1 /* Interchange heuristics and transform for loop interchange on
2 polyhedral representation.
4 Copyright (C) 2009, 2010, 2011 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"
38 #include "tree-flow.h"
41 #include "tree-chrec.h"
42 #include "tree-data-ref.h"
43 #include "tree-scalar-evolution.h"
47 #include "graphite-poly.h"
49 /* XXX isl rewrite following comment */
50 /* Builds a linear expression, of dimension DIM, representing PDR's
53 L = r_{n}*r_{n-1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n-1} + s_{n}.
55 For an array A[10][20] with two subscript locations s0 and s1, the
56 linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0
57 corresponds to a memory stride of 20.
59 OFFSET is a number of dimensions to prepend before the
60 subscript dimensions: s_0, s_1, ..., s_n.
62 Thus, the final linear expression has the following format:
63 0 .. 0_{offset} | 0 .. 0_{nit} | 0 .. 0_{gd} | 0 | c_0 c_1 ... c_n
64 where the expression itself is:
65 c_0 * s_0 + c_1 * s_1 + ... c_n * s_n. */
67 static isl_constraint
*
68 build_linearized_memory_access (isl_map
*map
, poly_dr_p pdr
)
71 isl_local_space
*ls
= isl_local_space_from_space (isl_map_get_space (map
));
72 unsigned offset
, nsubs
;
74 isl_int size
, subsize
;
76 res
= isl_equality_alloc (ls
);
78 isl_int_set_ui (size
, 1);
79 isl_int_init (subsize
);
80 isl_int_set_ui (subsize
, 1);
82 nsubs
= isl_set_dim (pdr
->extent
, isl_dim_set
);
83 /* -1 for the already included L dimension. */
84 offset
= isl_map_dim (map
, isl_dim_out
) - 1 - nsubs
;
85 res
= isl_constraint_set_coefficient_si (res
, isl_dim_out
, offset
+ nsubs
, -1);
86 /* Go through all subscripts from last to first. First dimension
87 is the alias set, ignore it. */
88 for (i
= nsubs
- 1; i
>= 1; i
--)
93 res
= isl_constraint_set_coefficient (res
, isl_dim_out
, offset
+ i
, size
);
95 dc
= isl_set_get_space (pdr
->extent
);
96 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
97 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, i
, 1);
98 isl_set_max (pdr
->extent
, aff
, &subsize
);
100 isl_int_mul (size
, size
, subsize
);
103 isl_int_clear (subsize
);
104 isl_int_clear (size
);
109 /* Set STRIDE to the stride of PDR in memory by advancing by one in
110 the loop at DEPTH. */
113 pdr_stride_in_loop (mpz_t stride
, graphite_dim_t depth
, poly_dr_p pdr
)
115 poly_bb_p pbb
= PDR_PBB (pdr
);
120 isl_constraint
*lma
, *c
;
122 graphite_dim_t time_depth
;
125 /* XXX isl rewrite following comments. */
126 /* Builds a partial difference equations and inserts them
127 into pointset powerset polyhedron P. Polyhedron is assumed
128 to have the format: T|I|T'|I'|G|S|S'|l1|l2.
130 TIME_DEPTH is the time dimension w.r.t. which we are
132 OFFSET represents the number of dimensions between
133 columns t_{time_depth} and t'_{time_depth}.
134 DIM_SCTR is the number of scattering dimensions. It is
135 essentially the dimensionality of the T vector.
137 The following equations are inserted into the polyhedron P:
140 | t_{time_depth-1} = t'_{time_depth-1}
141 | t_{time_depth} = t'_{time_depth} + 1
142 | t_{time_depth+1} = t'_{time_depth + 1}
144 | t_{dim_sctr} = t'_{dim_sctr}. */
146 /* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
147 This is the core part of this alogrithm, since this
148 constraint asks for the memory access stride (difference)
149 between two consecutive points in time dimensions. */
154 | t_{time_depth-1} = t'_{time_depth-1}
155 | t_{time_depth+1} = t'_{time_depth+1}
157 | t_{dim_sctr} = t'_{dim_sctr}
159 This means that all the time dimensions are equal except for
160 time_depth, where the constraint is t_{depth} = t'_{depth} + 1
161 step. More to this: we should be careful not to add equalities
162 to the 'coupled' dimensions, which happens when the one dimension
163 is stripmined dimension, and the other dimension corresponds
164 to the point loop inside stripmined dimension. */
166 /* pdr->accesses: [P1..nb_param,I1..nb_domain]->[a,S1..nb_subscript]
167 ??? [P] not used for PDRs?
168 pdr->extent: [a,S1..nb_subscript]
169 pbb->domain: [P1..nb_param,I1..nb_domain]
170 pbb->transformed: [P1..nb_param,I1..nb_domain]->[T1..Tnb_sctr]
171 [T] includes local vars (currently unused)
173 First we create [P,I] -> [T,a,S]. */
175 map
= isl_map_flat_range_product (isl_map_copy (pbb
->transformed
),
176 isl_map_copy (pdr
->accesses
));
177 /* Add a dimension for L: [P,I] -> [T,a,S,L].*/
178 map
= isl_map_add_dims (map
, isl_dim_out
, 1);
179 /* Build a constraint for "lma[S] - L == 0", effectively calculating
180 L in terms of subscripts. */
181 lma
= build_linearized_memory_access (map
, pdr
);
182 /* And add it to the map, so we now have:
183 [P,I] -> [T,a,S,L] : lma([S]) == L. */
184 map
= isl_map_add_constraint (map
, lma
);
186 /* Then we create [P,I,P',I'] -> [T,a,S,L,T',a',S',L']. */
187 map
= isl_map_flat_product (map
, isl_map_copy (map
));
189 /* Now add the equality T[time_depth] == T'[time_depth]+1. This will
190 force L' to be the linear address at T[time_depth] + 1. */
191 time_depth
= psct_dynamic_dim (pbb
, depth
);
192 /* Length of [a,S] plus [L] ... */
193 offset
= 1 + isl_map_dim (pdr
->accesses
, isl_dim_out
);
195 offset
+= isl_map_dim (pbb
->transformed
, isl_dim_out
);
197 c
= isl_equality_alloc (isl_local_space_from_space (isl_map_get_space (map
)));
198 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
, time_depth
, 1);
199 c
= isl_constraint_set_coefficient_si (c
, isl_dim_out
,
200 offset
+ time_depth
, -1);
201 c
= isl_constraint_set_constant_si (c
, 1);
202 map
= isl_map_add_constraint (map
, c
);
204 /* Now we equate most of the T/T' elements (making PITaSL nearly
205 the same is (PITaSL)', except for one dimension, namely for 'depth'
206 (an index into [I]), after translating to index into [T]. Take care
207 to not produce an empty map, which indicates we wanted to equate
208 two dimensions that are already coupled via the above time_depth
209 dimension. Happens with strip mining where several scatter dimension
210 are interdependend. */
212 nt
= pbb_nb_scattering_transform (pbb
) + pbb_nb_local_vars (pbb
);
213 for (i
= 0; i
< nt
; i
++)
216 isl_map
*temp
= isl_map_equate (isl_map_copy (map
),
218 isl_dim_out
, offset
+ i
);
219 if (isl_map_is_empty (temp
))
228 /* Now maximize the expression L' - L. */
229 set
= isl_map_range (map
);
230 dc
= isl_set_get_space (set
);
231 aff
= isl_aff_zero_on_domain (isl_local_space_from_space (dc
));
232 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
- 1, -1);
233 aff
= isl_aff_set_coefficient_si (aff
, isl_dim_in
, offset
+ offset
- 1, 1);
234 isl_int_init (islstride
);
235 isl_set_max (set
, aff
, &islstride
);
236 isl_int_get_gmp (islstride
, stride
);
237 isl_int_clear (islstride
);
241 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
244 void (*gmp_free
) (void *, size_t);
246 fprintf (dump_file
, "\nStride in BB_%d, DR_%d, depth %d:",
247 pbb_index (pbb
), PDR_ID (pdr
), (int) depth
);
248 str
= mpz_get_str (0, 10, stride
);
249 fprintf (dump_file
, " %s ", str
);
250 mp_get_memory_functions (NULL
, NULL
, &gmp_free
);
251 (*gmp_free
) (str
, strlen (str
) + 1);
255 /* Sets STRIDES to the sum of all the strides of the data references
256 accessed in LOOP at DEPTH. */
259 memory_strides_in_loop_1 (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
269 FOR_EACH_VEC_ELT (LST_SEQ (loop
), j
, l
)
271 memory_strides_in_loop_1 (l
, depth
, strides
);
273 FOR_EACH_VEC_ELT (PBB_DRS (LST_PBB (l
)), i
, pdr
)
275 pdr_stride_in_loop (s
, depth
, pdr
);
276 mpz_set_si (n
, PDR_NB_REFS (pdr
));
278 mpz_add (strides
, strides
, s
);
285 /* Sets STRIDES to the sum of all the strides of the data references
286 accessed in LOOP at DEPTH. */
289 memory_strides_in_loop (lst_p loop
, graphite_dim_t depth
, mpz_t strides
)
291 if (mpz_cmp_si (loop
->memory_strides
, -1) == 0)
293 mpz_set_si (strides
, 0);
294 memory_strides_in_loop_1 (loop
, depth
, strides
);
297 mpz_set (strides
, loop
->memory_strides
);
300 /* Return true when the interchange of loops LOOP1 and LOOP2 is
313 | for (i = 0; i < N; i++)
314 | for (j = 0; j < N; j++)
320 The data access A[j][i] is described like this:
328 | 0 0 0 0 -1 0 100 >= 0
329 | 0 0 0 0 0 -1 100 >= 0
331 The linearized memory access L to A[100][100] is:
336 TODO: the shown format is not valid as it does not show the fact
337 that the iteration domain "i j" is transformed using the scattering.
339 Next, to measure the impact of iterating once in loop "i", we build
340 a maximization problem: first, we add to DR accesses the dimensions
341 k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
342 L1 and L2 are the linearized memory access functions.
344 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
345 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
346 | 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
347 |-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
348 | 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
349 | 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
350 | 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
351 | 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
352 | 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
354 Then, we generate the polyhedron P2 by interchanging the dimensions
355 (s0, s2), (s1, s3), (L1, L2), (k, i)
357 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
358 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
359 | 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
360 | 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
361 | 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
362 | 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
363 | 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
364 | 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
365 | 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
367 then we add to P2 the equality k = i + 1:
369 |-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
371 and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
373 Similarly, to determine the impact of one iteration on loop "j", we
374 interchange (k, j), we add "k = j + 1", and we compute D2 the
375 maximal value of the difference.
377 Finally, the profitability test is D1 < D2: if in the outer loop
378 the strides are smaller than in the inner loop, then it is
379 profitable to interchange the loops at DEPTH1 and DEPTH2. */
382 lst_interchange_profitable_p (lst_p nest
, int depth1
, int depth2
)
387 gcc_assert (depth1
< depth2
);
392 memory_strides_in_loop (nest
, depth1
, d1
);
393 memory_strides_in_loop (nest
, depth2
, d2
);
395 res
= mpz_cmp (d1
, d2
) < 0;
403 /* Interchanges the loops at DEPTH1 and DEPTH2 of the original
404 scattering and assigns the resulting polyhedron to the transformed
408 pbb_interchange_loop_depths (graphite_dim_t depth1
, graphite_dim_t depth2
,
412 unsigned dim1
= psct_dynamic_dim (pbb
, depth1
);
413 unsigned dim2
= psct_dynamic_dim (pbb
, depth2
);
414 isl_space
*d
= isl_map_get_space (pbb
->transformed
);
415 isl_space
*d1
= isl_space_range (d
);
416 unsigned n
= isl_space_dim (d1
, isl_dim_out
);
417 isl_space
*d2
= isl_space_add_dims (d1
, isl_dim_in
, n
);
418 isl_map
*x
= isl_map_universe (d2
);
420 x
= isl_map_equate (x
, isl_dim_in
, dim1
, isl_dim_out
, dim2
);
421 x
= isl_map_equate (x
, isl_dim_in
, dim2
, isl_dim_out
, dim1
);
423 for (i
= 0; i
< n
; i
++)
424 if (i
!= dim1
&& i
!= dim2
)
425 x
= isl_map_equate (x
, isl_dim_in
, i
, isl_dim_out
, i
);
427 pbb
->transformed
= isl_map_apply_range (pbb
->transformed
, x
);
430 /* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
431 the statements below LST. */
434 lst_apply_interchange (lst_p lst
, int depth1
, int depth2
)
439 if (LST_LOOP_P (lst
))
444 FOR_EACH_VEC_ELT (LST_SEQ (lst
), i
, l
)
445 lst_apply_interchange (l
, depth1
, depth2
);
448 pbb_interchange_loop_depths (depth1
, depth2
, LST_PBB (lst
));
451 /* Return true when the nest starting at LOOP1 and ending on LOOP2 is
452 perfect: i.e. there are no sequence of statements. */
455 lst_perfectly_nested_p (lst_p loop1
, lst_p loop2
)
460 if (!LST_LOOP_P (loop1
))
463 return LST_SEQ (loop1
).length () == 1
464 && lst_perfectly_nested_p (LST_SEQ (loop1
)[0], loop2
);
467 /* Transform the loop nest between LOOP1 and LOOP2 into a perfect
468 nest. To continue the naming tradition, this function is called
469 after perfect_nestify. NEST is set to the perfectly nested loop
470 that is created. BEFORE/AFTER are set to the loops distributed
471 before/after the loop NEST. */
474 lst_perfect_nestify (lst_p loop1
, lst_p loop2
, lst_p
*before
,
475 lst_p
*nest
, lst_p
*after
)
477 poly_bb_p first
, last
;
479 gcc_assert (loop1
&& loop2
481 && LST_LOOP_P (loop1
) && LST_LOOP_P (loop2
));
483 first
= LST_PBB (lst_find_first_pbb (loop2
));
484 last
= LST_PBB (lst_find_last_pbb (loop2
));
486 *before
= copy_lst (loop1
);
487 *nest
= copy_lst (loop1
);
488 *after
= copy_lst (loop1
);
490 lst_remove_all_before_including_pbb (*before
, first
, false);
491 lst_remove_all_before_including_pbb (*after
, last
, true);
493 lst_remove_all_before_excluding_pbb (*nest
, first
, true);
494 lst_remove_all_before_excluding_pbb (*nest
, last
, false);
496 if (lst_empty_p (*before
))
501 if (lst_empty_p (*after
))
506 if (lst_empty_p (*nest
))
513 /* Try to interchange LOOP1 with LOOP2 for all the statements of the
514 body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
518 lst_try_interchange_loops (scop_p scop
, lst_p loop1
, lst_p loop2
)
520 int depth1
= lst_depth (loop1
);
521 int depth2
= lst_depth (loop2
);
524 lst_p before
= NULL
, nest
= NULL
, after
= NULL
;
526 if (!lst_perfectly_nested_p (loop1
, loop2
))
527 lst_perfect_nestify (loop1
, loop2
, &before
, &nest
, &after
);
529 if (!lst_interchange_profitable_p (loop2
, depth1
, depth2
))
532 lst_apply_interchange (loop2
, depth1
, depth2
);
534 /* Sync the transformed LST information and the PBB scatterings
535 before using the scatterings in the data dependence analysis. */
536 if (before
|| nest
|| after
)
538 transformed
= lst_substitute_3 (SCOP_TRANSFORMED_SCHEDULE (scop
), loop1
,
539 before
, nest
, after
);
540 lst_update_scattering (transformed
);
541 free_lst (transformed
);
544 if (graphite_legal_transform (scop
))
546 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
548 "Loops at depths %d and %d will be interchanged.\n",
551 /* Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP. */
552 lst_insert_in_sequence (before
, loop1
, true);
553 lst_insert_in_sequence (after
, loop1
, false);
557 lst_replace (loop1
, nest
);
564 /* Undo the transform. */
568 lst_apply_interchange (loop2
, depth2
, depth1
);
572 /* Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged
573 with the loop OUTER in LST_SEQ (OUTER_FATHER). */
576 lst_interchange_select_inner (scop_p scop
, lst_p outer_father
, int outer
,
582 gcc_assert (outer_father
583 && LST_LOOP_P (outer_father
)
584 && LST_LOOP_P (LST_SEQ (outer_father
)[outer
])
586 && LST_LOOP_P (inner_father
));
588 loop1
= LST_SEQ (outer_father
)[outer
];
590 FOR_EACH_VEC_ELT (LST_SEQ (inner_father
), inner
, loop2
)
591 if (LST_LOOP_P (loop2
)
592 && (lst_try_interchange_loops (scop
, loop1
, loop2
)
593 || lst_interchange_select_inner (scop
, outer_father
, outer
, loop2
)))
599 /* Interchanges all the loops of LOOP and the loops of its body that
600 are considered profitable to interchange. Return the number of
601 interchanged loops. OUTER is the index in LST_SEQ (LOOP) that
602 points to the next outer loop to be considered for interchange. */
605 lst_interchange_select_outer (scop_p scop
, lst_p loop
, int outer
)
612 if (!loop
|| !LST_LOOP_P (loop
))
615 father
= LST_LOOP_FATHER (loop
);
618 while (lst_interchange_select_inner (scop
, father
, outer
, loop
))
621 loop
= LST_SEQ (father
)[outer
];
625 if (LST_LOOP_P (loop
))
626 FOR_EACH_VEC_ELT (LST_SEQ (loop
), i
, l
)
628 res
+= lst_interchange_select_outer (scop
, l
, i
);
633 /* Interchanges all the loop depths that are considered profitable for
634 SCOP. Return the number of interchanged loops. */
637 scop_do_interchange (scop_p scop
)
639 int res
= lst_interchange_select_outer
640 (scop
, SCOP_TRANSFORMED_SCHEDULE (scop
), 0);
642 lst_update_scattering (SCOP_TRANSFORMED_SCHEDULE (scop
));