements that are assigned different classes.
6324 If only some of the elements are assigned a class, then those elements
6325 that are not assigned any class will be treated as belonging to a class
6326 that is separate from the explicitly assigned classes.
6327 The typical use case for this option is to separate full tiles from
6329 The other options, described below, are applied after the separation
6332 As an example, consider the separation into full and partial tiles
6333 of a tiling of a triangular domain.
6334 Take, for example, the domain
6336 { A[i,j] : 0 <= i,j and i + j <= 100 }
6338 and a tiling into tiles of 10 by 10. The input to the AST generator
6339 is then the schedule
6341 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6344 Without any options, the following AST is generated
6346 for (int c0 = 0; c0 <= 10; c0 += 1)
6347 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6348 for (int c2 = 10 * c0;
6349 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6351 for (int c3 = 10 * c1;
6352 c3 <= min(10 * c1 + 9, -c2 + 100);
6356 Separation into full and partial tiles can be obtained by assigning
6357 a class, say C<0>, to the full tiles. The full tiles are represented by those
6358 values of the first and second schedule dimensions for which there are
6359 values of the third and fourth dimensions to cover an entire tile.
6360 That is, we need to specify the following option
6362 { [a,b,c,d] -> separation_class[[0]->[0]] :
6363 exists b': 0 <= 10a,10b' and
6364 10a+9+10b'+9 <= 100;
6365 [a,b,c,d] -> separation_class[[1]->[0]] :
6366 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6370 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6371 a >= 0 and b >= 0 and b <= 8 - a;
6372 [a, b, c, d] -> separation_class[[0] -> [0]] :
6375 With this option, the generated AST is as follows
6378 for (int c0 = 0; c0 <= 8; c0 += 1) {
6379 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6380 for (int c2 = 10 * c0;
6381 c2 <= 10 * c0 + 9; c2 += 1)
6382 for (int c3 = 10 * c1;
6383 c3 <= 10 * c1 + 9; c3 += 1)
6385 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6386 for (int c2 = 10 * c0;
6387 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6389 for (int c3 = 10 * c1;
6390 c3 <= min(-c2 + 100, 10 * c1 + 9);
6394 for (int c0 = 9; c0 <= 10; c0 += 1)
6395 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6396 for (int c2 = 10 * c0;
6397 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6399 for (int c3 = 10 * c1;
6400 c3 <= min(10 * c1 + 9, -c2 + 100);
6407 This is a single-dimensional space representing the schedule dimension(s)
6408 to which ``separation'' should be applied. Separation tries to split
6409 a loop into several pieces if this can avoid the generation of guards
6411 See also the C<atomic> option.
6415 This is a single-dimensional space representing the schedule dimension(s)
6416 for which the domains should be considered ``atomic''. That is, the
6417 AST generator will make sure that any given domain space will only appear
6418 in a single loop at the specified level.
6420 Consider the following schedule
6422 { a[i] -> [i] : 0 <= i < 10;
6423 b[i] -> [i+1] : 0 <= i < 10 }
6425 If the following option is specified
6427 { [i] -> separate[x] }
6429 then the following AST will be generated
6433 for (int c0 = 1; c0 <= 9; c0 += 1) {
6440 If, on the other hand, the following option is specified
6442 { [i] -> atomic[x] }
6444 then the following AST will be generated
6446 for (int c0 = 0; c0 <= 10; c0 += 1) {
6453 If neither C<atomic> nor C<separate> is specified, then the AST generator
6454 may produce either of these two results or some intermediate form.
6458 This is a single-dimensional space representing the schedule dimension(s)
6459 that should be I<completely> unrolled.
6460 To obtain a partial unrolling, the user should apply an additional
6461 strip-mining to the schedule and fully unroll the inner loop.
6465 Additional control is available through the following functions.
6467 #include <isl/ast_build.h>
6468 __isl_give isl_ast_build *
6469 isl_ast_build_set_iterators(
6470 __isl_take isl_ast_build *control,
6471 __isl_take isl_id_list *iterators);
6473 The function C<isl_ast_build_set_iterators> allows the user to
6474 specify a list of iterator C<isl_id>s to be used as iterators.
6475 If the input schedule is injective, then
6476 the number of elements in this list should be as large as the dimension
6477 of the schedule space, but no direct correspondence should be assumed
6478 between dimensions and elements.
6479 If the input schedule is not injective, then an additional number
6480 of C<isl_id>s equal to the largest dimension of the input domains
6482 If the number of provided C<isl_id>s is insufficient, then additional
6483 names are automatically generated.
6485 #include <isl/ast_build.h>
6486 __isl_give isl_ast_build *
6487 isl_ast_build_set_create_leaf(
6488 __isl_take isl_ast_build *control,
6489 __isl_give isl_ast_node *(*fn)(
6490 __isl_take isl_ast_build *build,
6491 void *user), void *user);
6494 C<isl_ast_build_set_create_leaf> function allows for the
6495 specification of a callback that should be called whenever the AST
6496 generator arrives at an element of the schedule domain.
6497 The callback should return an AST node that should be inserted
6498 at the corresponding position of the AST. The default action (when
6499 the callback is not set) is to continue generating parts of the AST to scan
6500 all the domain elements associated to the schedule domain element
6501 and to insert user nodes, ``calling'' the domain element, for each of them.
6502 The C<build> argument contains the current state of the C<isl_ast_build>.
6503 To ease nested AST generation (see L</"Nested AST Generation">),
6504 all control information that is
6505 specific to the current AST generation such as the options and
6506 the callbacks has been removed from this C<isl_ast_build>.
6507 The callback would typically return the result of a nested
6509 user defined node created using the following function.
6511 #include <isl/ast.h>
6512 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6513 __isl_take isl_ast_expr *expr);
6515 #include <isl/ast_build.h>
6516 __isl_give isl_ast_build *
6517 isl_ast_build_set_at_each_domain(
6518 __isl_take isl_ast_build *build,
6519 __isl_give isl_ast_node *(*fn)(
6520 __isl_take isl_ast_node *node,
6521 __isl_keep isl_ast_build *build,
6522 void *user), void *user);
6523 __isl_give isl_ast_build *
6524 isl_ast_build_set_before_each_for(
6525 __isl_take isl_ast_build *build,
6526 __isl_give isl_id *(*fn)(
6527 __isl_keep isl_ast_build *build,
6528 void *user), void *user);
6529 __isl_give isl_ast_build *
6530 isl_ast_build_set_after_each_for(
6531 __isl_take isl_ast_build *build,
6532 __isl_give isl_ast_node *(*fn)(
6533 __isl_take isl_ast_node *node,
6534 __isl_keep isl_ast_build *build,
6535 void *user), void *user);
6537 The callback set by C<isl_ast_build_set_at_each_domain> will
6538 be called for each domain AST node.
6539 The callbacks set by C<isl_ast_build_set_before_each_for>
6540 and C<isl_ast_build_set_after_each_for> will be called
6541 for each for AST node. The first will be called in depth-first
6542 pre-order, while the second will be called in depth-first post-order.
6543 Since C<isl_ast_build_set_before_each_for> is called before the for
6544 node is actually constructed, it is only passed an C<isl_ast_build>.
6545 The returned C<isl_id> will be added as an annotation (using
6546 C<isl_ast_node_set_annotation>) to the constructed for node.
6547 In particular, if the user has also specified an C<after_each_for>
6548 callback, then the annotation can be retrieved from the node passed to
6549 that callback using C<isl_ast_node_get_annotation>.
6550 All callbacks should C<NULL> on failure.
6551 The given C<isl_ast_build> can be used to create new
6552 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6553 or C<isl_ast_build_call_from_pw_multi_aff>.
6555 =head3 Nested AST Generation
6557 C<isl> allows the user to create an AST within the context
6558 of another AST. These nested ASTs are created using the
6559 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6560 outer AST. The C<build> argument should be an C<isl_ast_build>
6561 passed to a callback set by
6562 C<isl_ast_build_set_create_leaf>.
6563 The space of the range of the C<schedule> argument should refer
6564 to this build. In particular, the space should be a wrapped
6565 relation and the domain of this wrapped relation should be the
6566 same as that of the range of the schedule returned by
6567 C<isl_ast_build_get_schedule> below.
6568 In practice, the new schedule is typically
6569 created by calling C<isl_union_map_range_product> on the old schedule
6570 and some extra piece of the schedule.
6571 The space of the schedule domain is also available from
6572 the C<isl_ast_build>.
6574 #include <isl/ast_build.h>
6575 __isl_give isl_union_map *isl_ast_build_get_schedule(
6576 __isl_keep isl_ast_build *build);
6577 __isl_give isl_space *isl_ast_build_get_schedule_space(
6578 __isl_keep isl_ast_build *build);
6579 __isl_give isl_ast_build *isl_ast_build_restrict(
6580 __isl_take isl_ast_build *build,
6581 __isl_take isl_set *set);
6583 The C<isl_ast_build_get_schedule> function returns a (partial)
6584 schedule for the domains elements for which part of the AST still needs to
6585 be generated in the current build.
6586 In particular, the domain elements are mapped to those iterations of the loops
6587 enclosing the current point of the AST generation inside which
6588 the domain elements are executed.
6589 No direct correspondence between
6590 the input schedule and this schedule should be assumed.
6591 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6592 to create a set for C<isl_ast_build_restrict> to intersect
6593 with the current build. In particular, the set passed to
6594 C<isl_ast_build_restrict> can have additional parameters.
6595 The ids of the set dimensions in the space returned by
6596 C<isl_ast_build_get_schedule_space> correspond to the
6597 iterators of the already generated loops.
6598 The user should not rely on the ids of the output dimensions
6599 of the relations in the union relation returned by
6600 C<isl_ast_build_get_schedule> having any particular value.
6604 Although C<isl> is mainly meant to be used as a library,
6605 it also contains some basic applications that use some
6606 of the functionality of C<isl>.
6607 The input may be specified in either the L<isl format>
6608 or the L<PolyLib format>.
6610 =head2 C<isl_polyhedron_sample>
6612 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6613 an integer element of the polyhedron, if there is any.
6614 The first column in the output is the denominator and is always
6615 equal to 1. If the polyhedron contains no integer points,
6616 then a vector of length zero is printed.
6620 C<isl_pip> takes the same input as the C<example> program
6621 from the C<piplib> distribution, i.e., a set of constraints
6622 on the parameters, a line containing only -1 and finally a set
6623 of constraints on a parametric polyhedron.
6624 The coefficients of the parameters appear in the last columns
6625 (but before the final constant column).
6626 The output is the lexicographic minimum of the parametric polyhedron.
6627 As C<isl> currently does not have its own output format, the output
6628 is just a dump of the internal state.
6630 =head2 C<isl_polyhedron_minimize>
6632 C<isl_polyhedron_minimize> computes the minimum of some linear
6633 or affine objective function over the integer points in a polyhedron.
6634 If an affine objective function
6635 is given, then the constant should appear in the last column.
6637 =head2 C<isl_polytope_scan>
6639 Given a polytope, C<isl_polytope_scan> prints
6640 all integer points in the polytope.
6642 =head2 C<isl_codegen>
6644 Given a schedule, a context set and an options relation,
6645 C<isl_codegen> prints out an AST that scans the domain elements
6646 of the schedule in the order of their image(s) taking into account
6647 the constraints in the context set.