| 1 |
684 |
jeremybenn |
/* Interchange heuristics and transform for loop interchange on
|
| 2 |
|
|
polyhedral representation.
|
| 3 |
|
|
|
| 4 |
|
|
Copyright (C) 2009, 2010 Free Software Foundation, Inc.
|
| 5 |
|
|
Contributed by Sebastian Pop <sebastian.pop@amd.com> and
|
| 6 |
|
|
Harsha Jagasia <harsha.jagasia@amd.com>.
|
| 7 |
|
|
|
| 8 |
|
|
This file is part of GCC.
|
| 9 |
|
|
|
| 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.
|
| 14 |
|
|
|
| 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.
|
| 19 |
|
|
|
| 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/>. */
|
| 23 |
|
|
#include "config.h"
|
| 24 |
|
|
#include "system.h"
|
| 25 |
|
|
#include "coretypes.h"
|
| 26 |
|
|
#include "tree-flow.h"
|
| 27 |
|
|
#include "tree-dump.h"
|
| 28 |
|
|
#include "cfgloop.h"
|
| 29 |
|
|
#include "tree-chrec.h"
|
| 30 |
|
|
#include "tree-data-ref.h"
|
| 31 |
|
|
#include "tree-scalar-evolution.h"
|
| 32 |
|
|
#include "sese.h"
|
| 33 |
|
|
|
| 34 |
|
|
#ifdef HAVE_cloog
|
| 35 |
|
|
#include "ppl_c.h"
|
| 36 |
|
|
#include "graphite-ppl.h"
|
| 37 |
|
|
#include "graphite-poly.h"
|
| 38 |
|
|
|
| 39 |
|
|
/* Builds a linear expression, of dimension DIM, representing PDR's
|
| 40 |
|
|
memory access:
|
| 41 |
|
|
|
| 42 |
|
|
L = r_{n}*r_{n-1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n-1} + s_{n}.
|
| 43 |
|
|
|
| 44 |
|
|
For an array A[10][20] with two subscript locations s0 and s1, the
|
| 45 |
|
|
linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0
|
| 46 |
|
|
corresponds to a memory stride of 20.
|
| 47 |
|
|
|
| 48 |
|
|
OFFSET is a number of dimensions to prepend before the
|
| 49 |
|
|
subscript dimensions: s_0, s_1, ..., s_n.
|
| 50 |
|
|
|
| 51 |
|
|
Thus, the final linear expression has the following format:
|
| 52 |
|
|
|
| 53 |
|
|
where the expression itself is:
|
| 54 |
|
|
c_0 * s_0 + c_1 * s_1 + ... c_n * s_n. */
|
| 55 |
|
|
|
| 56 |
|
|
static ppl_Linear_Expression_t
|
| 57 |
|
|
build_linearized_memory_access (ppl_dimension_type offset, poly_dr_p pdr)
|
| 58 |
|
|
{
|
| 59 |
|
|
ppl_Linear_Expression_t res;
|
| 60 |
|
|
ppl_Linear_Expression_t le;
|
| 61 |
|
|
ppl_dimension_type i;
|
| 62 |
|
|
ppl_dimension_type first = pdr_subscript_dim (pdr, 0);
|
| 63 |
|
|
ppl_dimension_type last = pdr_subscript_dim (pdr, PDR_NB_SUBSCRIPTS (pdr));
|
| 64 |
|
|
mpz_t size, sub_size;
|
| 65 |
|
|
graphite_dim_t dim = offset + pdr_dim (pdr);
|
| 66 |
|
|
|
| 67 |
|
|
ppl_new_Linear_Expression_with_dimension (&res, dim);
|
| 68 |
|
|
|
| 69 |
|
|
mpz_init (size);
|
| 70 |
|
|
mpz_set_si (size, 1);
|
| 71 |
|
|
mpz_init (sub_size);
|
| 72 |
|
|
mpz_set_si (sub_size, 1);
|
| 73 |
|
|
|
| 74 |
|
|
for (i = last - 1; i >= first; i--)
|
| 75 |
|
|
{
|
| 76 |
|
|
ppl_set_coef_gmp (res, i + offset, size);
|
| 77 |
|
|
|
| 78 |
|
|
ppl_new_Linear_Expression_with_dimension (&le, dim - offset);
|
| 79 |
|
|
ppl_set_coef (le, i, 1);
|
| 80 |
|
|
ppl_max_for_le_pointset (PDR_ACCESSES (pdr), le, sub_size);
|
| 81 |
|
|
mpz_mul (size, size, sub_size);
|
| 82 |
|
|
ppl_delete_Linear_Expression (le);
|
| 83 |
|
|
}
|
| 84 |
|
|
|
| 85 |
|
|
mpz_clear (sub_size);
|
| 86 |
|
|
mpz_clear (size);
|
| 87 |
|
|
return res;
|
| 88 |
|
|
}
|
| 89 |
|
|
|
| 90 |
|
|
/* Builds a partial difference equations and inserts them
|
| 91 |
|
|
into pointset powerset polyhedron P. Polyhedron is assumed
|
| 92 |
|
|
to have the format: T|I|T'|I'|G|S|S'|l1|l2.
|
| 93 |
|
|
|
| 94 |
|
|
TIME_DEPTH is the time dimension w.r.t. which we are
|
| 95 |
|
|
differentiating.
|
| 96 |
|
|
OFFSET represents the number of dimensions between
|
| 97 |
|
|
columns t_{time_depth} and t'_{time_depth}.
|
| 98 |
|
|
DIM_SCTR is the number of scattering dimensions. It is
|
| 99 |
|
|
essentially the dimensionality of the T vector.
|
| 100 |
|
|
|
| 101 |
|
|
The following equations are inserted into the polyhedron P:
|
| 102 |
|
|
| t_1 = t_1'
|
| 103 |
|
|
| ...
|
| 104 |
|
|
| t_{time_depth-1} = t'_{time_depth-1}
|
| 105 |
|
|
| t_{time_depth} = t'_{time_depth} + 1
|
| 106 |
|
|
| t_{time_depth+1} = t'_{time_depth + 1}
|
| 107 |
|
|
| ...
|
| 108 |
|
|
| t_{dim_sctr} = t'_{dim_sctr}. */
|
| 109 |
|
|
|
| 110 |
|
|
static void
|
| 111 |
|
|
build_partial_difference (ppl_Pointset_Powerset_C_Polyhedron_t *p,
|
| 112 |
|
|
ppl_dimension_type time_depth,
|
| 113 |
|
|
ppl_dimension_type offset,
|
| 114 |
|
|
ppl_dimension_type dim_sctr)
|
| 115 |
|
|
{
|
| 116 |
|
|
ppl_Constraint_t new_cstr;
|
| 117 |
|
|
ppl_Linear_Expression_t le;
|
| 118 |
|
|
ppl_dimension_type i;
|
| 119 |
|
|
ppl_dimension_type dim;
|
| 120 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_t temp;
|
| 121 |
|
|
|
| 122 |
|
|
/* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
|
| 123 |
|
|
This is the core part of this alogrithm, since this
|
| 124 |
|
|
constraint asks for the memory access stride (difference)
|
| 125 |
|
|
between two consecutive points in time dimensions. */
|
| 126 |
|
|
|
| 127 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_space_dimension (*p, &dim);
|
| 128 |
|
|
ppl_new_Linear_Expression_with_dimension (&le, dim);
|
| 129 |
|
|
ppl_set_coef (le, time_depth, 1);
|
| 130 |
|
|
ppl_set_coef (le, time_depth + offset, -1);
|
| 131 |
|
|
ppl_set_inhomogeneous (le, 1);
|
| 132 |
|
|
ppl_new_Constraint (&new_cstr, le, PPL_CONSTRAINT_TYPE_EQUAL);
|
| 133 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_constraint (*p, new_cstr);
|
| 134 |
|
|
ppl_delete_Linear_Expression (le);
|
| 135 |
|
|
ppl_delete_Constraint (new_cstr);
|
| 136 |
|
|
|
| 137 |
|
|
/* Add equalities:
|
| 138 |
|
|
| t1 = t1'
|
| 139 |
|
|
| ...
|
| 140 |
|
|
| t_{time_depth-1} = t'_{time_depth-1}
|
| 141 |
|
|
| t_{time_depth+1} = t'_{time_depth+1}
|
| 142 |
|
|
| ...
|
| 143 |
|
|
| t_{dim_sctr} = t'_{dim_sctr}
|
| 144 |
|
|
|
| 145 |
|
|
This means that all the time dimensions are equal except for
|
| 146 |
|
|
time_depth, where the constraint is t_{depth} = t'_{depth} + 1
|
| 147 |
|
|
step. More to this: we should be carefull not to add equalities
|
| 148 |
|
|
to the 'coupled' dimensions, which happens when the one dimension
|
| 149 |
|
|
is stripmined dimension, and the other dimension corresponds
|
| 150 |
|
|
to the point loop inside stripmined dimension. */
|
| 151 |
|
|
|
| 152 |
|
|
ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron (&temp, *p);
|
| 153 |
|
|
|
| 154 |
|
|
for (i = 0; i < dim_sctr; i++)
|
| 155 |
|
|
if (i != time_depth)
|
| 156 |
|
|
{
|
| 157 |
|
|
ppl_new_Linear_Expression_with_dimension (&le, dim);
|
| 158 |
|
|
ppl_set_coef (le, i, 1);
|
| 159 |
|
|
ppl_set_coef (le, i + offset, -1);
|
| 160 |
|
|
ppl_new_Constraint (&new_cstr, le, PPL_CONSTRAINT_TYPE_EQUAL);
|
| 161 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_constraint (temp, new_cstr);
|
| 162 |
|
|
|
| 163 |
|
|
if (ppl_Pointset_Powerset_C_Polyhedron_is_empty (temp))
|
| 164 |
|
|
{
|
| 165 |
|
|
ppl_delete_Pointset_Powerset_C_Polyhedron (temp);
|
| 166 |
|
|
ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron (&temp, *p);
|
| 167 |
|
|
}
|
| 168 |
|
|
else
|
| 169 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_constraint (*p, new_cstr);
|
| 170 |
|
|
ppl_delete_Linear_Expression (le);
|
| 171 |
|
|
ppl_delete_Constraint (new_cstr);
|
| 172 |
|
|
}
|
| 173 |
|
|
|
| 174 |
|
|
ppl_delete_Pointset_Powerset_C_Polyhedron (temp);
|
| 175 |
|
|
}
|
| 176 |
|
|
|
| 177 |
|
|
|
| 178 |
|
|
/* Set STRIDE to the stride of PDR in memory by advancing by one in
|
| 179 |
|
|
the loop at DEPTH. */
|
| 180 |
|
|
|
| 181 |
|
|
static void
|
| 182 |
|
|
pdr_stride_in_loop (mpz_t stride, graphite_dim_t depth, poly_dr_p pdr)
|
| 183 |
|
|
{
|
| 184 |
|
|
ppl_dimension_type time_depth;
|
| 185 |
|
|
ppl_Linear_Expression_t le, lma;
|
| 186 |
|
|
ppl_Constraint_t new_cstr;
|
| 187 |
|
|
ppl_dimension_type i, *map;
|
| 188 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_t p1, p2, sctr;
|
| 189 |
|
|
graphite_dim_t nb_subscripts = PDR_NB_SUBSCRIPTS (pdr) + 1;
|
| 190 |
|
|
poly_bb_p pbb = PDR_PBB (pdr);
|
| 191 |
|
|
ppl_dimension_type offset = pbb_nb_scattering_transform (pbb)
|
| 192 |
|
|
+ pbb_nb_local_vars (pbb)
|
| 193 |
|
|
+ pbb_dim_iter_domain (pbb);
|
| 194 |
|
|
ppl_dimension_type offsetg = offset + pbb_nb_params (pbb);
|
| 195 |
|
|
ppl_dimension_type dim_sctr = pbb_nb_scattering_transform (pbb)
|
| 196 |
|
|
+ pbb_nb_local_vars (pbb);
|
| 197 |
|
|
ppl_dimension_type dim_L1 = offset + offsetg + 2 * nb_subscripts;
|
| 198 |
|
|
ppl_dimension_type dim_L2 = offset + offsetg + 2 * nb_subscripts + 1;
|
| 199 |
|
|
ppl_dimension_type new_dim = offset + offsetg + 2 * nb_subscripts + 2;
|
| 200 |
|
|
|
| 201 |
|
|
/* The resulting polyhedron should have the following format:
|
| 202 |
|
|
T|I|T'|I'|G|S|S'|l1|l2
|
| 203 |
|
|
where:
|
| 204 |
|
|
| T = t_1..t_{dim_sctr}
|
| 205 |
|
|
| I = i_1..i_{dim_iter_domain}
|
| 206 |
|
|
| T'= t'_1..t'_{dim_sctr}
|
| 207 |
|
|
| I'= i'_1..i'_{dim_iter_domain}
|
| 208 |
|
|
| G = g_1..g_{nb_params}
|
| 209 |
|
|
| S = s_1..s_{nb_subscripts}
|
| 210 |
|
|
| S'= s'_1..s'_{nb_subscripts}
|
| 211 |
|
|
| l1 and l2 are scalars.
|
| 212 |
|
|
|
| 213 |
|
|
Some invariants:
|
| 214 |
|
|
offset = dim_sctr + dim_iter_domain + nb_local_vars
|
| 215 |
|
|
offsetg = dim_sctr + dim_iter_domain + nb_local_vars + nb_params. */
|
| 216 |
|
|
|
| 217 |
|
|
/* Construct the T|I|0|0|G|0|0|0|0 part. */
|
| 218 |
|
|
{
|
| 219 |
|
|
ppl_new_Pointset_Powerset_C_Polyhedron_from_C_Polyhedron
|
| 220 |
|
|
(&sctr, PBB_TRANSFORMED_SCATTERING (pbb));
|
| 221 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_space_dimensions_and_embed
|
| 222 |
|
|
(sctr, 2 * nb_subscripts + 2);
|
| 223 |
|
|
ppl_insert_dimensions_pointset (sctr, offset, offset);
|
| 224 |
|
|
}
|
| 225 |
|
|
|
| 226 |
|
|
/* Construct the 0|I|0|0|G|S|0|0|0 part. */
|
| 227 |
|
|
{
|
| 228 |
|
|
ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
|
| 229 |
|
|
(&p1, PDR_ACCESSES (pdr));
|
| 230 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_space_dimensions_and_embed
|
| 231 |
|
|
(p1, nb_subscripts + 2);
|
| 232 |
|
|
ppl_insert_dimensions_pointset (p1, 0, dim_sctr);
|
| 233 |
|
|
ppl_insert_dimensions_pointset (p1, offset, offset);
|
| 234 |
|
|
}
|
| 235 |
|
|
|
| 236 |
|
|
/* Construct the 0|0|0|0|0|S|0|l1|0 part. */
|
| 237 |
|
|
{
|
| 238 |
|
|
lma = build_linearized_memory_access (offset + dim_sctr, pdr);
|
| 239 |
|
|
ppl_set_coef (lma, dim_L1, -1);
|
| 240 |
|
|
ppl_new_Constraint (&new_cstr, lma, PPL_CONSTRAINT_TYPE_EQUAL);
|
| 241 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_add_constraint (p1, new_cstr);
|
| 242 |
|
|
ppl_delete_Linear_Expression (lma);
|
| 243 |
|
|
ppl_delete_Constraint (new_cstr);
|
| 244 |
|
|
}
|
| 245 |
|
|
|
| 246 |
|
|
/* Now intersect all the parts to get the polyhedron P1:
|
| 247 |
|
|
T|I|0|0|G|0|0|0 |0
|
| 248 |
|
|
0|I|0|0|G|S|0|0 |0
|
| 249 |
|
|
0|0|0|0|0|S|0|l1|0
|
| 250 |
|
|
------------------
|
| 251 |
|
|
T|I|0|0|G|S|0|l1|0. */
|
| 252 |
|
|
|
| 253 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (p1, sctr);
|
| 254 |
|
|
ppl_delete_Pointset_Powerset_C_Polyhedron (sctr);
|
| 255 |
|
|
|
| 256 |
|
|
/* Build P2, which would have the following form:
|
| 257 |
|
|
0|0|T'|I'|G|0|S'|0|l2
|
| 258 |
|
|
|
| 259 |
|
|
P2 is built, by remapping the P1 polyhedron:
|
| 260 |
|
|
T|I|0|0|G|S|0|l1|0
|
| 261 |
|
|
|
| 262 |
|
|
using the following mapping:
|
| 263 |
|
|
T->T'
|
| 264 |
|
|
I->I'
|
| 265 |
|
|
S->S'
|
| 266 |
|
|
l1->l2. */
|
| 267 |
|
|
{
|
| 268 |
|
|
ppl_new_Pointset_Powerset_C_Polyhedron_from_Pointset_Powerset_C_Polyhedron
|
| 269 |
|
|
(&p2, p1);
|
| 270 |
|
|
|
| 271 |
|
|
map = ppl_new_id_map (new_dim);
|
| 272 |
|
|
|
| 273 |
|
|
/* TI -> T'I'. */
|
| 274 |
|
|
for (i = 0; i < offset; i++)
|
| 275 |
|
|
ppl_interchange (map, i, i + offset);
|
| 276 |
|
|
|
| 277 |
|
|
/* l1 -> l2. */
|
| 278 |
|
|
ppl_interchange (map, dim_L1, dim_L2);
|
| 279 |
|
|
|
| 280 |
|
|
/* S -> S'. */
|
| 281 |
|
|
for (i = 0; i < nb_subscripts; i++)
|
| 282 |
|
|
ppl_interchange (map, offset + offsetg + i,
|
| 283 |
|
|
offset + offsetg + nb_subscripts + i);
|
| 284 |
|
|
|
| 285 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_map_space_dimensions (p2, map, new_dim);
|
| 286 |
|
|
free (map);
|
| 287 |
|
|
}
|
| 288 |
|
|
|
| 289 |
|
|
time_depth = psct_dynamic_dim (pbb, depth);
|
| 290 |
|
|
|
| 291 |
|
|
/* P1 = P1 inter P2. */
|
| 292 |
|
|
ppl_Pointset_Powerset_C_Polyhedron_intersection_assign (p1, p2);
|
| 293 |
|
|
build_partial_difference (&p1, time_depth, offset, dim_sctr);
|
| 294 |
|
|
|
| 295 |
|
|
/* Maximise the expression L2 - L1. */
|
| 296 |
|
|
{
|
| 297 |
|
|
ppl_new_Linear_Expression_with_dimension (&le, new_dim);
|
| 298 |
|
|
ppl_set_coef (le, dim_L2, 1);
|
| 299 |
|
|
ppl_set_coef (le, dim_L1, -1);
|
| 300 |
|
|
ppl_max_for_le_pointset (p1, le, stride);
|
| 301 |
|
|
}
|
| 302 |
|
|
|
| 303 |
|
|
if (dump_file && (dump_flags & TDF_DETAILS))
|
| 304 |
|
|
{
|
| 305 |
|
|
char *str;
|
| 306 |
|
|
void (*gmp_free) (void *, size_t);
|
| 307 |
|
|
|
| 308 |
|
|
fprintf (dump_file, "\nStride in BB_%d, DR_%d, depth %d:",
|
| 309 |
|
|
pbb_index (pbb), PDR_ID (pdr), (int) depth);
|
| 310 |
|
|
str = mpz_get_str (0, 10, stride);
|
| 311 |
|
|
fprintf (dump_file, " %s ", str);
|
| 312 |
|
|
mp_get_memory_functions (NULL, NULL, &gmp_free);
|
| 313 |
|
|
(*gmp_free) (str, strlen (str) + 1);
|
| 314 |
|
|
}
|
| 315 |
|
|
|
| 316 |
|
|
ppl_delete_Pointset_Powerset_C_Polyhedron (p1);
|
| 317 |
|
|
ppl_delete_Pointset_Powerset_C_Polyhedron (p2);
|
| 318 |
|
|
ppl_delete_Linear_Expression (le);
|
| 319 |
|
|
}
|
| 320 |
|
|
|
| 321 |
|
|
|
| 322 |
|
|
/* Sets STRIDES to the sum of all the strides of the data references
|
| 323 |
|
|
accessed in LOOP at DEPTH. */
|
| 324 |
|
|
|
| 325 |
|
|
static void
|
| 326 |
|
|
memory_strides_in_loop_1 (lst_p loop, graphite_dim_t depth, mpz_t strides)
|
| 327 |
|
|
{
|
| 328 |
|
|
int i, j;
|
| 329 |
|
|
lst_p l;
|
| 330 |
|
|
poly_dr_p pdr;
|
| 331 |
|
|
mpz_t s, n;
|
| 332 |
|
|
|
| 333 |
|
|
mpz_init (s);
|
| 334 |
|
|
mpz_init (n);
|
| 335 |
|
|
|
| 336 |
|
|
FOR_EACH_VEC_ELT (lst_p, LST_SEQ (loop), j, l)
|
| 337 |
|
|
if (LST_LOOP_P (l))
|
| 338 |
|
|
memory_strides_in_loop_1 (l, depth, strides);
|
| 339 |
|
|
else
|
| 340 |
|
|
FOR_EACH_VEC_ELT (poly_dr_p, PBB_DRS (LST_PBB (l)), i, pdr)
|
| 341 |
|
|
{
|
| 342 |
|
|
pdr_stride_in_loop (s, depth, pdr);
|
| 343 |
|
|
mpz_set_si (n, PDR_NB_REFS (pdr));
|
| 344 |
|
|
mpz_mul (s, s, n);
|
| 345 |
|
|
mpz_add (strides, strides, s);
|
| 346 |
|
|
}
|
| 347 |
|
|
|
| 348 |
|
|
mpz_clear (s);
|
| 349 |
|
|
mpz_clear (n);
|
| 350 |
|
|
}
|
| 351 |
|
|
|
| 352 |
|
|
/* Sets STRIDES to the sum of all the strides of the data references
|
| 353 |
|
|
accessed in LOOP at DEPTH. */
|
| 354 |
|
|
|
| 355 |
|
|
static void
|
| 356 |
|
|
memory_strides_in_loop (lst_p loop, graphite_dim_t depth, mpz_t strides)
|
| 357 |
|
|
{
|
| 358 |
|
|
if (mpz_cmp_si (loop->memory_strides, -1) == 0)
|
| 359 |
|
|
{
|
| 360 |
|
|
mpz_set_si (strides, 0);
|
| 361 |
|
|
memory_strides_in_loop_1 (loop, depth, strides);
|
| 362 |
|
|
}
|
| 363 |
|
|
else
|
| 364 |
|
|
mpz_set (strides, loop->memory_strides);
|
| 365 |
|
|
}
|
| 366 |
|
|
|
| 367 |
|
|
/* Return true when the interchange of loops LOOP1 and LOOP2 is
|
| 368 |
|
|
profitable.
|
| 369 |
|
|
|
| 370 |
|
|
Example:
|
| 371 |
|
|
|
| 372 |
|
|
| int a[100][100];
|
| 373 |
|
|
|
|
| 374 |
|
|
| int
|
| 375 |
|
|
| foo (int N)
|
| 376 |
|
|
| {
|
| 377 |
|
|
| int j;
|
| 378 |
|
|
| int i;
|
| 379 |
|
|
|
|
| 380 |
|
|
| for (i = 0; i < N; i++)
|
| 381 |
|
|
| for (j = 0; j < N; j++)
|
| 382 |
|
|
| a[j][2 * i] += 1;
|
| 383 |
|
|
|
|
| 384 |
|
|
| return a[N][12];
|
| 385 |
|
|
| }
|
| 386 |
|
|
|
| 387 |
|
|
The data access A[j][i] is described like this:
|
| 388 |
|
|
|
| 389 |
|
|
| i j N a s0 s1 1
|
| 390 |
|
|
| 0 0 0 1 0 0 -5 = 0
|
| 391 |
|
|
| 0 -1 0 0 1 0 0 = 0
|
| 392 |
|
|
|-2 0 0 0 0 1 0 = 0
|
| 393 |
|
|
| 0 0 0 0 1 0 0 >= 0
|
| 394 |
|
|
| 0 0 0 0 0 1 0 >= 0
|
| 395 |
|
|
| 0 0 0 0 -1 0 100 >= 0
|
| 396 |
|
|
| 0 0 0 0 0 -1 100 >= 0
|
| 397 |
|
|
|
| 398 |
|
|
The linearized memory access L to A[100][100] is:
|
| 399 |
|
|
|
| 400 |
|
|
| i j N a s0 s1 1
|
| 401 |
|
|
| 0 0 0 0 100 1 0
|
| 402 |
|
|
|
| 403 |
|
|
TODO: the shown format is not valid as it does not show the fact
|
| 404 |
|
|
that the iteration domain "i j" is transformed using the scattering.
|
| 405 |
|
|
|
| 406 |
|
|
Next, to measure the impact of iterating once in loop "i", we build
|
| 407 |
|
|
a maximization problem: first, we add to DR accesses the dimensions
|
| 408 |
|
|
k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1.
|
| 409 |
|
|
L1 and L2 are the linearized memory access functions.
|
| 410 |
|
|
|
| 411 |
|
|
| i j N a s0 s1 k s2 s3 L1 L2 D1 1
|
| 412 |
|
|
| 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
|
| 413 |
|
|
| 0 -1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j
|
| 414 |
|
|
|-2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i
|
| 415 |
|
|
| 0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0
|
| 416 |
|
|
| 0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0
|
| 417 |
|
|
| 0 0 0 0 -1 0 0 0 0 0 0 0 100 >= 0
|
| 418 |
|
|
| 0 0 0 0 0 -1 0 0 0 0 0 0 100 >= 0
|
| 419 |
|
|
| 0 0 0 0 100 1 0 0 0 -1 0 0 0 = 0 L1 = 100 * s0 + s1
|
| 420 |
|
|
|
| 421 |
|
|
Then, we generate the polyhedron P2 by interchanging the dimensions
|
| 422 |
|
|
(s0, s2), (s1, s3), (L1, L2), (k, i)
|
| 423 |
|
|
|
| 424 |
|
|
| i j N a s0 s1 k s2 s3 L1 L2 D1 1
|
| 425 |
|
|
| 0 0 0 1 0 0 0 0 0 0 0 0 -5 = 0 alias = 5
|
| 426 |
|
|
| 0 -1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j
|
| 427 |
|
|
| 0 0 0 0 0 0 -2 0 1 0 0 0 0 = 0 s3 = 2 * k
|
| 428 |
|
|
| 0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0
|
| 429 |
|
|
| 0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0
|
| 430 |
|
|
| 0 0 0 0 0 0 0 -1 0 0 0 0 100 >= 0
|
| 431 |
|
|
| 0 0 0 0 0 0 0 0 -1 0 0 0 100 >= 0
|
| 432 |
|
|
| 0 0 0 0 0 0 0 100 1 0 -1 0 0 = 0 L2 = 100 * s2 + s3
|
| 433 |
|
|
|
| 434 |
|
|
then we add to P2 the equality k = i + 1:
|
| 435 |
|
|
|
| 436 |
|
|
|-1 0 0 0 0 0 1 0 0 0 0 0 -1 = 0 k = i + 1
|
| 437 |
|
|
|
| 438 |
|
|
and finally we maximize the expression "D1 = max (P1 inter P2, L2 - L1)".
|
| 439 |
|
|
|
| 440 |
|
|
Similarly, to determine the impact of one iteration on loop "j", we
|
| 441 |
|
|
interchange (k, j), we add "k = j + 1", and we compute D2 the
|
| 442 |
|
|
maximal value of the difference.
|
| 443 |
|
|
|
| 444 |
|
|
Finally, the profitability test is D1 < D2: if in the outer loop
|
| 445 |
|
|
the strides are smaller than in the inner loop, then it is
|
| 446 |
|
|
profitable to interchange the loops at DEPTH1 and DEPTH2. */
|
| 447 |
|
|
|
| 448 |
|
|
static bool
|
| 449 |
|
|
lst_interchange_profitable_p (lst_p nest, int depth1, int depth2)
|
| 450 |
|
|
{
|
| 451 |
|
|
mpz_t d1, d2;
|
| 452 |
|
|
bool res;
|
| 453 |
|
|
|
| 454 |
|
|
gcc_assert (depth1 < depth2);
|
| 455 |
|
|
|
| 456 |
|
|
mpz_init (d1);
|
| 457 |
|
|
mpz_init (d2);
|
| 458 |
|
|
|
| 459 |
|
|
memory_strides_in_loop (nest, depth1, d1);
|
| 460 |
|
|
memory_strides_in_loop (nest, depth2, d2);
|
| 461 |
|
|
|
| 462 |
|
|
res = mpz_cmp (d1, d2) < 0;
|
| 463 |
|
|
|
| 464 |
|
|
mpz_clear (d1);
|
| 465 |
|
|
mpz_clear (d2);
|
| 466 |
|
|
|
| 467 |
|
|
return res;
|
| 468 |
|
|
}
|
| 469 |
|
|
|
| 470 |
|
|
/* Interchanges the loops at DEPTH1 and DEPTH2 of the original
|
| 471 |
|
|
scattering and assigns the resulting polyhedron to the transformed
|
| 472 |
|
|
scattering. */
|
| 473 |
|
|
|
| 474 |
|
|
static void
|
| 475 |
|
|
pbb_interchange_loop_depths (graphite_dim_t depth1, graphite_dim_t depth2,
|
| 476 |
|
|
poly_bb_p pbb)
|
| 477 |
|
|
{
|
| 478 |
|
|
ppl_dimension_type i, dim;
|
| 479 |
|
|
ppl_dimension_type *map;
|
| 480 |
|
|
ppl_Polyhedron_t poly = PBB_TRANSFORMED_SCATTERING (pbb);
|
| 481 |
|
|
ppl_dimension_type dim1 = psct_dynamic_dim (pbb, depth1);
|
| 482 |
|
|
ppl_dimension_type dim2 = psct_dynamic_dim (pbb, depth2);
|
| 483 |
|
|
|
| 484 |
|
|
ppl_Polyhedron_space_dimension (poly, &dim);
|
| 485 |
|
|
map = (ppl_dimension_type *) XNEWVEC (ppl_dimension_type, dim);
|
| 486 |
|
|
|
| 487 |
|
|
for (i = 0; i < dim; i++)
|
| 488 |
|
|
map[i] = i;
|
| 489 |
|
|
|
| 490 |
|
|
map[dim1] = dim2;
|
| 491 |
|
|
map[dim2] = dim1;
|
| 492 |
|
|
|
| 493 |
|
|
ppl_Polyhedron_map_space_dimensions (poly, map, dim);
|
| 494 |
|
|
free (map);
|
| 495 |
|
|
}
|
| 496 |
|
|
|
| 497 |
|
|
/* Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all
|
| 498 |
|
|
the statements below LST. */
|
| 499 |
|
|
|
| 500 |
|
|
static void
|
| 501 |
|
|
lst_apply_interchange (lst_p lst, int depth1, int depth2)
|
| 502 |
|
|
{
|
| 503 |
|
|
if (!lst)
|
| 504 |
|
|
return;
|
| 505 |
|
|
|
| 506 |
|
|
if (LST_LOOP_P (lst))
|
| 507 |
|
|
{
|
| 508 |
|
|
int i;
|
| 509 |
|
|
lst_p l;
|
| 510 |
|
|
|
| 511 |
|
|
FOR_EACH_VEC_ELT (lst_p, LST_SEQ (lst), i, l)
|
| 512 |
|
|
lst_apply_interchange (l, depth1, depth2);
|
| 513 |
|
|
}
|
| 514 |
|
|
else
|
| 515 |
|
|
pbb_interchange_loop_depths (depth1, depth2, LST_PBB (lst));
|
| 516 |
|
|
}
|
| 517 |
|
|
|
| 518 |
|
|
/* Return true when the nest starting at LOOP1 and ending on LOOP2 is
|
| 519 |
|
|
perfect: i.e. there are no sequence of statements. */
|
| 520 |
|
|
|
| 521 |
|
|
static bool
|
| 522 |
|
|
lst_perfectly_nested_p (lst_p loop1, lst_p loop2)
|
| 523 |
|
|
{
|
| 524 |
|
|
if (loop1 == loop2)
|
| 525 |
|
|
return true;
|
| 526 |
|
|
|
| 527 |
|
|
if (!LST_LOOP_P (loop1))
|
| 528 |
|
|
return false;
|
| 529 |
|
|
|
| 530 |
|
|
return VEC_length (lst_p, LST_SEQ (loop1)) == 1
|
| 531 |
|
|
&& lst_perfectly_nested_p (VEC_index (lst_p, LST_SEQ (loop1), 0), loop2);
|
| 532 |
|
|
}
|
| 533 |
|
|
|
| 534 |
|
|
/* Transform the loop nest between LOOP1 and LOOP2 into a perfect
|
| 535 |
|
|
nest. To continue the naming tradition, this function is called
|
| 536 |
|
|
after perfect_nestify. NEST is set to the perfectly nested loop
|
| 537 |
|
|
that is created. BEFORE/AFTER are set to the loops distributed
|
| 538 |
|
|
before/after the loop NEST. */
|
| 539 |
|
|
|
| 540 |
|
|
static void
|
| 541 |
|
|
lst_perfect_nestify (lst_p loop1, lst_p loop2, lst_p *before,
|
| 542 |
|
|
lst_p *nest, lst_p *after)
|
| 543 |
|
|
{
|
| 544 |
|
|
poly_bb_p first, last;
|
| 545 |
|
|
|
| 546 |
|
|
gcc_assert (loop1 && loop2
|
| 547 |
|
|
&& loop1 != loop2
|
| 548 |
|
|
&& LST_LOOP_P (loop1) && LST_LOOP_P (loop2));
|
| 549 |
|
|
|
| 550 |
|
|
first = LST_PBB (lst_find_first_pbb (loop2));
|
| 551 |
|
|
last = LST_PBB (lst_find_last_pbb (loop2));
|
| 552 |
|
|
|
| 553 |
|
|
*before = copy_lst (loop1);
|
| 554 |
|
|
*nest = copy_lst (loop1);
|
| 555 |
|
|
*after = copy_lst (loop1);
|
| 556 |
|
|
|
| 557 |
|
|
lst_remove_all_before_including_pbb (*before, first, false);
|
| 558 |
|
|
lst_remove_all_before_including_pbb (*after, last, true);
|
| 559 |
|
|
|
| 560 |
|
|
lst_remove_all_before_excluding_pbb (*nest, first, true);
|
| 561 |
|
|
lst_remove_all_before_excluding_pbb (*nest, last, false);
|
| 562 |
|
|
|
| 563 |
|
|
if (lst_empty_p (*before))
|
| 564 |
|
|
{
|
| 565 |
|
|
free_lst (*before);
|
| 566 |
|
|
*before = NULL;
|
| 567 |
|
|
}
|
| 568 |
|
|
if (lst_empty_p (*after))
|
| 569 |
|
|
{
|
| 570 |
|
|
free_lst (*after);
|
| 571 |
|
|
*after = NULL;
|
| 572 |
|
|
}
|
| 573 |
|
|
if (lst_empty_p (*nest))
|
| 574 |
|
|
{
|
| 575 |
|
|
free_lst (*nest);
|
| 576 |
|
|
*nest = NULL;
|
| 577 |
|
|
}
|
| 578 |
|
|
}
|
| 579 |
|
|
|
| 580 |
|
|
/* Try to interchange LOOP1 with LOOP2 for all the statements of the
|
| 581 |
|
|
body of LOOP2. LOOP1 contains LOOP2. Return true if it did the
|
| 582 |
|
|
interchange. */
|
| 583 |
|
|
|
| 584 |
|
|
static bool
|
| 585 |
|
|
lst_try_interchange_loops (scop_p scop, lst_p loop1, lst_p loop2)
|
| 586 |
|
|
{
|
| 587 |
|
|
int depth1 = lst_depth (loop1);
|
| 588 |
|
|
int depth2 = lst_depth (loop2);
|
| 589 |
|
|
lst_p transformed;
|
| 590 |
|
|
|
| 591 |
|
|
lst_p before = NULL, nest = NULL, after = NULL;
|
| 592 |
|
|
|
| 593 |
|
|
if (!lst_perfectly_nested_p (loop1, loop2))
|
| 594 |
|
|
lst_perfect_nestify (loop1, loop2, &before, &nest, &after);
|
| 595 |
|
|
|
| 596 |
|
|
if (!lst_interchange_profitable_p (loop2, depth1, depth2))
|
| 597 |
|
|
return false;
|
| 598 |
|
|
|
| 599 |
|
|
lst_apply_interchange (loop2, depth1, depth2);
|
| 600 |
|
|
|
| 601 |
|
|
/* Sync the transformed LST information and the PBB scatterings
|
| 602 |
|
|
before using the scatterings in the data dependence analysis. */
|
| 603 |
|
|
if (before || nest || after)
|
| 604 |
|
|
{
|
| 605 |
|
|
transformed = lst_substitute_3 (SCOP_TRANSFORMED_SCHEDULE (scop), loop1,
|
| 606 |
|
|
before, nest, after);
|
| 607 |
|
|
lst_update_scattering (transformed);
|
| 608 |
|
|
free_lst (transformed);
|
| 609 |
|
|
}
|
| 610 |
|
|
|
| 611 |
|
|
if (graphite_legal_transform (scop))
|
| 612 |
|
|
{
|
| 613 |
|
|
if (dump_file && (dump_flags & TDF_DETAILS))
|
| 614 |
|
|
fprintf (dump_file,
|
| 615 |
|
|
"Loops at depths %d and %d will be interchanged.\n",
|
| 616 |
|
|
depth1, depth2);
|
| 617 |
|
|
|
| 618 |
|
|
/* Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP. */
|
| 619 |
|
|
lst_insert_in_sequence (before, loop1, true);
|
| 620 |
|
|
lst_insert_in_sequence (after, loop1, false);
|
| 621 |
|
|
|
| 622 |
|
|
if (nest)
|
| 623 |
|
|
{
|
| 624 |
|
|
lst_replace (loop1, nest);
|
| 625 |
|
|
free_lst (loop1);
|
| 626 |
|
|
}
|
| 627 |
|
|
|
| 628 |
|
|
return true;
|
| 629 |
|
|
}
|
| 630 |
|
|
|
| 631 |
|
|
/* Undo the transform. */
|
| 632 |
|
|
free_lst (before);
|
| 633 |
|
|
free_lst (nest);
|
| 634 |
|
|
free_lst (after);
|
| 635 |
|
|
lst_apply_interchange (loop2, depth2, depth1);
|
| 636 |
|
|
return false;
|
| 637 |
|
|
}
|
| 638 |
|
|
|
| 639 |
|
|
/* Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged
|
| 640 |
|
|
with the loop OUTER in LST_SEQ (OUTER_FATHER). */
|
| 641 |
|
|
|
| 642 |
|
|
static bool
|
| 643 |
|
|
lst_interchange_select_inner (scop_p scop, lst_p outer_father, int outer,
|
| 644 |
|
|
lst_p inner_father)
|
| 645 |
|
|
{
|
| 646 |
|
|
int inner;
|
| 647 |
|
|
lst_p loop1, loop2;
|
| 648 |
|
|
|
| 649 |
|
|
gcc_assert (outer_father
|
| 650 |
|
|
&& LST_LOOP_P (outer_father)
|
| 651 |
|
|
&& LST_LOOP_P (VEC_index (lst_p, LST_SEQ (outer_father), outer))
|
| 652 |
|
|
&& inner_father
|
| 653 |
|
|
&& LST_LOOP_P (inner_father));
|
| 654 |
|
|
|
| 655 |
|
|
loop1 = VEC_index (lst_p, LST_SEQ (outer_father), outer);
|
| 656 |
|
|
|
| 657 |
|
|
FOR_EACH_VEC_ELT (lst_p, LST_SEQ (inner_father), inner, loop2)
|
| 658 |
|
|
if (LST_LOOP_P (loop2)
|
| 659 |
|
|
&& (lst_try_interchange_loops (scop, loop1, loop2)
|
| 660 |
|
|
|| lst_interchange_select_inner (scop, outer_father, outer, loop2)))
|
| 661 |
|
|
return true;
|
| 662 |
|
|
|
| 663 |
|
|
return false;
|
| 664 |
|
|
}
|
| 665 |
|
|
|
| 666 |
|
|
/* Interchanges all the loops of LOOP and the loops of its body that
|
| 667 |
|
|
are considered profitable to interchange. Return the number of
|
| 668 |
|
|
interchanged loops. OUTER is the index in LST_SEQ (LOOP) that
|
| 669 |
|
|
points to the next outer loop to be considered for interchange. */
|
| 670 |
|
|
|
| 671 |
|
|
static int
|
| 672 |
|
|
lst_interchange_select_outer (scop_p scop, lst_p loop, int outer)
|
| 673 |
|
|
{
|
| 674 |
|
|
lst_p l;
|
| 675 |
|
|
int res = 0;
|
| 676 |
|
|
int i = 0;
|
| 677 |
|
|
lst_p father;
|
| 678 |
|
|
|
| 679 |
|
|
if (!loop || !LST_LOOP_P (loop))
|
| 680 |
|
|
return 0;
|
| 681 |
|
|
|
| 682 |
|
|
father = LST_LOOP_FATHER (loop);
|
| 683 |
|
|
if (father)
|
| 684 |
|
|
{
|
| 685 |
|
|
while (lst_interchange_select_inner (scop, father, outer, loop))
|
| 686 |
|
|
{
|
| 687 |
|
|
res++;
|
| 688 |
|
|
loop = VEC_index (lst_p, LST_SEQ (father), outer);
|
| 689 |
|
|
}
|
| 690 |
|
|
}
|
| 691 |
|
|
|
| 692 |
|
|
if (LST_LOOP_P (loop))
|
| 693 |
|
|
FOR_EACH_VEC_ELT (lst_p, LST_SEQ (loop), i, l)
|
| 694 |
|
|
if (LST_LOOP_P (l))
|
| 695 |
|
|
res += lst_interchange_select_outer (scop, l, i);
|
| 696 |
|
|
|
| 697 |
|
|
return res;
|
| 698 |
|
|
}
|
| 699 |
|
|
|
| 700 |
|
|
/* Interchanges all the loop depths that are considered profitable for
|
| 701 |
|
|
SCOP. Return the number of interchanged loops. */
|
| 702 |
|
|
|
| 703 |
|
|
int
|
| 704 |
|
|
scop_do_interchange (scop_p scop)
|
| 705 |
|
|
{
|
| 706 |
|
|
int res = lst_interchange_select_outer
|
| 707 |
|
|
(scop, SCOP_TRANSFORMED_SCHEDULE (scop), 0);
|
| 708 |
|
|
|
| 709 |
|
|
lst_update_scattering (SCOP_TRANSFORMED_SCHEDULE (scop));
|
| 710 |
|
|
|
| 711 |
|
|
return res;
|
| 712 |
|
|
}
|
| 713 |
|
|
|
| 714 |
|
|
|
| 715 |
|
|
#endif
|
| 716 |
|
|
|