1 /* Interchange heuristics and transform for loop interchange on
2 polyhedral representation.
4 Copyright (C) 2009-2015 Free Software Foundation, Inc.
5 Contributed by Sebastian Pop <sebastian.pop@amd.com> and
6 Harsha Jagasia <harsha.jagasia@amd.com>.
8 This file is part of GCC.
10 GCC is free software; you can redistribute it and/or modify
11 it under the terms of the GNU General Public License as published by
12 the Free Software Foundation; either version 3, or (at your option)
15 GCC is distributed in the hope that it will be useful,
16 but WITHOUT ANY WARRANTY; without even the implied warranty of
17 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 GNU General Public License for more details.
20 You should have received a copy of the GNU General Public License
21 along with GCC; see the file COPYING3. If not see
22 <http://www.gnu.org/licenses/>. */
30 #include <isl/union_map.h>
34 /* Since ISL-0.13, the extern is in val_gmp.h. */
35 #if !defined(HAVE_ISL_SCHED_CONSTRAINTS_COMPUTE_SCHEDULE) && defined(__cplusplus)
38 #include <isl/val_gmp.h>
39 #if !defined(HAVE_ISL_SCHED_CONSTRAINTS_COMPUTE_SCHEDULE) && defined(__cplusplus)
45 #include "coretypes.h"
51 #include "fold-const.h"
54 #include "hard-reg-set.h"
57 #include "dominance.h"
59 #include "basic-block.h"
60 #include "tree-ssa-alias.h"
61 #include "internal-fn.h"
62 #include "gimple-expr.h"
65 #include "gimple-iterator.h"
66 #include "tree-ssa-loop.h"
69 #include "tree-chrec.h"
70 #include "tree-data-ref.h"
71 #include "tree-scalar-evolution.h"
75 #include "graphite-poly.h"
77 /* XXX isl rewrite following comment */
78 /* Builds a linear expression, of dimension DIM, representing PDR's
81 L = r_{n}*r_{n-1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n-1} + s_{n}.
83 For an array A[10][20] with two subscript locations s0 and s1, the
84 linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0
85 corresponds to a memory stride of 20.
87 OFFSET is a number of dimensions to prepend before the
88 subscript dimensions: s_0, s_1, ..., s_n.
90 Thus, the final linear expression has the following format:
91 0 .. 0_{offset} | 0 .. 0_{nit} | 0 .. 0_{gd} | 0 | c_0 c_1 ... c_n
92 where the expression itself is:
93 c_0 * s_0 + c_1 * s_1 + ... c_n * s_n. */
95 static isl_constraint
*
96 build_linearized_memory_access (isl_map
*map
, poly_dr_p pdr
)
99 isl_local_space
*ls
= isl_local_space_from_space (isl_map_get_space (map
));
100 unsigned offset
, nsubs
;
104 isl_val
*size
, *subsize
, *size1
;
106 res
= isl_equality_alloc (ls
);
107 ctx
= isl_local_space_get_ctx (ls
);
108 size
= isl_val_int_from_ui (ctx
, 1);
110 nsubs
= isl_set_dim (pdr
->extent
, isl_dim_set
);
111 /* -1 for the already included L dimension. */
112 offset
= isl_map_dim (map
, isl_dim_out
) - 1 - nsubs
;
113 res
= isl_constraint_set_coefficient_si (res
, isl_dim_out
, offset
+ nsubs
, -1);
114 /* Go through all subscripts from last to first. First dimension
115 is the alias set, ignore it. */
116 for (i
= nsubs
- 1; i
>= 1; i
--)
121 size1
= isl_val_copy (size
);
122 res
= isl_constraint_set_coefficient_val (res
, isl_dim_out
, offset
+ i
, size
);
123 dc
= isl_set_get_space (pdr
->extent
);
124 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
125 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, i
, 1);
126 subsize
= isl_set_max_val (pdr
->extent
, aff
);
128 size
= isl_val_mul (size1
, subsize
);
136 /* Set STRIDE to the stride of PDR in memory by advancing by one in
137 the loop at DEPTH. */
140 pdr_stride_in_loop (mpz_t stride
, graphite_dim_t depth
, poly_dr_p pdr
)
142 poly_bb_p pbb
= PDR_PBB (pdr
);
147 isl_constraint
*lma
, *c
;
149 graphite_dim_t time_depth
;
152 /* XXX isl rewrite following comments. */
153 /* Builds a partial difference equations and inserts them
154 into pointset powerset polyhedron P. Polyhedron is assumed
155 to have the format: T|I|T'|I'|G|S|S'|l1|l2.
157 TIME_DEPTH is the time dimension w.r.t. which we are
159 OFFSET represents the number of dimensions between
160 columns t_{time_depth} and t'_{time_depth}.
161 DIM_SCTR is the number of scattering dimensions. It is
162 essentially the dimensionality of the T vector.
164 The following equations are inserted into the polyhedron P:
167 | t_{time_depth-1} = t'_{time_depth-1}
168 | t_{time_depth} = t'_{time_depth} + 1
169 | t_{time_depth+1} = t'_{time_depth + 1}
171 | t_{dim_sctr} = t'_{dim_sctr}. */
173 /* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
174 This is the core part of this alogrithm, since this
175 constraint asks for the memory access stride (difference)
176 between two consecutive points in time dimensions. */
181 | t_{time_depth-1} = t'_{time_depth-1}
182 | t_{time_depth+1} = t'_{time_depth+1}
184 | t_{dim_sctr} = t'_{dim_sctr}
186 This means that all the time dimensions are equal except for
187 time_depth, where the constraint is t_{depth} = t'_{depth} + 1
188 step. More to this: we should be careful not to add equalities
189 to the 'coupled' dimensions, which happens when the one dimension
190 is stripmined dimension, and the other dimension corresponds
191 to the point loop inside stripmined dimension. */
193 /* pdr->accesses: [P1..nb_param,I1..nb_domain]->[a,S1..nb_subscript]
194 ??? [P] not used for PDRs?
195 pdr->extent: [a,S1..nb_subscript]
196 pbb->domain: [P1..nb_param,I1..nb_domain]
197 pbb->transformed: [P1..nb_param,I1..nb_domain]->[T1..Tnb_sctr]
198 [T] includes local vars (currently unused)
200 First we create [P,I] -> [T,a,S]. */
202 map
= isl_map_flat_range_product (isl_map_copy (pbb
->transformed
),
203 isl_map_copy (pdr
->accesses
));
204 /* Add a dimension for L: [P,I] -> [T,a,S,L].*/
205 map
= isl_map_add_dims (map
, isl_dim_out
, 1);
206 /* Build a constraint for "lma[S] - L == 0", effectively calculating
207 L in terms of subscripts. */
208 lma
= build_linearized_memory_access (map
, pdr
);
209 /* And add it to the map, so we now have:
210 [P,I] -> [T,a,S,L] : lma([S]) == L. */
211 map
= isl_map_add_constraint (map
, lma
);
213 /* Then we create [P,I,P',I'] -> [T,a,S,L,T',a',S',L']. */
214 map
= isl_map_flat_product (map
, isl_map_copy (map
));
216 /* Now add the equality T[time_depth] == T'[time_depth]+1. This will
217 force L' to be the linear address at T[time_depth] + 1. */
218 time_depth
= psct_dynamic_dim (pbb
, depth
);
219 /* Length of [a,S] plus [L] ... */
220 offset
= 1 + isl_map_dim (pdr
->accesses
, isl_dim_out
);
222 offset
+= isl_map_dim (pbb
->transformed
, isl_dim_out
);
224 c
= isl_equality_alloc (isl_local_space_from_space (isl_map_get_space (map
)));
225 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
, time_depth
, 1);
226 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
,
227 offset
+ time_depth
, -1);
228 c
= isl_constraint_set_constant_si (c
, 1);
229 map
= isl_map_add_constraint (map
, c
);
231 /* Now we equate most of the T/T' elements (making PITaSL nearly
232 the same is (PITaSL)', except for one dimension, namely for 'depth'
233 (an index into [I]), after translating to index into [T]. Take care
234 to not produce an empty map, which indicates we wanted to equate
235 two dimensions that are already coupled via the above time_depth
236 dimension. Happens with strip mining where several scatter dimension
237 are interdependend. */
239 nt
= pbb_nb_scattering_transform (pbb
) + pbb_nb_local_vars (pbb
);
240 for (i
= 0; i
< nt
; i
++)
243 isl_map
*temp
= isl_map_equate (isl_map_copy (map
),
245 isl_dim_out
, offset
+ i
);
246 if (isl_map_is_empty (temp
))
255 /* Now maximize the expression L' - L. */
256 set
= isl_map_range (map
);
257 dc
= isl_set_get_space (set
);
258 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
259 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
- 1, -1);
260 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
+ offset
- 1, 1);
261 islstride
= isl_set_max_val (set
, aff
);
262 isl_val_get_num_gmp (islstride
, stride
);
263 isl_val_free (islstride
);
267 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
269 gmp_fprintf (dump_file
, "\nStride in BB_%d, DR_%d, depth %d: %Zd ",
270 pbb_index (pbb
), PDR_ID (pdr
), (int) depth
, stride
);
274 /* Sets STRIDES to the sum of all the strides of the data references
275 accessed in LOOP at DEPTH. */
278 memory_strides_in_loop_1 (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
288 FOR_EACH_VEC_ELT (LST_SEQ (loop
), j
, l
)
290 memory_strides_in_loop_1 (l
, depth
, strides
);
292 FOR_EACH_VEC_ELT (PBB_DRS (LST_PBB (l
)), i
, pdr
)
294 pdr_stride_in_loop (s
, depth
, pdr
);
295 mpz_set_si (n
, PDR_NB_REFS (pdr
));
297 mpz_add (strides
, strides
, s
);
304 /* Sets STRIDES to the sum of all the strides of the data references
305 accessed in LOOP at DEPTH. */
308 memory_strides_in_loop (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
310 if (mpz_cmp_si (loop
->memory_strides
, -1) == 0)
312 mpz_set_si (strides
, 0);
313 memory_strides_in_loop_1 (loop
, depth
, strides
);
316 mpz_set (strides
, loop
->memory_strides
);
319 /* Return true when the interchange of loops LOOP1 and LOOP2 is
332 | for (i = 0; i < N; i++)
333 | for (j = 0; j < N; j++)
339 The data access A[j][i] is described like this:
347 | 0 0 0 0 -1 0 100 >= 0
348 | 0 0 0 0 0 -1 100 >= 0
350 The linearized memory access L to A[100][100] is:
355 TODO: the shown format is not valid as it does not show the fact
356 that the iteration domain "i j" is transformed using the scattering.
358 Next, to measure the impact of iterating once in loop "i", we build
359 a maximization problem: first, we add to DR accesses the dimensions
360 k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
361 L1 and L2 are the linearized memory access functions.
363 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
364 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
365 | 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
366 |-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
367 | 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
368 | 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
369 | 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
370 | 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
371 | 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
373 Then, we generate the polyhedron P2 by interchanging the dimensions
374 (s0, s2), (s1, s3), (L1, L2), (k, i)
376 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
377 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
378 | 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
379 | 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
380 | 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
381 | 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
382 | 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
383 | 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
384 | 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
386 then we add to P2 the equality k = i + 1:
388 |-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
390 and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
392 Similarly, to determine the impact of one iteration on loop "j", we
393 interchange (k, j), we add "k = j + 1", and we compute D2 the
394 maximal value of the difference.
396 Finally, the profitability test is D1 < D2: if in the outer loop
397 the strides are smaller than in the inner loop, then it is
398 profitable to interchange the loops at DEPTH1 and DEPTH2. */
401 lst_interchange_profitable_p (lst_p nest
, int depth1
, int depth2
)
406 gcc_assert (depth1
< depth2
);
411 memory_strides_in_loop (nest
, depth1
, d1
);
412 memory_strides_in_loop (nest
, depth2
, d2
);
414 res
= mpz_cmp (d1
, d2
) < 0;
422 /* Interchanges the loops at DEPTH1 and DEPTH2 of the original
423 scattering and assigns the resulting polyhedron to the transformed
427 pbb_interchange_loop_depths (graphite_dim_t depth1
, graphite_dim_t depth2
,
431 unsigned dim1
= psct_dynamic_dim (pbb
, depth1
);
432 unsigned dim2
= psct_dynamic_dim (pbb
, depth2
);
433 isl_space
*d
= isl_map_get_space (pbb
->transformed
);
434 isl_space
*d1
= isl_space_range (d
);
435 unsigned n
= isl_space_dim (d1
, isl_dim_out
);
436 isl_space
*d2
= isl_space_add_dims (d1
, isl_dim_in
, n
);
437 isl_map
*x
= isl_map_universe (d2
);
439 x
= isl_map_equate (x
, isl_dim_in
, dim1
, isl_dim_out
, dim2
);
440 x
= isl_map_equate (x
, isl_dim_in
, dim2
, isl_dim_out
, dim1
);
442 for (i
= 0; i
< n
; i
++)
443 if (i
!= dim1
&& i
!= dim2
)
444 x
= isl_map_equate (x
, isl_dim_in
, i
, isl_dim_out
, i
);
446 pbb
->transformed
= isl_map_apply_range (pbb
->transformed
, x
);
449 /* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
450 the statements below LST. */
453 lst_apply_interchange (lst_p lst
, int depth1
, int depth2
)
458 if (LST_LOOP_P (lst
))
463 FOR_EACH_VEC_ELT (LST_SEQ (lst
), i
, l
)
464 lst_apply_interchange (l
, depth1
, depth2
);
467 pbb_interchange_loop_depths (depth1
, depth2
, LST_PBB (lst
));
470 /* Return true when the nest starting at LOOP1 and ending on LOOP2 is
471 perfect: i.e. there are no sequence of statements. */
474 lst_perfectly_nested_p (lst_p loop1
, lst_p loop2
)
479 if (!LST_LOOP_P (loop1
))
482 return LST_SEQ (loop1
).length () == 1
483 && lst_perfectly_nested_p (LST_SEQ (loop1
)[0], loop2
);
486 /* Transform the loop nest between LOOP1 and LOOP2 into a perfect
487 nest. To continue the naming tradition, this function is called
488 after perfect_nestify. NEST is set to the perfectly nested loop
489 that is created. BEFORE/AFTER are set to the loops distributed
490 before/after the loop NEST. */
493 lst_perfect_nestify (lst_p loop1
, lst_p loop2
, lst_p
*before
,
494 lst_p
*nest
, lst_p
*after
)
496 poly_bb_p first
, last
;
498 gcc_assert (loop1
&& loop2
500 && LST_LOOP_P (loop1
) && LST_LOOP_P (loop2
));
502 first
= LST_PBB (lst_find_first_pbb (loop2
));
503 last
= LST_PBB (lst_find_last_pbb (loop2
));
505 *before
= copy_lst (loop1
);
506 *nest
= copy_lst (loop1
);
507 *after
= copy_lst (loop1
);
509 lst_remove_all_before_including_pbb (*before
, first
, false);
510 lst_remove_all_before_including_pbb (*after
, last
, true);
512 lst_remove_all_before_excluding_pbb (*nest
, first
, true);
513 lst_remove_all_before_excluding_pbb (*nest
, last
, false);
515 if (lst_empty_p (*before
))
520 if (lst_empty_p (*after
))
525 if (lst_empty_p (*nest
))
532 /* Try to interchange LOOP1 with LOOP2 for all the statements of the
533 body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
537 lst_try_interchange_loops (scop_p scop
, lst_p loop1
, lst_p loop2
)
539 int depth1
= lst_depth (loop1
);
540 int depth2
= lst_depth (loop2
);
543 lst_p before
= NULL
, nest
= NULL
, after
= NULL
;
545 if (!lst_perfectly_nested_p (loop1
, loop2
))
546 lst_perfect_nestify (loop1
, loop2
, &before
, &nest
, &after
);
548 if (!lst_interchange_profitable_p (loop2
, depth1
, depth2
))
551 lst_apply_interchange (loop2
, depth1
, depth2
);
553 /* Sync the transformed LST information and the PBB scatterings
554 before using the scatterings in the data dependence analysis. */
555 if (before
|| nest
|| after
)
557 transformed
= lst_substitute_3 (SCOP_TRANSFORMED_SCHEDULE (scop
), loop1
,
558 before
, nest
, after
);
559 lst_update_scattering (transformed
);
560 free_lst (transformed
);
563 if (graphite_legal_transform (scop
))
565 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
567 "Loops at depths %d and %d will be interchanged.\n",
570 /* Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP. */
571 lst_insert_in_sequence (before
, loop1
, true);
572 lst_insert_in_sequence (after
, loop1
, false);
576 lst_replace (loop1
, nest
);
583 /* Undo the transform. */
587 lst_apply_interchange (loop2
, depth2
, depth1
);
591 /* Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged
592 with the loop OUTER in LST_SEQ (OUTER_FATHER). */
595 lst_interchange_select_inner (scop_p scop
, lst_p outer_father
, int outer
,
601 gcc_assert (outer_father
602 && LST_LOOP_P (outer_father
)
603 && LST_LOOP_P (LST_SEQ (outer_father
)[outer
])
605 && LST_LOOP_P (inner_father
));
607 loop1
= LST_SEQ (outer_father
)[outer
];
609 FOR_EACH_VEC_ELT (LST_SEQ (inner_father
), inner
, loop2
)
610 if (LST_LOOP_P (loop2
)
611 && (lst_try_interchange_loops (scop
, loop1
, loop2
)
612 || lst_interchange_select_inner (scop
, outer_father
, outer
, loop2
)))
618 /* Interchanges all the loops of LOOP and the loops of its body that
619 are considered profitable to interchange. Return the number of
620 interchanged loops. OUTER is the index in LST_SEQ (LOOP) that
621 points to the next outer loop to be considered for interchange. */
624 lst_interchange_select_outer (scop_p scop
, lst_p loop
, int outer
)
631 if (!loop
|| !LST_LOOP_P (loop
))
634 father
= LST_LOOP_FATHER (loop
);
637 while (lst_interchange_select_inner (scop
, father
, outer
, loop
))
640 loop
= LST_SEQ (father
)[outer
];
644 if (LST_LOOP_P (loop
))
645 FOR_EACH_VEC_ELT (LST_SEQ (loop
), i
, l
)
647 res
+= lst_interchange_select_outer (scop
, l
, i
);
652 /* Interchanges all the loop depths that are considered profitable for
653 SCOP. Return the number of interchanged loops. */
656 scop_do_interchange (scop_p scop
)
658 int res
= lst_interchange_select_outer
659 (scop
, SCOP_TRANSFORMED_SCHEDULE (scop
), 0);
661 lst_update_scattering (SCOP_TRANSFORMED_SCHEDULE (scop
));