1 /* Interchange heuristics and transform for loop interchange on
2 polyhedral representation.
4 Copyright (C) 2009 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/>. */
25 #include "coretypes.h"
31 #include "basic-block.h"
32 #include "diagnostic.h"
33 #include "tree-flow.h"
35 #include "tree-dump.h"
38 #include "tree-chrec.h"
39 #include "tree-data-ref.h"
40 #include "tree-scalar-evolution.h"
41 #include "tree-pass.h"
43 #include "value-prof.h"
44 #include "pointer-set.h"
49 #include "cloog/cloog.h"
52 #include "graphite-ppl.h"
54 #include "graphite-poly.h"
56 /* Builds a linear expression, of dimension DIM, representing PDR's
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 ppl_Linear_Expression_t
74 build_linearized_memory_access (ppl_dimension_type offset, poly_dr_p pdr)
76 ppl_Linear_Expression_t res;
77 ppl_Linear_Expression_t le;
79 ppl_dimension_type first = pdr_subscript_dim (pdr, 0);
80 ppl_dimension_type last = pdr_subscript_dim (pdr, PDR_NB_SUBSCRIPTS (pdr));
82 graphite_dim_t dim = offset + pdr_dim (pdr);
84 ppl_new_Linear_Expression_with_dimension (&res, dim);
87 value_set_si (size, 1);
88 value_init (sub_size);
89 value_set_si (sub_size, 1);
91 for (i = last - 1; i >= first; i--)
93 ppl_set_coef_gmp (res, i + offset, size);
95 ppl_new_Linear_Expression_with_dimension (&le, dim - offset);
96 ppl_set_coef (le, i, 1);
97 ppl_max_for_le_pointset (PDR_ACCESSES (pdr), le, sub_size);
98 value_multiply (size, size, sub_size);
99 ppl_delete_Linear_Expression (le);
102 value_clear (sub_size);
107 /* Set STRIDE to the stride of PDR in memory by advancing by one in
108 time dimension DEPTH. */
111 memory_stride_in_loop (Value stride, graphite_dim_t depth, poly_dr_p pdr)
113 ppl_dimension_type time_depth;
114 ppl_Linear_Expression_t le, lma;
115 ppl_Constraint_t new_cstr;
116 ppl_dimension_type i, *map;
117 ppl_Pointset_Powerset_C_Polyhedron_t p1, p2, sctr;
118 graphite_dim_t nb_subscripts = PDR_NB_SUBSCRIPTS (pdr) + 1;
119 poly_bb_p pbb = PDR_PBB (pdr);
120 ppl_dimension_type offset = pbb_nb_scattering_transform (pbb)
121 + pbb_nb_local_vars (pbb)
122 + pbb_dim_iter_domain (pbb);
123 ppl_dimension_type offsetg = offset + pbb_nb_params (pbb);
124 ppl_dimension_type dim_sctr = pbb_nb_scattering_transform (pbb)
125 + pbb_nb_local_vars (pbb);
126 ppl_dimension_type dim_L1 = offset + offsetg + 2 * nb_subscripts;
127 ppl_dimension_type dim_L2 = offset + offsetg + 2 * nb_subscripts + 1;
128 ppl_dimension_type new_dim = offset + offsetg + 2 * nb_subscripts + 2;
130 /* The resulting polyhedron should have the following format:
131 T|I|T'|I'|G|S|S'|l1|l2
133 | T = t_1..t_{dim_sctr}
134 | I = i_1..i_{dim_iter_domain}
135 | T'= t'_1..t'_{dim_sctr}
136 | I'= i'_1..i'_{dim_iter_domain}
137 | G = g_1..g_{nb_params}
138 | S = s_1..s_{nb_subscripts}
139 | S'= s'_1..s'_{nb_subscripts}
140 | l1 and l2 are scalars.
143 offset = dim_sctr + dim_iter_domain + nb_local_vars
144 offsetg = dim_sctr + dim_iter_domain + nb_local_vars + nb_params. */
146 /* Construct the T|I|0|0|G|0|0|0|0 part. */
148 ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron
149 (&sctr, PBB_TRANSFORMED_SCATTERING (pbb));
150 ppl_Pointset_Powerset_C_Polyhedron_add_space_dimensions_and_embed
151 (sctr, 2 * nb_subscripts + 2);
152 ppl_insert_dimensions_pointset (sctr, offset, offset);
155 /* Construct the 0|I|0|0|G|S|0|0|0 part. */
157 ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
158 (&p1, PDR_ACCESSES (pdr));
159 ppl_Pointset_Powerset_C_Polyhedron_add_space_dimensions_and_embed
160 (p1, nb_subscripts + 2);
161 ppl_insert_dimensions_pointset (p1, 0, dim_sctr);
162 ppl_insert_dimensions_pointset (p1, offset, offset);
165 /* Construct the 0|0|0|0|0|S|0|l1|0 part. */
167 lma = build_linearized_memory_access (offset + dim_sctr, pdr);
168 ppl_set_coef (lma, dim_L1, -1);
169 ppl_new_Constraint (&new_cstr, lma, PPL_CONSTRAINT_TYPE_EQUAL);
170 ppl_Pointset_Powerset_C_Polyhedron_add_constraint (p1, new_cstr);
173 /* Now intersect all the parts to get the polyhedron P1:
178 T|I|0|0|G|S|0|l1|0. */
180 ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (p1, sctr);
181 ppl_delete_Pointset_Powerset_C_Polyhedron (sctr);
183 /* Build P2, which would have the following form:
184 0|0|T'|I'|G|0|S'|0|l2
186 P2 is built, by remapping the P1 polyhedron:
189 using the following mapping:
195 ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
198 map = ppl_new_id_map (new_dim);
201 for (i = 0; i < offset; i++)
202 ppl_interchange (map, i, i + offset);
205 ppl_interchange (map, dim_L1, dim_L2);
208 for (i = 0; i < nb_subscripts; i++)
209 ppl_interchange (map, offset + offsetg + i,
210 offset + offsetg + nb_subscripts + i);
212 ppl_Pointset_Powerset_C_Polyhedron_map_space_dimensions (p2, map, new_dim);
219 | t_{depth-1} = t'_{depth-1}
220 | t_{depth+1} = t'_{depth+1}
222 | t_{dim_sctr} = t'_{dim_sctr}
224 This means that all the time dimensions are equal except for
225 depth, where we will add t_{depth} = t'_{depth} + 1 in the next
228 time_depth = psct_dynamic_dim (pbb, depth);
229 for (i = 0; i < dim_sctr; i++)
232 ppl_new_Linear_Expression_with_dimension (&le, new_dim);
233 ppl_set_coef (le, i, 1);
234 ppl_set_coef (le, i + offset, -1);
235 ppl_new_Constraint (&new_cstr, le, PPL_CONSTRAINT_TYPE_EQUAL);
236 ppl_Pointset_Powerset_C_Polyhedron_add_constraint (p2, new_cstr);
237 ppl_delete_Linear_Expression (le);
238 ppl_delete_Constraint (new_cstr);
241 /* Add equality : t_{depth} = t'_{depth} + 1.
242 This is the core part of this alogrithm, since this
243 constraint asks for the memory access stride (difference)
244 between two consecutive points in time dimensions. */
246 ppl_new_Linear_Expression_with_dimension (&le, new_dim);
247 ppl_set_coef (le, time_depth, 1);
248 ppl_set_coef (le, time_depth + offset, -1);
249 ppl_set_inhomogeneous (le, 1);
250 ppl_new_Constraint (&new_cstr, le, PPL_CONSTRAINT_TYPE_EQUAL);
251 ppl_Pointset_Powerset_C_Polyhedron_add_constraint (p2, new_cstr);
252 ppl_delete_Linear_Expression (le);
253 ppl_delete_Constraint (new_cstr);
256 /* P1 = P1 inter P2. */
258 ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (p1, p2);
259 ppl_delete_Pointset_Powerset_C_Polyhedron (p2);
262 /* Maximise the expression L2 - L1. */
264 ppl_new_Linear_Expression_with_dimension (&le, new_dim);
265 ppl_set_coef (le, dim_L2, 1);
266 ppl_set_coef (le, dim_L1, -1);
267 ppl_max_for_le_pointset (p1, le, stride);
268 ppl_delete_Linear_Expression (le);
272 /* Returns true when it is profitable to interchange time dimensions DEPTH1
273 and DEPTH2 with DEPTH1 < DEPTH2 for PBB.
285 | for (i = 0; i < N; i++)
286 | for (j = 0; j < N; j++)
292 The data access A[j][i] is described like this:
300 | 0 0 0 0 -1 0 100 >= 0
301 | 0 0 0 0 0 -1 100 >= 0
303 The linearized memory access L to A[100][100] is:
308 TODO: the shown format is not valid as it does not show the fact
309 that the iteration domain "i j" is transformed using the scattering.
311 Next, to measure the impact of iterating once in loop "i", we build
312 a maximization problem: first, we add to DR accesses the dimensions
313 k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
314 L1 and L2 are the linearized memory access functions.
316 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
317 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
318 | 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
319 |-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
320 | 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
321 | 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
322 | 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
323 | 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
324 | 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
326 Then, we generate the polyhedron P2 by interchanging the dimensions
327 (s0, s2), (s1, s3), (L1, L2), (k, i)
329 | i j N a s0 s1 k s2 s3 L1 L2 D1 1
330 | 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
331 | 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
332 | 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
333 | 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
334 | 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
335 | 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
336 | 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
337 | 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
339 then we add to P2 the equality k = i + 1:
341 |-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
343 and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
345 Similarly, to determine the impact of one iteration on loop "j", we
346 interchange (k, j), we add "k = j + 1", and we compute D2 the
347 maximal value of the difference.
349 Finally, the profitability test is D1 < D2: if in the outer loop
350 the strides are smaller than in the inner loop, then it is
351 profitable to interchange the loops at DEPTH1 and DEPTH2. */
354 pbb_interchange_profitable_p (graphite_dim_t depth1, graphite_dim_t depth2,
362 gcc_assert (depth1 < depth2);
365 value_set_si (d1, 0);
367 value_set_si (d2, 0);
371 for (i = 0; VEC_iterate (poly_dr_p, PBB_DRS (pbb), i, pdr); i++)
373 value_set_si (n, PDR_NB_REFS (pdr));
375 memory_stride_in_loop (s, depth1, pdr);
376 value_multiply (s, s, n);
377 value_addto (d1, d1, s);
379 memory_stride_in_loop (s, depth2, pdr);
380 value_multiply (s, s, n);
381 value_addto (d2, d2, s);
384 res = value_lt (d1, d2);
394 /* Interchanges the loops at DEPTH1 and DEPTH2 of the original
395 scattering and assigns the resulting polyhedron to the transformed
399 pbb_interchange_loop_depths (graphite_dim_t depth1, graphite_dim_t depth2,
402 ppl_dimension_type i, dim;
403 ppl_dimension_type *map;
404 ppl_Polyhedron_t poly = PBB_TRANSFORMED_SCATTERING (pbb);
405 ppl_dimension_type dim1 = psct_dynamic_dim (pbb, depth1);
406 ppl_dimension_type dim2 = psct_dynamic_dim (pbb, depth2);
408 ppl_Polyhedron_space_dimension (poly, &dim);
409 map = (ppl_dimension_type *) XNEWVEC (ppl_dimension_type, dim);
411 for (i = 0; i < dim; i++)
417 ppl_Polyhedron_map_space_dimensions (poly, map, dim);
421 /* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
422 the statements below LST. */
425 lst_apply_interchange (lst_p lst, int depth1, int depth2)
430 if (LST_LOOP_P (lst))
435 for (i = 0; VEC_iterate (lst_p, LST_SEQ (lst), i, l); i++)
436 lst_apply_interchange (l, depth1, depth2);
439 pbb_interchange_loop_depths (depth1, depth2, LST_PBB (lst));
442 /* Return true when the interchange of loops at depths DEPTH1 and
443 DEPTH2 to all the statements below LST is profitable. */
446 lst_interchange_profitable_p (lst_p lst, int depth1, int depth2)
451 if (LST_LOOP_P (lst))
457 for (i = 0; VEC_iterate (lst_p, LST_SEQ (lst), i, l); i++)
459 bool profitable = lst_interchange_profitable_p (l, depth1, depth2);
461 if (profitable && !LST_LOOP_P (lst)
462 && dump_file && (dump_flags & TDF_DETAILS))
464 "Interchanging loops at depths %d and %d is profitable for stmt_%d.\n",
465 depth1, depth2, pbb_index (LST_PBB (lst)));
473 return pbb_interchange_profitable_p (depth1, depth2, LST_PBB (lst));
477 /* Try to interchange LOOP1 with LOOP2 for all the statements of the
478 body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
482 lst_try_interchange_loops (scop_p scop, lst_p loop1, lst_p loop2)
484 int depth1 = lst_depth (loop1);
485 int depth2 = lst_depth (loop2);
487 if (!lst_interchange_profitable_p (loop2, depth1, depth2))
490 lst_apply_interchange (loop2, depth1, depth2);
492 if (graphite_legal_transform (scop))
494 if (dump_file && (dump_flags & TDF_DETAILS))
496 "Loops at depths %d and %d will be interchanged.\n",
502 /* Undo the transform. */
503 lst_apply_interchange (loop2, depth2, depth1);
507 /* Try to interchange LOOP with all the loops contained in the body of
508 LST. Return true if it did interchanged some loops. */
511 lst_try_interchange (scop_p scop, lst_p loop, lst_p lst)
516 if (LST_LOOP_P (lst))
520 bool res = lst_try_interchange_loops (scop, loop, lst);
522 for (i = 0; VEC_iterate (lst_p, LST_SEQ (lst), i, l); i++)
523 res |= lst_try_interchange (scop, loop, l);
531 /* Interchanges all the loops of LST that are considered profitable to
532 interchange. Return true if it did interchanged some loops. */
535 lst_do_interchange (scop_p scop, lst_p lst)
540 if (LST_LOOP_P (lst))
546 if (lst_depth (lst) >= 0)
547 for (i = 0; VEC_iterate (lst_p, LST_SEQ (lst), i, l); i++)
548 res |= lst_try_interchange (scop, lst, l);
550 for (i = 0; VEC_iterate (lst_p, LST_SEQ (lst), i, l); i++)
551 res |= lst_do_interchange (scop, l);
559 /* Interchanges all the loop depths that are considered profitable for SCOP. */
562 scop_do_interchange (scop_p scop)
564 bool transform_done = false;
566 store_scattering (scop);
568 transform_done = lst_do_interchange (scop, SCOP_TRANSFORMED_SCHEDULE (scop));
573 if (!graphite_legal_transform (scop))
575 restore_scattering (scop);
579 return transform_done;