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[official-gcc.git] / gcc / graphite-interchange.c
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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)
13 any later version.
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/>. */
24 #include "config.h"
26 #ifdef HAVE_cloog
27 #include <isl/aff.h>
28 #include <isl/set.h>
29 #include <isl/map.h>
30 #include <isl/union_map.h>
31 #include <isl/ilp.h>
32 #include <cloog/cloog.h>
33 #include <cloog/isl/domain.h>
34 #ifdef HAVE_ISL_SCHED_CONSTRAINTS_COMPUTE_SCHEDULE
35 #include <isl/deprecated/int.h>
36 #include <isl/deprecated/aff_int.h>
37 #include <isl/deprecated/ilp_int.h>
38 #include <isl/deprecated/constraint_int.h>
39 #endif
40 #endif
42 #include "system.h"
43 #include "coretypes.h"
44 #include "tree-flow.h"
45 #include "dumpfile.h"
46 #include "cfgloop.h"
47 #include "tree-chrec.h"
48 #include "tree-data-ref.h"
49 #include "tree-scalar-evolution.h"
50 #include "sese.h"
52 #ifdef HAVE_cloog
53 #include "graphite-poly.h"
55 /* XXX isl rewrite following comment */
56 /* Builds a linear expression, of dimension DIM, representing PDR's
57 memory access:
59 L = r_{n}*r_{n-1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n-1} + s_{n}.
61 For an array A[10][20] with two subscript locations s0 and s1, the
62 linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0
63 corresponds to a memory stride of 20.
65 OFFSET is a number of dimensions to prepend before the
66 subscript dimensions: s_0, s_1, ..., s_n.
68 Thus, the final linear expression has the following format:
69 0 .. 0_{offset} | 0 .. 0_{nit} | 0 .. 0_{gd} | 0 | c_0 c_1 ... c_n
70 where the expression itself is:
71 c_0 * s_0 + c_1 * s_1 + ... c_n * s_n. */
73 static isl_constraint *
74 build_linearized_memory_access (isl_map *map, poly_dr_p pdr)
76 isl_constraint *res;
77 isl_local_space *ls = isl_local_space_from_space (isl_map_get_space (map));
78 unsigned offset, nsubs;
79 int i;
80 isl_int size, subsize;
82 res = isl_equality_alloc (ls);
83 isl_int_init (size);
84 isl_int_set_ui (size, 1);
85 isl_int_init (subsize);
86 isl_int_set_ui (subsize, 1);
88 nsubs = isl_set_dim (pdr->extent, isl_dim_set);
89 /* -1 for the already included L dimension. */
90 offset = isl_map_dim (map, isl_dim_out) - 1 - nsubs;
91 res = isl_constraint_set_coefficient_si (res, isl_dim_out, offset + nsubs, -1);
92 /* Go through all subscripts from last to first. First dimension
93 is the alias set, ignore it. */
94 for (i = nsubs - 1; i >= 1; i--)
96 isl_space *dc;
97 isl_aff *aff;
99 res = isl_constraint_set_coefficient (res, isl_dim_out, offset + i, size);
101 dc = isl_set_get_space (pdr->extent);
102 aff = isl_aff_zero_on_domain (isl_local_space_from_space (dc));
103 aff = isl_aff_set_coefficient_si (aff, isl_dim_in, i, 1);
104 isl_set_max (pdr->extent, aff, &subsize);
105 isl_aff_free (aff);
106 isl_int_mul (size, size, subsize);
109 isl_int_clear (subsize);
110 isl_int_clear (size);
112 return res;
115 /* Set STRIDE to the stride of PDR in memory by advancing by one in
116 the loop at DEPTH. */
118 static void
119 pdr_stride_in_loop (mpz_t stride, graphite_dim_t depth, poly_dr_p pdr)
121 poly_bb_p pbb = PDR_PBB (pdr);
122 isl_map *map;
123 isl_set *set;
124 isl_aff *aff;
125 isl_space *dc;
126 isl_constraint *lma, *c;
127 isl_int islstride;
128 graphite_dim_t time_depth;
129 unsigned offset, nt;
130 unsigned i;
131 /* XXX isl rewrite following comments. */
132 /* Builds a partial difference equations and inserts them
133 into pointset powerset polyhedron P. Polyhedron is assumed
134 to have the format: T|I|T'|I'|G|S|S'|l1|l2.
136 TIME_DEPTH is the time dimension w.r.t. which we are
137 differentiating.
138 OFFSET represents the number of dimensions between
139 columns t_{time_depth} and t'_{time_depth}.
140 DIM_SCTR is the number of scattering dimensions. It is
141 essentially the dimensionality of the T vector.
143 The following equations are inserted into the polyhedron P:
144 | t_1 = t_1'
145 | ...
146 | t_{time_depth-1} = t'_{time_depth-1}
147 | t_{time_depth} = t'_{time_depth} + 1
148 | t_{time_depth+1} = t'_{time_depth + 1}
149 | ...
150 | t_{dim_sctr} = t'_{dim_sctr}. */
152 /* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
153 This is the core part of this alogrithm, since this
154 constraint asks for the memory access stride (difference)
155 between two consecutive points in time dimensions. */
157 /* Add equalities:
158 | t1 = t1'
159 | ...
160 | t_{time_depth-1} = t'_{time_depth-1}
161 | t_{time_depth+1} = t'_{time_depth+1}
162 | ...
163 | t_{dim_sctr} = t'_{dim_sctr}
165 This means that all the time dimensions are equal except for
166 time_depth, where the constraint is t_{depth} = t'_{depth} + 1
167 step. More to this: we should be careful not to add equalities
168 to the 'coupled' dimensions, which happens when the one dimension
169 is stripmined dimension, and the other dimension corresponds
170 to the point loop inside stripmined dimension. */
172 /* pdr->accesses: [P1..nb_param,I1..nb_domain]->[a,S1..nb_subscript]
173 ??? [P] not used for PDRs?
174 pdr->extent: [a,S1..nb_subscript]
175 pbb->domain: [P1..nb_param,I1..nb_domain]
176 pbb->transformed: [P1..nb_param,I1..nb_domain]->[T1..Tnb_sctr]
177 [T] includes local vars (currently unused)
179 First we create [P,I] -> [T,a,S]. */
181 map = isl_map_flat_range_product (isl_map_copy (pbb->transformed),
182 isl_map_copy (pdr->accesses));
183 /* Add a dimension for L: [P,I] -> [T,a,S,L].*/
184 map = isl_map_add_dims (map, isl_dim_out, 1);
185 /* Build a constraint for "lma[S] - L == 0", effectively calculating
186 L in terms of subscripts. */
187 lma = build_linearized_memory_access (map, pdr);
188 /* And add it to the map, so we now have:
189 [P,I] -> [T,a,S,L] : lma([S]) == L. */
190 map = isl_map_add_constraint (map, lma);
192 /* Then we create [P,I,P',I'] -> [T,a,S,L,T',a',S',L']. */
193 map = isl_map_flat_product (map, isl_map_copy (map));
195 /* Now add the equality T[time_depth] == T'[time_depth]+1. This will
196 force L' to be the linear address at T[time_depth] + 1. */
197 time_depth = psct_dynamic_dim (pbb, depth);
198 /* Length of [a,S] plus [L] ... */
199 offset = 1 + isl_map_dim (pdr->accesses, isl_dim_out);
200 /* ... plus [T]. */
201 offset += isl_map_dim (pbb->transformed, isl_dim_out);
203 c = isl_equality_alloc (isl_local_space_from_space (isl_map_get_space (map)));
204 c = isl_constraint_set_coefficient_si (c, isl_dim_out, time_depth, 1);
205 c = isl_constraint_set_coefficient_si (c, isl_dim_out,
206 offset + time_depth, -1);
207 c = isl_constraint_set_constant_si (c, 1);
208 map = isl_map_add_constraint (map, c);
210 /* Now we equate most of the T/T' elements (making PITaSL nearly
211 the same is (PITaSL)', except for one dimension, namely for 'depth'
212 (an index into [I]), after translating to index into [T]. Take care
213 to not produce an empty map, which indicates we wanted to equate
214 two dimensions that are already coupled via the above time_depth
215 dimension. Happens with strip mining where several scatter dimension
216 are interdependend. */
217 /* Length of [T]. */
218 nt = pbb_nb_scattering_transform (pbb) + pbb_nb_local_vars (pbb);
219 for (i = 0; i < nt; i++)
220 if (i != time_depth)
222 isl_map *temp = isl_map_equate (isl_map_copy (map),
223 isl_dim_out, i,
224 isl_dim_out, offset + i);
225 if (isl_map_is_empty (temp))
226 isl_map_free (temp);
227 else
229 isl_map_free (map);
230 map = temp;
234 /* Now maximize the expression L' - L. */
235 set = isl_map_range (map);
236 dc = isl_set_get_space (set);
237 aff = isl_aff_zero_on_domain (isl_local_space_from_space (dc));
238 aff = isl_aff_set_coefficient_si (aff, isl_dim_in, offset - 1, -1);
239 aff = isl_aff_set_coefficient_si (aff, isl_dim_in, offset + offset - 1, 1);
240 isl_int_init (islstride);
241 isl_set_max (set, aff, &islstride);
242 isl_int_get_gmp (islstride, stride);
243 isl_int_clear (islstride);
244 isl_aff_free (aff);
245 isl_set_free (set);
247 if (dump_file && (dump_flags & TDF_DETAILS))
249 gmp_fprintf (dump_file, "\nStride in BB_%d, DR_%d, depth %d: %Zd ",
250 pbb_index (pbb), PDR_ID (pdr), (int) depth, stride);
254 /* Sets STRIDES to the sum of all the strides of the data references
255 accessed in LOOP at DEPTH. */
257 static void
258 memory_strides_in_loop_1 (lst_p loop, graphite_dim_t depth, mpz_t strides)
260 int i, j;
261 lst_p l;
262 poly_dr_p pdr;
263 mpz_t s, n;
265 mpz_init (s);
266 mpz_init (n);
268 FOR_EACH_VEC_ELT (LST_SEQ (loop), j, l)
269 if (LST_LOOP_P (l))
270 memory_strides_in_loop_1 (l, depth, strides);
271 else
272 FOR_EACH_VEC_ELT (PBB_DRS (LST_PBB (l)), i, pdr)
274 pdr_stride_in_loop (s, depth, pdr);
275 mpz_set_si (n, PDR_NB_REFS (pdr));
276 mpz_mul (s, s, n);
277 mpz_add (strides, strides, s);
280 mpz_clear (s);
281 mpz_clear (n);
284 /* Sets STRIDES to the sum of all the strides of the data references
285 accessed in LOOP at DEPTH. */
287 static void
288 memory_strides_in_loop (lst_p loop, graphite_dim_t depth, mpz_t strides)
290 if (mpz_cmp_si (loop->memory_strides, -1) == 0)
292 mpz_set_si (strides, 0);
293 memory_strides_in_loop_1 (loop, depth, strides);
295 else
296 mpz_set (strides, loop->memory_strides);
299 /* Return true when the interchange of loops LOOP1 and LOOP2 is
300 profitable.
302 Example:
304 | int a[100][100];
306 | int
307 | foo (int N)
309 | int j;
310 | int i;
312 | for (i = 0; i < N; i++)
313 | for (j = 0; j < N; j++)
314 | a[j][2 * i] += 1;
316 | return a[N][12];
319 The data access A[j][i] is described like this:
321 | i j N a s0 s1 1
322 | 0 0 0 1 0 0 -5 = 0
323 | 0 -1 0 0 1 0 0 = 0
324 |-2 0 0 0 0 1 0 = 0
325 | 0 0 0 0 1 0 0 >= 0
326 | 0 0 0 0 0 1 0 >= 0
327 | 0 0 0 0 -1 0 100 >= 0
328 | 0 0 0 0 0 -1 100 >= 0
330 The linearized memory access L to A[100][100] is:
332 | i j N a s0 s1 1
333 | 0 0 0 0 100 1 0
335 TODO: the shown format is not valid as it does not show the fact
336 that the iteration domain "i j" is transformed using the scattering.
338 Next, to measure the impact of iterating once in loop "i", we build
339 a maximization problem: first, we add to DR accesses the dimensions
340 k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
341 L1 and L2 are the linearized memory access functions.
343 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
344 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
345 | 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
346 |-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
347 | 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
348 | 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
349 | 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
350 | 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
351 | 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
353 Then, we generate the polyhedron P2 by interchanging the dimensions
354 (s0, s2), (s1, s3), (L1, L2), (k, i)
356 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
357 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
358 | 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
359 | 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
360 | 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
361 | 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
362 | 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
363 | 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
364 | 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
366 then we add to P2 the equality k = i + 1:
368 |-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
370 and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
372 Similarly, to determine the impact of one iteration on loop "j", we
373 interchange (k, j), we add "k = j + 1", and we compute D2 the
374 maximal value of the difference.
376 Finally, the profitability test is D1 < D2: if in the outer loop
377 the strides are smaller than in the inner loop, then it is
378 profitable to interchange the loops at DEPTH1 and DEPTH2. */
380 static bool
381 lst_interchange_profitable_p (lst_p nest, int depth1, int depth2)
383 mpz_t d1, d2;
384 bool res;
386 gcc_assert (depth1 < depth2);
388 mpz_init (d1);
389 mpz_init (d2);
391 memory_strides_in_loop (nest, depth1, d1);
392 memory_strides_in_loop (nest, depth2, d2);
394 res = mpz_cmp (d1, d2) < 0;
396 mpz_clear (d1);
397 mpz_clear (d2);
399 return res;
402 /* Interchanges the loops at DEPTH1 and DEPTH2 of the original
403 scattering and assigns the resulting polyhedron to the transformed
404 scattering. */
406 static void
407 pbb_interchange_loop_depths (graphite_dim_t depth1, graphite_dim_t depth2,
408 poly_bb_p pbb)
410 unsigned i;
411 unsigned dim1 = psct_dynamic_dim (pbb, depth1);
412 unsigned dim2 = psct_dynamic_dim (pbb, depth2);
413 isl_space *d = isl_map_get_space (pbb->transformed);
414 isl_space *d1 = isl_space_range (d);
415 unsigned n = isl_space_dim (d1, isl_dim_out);
416 isl_space *d2 = isl_space_add_dims (d1, isl_dim_in, n);
417 isl_map *x = isl_map_universe (d2);
419 x = isl_map_equate (x, isl_dim_in, dim1, isl_dim_out, dim2);
420 x = isl_map_equate (x, isl_dim_in, dim2, isl_dim_out, dim1);
422 for (i = 0; i < n; i++)
423 if (i != dim1 && i != dim2)
424 x = isl_map_equate (x, isl_dim_in, i, isl_dim_out, i);
426 pbb->transformed = isl_map_apply_range (pbb->transformed, x);
429 /* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
430 the statements below LST. */
432 static void
433 lst_apply_interchange (lst_p lst, int depth1, int depth2)
435 if (!lst)
436 return;
438 if (LST_LOOP_P (lst))
440 int i;
441 lst_p l;
443 FOR_EACH_VEC_ELT (LST_SEQ (lst), i, l)
444 lst_apply_interchange (l, depth1, depth2);
446 else
447 pbb_interchange_loop_depths (depth1, depth2, LST_PBB (lst));
450 /* Return true when the nest starting at LOOP1 and ending on LOOP2 is
451 perfect: i.e. there are no sequence of statements. */
453 static bool
454 lst_perfectly_nested_p (lst_p loop1, lst_p loop2)
456 if (loop1 == loop2)
457 return true;
459 if (!LST_LOOP_P (loop1))
460 return false;
462 return LST_SEQ (loop1).length () == 1
463 && lst_perfectly_nested_p (LST_SEQ (loop1)[0], loop2);
466 /* Transform the loop nest between LOOP1 and LOOP2 into a perfect
467 nest. To continue the naming tradition, this function is called
468 after perfect_nestify. NEST is set to the perfectly nested loop
469 that is created. BEFORE/AFTER are set to the loops distributed
470 before/after the loop NEST. */
472 static void
473 lst_perfect_nestify (lst_p loop1, lst_p loop2, lst_p *before,
474 lst_p *nest, lst_p *after)
476 poly_bb_p first, last;
478 gcc_assert (loop1 && loop2
479 && loop1 != loop2
480 && LST_LOOP_P (loop1) && LST_LOOP_P (loop2));
482 first = LST_PBB (lst_find_first_pbb (loop2));
483 last = LST_PBB (lst_find_last_pbb (loop2));
485 *before = copy_lst (loop1);
486 *nest = copy_lst (loop1);
487 *after = copy_lst (loop1);
489 lst_remove_all_before_including_pbb (*before, first, false);
490 lst_remove_all_before_including_pbb (*after, last, true);
492 lst_remove_all_before_excluding_pbb (*nest, first, true);
493 lst_remove_all_before_excluding_pbb (*nest, last, false);
495 if (lst_empty_p (*before))
497 free_lst (*before);
498 *before = NULL;
500 if (lst_empty_p (*after))
502 free_lst (*after);
503 *after = NULL;
505 if (lst_empty_p (*nest))
507 free_lst (*nest);
508 *nest = NULL;
512 /* Try to interchange LOOP1 with LOOP2 for all the statements of the
513 body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
514 interchange. */
516 static bool
517 lst_try_interchange_loops (scop_p scop, lst_p loop1, lst_p loop2)
519 int depth1 = lst_depth (loop1);
520 int depth2 = lst_depth (loop2);
521 lst_p transformed;
523 lst_p before = NULL, nest = NULL, after = NULL;
525 if (!lst_perfectly_nested_p (loop1, loop2))
526 lst_perfect_nestify (loop1, loop2, &before, &nest, &after);
528 if (!lst_interchange_profitable_p (loop2, depth1, depth2))
529 return false;
531 lst_apply_interchange (loop2, depth1, depth2);
533 /* Sync the transformed LST information and the PBB scatterings
534 before using the scatterings in the data dependence analysis. */
535 if (before || nest || after)
537 transformed = lst_substitute_3 (SCOP_TRANSFORMED_SCHEDULE (scop), loop1,
538 before, nest, after);
539 lst_update_scattering (transformed);
540 free_lst (transformed);
543 if (graphite_legal_transform (scop))
545 if (dump_file && (dump_flags & TDF_DETAILS))
546 fprintf (dump_file,
547 "Loops at depths %d and %d will be interchanged.\n",
548 depth1, depth2);
550 /* Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP. */
551 lst_insert_in_sequence (before, loop1, true);
552 lst_insert_in_sequence (after, loop1, false);
554 if (nest)
556 lst_replace (loop1, nest);
557 free_lst (loop1);
560 return true;
563 /* Undo the transform. */
564 free_lst (before);
565 free_lst (nest);
566 free_lst (after);
567 lst_apply_interchange (loop2, depth2, depth1);
568 return false;
571 /* Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged
572 with the loop OUTER in LST_SEQ (OUTER_FATHER). */
574 static bool
575 lst_interchange_select_inner (scop_p scop, lst_p outer_father, int outer,
576 lst_p inner_father)
578 int inner;
579 lst_p loop1, loop2;
581 gcc_assert (outer_father
582 && LST_LOOP_P (outer_father)
583 && LST_LOOP_P (LST_SEQ (outer_father)[outer])
584 && inner_father
585 && LST_LOOP_P (inner_father));
587 loop1 = LST_SEQ (outer_father)[outer];
589 FOR_EACH_VEC_ELT (LST_SEQ (inner_father), inner, loop2)
590 if (LST_LOOP_P (loop2)
591 && (lst_try_interchange_loops (scop, loop1, loop2)
592 || lst_interchange_select_inner (scop, outer_father, outer, loop2)))
593 return true;
595 return false;
598 /* Interchanges all the loops of LOOP and the loops of its body that
599 are considered profitable to interchange. Return the number of
600 interchanged loops. OUTER is the index in LST_SEQ (LOOP) that
601 points to the next outer loop to be considered for interchange. */
603 static int
604 lst_interchange_select_outer (scop_p scop, lst_p loop, int outer)
606 lst_p l;
607 int res = 0;
608 int i = 0;
609 lst_p father;
611 if (!loop || !LST_LOOP_P (loop))
612 return 0;
614 father = LST_LOOP_FATHER (loop);
615 if (father)
617 while (lst_interchange_select_inner (scop, father, outer, loop))
619 res++;
620 loop = LST_SEQ (father)[outer];
624 if (LST_LOOP_P (loop))
625 FOR_EACH_VEC_ELT (LST_SEQ (loop), i, l)
626 if (LST_LOOP_P (l))
627 res += lst_interchange_select_outer (scop, l, i);
629 return res;
632 /* Interchanges all the loop depths that are considered profitable for
633 SCOP. Return the number of interchanged loops. */
636 scop_do_interchange (scop_p scop)
638 int res = lst_interchange_select_outer
639 (scop, SCOP_TRANSFORMED_SCHEDULE (scop), 0);
641 lst_update_scattering (SCOP_TRANSFORMED_SCHEDULE (scop));
643 return res;
647 #endif