2 * Copyright (C) 1995-2008 University of Karlsruhe. All right reserved.
4 * This file is part of libFirm.
6 * This file may be distributed and/or modified under the terms of the
7 * GNU General Public License version 2 as published by the Free Software
8 * Foundation and appearing in the file LICENSE.GPL included in the
9 * packaging of this file.
11 * Licensees holding valid libFirm Professional Edition licenses may use
12 * this file in accordance with the libFirm Commercial License.
13 * Agreement provided with the Software.
15 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
16 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * @brief Compute an estimate of basic block executions.
23 * @author Adam M. Szalkowski
34 #include "gaussseidel.h"
44 #include "irgraph_t.h"
56 /* enable to also solve the equations with Gauss-Jordan */
57 #undef COMPARE_AGAINST_GAUSSJORDAN
59 #ifdef COMPARE_AGAINST_GAUSSJORDAN
60 #include "gaussjordan.h"
65 #define UNDEF(x) (fabs(x) < EPSILON)
66 #define SEIDEL_TOLERANCE 1e-7
68 #define MAX_INT_FREQ 1000000
70 #define set_foreach(s,i) for ((i)=set_first((s)); (i); (i)=set_next((s)))
72 typedef struct _freq_t {
84 unsigned infeasible : 1;
87 static int cmp_freq(const void *a, const void *b, size_t size)
93 return !(p->irn == q->irn);
96 static freq_t *set_find_freq(set *set, const ir_node *irn)
101 return set_find(set, &query, sizeof(query), HASH_PTR(irn));
104 static freq_t *set_insert_freq(set *set, const ir_node *irn)
111 return set_insert(set, &query, sizeof(query), HASH_PTR(irn));
114 double get_block_execfreq(const ir_exec_freq *ef, const ir_node *irn)
116 if (!ef->infeasible) {
117 set *freqs = ef->set;
119 assert(is_Block(irn));
120 freq = set_find_freq(freqs, irn);
123 assert(freq->freq >= 0);
131 get_block_execfreq_ulong(const ir_exec_freq *ef, const ir_node *bb)
133 double f = get_block_execfreq(ef, bb);
134 int res = (int) (f > ef->min_non_zero ? ef->m * f + ef->b : 1.0);
138 static double *solve_lgs(gs_matrix_t *mat, double *x, int size)
140 double init = 1.0 / size;
144 /* better convergence. */
145 for (i = 0; i < size; ++i)
148 stat_ev_dbl("execfreq_matrix_size", size);
152 dev = gs_matrix_gauss_seidel(mat, x, size);
153 } while (fabs(dev) > SEIDEL_TOLERANCE);
154 stat_ev_tim_pop("execfreq_seidel_time");
155 stat_ev_dbl("execfreq_seidel_iter", iter);
157 #ifdef COMPARE_AGAINST_GAUSSJORDAN
159 double *nw = XMALLOCN(double, size * size);
160 double *nx = XMALLOCNZ(double, size);
162 gs_matrix_export(mat, nw, size);
165 firm_gaussjordansolve(nw, nx, size);
166 stat_ev_tim_pop("execfreq_jordan_time");
177 * Determine probability that predecessor pos takes this cf edge.
179 static double get_cf_probability(ir_node *bb, int pos, double loop_weight)
183 double inv_loop_weight = 1./loop_weight;
184 const ir_node *pred = get_Block_cfgpred_block(bb, pos);
185 const ir_loop *pred_loop;
187 const ir_edge_t *edge;
195 loop = get_irn_loop(bb);
196 depth = get_loop_depth(loop);
197 pred_loop = get_irn_loop(pred);
198 pred_depth = get_loop_depth(pred_loop);
200 for (d = depth; d < pred_depth; ++d) {
201 cur *= inv_loop_weight;
204 foreach_block_succ(pred, edge) {
205 const ir_node *succ = get_edge_src_irn(edge);
206 const ir_loop *succ_loop = get_irn_loop(succ);
207 int succ_depth = get_loop_depth(succ_loop);
210 for (d = succ_depth; d < pred_depth; ++d) {
211 fac *= inv_loop_weight;
219 static void exec_freq_node_info(void *ctx, FILE *f, const ir_node *irn)
222 ir_exec_freq *ef = ctx;
223 fprintf(f, "execution frequency: %g/%lu\n", get_block_execfreq(ef, irn), get_block_execfreq_ulong(ef, irn));
227 ir_exec_freq *create_execfreq(ir_graph *irg)
229 ir_exec_freq *execfreq = XMALLOCZ(ir_exec_freq);
230 execfreq->set = new_set(cmp_freq, 32);
232 memset(&execfreq->hook, 0, sizeof(execfreq->hook));
234 // set reasonable values to convert double execfreq to ulong execfreq
237 execfreq->hook.context = execfreq;
238 execfreq->hook.hook._hook_node_info = exec_freq_node_info;
239 register_hook(hook_node_info, &execfreq->hook);
245 void set_execfreq(ir_exec_freq *execfreq, const ir_node *block, double freq)
247 freq_t *f = set_insert_freq(execfreq->set, block);
251 static void collect_blocks(ir_node *bl, void *data)
254 set_insert_freq(freqs, bl);
257 ir_exec_freq *compute_execfreq(ir_graph *irg, double loop_weight)
263 freq_t *freq, *s, *e;
265 ir_node *end = get_irg_end(irg);
273 * using a toposort on the CFG (without back edges) will propagate
274 * the values better for the gauss/seidel iteration.
275 * => they can "flow" from start to end.
277 dfs = dfs_new(&absgraph_irg_cfg_succ, irg);
278 ef = XMALLOCZ(ir_exec_freq);
279 ef->min_non_zero = HUGE_VAL; /* initialize with a reasonable large number. */
280 freqs = ef->set = new_set(cmp_freq, dfs_get_n_nodes(dfs));
283 * Populate the exec freq set.
284 * The DFS cannot be used alone, since the CFG might not be connected
285 * due to unreachable code.
287 irg_block_walk_graph(irg, collect_blocks, NULL, freqs);
289 construct_cf_backedges(irg);
292 size = dfs_get_n_nodes(dfs);
293 mat = gs_new_matrix(size, size);
294 x = XMALLOCN(double, size);
296 for (idx = dfs_get_n_nodes(dfs) - 1; idx >= 0; --idx) {
297 ir_node *bb = (ir_node *) dfs_get_post_num_node(dfs, size - idx - 1);
301 freq = set_insert_freq(freqs, bb);
304 /* Sum of (execution frequency of predecessor * probability of cf edge) ... */
305 for (i = get_Block_n_cfgpreds(bb) - 1; i >= 0; --i) {
306 ir_node *pred = get_Block_cfgpred_block(bb, i);
307 int pred_idx = size - dfs_get_post_num(dfs, pred) - 1;
309 gs_matrix_set(mat, idx, pred_idx, get_cf_probability(bb, i, loop_weight));
311 /* ... equals my execution frequency */
312 gs_matrix_set(mat, idx, idx, -1.0);
318 * Add an edge from end to start.
319 * The problem is then an eigenvalue problem:
320 * Solve A*x = 1*x => (A-I)x = 0
322 s = set_find_freq(freqs, get_irg_start_block(irg));
324 e = set_find_freq(freqs, get_irg_end_block(irg));
326 gs_matrix_set(mat, s->idx, e->idx, 1.0);
329 * Also add an edge for each kept block to start.
331 * This avoid strange results for e.g. an irg containing a exit()-call
332 * which block has no cfg successor.
334 n_keepalives = get_End_n_keepalives(end);
335 for (idx = n_keepalives - 1; idx >= 0; --idx) {
336 ir_node *keep = get_End_keepalive(end, idx);
338 if (is_Block(keep) && get_Block_n_cfg_outs(keep) == 0) {
339 freq_t *k = set_find_freq(freqs, keep);
341 gs_matrix_set(mat, s->idx, k->idx, 1.0);
345 /* solve the system and delete the matrix */
346 solve_lgs(mat, x, size);
347 gs_delete_matrix(mat);
350 * compute the normalization factor.
351 * 1.0 / exec freq of start block.
353 norm = x[s->idx] != 0.0 ? 1.0 / x[s->idx] : 1.0;
356 set_foreach(freqs, freq) {
359 /* take abs because it sometimes can be -0 in case of endless loops */
360 freq->freq = fabs(x[idx]) * norm;
362 /* get the maximum exec freq */
363 ef->max = MAX(ef->max, freq->freq);
365 /* Get the minimum non-zero execution frequency. */
366 if (freq->freq > 0.0)
367 ef->min_non_zero = MIN(ef->min_non_zero, freq->freq);
370 /* compute m and b of the transformation used to convert the doubles into scaled ints */
372 double smallest_diff = 1.0;
374 double l2 = ef->min_non_zero;
377 double h1 = MAX_INT_FREQ;
379 double *fs = malloc(set_count(freqs) * sizeof(fs[0]));
382 set_foreach(freqs, freq)
383 fs[n++] = freq->freq;
386 * find the smallest difference of the execution frequencies
387 * we try to ressolve it with 1 integer.
389 for (i = 0; i < n; ++i) {
393 for (j = i + 1; j < n; ++j) {
394 double diff = fabs(fs[i] - fs[j]);
397 smallest_diff = MIN(diff, smallest_diff);
401 /* according to that the slope of the translation function is 1.0 / smallest diff */
402 ef->m = 1.0 / smallest_diff;
404 /* the abscissa is then given by */
405 ef->b = l1 - ef->m * l2;
408 * if the slope is so high that the largest integer would be larger than MAX_INT_FREQ
409 * set the largest int freq to that upper limit and recompute the translation function
411 if (ef->m * h2 + ef->b > MAX_INT_FREQ) {
412 ef->m = (h1 - l1) / (h2 - l2);
413 ef->b = l1 - ef->m * l2;
419 memset(&ef->hook, 0, sizeof(ef->hook));
420 ef->hook.context = ef;
421 ef->hook.hook._hook_node_info = exec_freq_node_info;
422 register_hook(hook_node_info, &ef->hook);
429 void free_execfreq(ir_exec_freq *ef)
432 unregister_hook(hook_node_info, &ef->hook);