1 /* Interchange heuristics and transform for loop interchange on
2 polyhedral representation.
4 Copyright (C) 2009-2013 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>
32 #include <cloog/cloog.h>
33 #include <cloog/isl/domain.h>
37 #include "coretypes.h"
40 #include "gimple-iterator.h"
41 #include "tree-ssa-loop.h"
44 #include "tree-chrec.h"
45 #include "tree-data-ref.h"
46 #include "tree-scalar-evolution.h"
50 #include "graphite-poly.h"
52 /* XXX isl rewrite following comment */
53 /* Builds a linear expression, of dimension DIM, representing PDR's
56 L = r_{n}*r_{n-1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n-1} + s_{n}.
58 For an array A[10][20] with two subscript locations s0 and s1, the
59 linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0
60 corresponds to a memory stride of 20.
62 OFFSET is a number of dimensions to prepend before the
63 subscript dimensions: s_0, s_1, ..., s_n.
65 Thus, the final linear expression has the following format:
66 0 .. 0_{offset} | 0 .. 0_{nit} | 0 .. 0_{gd} | 0 | c_0 c_1 ... c_n
67 where the expression itself is:
68 c_0 * s_0 + c_1 * s_1 + ... c_n * s_n. */
70 static isl_constraint
*
71 build_linearized_memory_access (isl_map
*map
, poly_dr_p pdr
)
74 isl_local_space
*ls
= isl_local_space_from_space (isl_map_get_space (map
));
75 unsigned offset
, nsubs
;
77 isl_int size
, subsize
;
79 res
= isl_equality_alloc (ls
);
81 isl_int_set_ui (size
, 1);
82 isl_int_init (subsize
);
83 isl_int_set_ui (subsize
, 1);
85 nsubs
= isl_set_dim (pdr
->extent
, isl_dim_set
);
86 /* -1 for the already included L dimension. */
87 offset
= isl_map_dim (map
, isl_dim_out
) - 1 - nsubs
;
88 res
= isl_constraint_set_coefficient_si (res
, isl_dim_out
, offset
+ nsubs
, -1);
89 /* Go through all subscripts from last to first. First dimension
90 is the alias set, ignore it. */
91 for (i
= nsubs
- 1; i
>= 1; i
--)
96 res
= isl_constraint_set_coefficient (res
, isl_dim_out
, offset
+ i
, size
);
98 dc
= isl_set_get_space (pdr
->extent
);
99 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
100 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, i
, 1);
101 isl_set_max (pdr
->extent
, aff
, &subsize
);
103 isl_int_mul (size
, size
, subsize
);
106 isl_int_clear (subsize
);
107 isl_int_clear (size
);
112 /* Set STRIDE to the stride of PDR in memory by advancing by one in
113 the loop at DEPTH. */
116 pdr_stride_in_loop (mpz_t stride
, graphite_dim_t depth
, poly_dr_p pdr
)
118 poly_bb_p pbb
= PDR_PBB (pdr
);
123 isl_constraint
*lma
, *c
;
125 graphite_dim_t time_depth
;
128 /* XXX isl rewrite following comments. */
129 /* Builds a partial difference equations and inserts them
130 into pointset powerset polyhedron P. Polyhedron is assumed
131 to have the format: T|I|T'|I'|G|S|S'|l1|l2.
133 TIME_DEPTH is the time dimension w.r.t. which we are
135 OFFSET represents the number of dimensions between
136 columns t_{time_depth} and t'_{time_depth}.
137 DIM_SCTR is the number of scattering dimensions. It is
138 essentially the dimensionality of the T vector.
140 The following equations are inserted into the polyhedron P:
143 | t_{time_depth-1} = t'_{time_depth-1}
144 | t_{time_depth} = t'_{time_depth} + 1
145 | t_{time_depth+1} = t'_{time_depth + 1}
147 | t_{dim_sctr} = t'_{dim_sctr}. */
149 /* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
150 This is the core part of this alogrithm, since this
151 constraint asks for the memory access stride (difference)
152 between two consecutive points in time dimensions. */
157 | t_{time_depth-1} = t'_{time_depth-1}
158 | t_{time_depth+1} = t'_{time_depth+1}
160 | t_{dim_sctr} = t'_{dim_sctr}
162 This means that all the time dimensions are equal except for
163 time_depth, where the constraint is t_{depth} = t'_{depth} + 1
164 step. More to this: we should be careful not to add equalities
165 to the 'coupled' dimensions, which happens when the one dimension
166 is stripmined dimension, and the other dimension corresponds
167 to the point loop inside stripmined dimension. */
169 /* pdr->accesses: [P1..nb_param,I1..nb_domain]->[a,S1..nb_subscript]
170 ??? [P] not used for PDRs?
171 pdr->extent: [a,S1..nb_subscript]
172 pbb->domain: [P1..nb_param,I1..nb_domain]
173 pbb->transformed: [P1..nb_param,I1..nb_domain]->[T1..Tnb_sctr]
174 [T] includes local vars (currently unused)
176 First we create [P,I] -> [T,a,S]. */
178 map
= isl_map_flat_range_product (isl_map_copy (pbb
->transformed
),
179 isl_map_copy (pdr
->accesses
));
180 /* Add a dimension for L: [P,I] -> [T,a,S,L].*/
181 map
= isl_map_add_dims (map
, isl_dim_out
, 1);
182 /* Build a constraint for "lma[S] - L == 0", effectively calculating
183 L in terms of subscripts. */
184 lma
= build_linearized_memory_access (map
, pdr
);
185 /* And add it to the map, so we now have:
186 [P,I] -> [T,a,S,L] : lma([S]) == L. */
187 map
= isl_map_add_constraint (map
, lma
);
189 /* Then we create [P,I,P',I'] -> [T,a,S,L,T',a',S',L']. */
190 map
= isl_map_flat_product (map
, isl_map_copy (map
));
192 /* Now add the equality T[time_depth] == T'[time_depth]+1. This will
193 force L' to be the linear address at T[time_depth] + 1. */
194 time_depth
= psct_dynamic_dim (pbb
, depth
);
195 /* Length of [a,S] plus [L] ... */
196 offset
= 1 + isl_map_dim (pdr
->accesses
, isl_dim_out
);
198 offset
+= isl_map_dim (pbb
->transformed
, isl_dim_out
);
200 c
= isl_equality_alloc (isl_local_space_from_space (isl_map_get_space (map
)));
201 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
, time_depth
, 1);
202 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
,
203 offset
+ time_depth
, -1);
204 c
= isl_constraint_set_constant_si (c
, 1);
205 map
= isl_map_add_constraint (map
, c
);
207 /* Now we equate most of the T/T' elements (making PITaSL nearly
208 the same is (PITaSL)', except for one dimension, namely for 'depth'
209 (an index into [I]), after translating to index into [T]. Take care
210 to not produce an empty map, which indicates we wanted to equate
211 two dimensions that are already coupled via the above time_depth
212 dimension. Happens with strip mining where several scatter dimension
213 are interdependend. */
215 nt
= pbb_nb_scattering_transform (pbb
) + pbb_nb_local_vars (pbb
);
216 for (i
= 0; i
< nt
; i
++)
219 isl_map
*temp
= isl_map_equate (isl_map_copy (map
),
221 isl_dim_out
, offset
+ i
);
222 if (isl_map_is_empty (temp
))
231 /* Now maximize the expression L' - L. */
232 set
= isl_map_range (map
);
233 dc
= isl_set_get_space (set
);
234 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
235 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
- 1, -1);
236 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
+ offset
- 1, 1);
237 isl_int_init (islstride
);
238 isl_set_max (set
, aff
, &islstride
);
239 isl_int_get_gmp (islstride
, stride
);
240 isl_int_clear (islstride
);
244 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
246 gmp_fprintf (dump_file
, "\nStride in BB_%d, DR_%d, depth %d: %Zd ",
247 pbb_index (pbb
), PDR_ID (pdr
), (int) depth
, stride
);
251 /* Sets STRIDES to the sum of all the strides of the data references
252 accessed in LOOP at DEPTH. */
255 memory_strides_in_loop_1 (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
265 FOR_EACH_VEC_ELT (LST_SEQ (loop
), j
, l
)
267 memory_strides_in_loop_1 (l
, depth
, strides
);
269 FOR_EACH_VEC_ELT (PBB_DRS (LST_PBB (l
)), i
, pdr
)
271 pdr_stride_in_loop (s
, depth
, pdr
);
272 mpz_set_si (n
, PDR_NB_REFS (pdr
));
274 mpz_add (strides
, strides
, s
);
281 /* Sets STRIDES to the sum of all the strides of the data references
282 accessed in LOOP at DEPTH. */
285 memory_strides_in_loop (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
287 if (mpz_cmp_si (loop
->memory_strides
, -1) == 0)
289 mpz_set_si (strides
, 0);
290 memory_strides_in_loop_1 (loop
, depth
, strides
);
293 mpz_set (strides
, loop
->memory_strides
);
296 /* Return true when the interchange of loops LOOP1 and LOOP2 is
309 | for (i = 0; i < N; i++)
310 | for (j = 0; j < N; j++)
316 The data access A[j][i] is described like this:
324 | 0 0 0 0 -1 0 100 >= 0
325 | 0 0 0 0 0 -1 100 >= 0
327 The linearized memory access L to A[100][100] is:
332 TODO: the shown format is not valid as it does not show the fact
333 that the iteration domain "i j" is transformed using the scattering.
335 Next, to measure the impact of iterating once in loop "i", we build
336 a maximization problem: first, we add to DR accesses the dimensions
337 k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
338 L1 and L2 are the linearized memory access functions.
340 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
341 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
342 | 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
343 |-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
344 | 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
345 | 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
346 | 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
347 | 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
348 | 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
350 Then, we generate the polyhedron P2 by interchanging the dimensions
351 (s0, s2), (s1, s3), (L1, L2), (k, i)
353 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
354 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
355 | 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
356 | 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
357 | 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
358 | 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
359 | 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
360 | 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
361 | 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
363 then we add to P2 the equality k = i + 1:
365 |-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
367 and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
369 Similarly, to determine the impact of one iteration on loop "j", we
370 interchange (k, j), we add "k = j + 1", and we compute D2 the
371 maximal value of the difference.
373 Finally, the profitability test is D1 < D2: if in the outer loop
374 the strides are smaller than in the inner loop, then it is
375 profitable to interchange the loops at DEPTH1 and DEPTH2. */
378 lst_interchange_profitable_p (lst_p nest
, int depth1
, int depth2
)
383 gcc_assert (depth1
< depth2
);
388 memory_strides_in_loop (nest
, depth1
, d1
);
389 memory_strides_in_loop (nest
, depth2
, d2
);
391 res
= mpz_cmp (d1
, d2
) < 0;
399 /* Interchanges the loops at DEPTH1 and DEPTH2 of the original
400 scattering and assigns the resulting polyhedron to the transformed
404 pbb_interchange_loop_depths (graphite_dim_t depth1
, graphite_dim_t depth2
,
408 unsigned dim1
= psct_dynamic_dim (pbb
, depth1
);
409 unsigned dim2
= psct_dynamic_dim (pbb
, depth2
);
410 isl_space
*d
= isl_map_get_space (pbb
->transformed
);
411 isl_space
*d1
= isl_space_range (d
);
412 unsigned n
= isl_space_dim (d1
, isl_dim_out
);
413 isl_space
*d2
= isl_space_add_dims (d1
, isl_dim_in
, n
);
414 isl_map
*x
= isl_map_universe (d2
);
416 x
= isl_map_equate (x
, isl_dim_in
, dim1
, isl_dim_out
, dim2
);
417 x
= isl_map_equate (x
, isl_dim_in
, dim2
, isl_dim_out
, dim1
);
419 for (i
= 0; i
< n
; i
++)
420 if (i
!= dim1
&& i
!= dim2
)
421 x
= isl_map_equate (x
, isl_dim_in
, i
, isl_dim_out
, i
);
423 pbb
->transformed
= isl_map_apply_range (pbb
->transformed
, x
);
426 /* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
427 the statements below LST. */
430 lst_apply_interchange (lst_p lst
, int depth1
, int depth2
)
435 if (LST_LOOP_P (lst
))
440 FOR_EACH_VEC_ELT (LST_SEQ (lst
), i
, l
)
441 lst_apply_interchange (l
, depth1
, depth2
);
444 pbb_interchange_loop_depths (depth1
, depth2
, LST_PBB (lst
));
447 /* Return true when the nest starting at LOOP1 and ending on LOOP2 is
448 perfect: i.e. there are no sequence of statements. */
451 lst_perfectly_nested_p (lst_p loop1
, lst_p loop2
)
456 if (!LST_LOOP_P (loop1
))
459 return LST_SEQ (loop1
).length () == 1
460 && lst_perfectly_nested_p (LST_SEQ (loop1
)[0], loop2
);
463 /* Transform the loop nest between LOOP1 and LOOP2 into a perfect
464 nest. To continue the naming tradition, this function is called
465 after perfect_nestify. NEST is set to the perfectly nested loop
466 that is created. BEFORE/AFTER are set to the loops distributed
467 before/after the loop NEST. */
470 lst_perfect_nestify (lst_p loop1
, lst_p loop2
, lst_p
*before
,
471 lst_p
*nest
, lst_p
*after
)
473 poly_bb_p first
, last
;
475 gcc_assert (loop1
&& loop2
477 && LST_LOOP_P (loop1
) && LST_LOOP_P (loop2
));
479 first
= LST_PBB (lst_find_first_pbb (loop2
));
480 last
= LST_PBB (lst_find_last_pbb (loop2
));
482 *before
= copy_lst (loop1
);
483 *nest
= copy_lst (loop1
);
484 *after
= copy_lst (loop1
);
486 lst_remove_all_before_including_pbb (*before
, first
, false);
487 lst_remove_all_before_including_pbb (*after
, last
, true);
489 lst_remove_all_before_excluding_pbb (*nest
, first
, true);
490 lst_remove_all_before_excluding_pbb (*nest
, last
, false);
492 if (lst_empty_p (*before
))
497 if (lst_empty_p (*after
))
502 if (lst_empty_p (*nest
))
509 /* Try to interchange LOOP1 with LOOP2 for all the statements of the
510 body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
514 lst_try_interchange_loops (scop_p scop
, lst_p loop1
, lst_p loop2
)
516 int depth1
= lst_depth (loop1
);
517 int depth2
= lst_depth (loop2
);
520 lst_p before
= NULL
, nest
= NULL
, after
= NULL
;
522 if (!lst_perfectly_nested_p (loop1
, loop2
))
523 lst_perfect_nestify (loop1
, loop2
, &before
, &nest
, &after
);
525 if (!lst_interchange_profitable_p (loop2
, depth1
, depth2
))
528 lst_apply_interchange (loop2
, depth1
, depth2
);
530 /* Sync the transformed LST information and the PBB scatterings
531 before using the scatterings in the data dependence analysis. */
532 if (before
|| nest
|| after
)
534 transformed
= lst_substitute_3 (SCOP_TRANSFORMED_SCHEDULE (scop
), loop1
,
535 before
, nest
, after
);
536 lst_update_scattering (transformed
);
537 free_lst (transformed
);
540 if (graphite_legal_transform (scop
))
542 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
544 "Loops at depths %d and %d will be interchanged.\n",
547 /* Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP. */
548 lst_insert_in_sequence (before
, loop1
, true);
549 lst_insert_in_sequence (after
, loop1
, false);
553 lst_replace (loop1
, nest
);
560 /* Undo the transform. */
564 lst_apply_interchange (loop2
, depth2
, depth1
);
568 /* Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged
569 with the loop OUTER in LST_SEQ (OUTER_FATHER). */
572 lst_interchange_select_inner (scop_p scop
, lst_p outer_father
, int outer
,
578 gcc_assert (outer_father
579 && LST_LOOP_P (outer_father
)
580 && LST_LOOP_P (LST_SEQ (outer_father
)[outer
])
582 && LST_LOOP_P (inner_father
));
584 loop1
= LST_SEQ (outer_father
)[outer
];
586 FOR_EACH_VEC_ELT (LST_SEQ (inner_father
), inner
, loop2
)
587 if (LST_LOOP_P (loop2
)
588 && (lst_try_interchange_loops (scop
, loop1
, loop2
)
589 || lst_interchange_select_inner (scop
, outer_father
, outer
, loop2
)))
595 /* Interchanges all the loops of LOOP and the loops of its body that
596 are considered profitable to interchange. Return the number of
597 interchanged loops. OUTER is the index in LST_SEQ (LOOP) that
598 points to the next outer loop to be considered for interchange. */
601 lst_interchange_select_outer (scop_p scop
, lst_p loop
, int outer
)
608 if (!loop
|| !LST_LOOP_P (loop
))
611 father
= LST_LOOP_FATHER (loop
);
614 while (lst_interchange_select_inner (scop
, father
, outer
, loop
))
617 loop
= LST_SEQ (father
)[outer
];
621 if (LST_LOOP_P (loop
))
622 FOR_EACH_VEC_ELT (LST_SEQ (loop
), i
, l
)
624 res
+= lst_interchange_select_outer (scop
, l
, i
);
629 /* Interchanges all the loop depths that are considered profitable for
630 SCOP. Return the number of interchanged loops. */
633 scop_do_interchange (scop_p scop
)
635 int res
= lst_interchange_select_outer
636 (scop
, SCOP_TRANSFORMED_SCHEDULE (scop
), 0);
638 lst_update_scattering (SCOP_TRANSFORMED_SCHEDULE (scop
));