2 * Copyright 2012-2014 Ecole Normale Superieure
3 * Copyright 2014 INRIA Rocquencourt
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege,
8 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
9 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
10 * B.P. 105 - 78153 Le Chesnay, France
14 #include <isl/space.h>
15 #include <isl/constraint.h>
18 #include <isl_ast_build_expr.h>
19 #include <isl_ast_private.h>
20 #include <isl_ast_build_private.h>
23 /* Compute the "opposite" of the (numerator of the) argument of a div
24 * with denominator "d".
26 * In particular, compute
30 static __isl_give isl_aff
*oppose_div_arg(__isl_take isl_aff
*aff
,
31 __isl_take isl_val
*d
)
33 aff
= isl_aff_neg(aff
);
34 aff
= isl_aff_add_constant_val(aff
, d
);
35 aff
= isl_aff_add_constant_si(aff
, -1);
40 /* Internal data structure used inside isl_ast_expr_add_term.
41 * The domain of "build" is used to simplify the expressions.
42 * "build" needs to be set by the caller of isl_ast_expr_add_term.
43 * "cst" is the constant term of the expression in which the added term
44 * appears. It may be modified by isl_ast_expr_add_term.
46 * "v" is the coefficient of the term that is being constructed and
47 * is set internally by isl_ast_expr_add_term.
49 struct isl_ast_add_term_data
{
55 /* Given the numerator "aff" of the argument of an integer division
56 * with denominator "d", check if it can be made non-negative over
57 * data->build->domain by stealing part of the constant term of
58 * the expression in which the integer division appears.
60 * In particular, the outer expression is of the form
62 * v * floor(aff/d) + cst
64 * We already know that "aff" itself may attain negative values.
65 * Here we check if aff + d*floor(cst/v) is non-negative, such
66 * that we could rewrite the expression to
68 * v * floor((aff + d*floor(cst/v))/d) + cst - v*floor(cst/v)
70 * Note that aff + d*floor(cst/v) can only possibly be non-negative
71 * if data->cst and data->v have the same sign.
72 * Similarly, if floor(cst/v) is zero, then there is no point in
75 static int is_non_neg_after_stealing(__isl_keep isl_aff
*aff
,
76 __isl_keep isl_val
*d
, struct isl_ast_add_term_data
*data
)
83 if (isl_val_sgn(data
->cst
) != isl_val_sgn(data
->v
))
86 shift
= isl_val_div(isl_val_copy(data
->cst
), isl_val_copy(data
->v
));
87 shift
= isl_val_floor(shift
);
88 is_zero
= isl_val_is_zero(shift
);
89 if (is_zero
< 0 || is_zero
) {
91 return is_zero
< 0 ? -1 : 0;
93 shift
= isl_val_mul(shift
, isl_val_copy(d
));
94 shifted
= isl_aff_copy(aff
);
95 shifted
= isl_aff_add_constant_val(shifted
, shift
);
96 non_neg
= isl_ast_build_aff_is_nonneg(data
->build
, shifted
);
97 isl_aff_free(shifted
);
102 /* Given the numerator "aff' of the argument of an integer division
103 * with denominator "d", steal part of the constant term of
104 * the expression in which the integer division appears to make it
105 * non-negative over data->build->domain.
107 * In particular, the outer expression is of the form
109 * v * floor(aff/d) + cst
111 * We know that "aff" itself may attain negative values,
112 * but that aff + d*floor(cst/v) is non-negative.
113 * Find the minimal positive value that we need to add to "aff"
114 * to make it positive and adjust data->cst accordingly.
115 * That is, compute the minimal value "m" of "aff" over
116 * data->build->domain and take
124 * and rewrite the expression to
126 * v * floor((aff + s*d)/d) + (cst - v*s)
128 static __isl_give isl_aff
*steal_from_cst(__isl_take isl_aff
*aff
,
129 __isl_keep isl_val
*d
, struct isl_ast_add_term_data
*data
)
134 domain
= isl_ast_build_get_domain(data
->build
);
135 shift
= isl_set_min_val(domain
, aff
);
136 isl_set_free(domain
);
138 shift
= isl_val_neg(shift
);
139 shift
= isl_val_div(shift
, isl_val_copy(d
));
140 shift
= isl_val_ceil(shift
);
142 t
= isl_val_copy(shift
);
143 t
= isl_val_mul(t
, isl_val_copy(data
->v
));
144 data
->cst
= isl_val_sub(data
->cst
, t
);
146 shift
= isl_val_mul(shift
, isl_val_copy(d
));
147 return isl_aff_add_constant_val(aff
, shift
);
150 /* Create an isl_ast_expr evaluating the div at position "pos" in "ls".
151 * The result is simplified in terms of data->build->domain.
152 * This function may change (the sign of) data->v.
154 * "ls" is known to be non-NULL.
156 * Let the div be of the form floor(e/d).
157 * If the ast_build_prefer_pdiv option is set then we check if "e"
158 * is non-negative, so that we can generate
160 * (pdiv_q, expr(e), expr(d))
164 * (fdiv_q, expr(e), expr(d))
166 * If the ast_build_prefer_pdiv option is set and
167 * if "e" is not non-negative, then we check if "-e + d - 1" is non-negative.
168 * If so, we can rewrite
170 * floor(e/d) = -ceil(-e/d) = -floor((-e + d - 1)/d)
172 * and still use pdiv_q, while changing the sign of data->v.
174 * Otherwise, we check if
178 * is non-negative and if so, replace floor(e/d) by
180 * floor((e + s*d)/d) - s
182 * with s the minimal shift that makes the argument non-negative.
184 static __isl_give isl_ast_expr
*var_div(struct isl_ast_add_term_data
*data
,
185 __isl_keep isl_local_space
*ls
, int pos
)
187 isl_ctx
*ctx
= isl_local_space_get_ctx(ls
);
189 isl_ast_expr
*num
, *den
;
191 enum isl_ast_op_type type
;
193 aff
= isl_local_space_get_div(ls
, pos
);
194 d
= isl_aff_get_denominator_val(aff
);
195 aff
= isl_aff_scale_val(aff
, isl_val_copy(d
));
196 den
= isl_ast_expr_from_val(isl_val_copy(d
));
198 type
= isl_ast_op_fdiv_q
;
199 if (isl_options_get_ast_build_prefer_pdiv(ctx
)) {
200 int non_neg
= isl_ast_build_aff_is_nonneg(data
->build
, aff
);
201 if (non_neg
>= 0 && !non_neg
) {
202 isl_aff
*opp
= oppose_div_arg(isl_aff_copy(aff
),
204 non_neg
= isl_ast_build_aff_is_nonneg(data
->build
, opp
);
205 if (non_neg
>= 0 && non_neg
) {
206 data
->v
= isl_val_neg(data
->v
);
212 if (non_neg
>= 0 && !non_neg
) {
213 non_neg
= is_non_neg_after_stealing(aff
, d
, data
);
214 if (non_neg
>= 0 && non_neg
)
215 aff
= steal_from_cst(aff
, d
, data
);
218 aff
= isl_aff_free(aff
);
220 type
= isl_ast_op_pdiv_q
;
224 num
= isl_ast_expr_from_aff(aff
, data
->build
);
225 return isl_ast_expr_alloc_binary(type
, num
, den
);
228 /* Create an isl_ast_expr evaluating the specified dimension of "ls".
229 * The result is simplified in terms of data->build->domain.
230 * This function may change (the sign of) data->v.
232 * The isl_ast_expr is constructed based on the type of the dimension.
233 * - divs are constructed by var_div
234 * - set variables are constructed from the iterator isl_ids in data->build
235 * - parameters are constructed from the isl_ids in "ls"
237 static __isl_give isl_ast_expr
*var(struct isl_ast_add_term_data
*data
,
238 __isl_keep isl_local_space
*ls
, enum isl_dim_type type
, int pos
)
240 isl_ctx
*ctx
= isl_local_space_get_ctx(ls
);
243 if (type
== isl_dim_div
)
244 return var_div(data
, ls
, pos
);
246 if (type
== isl_dim_set
) {
247 id
= isl_ast_build_get_iterator_id(data
->build
, pos
);
248 return isl_ast_expr_from_id(id
);
251 if (!isl_local_space_has_dim_id(ls
, type
, pos
))
252 isl_die(ctx
, isl_error_internal
, "unnamed dimension",
254 id
= isl_local_space_get_dim_id(ls
, type
, pos
);
255 return isl_ast_expr_from_id(id
);
258 /* Does "expr" represent the zero integer?
260 static int ast_expr_is_zero(__isl_keep isl_ast_expr
*expr
)
264 if (expr
->type
!= isl_ast_expr_int
)
266 return isl_val_is_zero(expr
->u
.v
);
269 /* Create an expression representing the sum of "expr1" and "expr2",
270 * provided neither of the two expressions is identically zero.
272 static __isl_give isl_ast_expr
*ast_expr_add(__isl_take isl_ast_expr
*expr1
,
273 __isl_take isl_ast_expr
*expr2
)
275 if (!expr1
|| !expr2
)
278 if (ast_expr_is_zero(expr1
)) {
279 isl_ast_expr_free(expr1
);
283 if (ast_expr_is_zero(expr2
)) {
284 isl_ast_expr_free(expr2
);
288 return isl_ast_expr_add(expr1
, expr2
);
290 isl_ast_expr_free(expr1
);
291 isl_ast_expr_free(expr2
);
295 /* Subtract expr2 from expr1.
297 * If expr2 is zero, we simply return expr1.
298 * If expr1 is zero, we return
300 * (isl_ast_op_minus, expr2)
302 * Otherwise, we return
304 * (isl_ast_op_sub, expr1, expr2)
306 static __isl_give isl_ast_expr
*ast_expr_sub(__isl_take isl_ast_expr
*expr1
,
307 __isl_take isl_ast_expr
*expr2
)
309 if (!expr1
|| !expr2
)
312 if (ast_expr_is_zero(expr2
)) {
313 isl_ast_expr_free(expr2
);
317 if (ast_expr_is_zero(expr1
)) {
318 isl_ast_expr_free(expr1
);
319 return isl_ast_expr_neg(expr2
);
322 return isl_ast_expr_sub(expr1
, expr2
);
324 isl_ast_expr_free(expr1
);
325 isl_ast_expr_free(expr2
);
329 /* Return an isl_ast_expr that represents
333 * v is assumed to be non-negative.
334 * The result is simplified in terms of build->domain.
336 static __isl_give isl_ast_expr
*isl_ast_expr_mod(__isl_keep isl_val
*v
,
337 __isl_keep isl_aff
*aff
, __isl_keep isl_val
*d
,
338 __isl_keep isl_ast_build
*build
)
346 expr
= isl_ast_expr_from_aff(isl_aff_copy(aff
), build
);
348 c
= isl_ast_expr_from_val(isl_val_copy(d
));
349 expr
= isl_ast_expr_alloc_binary(isl_ast_op_pdiv_r
, expr
, c
);
351 if (!isl_val_is_one(v
)) {
352 c
= isl_ast_expr_from_val(isl_val_copy(v
));
353 expr
= isl_ast_expr_mul(c
, expr
);
359 /* Create an isl_ast_expr that scales "expr" by "v".
361 * If v is 1, we simply return expr.
362 * If v is -1, we return
364 * (isl_ast_op_minus, expr)
366 * Otherwise, we return
368 * (isl_ast_op_mul, expr(v), expr)
370 static __isl_give isl_ast_expr
*scale(__isl_take isl_ast_expr
*expr
,
371 __isl_take isl_val
*v
)
377 if (isl_val_is_one(v
)) {
382 if (isl_val_is_negone(v
)) {
384 expr
= isl_ast_expr_neg(expr
);
386 c
= isl_ast_expr_from_val(v
);
387 expr
= isl_ast_expr_mul(c
, expr
);
393 isl_ast_expr_free(expr
);
397 /* Add an expression for "*v" times the specified dimension of "ls"
399 * If the dimension is an integer division, then this function
400 * may modify data->cst in order to make the numerator non-negative.
401 * The result is simplified in terms of data->build->domain.
403 * Let e be the expression for the specified dimension,
404 * multiplied by the absolute value of "*v".
405 * If "*v" is negative, we create
407 * (isl_ast_op_sub, expr, e)
409 * except when expr is trivially zero, in which case we create
411 * (isl_ast_op_minus, e)
415 * If "*v" is positive, we simply create
417 * (isl_ast_op_add, expr, e)
420 static __isl_give isl_ast_expr
*isl_ast_expr_add_term(
421 __isl_take isl_ast_expr
*expr
,
422 __isl_keep isl_local_space
*ls
, enum isl_dim_type type
, int pos
,
423 __isl_take isl_val
*v
, struct isl_ast_add_term_data
*data
)
431 term
= var(data
, ls
, type
, pos
);
434 if (isl_val_is_neg(v
) && !ast_expr_is_zero(expr
)) {
436 term
= scale(term
, v
);
437 return ast_expr_sub(expr
, term
);
439 term
= scale(term
, v
);
440 return ast_expr_add(expr
, term
);
444 /* Add an expression for "v" to expr.
446 static __isl_give isl_ast_expr
*isl_ast_expr_add_int(
447 __isl_take isl_ast_expr
*expr
, __isl_take isl_val
*v
)
449 isl_ast_expr
*expr_int
;
454 if (isl_val_is_zero(v
)) {
459 if (isl_val_is_neg(v
) && !ast_expr_is_zero(expr
)) {
461 expr_int
= isl_ast_expr_from_val(v
);
462 return ast_expr_sub(expr
, expr_int
);
464 expr_int
= isl_ast_expr_from_val(v
);
465 return ast_expr_add(expr
, expr_int
);
468 isl_ast_expr_free(expr
);
473 /* Internal data structure used inside extract_modulos.
475 * If any modulo expressions are detected in "aff", then the
476 * expression is removed from "aff" and added to either "pos" or "neg"
477 * depending on the sign of the coefficient of the modulo expression
480 * "add" is an expression that needs to be added to "aff" at the end of
481 * the computation. It is NULL as long as no modulos have been extracted.
483 * "i" is the position in "aff" of the div under investigation
484 * "v" is the coefficient in "aff" of the div
485 * "div" is the argument of the div, with the denominator removed
486 * "d" is the original denominator of the argument of the div
488 * "nonneg" is an affine expression that is non-negative over "build"
489 * and that can be used to extract a modulo expression from "div".
490 * In particular, if "sign" is 1, then the coefficients of "nonneg"
491 * are equal to those of "div" modulo "d". If "sign" is -1, then
492 * the coefficients of "nonneg" are opposite to those of "div" modulo "d".
493 * If "sign" is 0, then no such affine expression has been found (yet).
495 struct isl_extract_mod_data
{
496 isl_ast_build
*build
;
513 /* Given that data->v * div_i in data->aff is equal to
515 * f * (term - (arg mod d))
517 * with data->d * f = data->v, add
523 * abs(f) * (arg mod d)
525 * to data->neg or data->pos depending on the sign of -f.
527 static int extract_term_and_mod(struct isl_extract_mod_data
*data
,
528 __isl_take isl_aff
*term
, __isl_take isl_aff
*arg
)
533 data
->v
= isl_val_div(data
->v
, isl_val_copy(data
->d
));
534 s
= isl_val_sgn(data
->v
);
535 data
->v
= isl_val_abs(data
->v
);
536 expr
= isl_ast_expr_mod(data
->v
, arg
, data
->d
, data
->build
);
539 data
->neg
= ast_expr_add(data
->neg
, expr
);
541 data
->pos
= ast_expr_add(data
->pos
, expr
);
542 data
->aff
= isl_aff_set_coefficient_si(data
->aff
,
543 isl_dim_div
, data
->i
, 0);
545 data
->v
= isl_val_neg(data
->v
);
546 term
= isl_aff_scale_val(term
, isl_val_copy(data
->v
));
551 data
->add
= isl_aff_add(data
->add
, term
);
558 /* Given that data->v * div_i in data->aff is of the form
560 * f * d * floor(div/d)
562 * with div nonnegative on data->build, rewrite it as
564 * f * (div - (div mod d)) = f * div - f * (div mod d)
572 * abs(f) * (div mod d)
574 * to data->neg or data->pos depending on the sign of -f.
576 static int extract_mod(struct isl_extract_mod_data
*data
)
578 return extract_term_and_mod(data
, isl_aff_copy(data
->div
),
579 isl_aff_copy(data
->div
));
582 /* Given that data->v * div_i in data->aff is of the form
584 * f * d * floor(div/d) (1)
586 * check if div is non-negative on data->build and, if so,
587 * extract the corresponding modulo from data->aff.
588 * If not, then check if
592 * is non-negative on data->build. If so, replace (1) by
594 * -f * d * floor((-div + d - 1)/d)
596 * and extract the corresponding modulo from data->aff.
598 * This function may modify data->div.
600 static int extract_nonneg_mod(struct isl_extract_mod_data
*data
)
604 mod
= isl_ast_build_aff_is_nonneg(data
->build
, data
->div
);
608 return extract_mod(data
);
610 data
->div
= oppose_div_arg(data
->div
, isl_val_copy(data
->d
));
611 mod
= isl_ast_build_aff_is_nonneg(data
->build
, data
->div
);
615 data
->v
= isl_val_neg(data
->v
);
616 return extract_mod(data
);
621 data
->aff
= isl_aff_free(data
->aff
);
625 /* Is the affine expression of constraint "c" "simpler" than data->nonneg
626 * for use in extracting a modulo expression?
628 * We currently only consider the constant term of the affine expression.
629 * In particular, we prefer the affine expression with the smallest constant
631 * This means that if there are two constraints, say x >= 0 and -x + 10 >= 0,
632 * then we would pick x >= 0
634 * More detailed heuristics could be used if it turns out that there is a need.
636 static int mod_constraint_is_simpler(struct isl_extract_mod_data
*data
,
637 __isl_keep isl_constraint
*c
)
645 v1
= isl_val_abs(isl_constraint_get_constant_val(c
));
646 v2
= isl_val_abs(isl_aff_get_constant_val(data
->nonneg
));
647 simpler
= isl_val_lt(v1
, v2
);
654 /* Check if the coefficients of "c" are either equal or opposite to those
655 * of data->div modulo data->d. If so, and if "c" is "simpler" than
656 * data->nonneg, then replace data->nonneg by the affine expression of "c"
657 * and set data->sign accordingly.
659 * Both "c" and data->div are assumed not to involve any integer divisions.
661 * Before we start the actual comparison, we first quickly check if
662 * "c" and data->div have the same non-zero coefficients.
663 * If not, then we assume that "c" is not of the desired form.
664 * Note that while the coefficients of data->div can be reasonably expected
665 * not to involve any coefficients that are multiples of d, "c" may
666 * very well involve such coefficients. This means that we may actually
669 * If the constant term is "too large", then the constraint is rejected,
670 * where "too large" is fairly arbitrarily set to 1 << 15.
671 * We do this to avoid picking up constraints that bound a variable
672 * by a very large number, say the largest or smallest possible
673 * variable in the representation of some integer type.
675 static isl_stat
check_parallel_or_opposite(__isl_take isl_constraint
*c
,
678 struct isl_extract_mod_data
*data
= user
;
679 enum isl_dim_type c_type
[2] = { isl_dim_param
, isl_dim_set
};
680 enum isl_dim_type a_type
[2] = { isl_dim_param
, isl_dim_in
};
683 int parallel
= 1, opposite
= 1;
685 for (t
= 0; t
< 2; ++t
) {
686 n
[t
] = isl_constraint_dim(c
, c_type
[t
]);
688 return isl_stat_error
;
689 for (i
= 0; i
< n
[t
]; ++i
) {
692 a
= isl_constraint_involves_dims(c
, c_type
[t
], i
, 1);
693 b
= isl_aff_involves_dims(data
->div
, a_type
[t
], i
, 1);
695 parallel
= opposite
= 0;
699 if (parallel
|| opposite
) {
702 v
= isl_val_abs(isl_constraint_get_constant_val(c
));
703 if (isl_val_cmp_si(v
, 1 << 15) > 0)
704 parallel
= opposite
= 0;
708 for (t
= 0; t
< 2; ++t
) {
709 for (i
= 0; i
< n
[t
]; ++i
) {
712 if (!parallel
&& !opposite
)
714 v1
= isl_constraint_get_coefficient_val(c
,
716 v2
= isl_aff_get_coefficient_val(data
->div
,
719 v1
= isl_val_sub(v1
, isl_val_copy(v2
));
720 parallel
= isl_val_is_divisible_by(v1
, data
->d
);
721 v1
= isl_val_add(v1
, isl_val_copy(v2
));
724 v1
= isl_val_add(v1
, isl_val_copy(v2
));
725 opposite
= isl_val_is_divisible_by(v1
, data
->d
);
732 if ((parallel
|| opposite
) && mod_constraint_is_simpler(data
, c
)) {
733 isl_aff_free(data
->nonneg
);
734 data
->nonneg
= isl_constraint_get_aff(c
);
735 data
->sign
= parallel
? 1 : -1;
738 isl_constraint_free(c
);
740 if (data
->sign
!= 0 && data
->nonneg
== NULL
)
741 return isl_stat_error
;
746 /* Given that data->v * div_i in data->aff is of the form
748 * f * d * floor(div/d) (1)
750 * see if we can find an expression div' that is non-negative over data->build
751 * and that is related to div through
757 * div' = -div + d - 1 + d * e
759 * with e some affine expression.
760 * If so, we write (1) as
762 * f * div + f * (div' mod d)
766 * -f * (-div + d - 1) - f * (div' mod d)
768 * exploiting (in the second case) the fact that
770 * f * d * floor(div/d) = -f * d * floor((-div + d - 1)/d)
773 * We first try to find an appropriate expression for div'
774 * from the constraints of data->build->domain (which is therefore
775 * guaranteed to be non-negative on data->build), where we remove
776 * any integer divisions from the constraints and skip this step
777 * if "div" itself involves any integer divisions.
778 * If we cannot find an appropriate expression this way, then
779 * we pass control to extract_nonneg_mod where check
780 * if div or "-div + d -1" themselves happen to be
781 * non-negative on data->build.
783 * While looking for an appropriate constraint in data->build->domain,
784 * we ignore the constant term, so after finding such a constraint,
785 * we still need to fix up the constant term.
786 * In particular, if a is the constant term of "div"
787 * (or d - 1 - the constant term of "div" if data->sign < 0)
788 * and b is the constant term of the constraint, then we need to find
789 * a non-negative constant c such that
791 * b + c \equiv a mod d
797 * and add it to b to obtain the constant term of div'.
798 * If this constant term is "too negative", then we add an appropriate
799 * multiple of d to make it positive.
802 * Note that the above is a only a very simple heuristic for finding an
803 * appropriate expression. We could try a bit harder by also considering
804 * sums of constraints that involve disjoint sets of variables or
805 * we could consider arbitrary linear combinations of constraints,
806 * although that could potentially be much more expensive as it involves
807 * the solution of an LP problem.
809 * In particular, if v_i is a column vector representing constraint i,
810 * w represents div and e_i is the i-th unit vector, then we are looking
811 * for a solution of the constraints
813 * \sum_i lambda_i v_i = w + \sum_i alpha_i d e_i
815 * with \lambda_i >= 0 and alpha_i of unrestricted sign.
816 * If we are not just interested in a non-negative expression, but
817 * also in one with a minimal range, then we don't just want
818 * c = \sum_i lambda_i v_i to be non-negative over the domain,
819 * but also beta - c = \sum_i mu_i v_i, where beta is a scalar
820 * that we want to minimize and we now also have to take into account
821 * the constant terms of the constraints.
822 * Alternatively, we could first compute the dual of the domain
823 * and plug in the constraints on the coefficients.
825 static int try_extract_mod(struct isl_extract_mod_data
*data
)
835 n
= isl_aff_dim(data
->div
, isl_dim_div
);
839 if (isl_aff_involves_dims(data
->div
, isl_dim_div
, 0, n
))
840 return extract_nonneg_mod(data
);
842 hull
= isl_set_simple_hull(isl_set_copy(data
->build
->domain
));
843 hull
= isl_basic_set_remove_divs(hull
);
846 r
= isl_basic_set_foreach_constraint(hull
, &check_parallel_or_opposite
,
848 isl_basic_set_free(hull
);
850 if (!data
->sign
|| r
< 0) {
851 isl_aff_free(data
->nonneg
);
854 return extract_nonneg_mod(data
);
857 v1
= isl_aff_get_constant_val(data
->div
);
858 v2
= isl_aff_get_constant_val(data
->nonneg
);
859 if (data
->sign
< 0) {
860 v1
= isl_val_neg(v1
);
861 v1
= isl_val_add(v1
, isl_val_copy(data
->d
));
862 v1
= isl_val_sub_ui(v1
, 1);
864 v1
= isl_val_sub(v1
, isl_val_copy(v2
));
865 v1
= isl_val_mod(v1
, isl_val_copy(data
->d
));
866 v1
= isl_val_add(v1
, v2
);
867 v2
= isl_val_div(isl_val_copy(v1
), isl_val_copy(data
->d
));
868 v2
= isl_val_ceil(v2
);
869 if (isl_val_is_neg(v2
)) {
870 v2
= isl_val_mul(v2
, isl_val_copy(data
->d
));
871 v1
= isl_val_sub(v1
, isl_val_copy(v2
));
873 data
->nonneg
= isl_aff_set_constant_val(data
->nonneg
, v1
);
876 if (data
->sign
< 0) {
877 data
->div
= oppose_div_arg(data
->div
, isl_val_copy(data
->d
));
878 data
->v
= isl_val_neg(data
->v
);
881 return extract_term_and_mod(data
,
882 isl_aff_copy(data
->div
), data
->nonneg
);
884 data
->aff
= isl_aff_free(data
->aff
);
888 /* Check if "data->aff" involves any (implicit) modulo computations based
890 * If so, remove them from aff and add expressions corresponding
891 * to those modulo computations to data->pos and/or data->neg.
893 * "aff" is assumed to be an integer affine expression.
895 * In particular, check if (v * div_j) is of the form
897 * f * m * floor(a / m)
899 * and, if so, rewrite it as
901 * f * (a - (a mod m)) = f * a - f * (a mod m)
903 * and extract out -f * (a mod m).
904 * In particular, if f > 0, we add (f * (a mod m)) to *neg.
905 * If f < 0, we add ((-f) * (a mod m)) to *pos.
907 * Note that in order to represent "a mod m" as
909 * (isl_ast_op_pdiv_r, a, m)
911 * we need to make sure that a is non-negative.
912 * If not, we check if "-a + m - 1" is non-negative.
913 * If so, we can rewrite
915 * floor(a/m) = -ceil(-a/m) = -floor((-a + m - 1)/m)
917 * and still extract a modulo.
919 static int extract_modulo(struct isl_extract_mod_data
*data
)
921 data
->div
= isl_aff_get_div(data
->aff
, data
->i
);
922 data
->d
= isl_aff_get_denominator_val(data
->div
);
923 if (isl_val_is_divisible_by(data
->v
, data
->d
)) {
924 data
->div
= isl_aff_scale_val(data
->div
, isl_val_copy(data
->d
));
925 if (try_extract_mod(data
) < 0)
926 data
->aff
= isl_aff_free(data
->aff
);
928 isl_aff_free(data
->div
);
929 isl_val_free(data
->d
);
933 /* Check if "aff" involves any (implicit) modulo computations.
934 * If so, remove them from aff and add expressions corresponding
935 * to those modulo computations to *pos and/or *neg.
936 * We only do this if the option ast_build_prefer_pdiv is set.
938 * "aff" is assumed to be an integer affine expression.
940 * A modulo expression is of the form
942 * a mod m = a - m * floor(a / m)
944 * To detect them in aff, we look for terms of the form
946 * f * m * floor(a / m)
950 * f * (a - (a mod m)) = f * a - f * (a mod m)
952 * and extract out -f * (a mod m).
953 * In particular, if f > 0, we add (f * (a mod m)) to *neg.
954 * If f < 0, we add ((-f) * (a mod m)) to *pos.
956 static __isl_give isl_aff
*extract_modulos(__isl_take isl_aff
*aff
,
957 __isl_keep isl_ast_expr
**pos
, __isl_keep isl_ast_expr
**neg
,
958 __isl_keep isl_ast_build
*build
)
960 struct isl_extract_mod_data data
= { build
, aff
, *pos
, *neg
};
967 ctx
= isl_aff_get_ctx(aff
);
968 if (!isl_options_get_ast_build_prefer_pdiv(ctx
))
971 n
= isl_aff_dim(data
.aff
, isl_dim_div
);
973 return isl_aff_free(aff
);
974 for (data
.i
= 0; data
.i
< n
; ++data
.i
) {
975 data
.v
= isl_aff_get_coefficient_val(data
.aff
,
976 isl_dim_div
, data
.i
);
978 return isl_aff_free(aff
);
979 if (isl_val_is_zero(data
.v
) ||
980 isl_val_is_one(data
.v
) || isl_val_is_negone(data
.v
)) {
981 isl_val_free(data
.v
);
984 if (extract_modulo(&data
) < 0)
985 data
.aff
= isl_aff_free(data
.aff
);
986 isl_val_free(data
.v
);
992 data
.aff
= isl_aff_add(data
.aff
, data
.add
);
999 /* Check if aff involves any non-integer coefficients.
1000 * If so, split aff into
1002 * aff = aff1 + (aff2 / d)
1004 * with both aff1 and aff2 having only integer coefficients.
1005 * Return aff1 and add (aff2 / d) to *expr.
1007 static __isl_give isl_aff
*extract_rational(__isl_take isl_aff
*aff
,
1008 __isl_keep isl_ast_expr
**expr
, __isl_keep isl_ast_build
*build
)
1012 isl_aff
*rat
= NULL
;
1013 isl_local_space
*ls
= NULL
;
1014 isl_ast_expr
*rat_expr
;
1016 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_div
};
1017 enum isl_dim_type l
[] = { isl_dim_param
, isl_dim_set
, isl_dim_div
};
1021 d
= isl_aff_get_denominator_val(aff
);
1024 if (isl_val_is_one(d
)) {
1029 aff
= isl_aff_scale_val(aff
, isl_val_copy(d
));
1031 ls
= isl_aff_get_domain_local_space(aff
);
1032 rat
= isl_aff_zero_on_domain(isl_local_space_copy(ls
));
1034 for (i
= 0; i
< 3; ++i
) {
1035 n
= isl_aff_dim(aff
, t
[i
]);
1038 for (j
= 0; j
< n
; ++j
) {
1041 v
= isl_aff_get_coefficient_val(aff
, t
[i
], j
);
1044 if (isl_val_is_divisible_by(v
, d
)) {
1048 rat_j
= isl_aff_var_on_domain(isl_local_space_copy(ls
),
1050 rat_j
= isl_aff_scale_val(rat_j
, v
);
1051 rat
= isl_aff_add(rat
, rat_j
);
1055 v
= isl_aff_get_constant_val(aff
);
1056 if (isl_val_is_divisible_by(v
, d
)) {
1061 rat_0
= isl_aff_val_on_domain(isl_local_space_copy(ls
), v
);
1062 rat
= isl_aff_add(rat
, rat_0
);
1065 isl_local_space_free(ls
);
1067 aff
= isl_aff_sub(aff
, isl_aff_copy(rat
));
1068 aff
= isl_aff_scale_down_val(aff
, isl_val_copy(d
));
1070 rat_expr
= isl_ast_expr_from_aff(rat
, build
);
1071 rat_expr
= isl_ast_expr_div(rat_expr
, isl_ast_expr_from_val(d
));
1072 *expr
= ast_expr_add(*expr
, rat_expr
);
1077 isl_local_space_free(ls
);
1083 /* Construct an isl_ast_expr that evaluates the affine expression "aff",
1084 * The result is simplified in terms of build->domain.
1086 * We first extract hidden modulo computations from the affine expression
1087 * and then add terms for each variable with a non-zero coefficient.
1088 * Finally, if the affine expression has a non-trivial denominator,
1089 * we divide the resulting isl_ast_expr by this denominator.
1091 __isl_give isl_ast_expr
*isl_ast_expr_from_aff(__isl_take isl_aff
*aff
,
1092 __isl_keep isl_ast_build
*build
)
1097 isl_ctx
*ctx
= isl_aff_get_ctx(aff
);
1098 isl_ast_expr
*expr
, *expr_neg
;
1099 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_div
};
1100 enum isl_dim_type l
[] = { isl_dim_param
, isl_dim_set
, isl_dim_div
};
1101 isl_local_space
*ls
;
1102 struct isl_ast_add_term_data data
;
1107 expr
= isl_ast_expr_alloc_int_si(ctx
, 0);
1108 expr_neg
= isl_ast_expr_alloc_int_si(ctx
, 0);
1110 aff
= extract_rational(aff
, &expr
, build
);
1112 aff
= extract_modulos(aff
, &expr
, &expr_neg
, build
);
1113 expr
= ast_expr_sub(expr
, expr_neg
);
1115 ls
= isl_aff_get_domain_local_space(aff
);
1118 data
.cst
= isl_aff_get_constant_val(aff
);
1119 for (i
= 0; i
< 3; ++i
) {
1120 n
= isl_aff_dim(aff
, t
[i
]);
1122 expr
= isl_ast_expr_free(expr
);
1123 for (j
= 0; j
< n
; ++j
) {
1124 v
= isl_aff_get_coefficient_val(aff
, t
[i
], j
);
1126 expr
= isl_ast_expr_free(expr
);
1127 if (isl_val_is_zero(v
)) {
1131 expr
= isl_ast_expr_add_term(expr
,
1132 ls
, l
[i
], j
, v
, &data
);
1136 expr
= isl_ast_expr_add_int(expr
, data
.cst
);
1138 isl_local_space_free(ls
);
1143 /* Add terms to "expr" for each variable in "aff" with a coefficient
1144 * with sign equal to "sign".
1145 * The result is simplified in terms of data->build->domain.
1147 static __isl_give isl_ast_expr
*add_signed_terms(__isl_take isl_ast_expr
*expr
,
1148 __isl_keep isl_aff
*aff
, int sign
, struct isl_ast_add_term_data
*data
)
1152 enum isl_dim_type t
[] = { isl_dim_param
, isl_dim_in
, isl_dim_div
};
1153 enum isl_dim_type l
[] = { isl_dim_param
, isl_dim_set
, isl_dim_div
};
1154 isl_local_space
*ls
;
1156 ls
= isl_aff_get_domain_local_space(aff
);
1158 for (i
= 0; i
< 3; ++i
) {
1159 isl_size n
= isl_aff_dim(aff
, t
[i
]);
1161 expr
= isl_ast_expr_free(expr
);
1162 for (j
= 0; j
< n
; ++j
) {
1163 v
= isl_aff_get_coefficient_val(aff
, t
[i
], j
);
1164 if (sign
* isl_val_sgn(v
) <= 0) {
1169 expr
= isl_ast_expr_add_term(expr
,
1170 ls
, l
[i
], j
, v
, data
);
1174 isl_local_space_free(ls
);
1179 /* Should the constant term "v" be considered positive?
1181 * A positive constant will be added to "pos" by the caller,
1182 * while a negative constant will be added to "neg".
1183 * If either "pos" or "neg" is exactly zero, then we prefer
1184 * to add the constant "v" to that side, irrespective of the sign of "v".
1185 * This results in slightly shorter expressions and may reduce the risk
1188 static int constant_is_considered_positive(__isl_keep isl_val
*v
,
1189 __isl_keep isl_ast_expr
*pos
, __isl_keep isl_ast_expr
*neg
)
1191 if (ast_expr_is_zero(pos
))
1193 if (ast_expr_is_zero(neg
))
1195 return isl_val_is_pos(v
);
1198 /* Check if the equality
1202 * represents a stride constraint on the integer division "pos".
1204 * In particular, if the integer division "pos" is equal to
1208 * then check if aff is equal to
1214 * If so, the equality is exactly
1218 * Note that in principle we could also accept
1222 * where e and e' differ by a constant.
1224 static int is_stride_constraint(__isl_keep isl_aff
*aff
, int pos
)
1230 div
= isl_aff_get_div(aff
, pos
);
1231 c
= isl_aff_get_coefficient_val(aff
, isl_dim_div
, pos
);
1232 d
= isl_aff_get_denominator_val(div
);
1233 eq
= isl_val_abs_eq(c
, d
);
1234 if (eq
>= 0 && eq
) {
1235 aff
= isl_aff_copy(aff
);
1236 aff
= isl_aff_set_coefficient_si(aff
, isl_dim_div
, pos
, 0);
1237 div
= isl_aff_scale_val(div
, d
);
1238 if (isl_val_is_pos(c
))
1239 div
= isl_aff_neg(div
);
1240 eq
= isl_aff_plain_is_equal(div
, aff
);
1250 /* Are all coefficients of "aff" (zero or) negative?
1252 static isl_bool
all_negative_coefficients(__isl_keep isl_aff
*aff
)
1257 n
= isl_aff_dim(aff
, isl_dim_param
);
1259 return isl_bool_error
;
1260 for (i
= 0; i
< n
; ++i
)
1261 if (isl_aff_coefficient_sgn(aff
, isl_dim_param
, i
) > 0)
1262 return isl_bool_false
;
1264 n
= isl_aff_dim(aff
, isl_dim_in
);
1266 return isl_bool_error
;
1267 for (i
= 0; i
< n
; ++i
)
1268 if (isl_aff_coefficient_sgn(aff
, isl_dim_in
, i
) > 0)
1269 return isl_bool_false
;
1271 return isl_bool_true
;
1274 /* Give an equality of the form
1276 * aff = e - d floor(e/d) = 0
1280 * aff = -e + d floor(e/d) = 0
1282 * with the integer division "pos" equal to floor(e/d),
1283 * construct the AST expression
1285 * (isl_ast_op_eq, (isl_ast_op_zdiv_r, expr(e), expr(d)), expr(0))
1287 * If e only has negative coefficients, then construct
1289 * (isl_ast_op_eq, (isl_ast_op_zdiv_r, expr(-e), expr(d)), expr(0))
1293 static __isl_give isl_ast_expr
*extract_stride_constraint(
1294 __isl_take isl_aff
*aff
, int pos
, __isl_keep isl_ast_build
*build
)
1299 isl_ast_expr
*expr
, *cst
;
1304 ctx
= isl_aff_get_ctx(aff
);
1306 c
= isl_aff_get_coefficient_val(aff
, isl_dim_div
, pos
);
1307 aff
= isl_aff_set_coefficient_si(aff
, isl_dim_div
, pos
, 0);
1309 all_neg
= all_negative_coefficients(aff
);
1311 aff
= isl_aff_free(aff
);
1313 aff
= isl_aff_neg(aff
);
1315 cst
= isl_ast_expr_from_val(isl_val_abs(c
));
1316 expr
= isl_ast_expr_from_aff(aff
, build
);
1318 expr
= isl_ast_expr_alloc_binary(isl_ast_op_zdiv_r
, expr
, cst
);
1319 cst
= isl_ast_expr_alloc_int_si(ctx
, 0);
1320 expr
= isl_ast_expr_alloc_binary(isl_ast_op_eq
, expr
, cst
);
1325 /* Construct an isl_ast_expr that evaluates the condition "constraint",
1326 * The result is simplified in terms of build->domain.
1328 * We first check if the constraint is an equality of the form
1330 * e - d floor(e/d) = 0
1336 * If so, we convert it to
1338 * (isl_ast_op_eq, (isl_ast_op_zdiv_r, expr(e), expr(d)), expr(0))
1340 * Otherwise, let the constraint by either "a >= 0" or "a == 0".
1341 * We first extract hidden modulo computations from "a"
1342 * and then collect all the terms with a positive coefficient in cons_pos
1343 * and the terms with a negative coefficient in cons_neg.
1345 * The result is then of the form
1347 * (isl_ast_op_ge, expr(pos), expr(-neg)))
1351 * (isl_ast_op_eq, expr(pos), expr(-neg)))
1353 * However, if the first expression is an integer constant (and the second
1354 * is not), then we swap the two expressions. This ensures that we construct,
1355 * e.g., "i <= 5" rather than "5 >= i".
1357 * Furthermore, is there are no terms with positive coefficients (or no terms
1358 * with negative coefficients), then the constant term is added to "pos"
1359 * (or "neg"), ignoring the sign of the constant term.
1361 static __isl_give isl_ast_expr
*isl_ast_expr_from_constraint(
1362 __isl_take isl_constraint
*constraint
, __isl_keep isl_ast_build
*build
)
1367 isl_ast_expr
*expr_pos
;
1368 isl_ast_expr
*expr_neg
;
1372 enum isl_ast_op_type type
;
1373 struct isl_ast_add_term_data data
;
1378 aff
= isl_constraint_get_aff(constraint
);
1379 eq
= isl_constraint_is_equality(constraint
);
1380 isl_constraint_free(constraint
);
1382 n
= isl_aff_dim(aff
, isl_dim_div
);
1384 aff
= isl_aff_free(aff
);
1386 for (i
= 0; i
< n
; ++i
) {
1388 is_stride
= is_stride_constraint(aff
, i
);
1392 return extract_stride_constraint(aff
, i
, build
);
1395 ctx
= isl_aff_get_ctx(aff
);
1396 expr_pos
= isl_ast_expr_alloc_int_si(ctx
, 0);
1397 expr_neg
= isl_ast_expr_alloc_int_si(ctx
, 0);
1399 aff
= extract_modulos(aff
, &expr_pos
, &expr_neg
, build
);
1402 data
.cst
= isl_aff_get_constant_val(aff
);
1403 expr_pos
= add_signed_terms(expr_pos
, aff
, 1, &data
);
1404 data
.cst
= isl_val_neg(data
.cst
);
1405 expr_neg
= add_signed_terms(expr_neg
, aff
, -1, &data
);
1406 data
.cst
= isl_val_neg(data
.cst
);
1408 if (constant_is_considered_positive(data
.cst
, expr_pos
, expr_neg
)) {
1409 expr_pos
= isl_ast_expr_add_int(expr_pos
, data
.cst
);
1411 data
.cst
= isl_val_neg(data
.cst
);
1412 expr_neg
= isl_ast_expr_add_int(expr_neg
, data
.cst
);
1415 if (isl_ast_expr_get_type(expr_pos
) == isl_ast_expr_int
&&
1416 isl_ast_expr_get_type(expr_neg
) != isl_ast_expr_int
) {
1417 type
= eq
? isl_ast_op_eq
: isl_ast_op_le
;
1418 expr
= isl_ast_expr_alloc_binary(type
, expr_neg
, expr_pos
);
1420 type
= eq
? isl_ast_op_eq
: isl_ast_op_ge
;
1421 expr
= isl_ast_expr_alloc_binary(type
, expr_pos
, expr_neg
);
1431 /* Wrapper around isl_constraint_cmp_last_non_zero for use
1432 * as a callback to isl_constraint_list_sort.
1433 * If isl_constraint_cmp_last_non_zero cannot tell the constraints
1434 * apart, then use isl_constraint_plain_cmp instead.
1436 static int cmp_constraint(__isl_keep isl_constraint
*a
,
1437 __isl_keep isl_constraint
*b
, void *user
)
1441 cmp
= isl_constraint_cmp_last_non_zero(a
, b
);
1444 return isl_constraint_plain_cmp(a
, b
);
1447 /* Construct an isl_ast_expr that evaluates the conditions defining "bset".
1448 * The result is simplified in terms of build->domain.
1450 * If "bset" is not bounded by any constraint, then we construct
1451 * the expression "1", i.e., "true".
1453 * Otherwise, we sort the constraints, putting constraints that involve
1454 * integer divisions after those that do not, and construct an "and"
1455 * of the ast expressions of the individual constraints.
1457 * Each constraint is added to the generated constraints of the build
1458 * after it has been converted to an AST expression so that it can be used
1459 * to simplify the following constraints. This may change the truth value
1460 * of subsequent constraints that do not satisfy the earlier constraints,
1461 * but this does not affect the outcome of the conjunction as it is
1462 * only true if all the conjuncts are true (no matter in what order
1463 * they are evaluated). In particular, the constraints that do not
1464 * involve integer divisions may serve to simplify some constraints
1465 * that do involve integer divisions.
1467 __isl_give isl_ast_expr
*isl_ast_build_expr_from_basic_set(
1468 __isl_keep isl_ast_build
*build
, __isl_take isl_basic_set
*bset
)
1473 isl_constraint_list
*list
;
1477 list
= isl_basic_set_get_constraint_list(bset
);
1478 isl_basic_set_free(bset
);
1479 list
= isl_constraint_list_sort(list
, &cmp_constraint
, NULL
);
1480 n
= isl_constraint_list_n_constraint(list
);
1484 isl_ctx
*ctx
= isl_constraint_list_get_ctx(list
);
1485 isl_constraint_list_free(list
);
1486 return isl_ast_expr_alloc_int_si(ctx
, 1);
1489 build
= isl_ast_build_copy(build
);
1491 c
= isl_constraint_list_get_constraint(list
, 0);
1492 bset
= isl_basic_set_from_constraint(isl_constraint_copy(c
));
1493 set
= isl_set_from_basic_set(bset
);
1494 res
= isl_ast_expr_from_constraint(c
, build
);
1495 build
= isl_ast_build_restrict_generated(build
, set
);
1497 for (i
= 1; i
< n
; ++i
) {
1500 c
= isl_constraint_list_get_constraint(list
, i
);
1501 bset
= isl_basic_set_from_constraint(isl_constraint_copy(c
));
1502 set
= isl_set_from_basic_set(bset
);
1503 expr
= isl_ast_expr_from_constraint(c
, build
);
1504 build
= isl_ast_build_restrict_generated(build
, set
);
1505 res
= isl_ast_expr_and(res
, expr
);
1508 isl_constraint_list_free(list
);
1509 isl_ast_build_free(build
);
1513 /* Construct an isl_ast_expr that evaluates the conditions defining "set".
1514 * The result is simplified in terms of build->domain.
1516 * If "set" is an (obviously) empty set, then return the expression "0".
1518 * If there are multiple disjuncts in the description of the set,
1519 * then subsequent disjuncts are simplified in a context where
1520 * the previous disjuncts have been removed from build->domain.
1521 * In particular, constraints that ensure that there is no overlap
1522 * with these previous disjuncts, can be removed.
1523 * This is mostly useful for disjuncts that are only defined by
1524 * a single constraint (relative to the build domain) as the opposite
1525 * of that single constraint can then be removed from the other disjuncts.
1526 * In order not to increase the number of disjuncts in the build domain
1527 * after subtracting the previous disjuncts of "set", the simple hull
1528 * is computed after taking the difference with each of these disjuncts.
1529 * This means that constraints that prevent overlap with a union
1530 * of multiple previous disjuncts are not removed.
1532 * "set" lives in the internal schedule space.
1534 __isl_give isl_ast_expr
*isl_ast_build_expr_from_set_internal(
1535 __isl_keep isl_ast_build
*build
, __isl_take isl_set
*set
)
1539 isl_basic_set
*bset
;
1540 isl_basic_set_list
*list
;
1544 list
= isl_set_get_basic_set_list(set
);
1547 n
= isl_basic_set_list_n_basic_set(list
);
1551 isl_ctx
*ctx
= isl_ast_build_get_ctx(build
);
1552 isl_basic_set_list_free(list
);
1553 return isl_ast_expr_from_val(isl_val_zero(ctx
));
1556 domain
= isl_ast_build_get_domain(build
);
1558 bset
= isl_basic_set_list_get_basic_set(list
, 0);
1559 set
= isl_set_from_basic_set(isl_basic_set_copy(bset
));
1560 res
= isl_ast_build_expr_from_basic_set(build
, bset
);
1562 for (i
= 1; i
< n
; ++i
) {
1566 rest
= isl_set_subtract(isl_set_copy(domain
), set
);
1567 rest
= isl_set_from_basic_set(isl_set_simple_hull(rest
));
1568 domain
= isl_set_intersect(domain
, rest
);
1569 bset
= isl_basic_set_list_get_basic_set(list
, i
);
1570 set
= isl_set_from_basic_set(isl_basic_set_copy(bset
));
1571 bset
= isl_basic_set_gist(bset
,
1572 isl_set_simple_hull(isl_set_copy(domain
)));
1573 expr
= isl_ast_build_expr_from_basic_set(build
, bset
);
1574 res
= isl_ast_expr_or(res
, expr
);
1577 isl_set_free(domain
);
1579 isl_basic_set_list_free(list
);
1583 /* Construct an isl_ast_expr that evaluates the conditions defining "set".
1584 * The result is simplified in terms of build->domain.
1586 * If "set" is an (obviously) empty set, then return the expression "0".
1588 * "set" lives in the external schedule space.
1590 * The internal AST expression generation assumes that there are
1591 * no unknown divs, so make sure an explicit representation is available.
1592 * Since the set comes from the outside, it may have constraints that
1593 * are redundant with respect to the build domain. Remove them first.
1595 __isl_give isl_ast_expr
*isl_ast_build_expr_from_set(
1596 __isl_keep isl_ast_build
*build
, __isl_take isl_set
*set
)
1600 needs_map
= isl_ast_build_need_schedule_map(build
);
1601 if (needs_map
< 0) {
1602 set
= isl_set_free(set
);
1603 } else if (needs_map
) {
1605 ma
= isl_ast_build_get_schedule_map_multi_aff(build
);
1606 set
= isl_set_preimage_multi_aff(set
, ma
);
1609 set
= isl_set_compute_divs(set
);
1610 set
= isl_ast_build_compute_gist(build
, set
);
1611 return isl_ast_build_expr_from_set_internal(build
, set
);
1614 /* State of data about previous pieces in
1615 * isl_ast_build_expr_from_pw_aff_internal.
1617 * isl_state_none: no data about previous pieces
1618 * isl_state_single: data about a single previous piece
1619 * isl_state_min: data represents minimum of several pieces
1620 * isl_state_max: data represents maximum of several pieces
1622 enum isl_from_pw_aff_state
{
1629 /* Internal date structure representing a single piece in the input of
1630 * isl_ast_build_expr_from_pw_aff_internal.
1632 * If "state" is isl_state_none, then "set_list" and "aff_list" are not used.
1633 * If "state" is isl_state_single, then "set_list" and "aff_list" contain the
1634 * single previous subpiece.
1635 * If "state" is isl_state_min, then "set_list" and "aff_list" contain
1636 * a sequence of several previous subpieces that are equal to the minimum
1637 * of the entries in "aff_list" over the union of "set_list"
1638 * If "state" is isl_state_max, then "set_list" and "aff_list" contain
1639 * a sequence of several previous subpieces that are equal to the maximum
1640 * of the entries in "aff_list" over the union of "set_list"
1642 * During the construction of the pieces, "set" is NULL.
1643 * After the construction, "set" is set to the union of the elements
1644 * in "set_list", at which point "set_list" is set to NULL.
1646 struct isl_from_pw_aff_piece
{
1647 enum isl_from_pw_aff_state state
;
1649 isl_set_list
*set_list
;
1650 isl_aff_list
*aff_list
;
1653 /* Internal data structure for isl_ast_build_expr_from_pw_aff_internal.
1655 * "build" specifies the domain against which the result is simplified.
1656 * "dom" is the domain of the entire isl_pw_aff.
1658 * "n" is the number of pieces constructed already.
1659 * In particular, during the construction of the pieces, "n" points to
1660 * the piece that is being constructed. After the construction of the
1661 * pieces, "n" is set to the total number of pieces.
1662 * "max" is the total number of allocated entries.
1663 * "p" contains the individual pieces.
1665 struct isl_from_pw_aff_data
{
1666 isl_ast_build
*build
;
1671 struct isl_from_pw_aff_piece
*p
;
1674 /* Initialize "data" based on "build" and "pa".
1676 static isl_stat
isl_from_pw_aff_data_init(struct isl_from_pw_aff_data
*data
,
1677 __isl_keep isl_ast_build
*build
, __isl_keep isl_pw_aff
*pa
)
1682 ctx
= isl_pw_aff_get_ctx(pa
);
1683 n
= isl_pw_aff_n_piece(pa
);
1685 return isl_stat_error
;
1687 isl_die(ctx
, isl_error_invalid
,
1688 "cannot handle void expression", return isl_stat_error
);
1690 data
->p
= isl_calloc_array(ctx
, struct isl_from_pw_aff_piece
, n
);
1692 return isl_stat_error
;
1693 data
->build
= build
;
1694 data
->dom
= isl_pw_aff_domain(isl_pw_aff_copy(pa
));
1700 /* Free all memory allocated for "data".
1702 static void isl_from_pw_aff_data_clear(struct isl_from_pw_aff_data
*data
)
1706 isl_set_free(data
->dom
);
1710 for (i
= 0; i
< data
->max
; ++i
) {
1711 isl_set_free(data
->p
[i
].set
);
1712 isl_set_list_free(data
->p
[i
].set_list
);
1713 isl_aff_list_free(data
->p
[i
].aff_list
);
1718 /* Initialize the current entry of "data" to an unused piece.
1720 static void set_none(struct isl_from_pw_aff_data
*data
)
1722 data
->p
[data
->n
].state
= isl_state_none
;
1723 data
->p
[data
->n
].set_list
= NULL
;
1724 data
->p
[data
->n
].aff_list
= NULL
;
1727 /* Store "set" and "aff" in the current entry of "data" as a single subpiece.
1729 static void set_single(struct isl_from_pw_aff_data
*data
,
1730 __isl_take isl_set
*set
, __isl_take isl_aff
*aff
)
1732 data
->p
[data
->n
].state
= isl_state_single
;
1733 data
->p
[data
->n
].set_list
= isl_set_list_from_set(set
);
1734 data
->p
[data
->n
].aff_list
= isl_aff_list_from_aff(aff
);
1737 /* Extend the current entry of "data" with "set" and "aff"
1738 * as a minimum expression.
1740 static isl_stat
extend_min(struct isl_from_pw_aff_data
*data
,
1741 __isl_take isl_set
*set
, __isl_take isl_aff
*aff
)
1744 data
->p
[n
].state
= isl_state_min
;
1745 data
->p
[n
].set_list
= isl_set_list_add(data
->p
[n
].set_list
, set
);
1746 data
->p
[n
].aff_list
= isl_aff_list_add(data
->p
[n
].aff_list
, aff
);
1748 if (!data
->p
[n
].set_list
|| !data
->p
[n
].aff_list
)
1749 return isl_stat_error
;
1753 /* Extend the current entry of "data" with "set" and "aff"
1754 * as a maximum expression.
1756 static isl_stat
extend_max(struct isl_from_pw_aff_data
*data
,
1757 __isl_take isl_set
*set
, __isl_take isl_aff
*aff
)
1760 data
->p
[n
].state
= isl_state_max
;
1761 data
->p
[n
].set_list
= isl_set_list_add(data
->p
[n
].set_list
, set
);
1762 data
->p
[n
].aff_list
= isl_aff_list_add(data
->p
[n
].aff_list
, aff
);
1764 if (!data
->p
[n
].set_list
|| !data
->p
[n
].aff_list
)
1765 return isl_stat_error
;
1769 /* Extend the domain of the current entry of "data", which is assumed
1770 * to contain a single subpiece, with "set". If "replace" is set,
1771 * then also replace the affine function by "aff". Otherwise,
1772 * simply free "aff".
1774 static isl_stat
extend_domain(struct isl_from_pw_aff_data
*data
,
1775 __isl_take isl_set
*set
, __isl_take isl_aff
*aff
, int replace
)
1780 set_n
= isl_set_list_get_set(data
->p
[n
].set_list
, 0);
1781 set_n
= isl_set_union(set_n
, set
);
1782 data
->p
[n
].set_list
=
1783 isl_set_list_set_set(data
->p
[n
].set_list
, 0, set_n
);
1786 data
->p
[n
].aff_list
=
1787 isl_aff_list_set_aff(data
->p
[n
].aff_list
, 0, aff
);
1791 if (!data
->p
[n
].set_list
|| !data
->p
[n
].aff_list
)
1792 return isl_stat_error
;
1796 /* Construct an isl_ast_expr from "list" within "build".
1797 * If "state" is isl_state_single, then "list" contains a single entry and
1798 * an isl_ast_expr is constructed for that entry.
1799 * Otherwise a min or max expression is constructed from "list"
1800 * depending on "state".
1802 static __isl_give isl_ast_expr
*ast_expr_from_aff_list(
1803 __isl_take isl_aff_list
*list
, enum isl_from_pw_aff_state state
,
1804 __isl_keep isl_ast_build
*build
)
1809 isl_ast_expr
*expr
= NULL
;
1810 enum isl_ast_op_type op_type
;
1812 if (state
== isl_state_single
) {
1813 aff
= isl_aff_list_get_aff(list
, 0);
1814 isl_aff_list_free(list
);
1815 return isl_ast_expr_from_aff(aff
, build
);
1817 n
= isl_aff_list_n_aff(list
);
1820 op_type
= state
== isl_state_min
? isl_ast_op_min
: isl_ast_op_max
;
1821 expr
= isl_ast_expr_alloc_op(isl_ast_build_get_ctx(build
), op_type
, n
);
1825 for (i
= 0; i
< n
; ++i
) {
1826 isl_ast_expr
*expr_i
;
1828 aff
= isl_aff_list_get_aff(list
, i
);
1829 expr_i
= isl_ast_expr_from_aff(aff
, build
);
1832 expr
->u
.op
.args
[i
] = expr_i
;
1835 isl_aff_list_free(list
);
1838 isl_aff_list_free(list
);
1839 isl_ast_expr_free(expr
);
1843 /* Extend the expression in "next" to take into account
1844 * the piece at position "pos" in "data", allowing for a further extension
1845 * for the next piece(s).
1846 * In particular, "next" is set to a select operation that selects
1847 * an isl_ast_expr corresponding to data->aff_list on data->set and
1848 * to an expression that will be filled in by later calls.
1849 * Return a pointer to this location.
1850 * Afterwards, the state of "data" is set to isl_state_none.
1852 * The constraints of data->set are added to the generated
1853 * constraints of the build such that they can be exploited to simplify
1854 * the AST expression constructed from data->aff_list.
1856 static isl_ast_expr
**add_intermediate_piece(struct isl_from_pw_aff_data
*data
,
1857 int pos
, isl_ast_expr
**next
)
1860 isl_ast_build
*build
;
1861 isl_ast_expr
*ternary
, *arg
;
1862 isl_set
*set
, *gist
;
1864 set
= data
->p
[pos
].set
;
1865 data
->p
[pos
].set
= NULL
;
1866 ctx
= isl_ast_build_get_ctx(data
->build
);
1867 ternary
= isl_ast_expr_alloc_op(ctx
, isl_ast_op_select
, 3);
1868 gist
= isl_set_gist(isl_set_copy(set
), isl_set_copy(data
->dom
));
1869 arg
= isl_ast_build_expr_from_set_internal(data
->build
, gist
);
1870 ternary
= isl_ast_expr_set_op_arg(ternary
, 0, arg
);
1871 build
= isl_ast_build_copy(data
->build
);
1872 build
= isl_ast_build_restrict_generated(build
, set
);
1873 arg
= ast_expr_from_aff_list(data
->p
[pos
].aff_list
,
1874 data
->p
[pos
].state
, build
);
1875 data
->p
[pos
].aff_list
= NULL
;
1876 isl_ast_build_free(build
);
1877 ternary
= isl_ast_expr_set_op_arg(ternary
, 1, arg
);
1878 data
->p
[pos
].state
= isl_state_none
;
1883 return &ternary
->u
.op
.args
[2];
1886 /* Extend the expression in "next" to take into account
1887 * the final piece, located at position "pos" in "data".
1888 * In particular, "next" is set to evaluate data->aff_list
1889 * and the domain is ignored.
1890 * Return isl_stat_ok on success and isl_stat_error on failure.
1892 * The constraints of data->set are however added to the generated
1893 * constraints of the build such that they can be exploited to simplify
1894 * the AST expression constructed from data->aff_list.
1896 static isl_stat
add_last_piece(struct isl_from_pw_aff_data
*data
,
1897 int pos
, isl_ast_expr
**next
)
1899 isl_ast_build
*build
;
1901 if (data
->p
[pos
].state
== isl_state_none
)
1902 isl_die(isl_ast_build_get_ctx(data
->build
), isl_error_invalid
,
1903 "cannot handle void expression", return isl_stat_error
);
1905 build
= isl_ast_build_copy(data
->build
);
1906 build
= isl_ast_build_restrict_generated(build
, data
->p
[pos
].set
);
1907 data
->p
[pos
].set
= NULL
;
1908 *next
= ast_expr_from_aff_list(data
->p
[pos
].aff_list
,
1909 data
->p
[pos
].state
, build
);
1910 data
->p
[pos
].aff_list
= NULL
;
1911 isl_ast_build_free(build
);
1912 data
->p
[pos
].state
= isl_state_none
;
1914 return isl_stat_error
;
1919 /* Return -1 if the piece "p1" should be sorted before "p2"
1920 * and 1 if it should be sorted after "p2".
1921 * Return 0 if they do not need to be sorted in a specific order.
1923 * Pieces are sorted according to the number of disjuncts
1926 static int sort_pieces_cmp(const void *p1
, const void *p2
, void *arg
)
1928 const struct isl_from_pw_aff_piece
*piece1
= p1
;
1929 const struct isl_from_pw_aff_piece
*piece2
= p2
;
1932 n1
= isl_set_n_basic_set(piece1
->set
);
1933 n2
= isl_set_n_basic_set(piece2
->set
);
1938 /* Construct an isl_ast_expr from the pieces in "data".
1939 * Return the result or NULL on failure.
1941 * When this function is called, data->n points to the current piece.
1942 * If this is an effective piece, then first increment data->n such
1943 * that data->n contains the number of pieces.
1944 * The "set_list" fields are subsequently replaced by the corresponding
1945 * "set" fields, after which the pieces are sorted according to
1946 * the number of disjuncts in these "set" fields.
1948 * Construct intermediate AST expressions for the initial pieces and
1949 * finish off with the final pieces.
1951 static isl_ast_expr
*build_pieces(struct isl_from_pw_aff_data
*data
)
1954 isl_ast_expr
*res
= NULL
;
1955 isl_ast_expr
**next
= &res
;
1957 if (data
->p
[data
->n
].state
!= isl_state_none
)
1960 isl_die(isl_ast_build_get_ctx(data
->build
), isl_error_invalid
,
1961 "cannot handle void expression", return NULL
);
1963 for (i
= 0; i
< data
->n
; ++i
) {
1964 data
->p
[i
].set
= isl_set_list_union(data
->p
[i
].set_list
);
1965 if (data
->p
[i
].state
!= isl_state_single
)
1966 data
->p
[i
].set
= isl_set_coalesce(data
->p
[i
].set
);
1967 data
->p
[i
].set_list
= NULL
;
1970 if (isl_sort(data
->p
, data
->n
, sizeof(data
->p
[0]),
1971 &sort_pieces_cmp
, NULL
) < 0)
1972 return isl_ast_expr_free(res
);
1974 for (i
= 0; i
+ 1 < data
->n
; ++i
) {
1975 next
= add_intermediate_piece(data
, i
, next
);
1977 return isl_ast_expr_free(res
);
1980 if (add_last_piece(data
, data
->n
- 1, next
) < 0)
1981 return isl_ast_expr_free(res
);
1986 /* Is the domain of the current entry of "data", which is assumed
1987 * to contain a single subpiece, a subset of "set"?
1989 static isl_bool
single_is_subset(struct isl_from_pw_aff_data
*data
,
1990 __isl_keep isl_set
*set
)
1995 set_n
= isl_set_list_get_set(data
->p
[data
->n
].set_list
, 0);
1996 subset
= isl_set_is_subset(set_n
, set
);
1997 isl_set_free(set_n
);
2002 /* Is "aff" a rational expression, i.e., does it have a denominator
2003 * different from one?
2005 static isl_bool
aff_is_rational(__isl_keep isl_aff
*aff
)
2010 den
= isl_aff_get_denominator_val(aff
);
2011 rational
= isl_bool_not(isl_val_is_one(den
));
2017 /* Does "list" consist of a single rational affine expression?
2019 static isl_bool
is_single_rational_aff(__isl_keep isl_aff_list
*list
)
2025 n
= isl_aff_list_n_aff(list
);
2027 return isl_bool_error
;
2029 return isl_bool_false
;
2030 aff
= isl_aff_list_get_aff(list
, 0);
2031 rational
= aff_is_rational(aff
);
2037 /* Can the list of subpieces in the last piece of "data" be extended with
2038 * "set" and "aff" based on "test"?
2039 * In particular, is it the case for each entry (set_i, aff_i) that
2041 * test(aff, aff_i) holds on set_i, and
2042 * test(aff_i, aff) holds on set?
2044 * "test" returns the set of elements where the tests holds, meaning
2045 * that test(aff_i, aff) holds on set if set is a subset of test(aff_i, aff).
2047 * This function is used to detect min/max expressions.
2048 * If the ast_build_detect_min_max option is turned off, then
2049 * do not even try and perform any detection and return false instead.
2051 * Rational affine expressions are not considered for min/max expressions
2052 * since the combined expression will be defined on the union of the domains,
2053 * while a rational expression may only yield integer values
2054 * on its own definition domain.
2056 static isl_bool
extends(struct isl_from_pw_aff_data
*data
,
2057 __isl_keep isl_set
*set
, __isl_keep isl_aff
*aff
,
2058 __isl_give isl_basic_set
*(*test
)(__isl_take isl_aff
*aff1
,
2059 __isl_take isl_aff
*aff2
))
2063 isl_bool is_rational
;
2067 is_rational
= aff_is_rational(aff
);
2068 if (is_rational
>= 0 && !is_rational
)
2069 is_rational
= is_single_rational_aff(data
->p
[data
->n
].aff_list
);
2070 if (is_rational
< 0 || is_rational
)
2071 return isl_bool_not(is_rational
);
2073 ctx
= isl_ast_build_get_ctx(data
->build
);
2074 if (!isl_options_get_ast_build_detect_min_max(ctx
))
2075 return isl_bool_false
;
2077 n
= isl_set_list_n_set(data
->p
[data
->n
].set_list
);
2079 return isl_bool_error
;
2081 dom
= isl_ast_build_get_domain(data
->build
);
2082 set
= isl_set_intersect(dom
, isl_set_copy(set
));
2084 for (i
= 0; i
< n
; ++i
) {
2087 isl_set
*dom
, *required
;
2090 aff_i
= isl_aff_list_get_aff(data
->p
[data
->n
].aff_list
, i
);
2091 valid
= isl_set_from_basic_set(test(isl_aff_copy(aff
), aff_i
));
2092 required
= isl_set_list_get_set(data
->p
[data
->n
].set_list
, i
);
2093 dom
= isl_ast_build_get_domain(data
->build
);
2094 required
= isl_set_intersect(dom
, required
);
2095 is_valid
= isl_set_is_subset(required
, valid
);
2096 isl_set_free(required
);
2097 isl_set_free(valid
);
2098 if (is_valid
< 0 || !is_valid
) {
2103 aff_i
= isl_aff_list_get_aff(data
->p
[data
->n
].aff_list
, i
);
2104 valid
= isl_set_from_basic_set(test(aff_i
, isl_aff_copy(aff
)));
2105 is_valid
= isl_set_is_subset(set
, valid
);
2106 isl_set_free(valid
);
2107 if (is_valid
< 0 || !is_valid
) {
2114 return isl_bool_true
;
2117 /* Can the list of pieces in "data" be extended with "set" and "aff"
2118 * to form/preserve a minimum expression?
2119 * In particular, is it the case for each entry (set_i, aff_i) that
2121 * aff >= aff_i on set_i, and
2122 * aff_i >= aff on set?
2124 static isl_bool
extends_min(struct isl_from_pw_aff_data
*data
,
2125 __isl_keep isl_set
*set
, __isl_keep isl_aff
*aff
)
2127 return extends(data
, set
, aff
, &isl_aff_ge_basic_set
);
2130 /* Can the list of pieces in "data" be extended with "set" and "aff"
2131 * to form/preserve a maximum expression?
2132 * In particular, is it the case for each entry (set_i, aff_i) that
2134 * aff <= aff_i on set_i, and
2135 * aff_i <= aff on set?
2137 static isl_bool
extends_max(struct isl_from_pw_aff_data
*data
,
2138 __isl_keep isl_set
*set
, __isl_keep isl_aff
*aff
)
2140 return extends(data
, set
, aff
, &isl_aff_le_basic_set
);
2143 /* This function is called during the construction of an isl_ast_expr
2144 * that evaluates an isl_pw_aff.
2145 * If the last piece of "data" contains a single subpiece and
2146 * if its affine function is equal to "aff" on a part of the domain
2147 * that includes either "set" or the domain of that single subpiece,
2148 * then extend the domain of that single subpiece with "set".
2149 * If it was the original domain of the single subpiece where
2150 * the two affine functions are equal, then also replace
2151 * the affine function of the single subpiece by "aff".
2152 * If the last piece of "data" contains either a single subpiece
2153 * or a minimum, then check if this minimum expression can be extended
2155 * If so, extend the sequence and return.
2156 * Perform the same operation for maximum expressions.
2157 * If no such extension can be performed, then move to the next piece
2158 * in "data" (if the current piece contains any data), and then store
2159 * the current subpiece in the current piece of "data" for later handling.
2161 static isl_stat
ast_expr_from_pw_aff(__isl_take isl_set
*set
,
2162 __isl_take isl_aff
*aff
, void *user
)
2164 struct isl_from_pw_aff_data
*data
= user
;
2166 enum isl_from_pw_aff_state state
;
2168 state
= data
->p
[data
->n
].state
;
2169 if (state
== isl_state_single
) {
2172 isl_bool subset1
, subset2
= isl_bool_false
;
2173 aff0
= isl_aff_list_get_aff(data
->p
[data
->n
].aff_list
, 0);
2174 eq
= isl_aff_eq_set(isl_aff_copy(aff
), aff0
);
2175 subset1
= isl_set_is_subset(set
, eq
);
2176 if (subset1
>= 0 && !subset1
)
2177 subset2
= single_is_subset(data
, eq
);
2179 if (subset1
< 0 || subset2
< 0)
2182 return extend_domain(data
, set
, aff
, 0);
2184 return extend_domain(data
, set
, aff
, 1);
2186 if (state
== isl_state_single
|| state
== isl_state_min
) {
2187 test
= extends_min(data
, set
, aff
);
2191 return extend_min(data
, set
, aff
);
2193 if (state
== isl_state_single
|| state
== isl_state_max
) {
2194 test
= extends_max(data
, set
, aff
);
2198 return extend_max(data
, set
, aff
);
2200 if (state
!= isl_state_none
)
2202 set_single(data
, set
, aff
);
2208 return isl_stat_error
;
2211 /* Construct an isl_ast_expr that evaluates "pa".
2212 * The result is simplified in terms of build->domain.
2214 * The domain of "pa" lives in the internal schedule space.
2216 __isl_give isl_ast_expr
*isl_ast_build_expr_from_pw_aff_internal(
2217 __isl_keep isl_ast_build
*build
, __isl_take isl_pw_aff
*pa
)
2219 struct isl_from_pw_aff_data data
= { NULL
};
2220 isl_ast_expr
*res
= NULL
;
2222 pa
= isl_ast_build_compute_gist_pw_aff(build
, pa
);
2223 pa
= isl_pw_aff_coalesce(pa
);
2227 if (isl_from_pw_aff_data_init(&data
, build
, pa
) < 0)
2231 if (isl_pw_aff_foreach_piece(pa
, &ast_expr_from_pw_aff
, &data
) >= 0)
2232 res
= build_pieces(&data
);
2234 isl_pw_aff_free(pa
);
2235 isl_from_pw_aff_data_clear(&data
);
2238 isl_pw_aff_free(pa
);
2239 isl_from_pw_aff_data_clear(&data
);
2243 /* Construct an isl_ast_expr that evaluates "pa".
2244 * The result is simplified in terms of build->domain.
2246 * The domain of "pa" lives in the external schedule space.
2248 __isl_give isl_ast_expr
*isl_ast_build_expr_from_pw_aff(
2249 __isl_keep isl_ast_build
*build
, __isl_take isl_pw_aff
*pa
)
2254 needs_map
= isl_ast_build_need_schedule_map(build
);
2255 if (needs_map
< 0) {
2256 pa
= isl_pw_aff_free(pa
);
2257 } else if (needs_map
) {
2259 ma
= isl_ast_build_get_schedule_map_multi_aff(build
);
2260 pa
= isl_pw_aff_pullback_multi_aff(pa
, ma
);
2262 expr
= isl_ast_build_expr_from_pw_aff_internal(build
, pa
);
2266 /* Set the ids of the input dimensions of "mpa" to the iterator ids
2269 * The domain of "mpa" is assumed to live in the internal schedule domain.
2271 static __isl_give isl_multi_pw_aff
*set_iterator_names(
2272 __isl_keep isl_ast_build
*build
, __isl_take isl_multi_pw_aff
*mpa
)
2277 n
= isl_multi_pw_aff_dim(mpa
, isl_dim_in
);
2279 return isl_multi_pw_aff_free(mpa
);
2280 for (i
= 0; i
< n
; ++i
) {
2283 id
= isl_ast_build_get_iterator_id(build
, i
);
2284 mpa
= isl_multi_pw_aff_set_dim_id(mpa
, isl_dim_in
, i
, id
);
2290 /* Construct an isl_ast_expr of type "type" with as first argument "arg0" and
2291 * the remaining arguments derived from "mpa".
2292 * That is, construct a call or access expression that calls/accesses "arg0"
2293 * with arguments/indices specified by "mpa".
2295 static __isl_give isl_ast_expr
*isl_ast_build_with_arguments(
2296 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2297 __isl_take isl_ast_expr
*arg0
, __isl_take isl_multi_pw_aff
*mpa
)
2304 ctx
= isl_ast_build_get_ctx(build
);
2306 n
= isl_multi_pw_aff_dim(mpa
, isl_dim_out
);
2307 expr
= n
>= 0 ? isl_ast_expr_alloc_op(ctx
, type
, 1 + n
) : NULL
;
2308 expr
= isl_ast_expr_set_op_arg(expr
, 0, arg0
);
2309 for (i
= 0; i
< n
; ++i
) {
2313 pa
= isl_multi_pw_aff_get_pw_aff(mpa
, i
);
2314 arg
= isl_ast_build_expr_from_pw_aff_internal(build
, pa
);
2315 expr
= isl_ast_expr_set_op_arg(expr
, 1 + i
, arg
);
2318 isl_multi_pw_aff_free(mpa
);
2322 static __isl_give isl_ast_expr
*isl_ast_build_from_multi_pw_aff_internal(
2323 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2324 __isl_take isl_multi_pw_aff
*mpa
);
2326 /* Construct an isl_ast_expr that accesses the member specified by "mpa".
2327 * The range of "mpa" is assumed to be wrapped relation.
2328 * The domain of this wrapped relation specifies the structure being
2329 * accessed, while the range of this wrapped relation spacifies the
2330 * member of the structure being accessed.
2332 * The domain of "mpa" is assumed to live in the internal schedule domain.
2334 static __isl_give isl_ast_expr
*isl_ast_build_from_multi_pw_aff_member(
2335 __isl_keep isl_ast_build
*build
, __isl_take isl_multi_pw_aff
*mpa
)
2338 isl_multi_pw_aff
*domain
;
2339 isl_ast_expr
*domain_expr
, *expr
;
2340 enum isl_ast_op_type type
= isl_ast_op_access
;
2342 domain
= isl_multi_pw_aff_copy(mpa
);
2343 domain
= isl_multi_pw_aff_range_factor_domain(domain
);
2344 domain_expr
= isl_ast_build_from_multi_pw_aff_internal(build
,
2346 mpa
= isl_multi_pw_aff_range_factor_range(mpa
);
2347 if (!isl_multi_pw_aff_has_tuple_id(mpa
, isl_dim_out
))
2348 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
2349 "missing field name", goto error
);
2350 id
= isl_multi_pw_aff_get_tuple_id(mpa
, isl_dim_out
);
2351 expr
= isl_ast_expr_from_id(id
);
2352 expr
= isl_ast_expr_alloc_binary(isl_ast_op_member
, domain_expr
, expr
);
2353 return isl_ast_build_with_arguments(build
, type
, expr
, mpa
);
2355 isl_multi_pw_aff_free(mpa
);
2359 /* Construct an isl_ast_expr of type "type" that calls or accesses
2360 * the element specified by "mpa".
2361 * The first argument is obtained from the output tuple name.
2362 * The remaining arguments are given by the piecewise affine expressions.
2364 * If the range of "mpa" is a mapped relation, then we assume it
2365 * represents an access to a member of a structure.
2367 * The domain of "mpa" is assumed to live in the internal schedule domain.
2369 static __isl_give isl_ast_expr
*isl_ast_build_from_multi_pw_aff_internal(
2370 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2371 __isl_take isl_multi_pw_aff
*mpa
)
2380 if (type
== isl_ast_op_access
&&
2381 isl_multi_pw_aff_range_is_wrapping(mpa
))
2382 return isl_ast_build_from_multi_pw_aff_member(build
, mpa
);
2384 mpa
= set_iterator_names(build
, mpa
);
2388 ctx
= isl_ast_build_get_ctx(build
);
2390 if (isl_multi_pw_aff_has_tuple_id(mpa
, isl_dim_out
))
2391 id
= isl_multi_pw_aff_get_tuple_id(mpa
, isl_dim_out
);
2393 id
= isl_id_alloc(ctx
, "", NULL
);
2395 expr
= isl_ast_expr_from_id(id
);
2396 return isl_ast_build_with_arguments(build
, type
, expr
, mpa
);
2398 isl_multi_pw_aff_free(mpa
);
2402 /* Construct an isl_ast_expr of type "type" that calls or accesses
2403 * the element specified by "pma".
2404 * The first argument is obtained from the output tuple name.
2405 * The remaining arguments are given by the piecewise affine expressions.
2407 * The domain of "pma" is assumed to live in the internal schedule domain.
2409 static __isl_give isl_ast_expr
*isl_ast_build_from_pw_multi_aff_internal(
2410 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2411 __isl_take isl_pw_multi_aff
*pma
)
2413 isl_multi_pw_aff
*mpa
;
2415 mpa
= isl_multi_pw_aff_from_pw_multi_aff(pma
);
2416 return isl_ast_build_from_multi_pw_aff_internal(build
, type
, mpa
);
2419 /* Construct an isl_ast_expr of type "type" that calls or accesses
2420 * the element specified by "mpa".
2421 * The first argument is obtained from the output tuple name.
2422 * The remaining arguments are given by the piecewise affine expressions.
2424 * The domain of "mpa" is assumed to live in the external schedule domain.
2426 static __isl_give isl_ast_expr
*isl_ast_build_from_multi_pw_aff(
2427 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2428 __isl_take isl_multi_pw_aff
*mpa
)
2433 isl_space
*space_build
, *space_mpa
;
2435 space_build
= isl_ast_build_get_space(build
, 0);
2436 space_mpa
= isl_multi_pw_aff_get_space(mpa
);
2437 is_domain
= isl_space_tuple_is_equal(space_build
, isl_dim_set
,
2438 space_mpa
, isl_dim_in
);
2439 isl_space_free(space_build
);
2440 isl_space_free(space_mpa
);
2444 isl_die(isl_ast_build_get_ctx(build
), isl_error_invalid
,
2445 "spaces don't match", goto error
);
2447 needs_map
= isl_ast_build_need_schedule_map(build
);
2452 ma
= isl_ast_build_get_schedule_map_multi_aff(build
);
2453 mpa
= isl_multi_pw_aff_pullback_multi_aff(mpa
, ma
);
2456 expr
= isl_ast_build_from_multi_pw_aff_internal(build
, type
, mpa
);
2459 isl_multi_pw_aff_free(mpa
);
2463 /* Construct an isl_ast_expr that calls the domain element specified by "mpa".
2464 * The name of the function is obtained from the output tuple name.
2465 * The arguments are given by the piecewise affine expressions.
2467 * The domain of "mpa" is assumed to live in the external schedule domain.
2469 __isl_give isl_ast_expr
*isl_ast_build_call_from_multi_pw_aff(
2470 __isl_keep isl_ast_build
*build
, __isl_take isl_multi_pw_aff
*mpa
)
2472 return isl_ast_build_from_multi_pw_aff(build
, isl_ast_op_call
, mpa
);
2475 /* Construct an isl_ast_expr that accesses the array element specified by "mpa".
2476 * The name of the array is obtained from the output tuple name.
2477 * The index expressions are given by the piecewise affine expressions.
2479 * The domain of "mpa" is assumed to live in the external schedule domain.
2481 __isl_give isl_ast_expr
*isl_ast_build_access_from_multi_pw_aff(
2482 __isl_keep isl_ast_build
*build
, __isl_take isl_multi_pw_aff
*mpa
)
2484 return isl_ast_build_from_multi_pw_aff(build
, isl_ast_op_access
, mpa
);
2487 /* Construct an isl_ast_expr of type "type" that calls or accesses
2488 * the element specified by "pma".
2489 * The first argument is obtained from the output tuple name.
2490 * The remaining arguments are given by the piecewise affine expressions.
2492 * The domain of "pma" is assumed to live in the external schedule domain.
2494 static __isl_give isl_ast_expr
*isl_ast_build_from_pw_multi_aff(
2495 __isl_keep isl_ast_build
*build
, enum isl_ast_op_type type
,
2496 __isl_take isl_pw_multi_aff
*pma
)
2498 isl_multi_pw_aff
*mpa
;
2500 mpa
= isl_multi_pw_aff_from_pw_multi_aff(pma
);
2501 return isl_ast_build_from_multi_pw_aff(build
, type
, mpa
);
2504 /* Construct an isl_ast_expr that calls the domain element specified by "pma".
2505 * The name of the function is obtained from the output tuple name.
2506 * The arguments are given by the piecewise affine expressions.
2508 * The domain of "pma" is assumed to live in the external schedule domain.
2510 __isl_give isl_ast_expr
*isl_ast_build_call_from_pw_multi_aff(
2511 __isl_keep isl_ast_build
*build
, __isl_take isl_pw_multi_aff
*pma
)
2513 return isl_ast_build_from_pw_multi_aff(build
, isl_ast_op_call
, pma
);
2516 /* Construct an isl_ast_expr that accesses the array element specified by "pma".
2517 * The name of the array is obtained from the output tuple name.
2518 * The index expressions are given by the piecewise affine expressions.
2520 * The domain of "pma" is assumed to live in the external schedule domain.
2522 __isl_give isl_ast_expr
*isl_ast_build_access_from_pw_multi_aff(
2523 __isl_keep isl_ast_build
*build
, __isl_take isl_pw_multi_aff
*pma
)
2525 return isl_ast_build_from_pw_multi_aff(build
, isl_ast_op_access
, pma
);
2528 /* Construct an isl_ast_expr that calls the domain element
2529 * specified by "executed".
2531 * "executed" is assumed to be single-valued, with a domain that lives
2532 * in the internal schedule space.
2534 __isl_give isl_ast_node
*isl_ast_build_call_from_executed(
2535 __isl_keep isl_ast_build
*build
, __isl_take isl_map
*executed
)
2537 isl_pw_multi_aff
*iteration
;
2540 iteration
= isl_pw_multi_aff_from_map(executed
);
2541 iteration
= isl_ast_build_compute_gist_pw_multi_aff(build
, iteration
);
2542 iteration
= isl_pw_multi_aff_intersect_domain(iteration
,
2543 isl_ast_build_get_domain(build
));
2544 expr
= isl_ast_build_from_pw_multi_aff_internal(build
, isl_ast_op_call
,
2546 return isl_ast_node_alloc_user(expr
);