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
33 #include "gaussseidel.h"
43 #include "irgraph_t.h"
55 /* enable to also solve the equations with Gauss-Jordan */
56 #undef COMPARE_AGAINST_GAUSSJORDAN
58 #ifdef COMPARE_AGAINST_GAUSSJORDAN
59 #include "gaussjordan.h"
64 #define UNDEF(x) (fabs(x) < EPSILON)
65 #define SEIDEL_TOLERANCE 1e-7
67 #define MAX_INT_FREQ 1000000
69 #define set_foreach(s,type,i) for ((i)=(type)set_first((s)); (i); (i)=(type)set_next((s)))
71 typedef struct freq_t {
83 unsigned infeasible : 1;
86 static int cmp_freq(const void *a, const void *b, size_t size)
88 const freq_t *p = (const freq_t*) a;
89 const freq_t *q = (const freq_t*) b;
92 return !(p->irn == q->irn);
95 static freq_t *set_find_freq(set *freqs, const ir_node *irn)
99 return (freq_t*) set_find(freqs, &query, sizeof(query), HASH_PTR(irn));
102 static freq_t *set_insert_freq(set *freqs, const ir_node *irn)
109 return (freq_t*) set_insert(freqs, &query, sizeof(query), HASH_PTR(irn));
112 double get_block_execfreq(const ir_exec_freq *ef, const ir_node *irn)
114 if (!ef->infeasible) {
115 set *freqs = ef->freqs;
117 assert(is_Block(irn));
118 freq = set_find_freq(freqs, irn);
121 assert(freq->freq >= 0);
129 get_block_execfreq_ulong(const ir_exec_freq *ef, const ir_node *bb)
131 double f = get_block_execfreq(ef, bb);
132 int res = (int) (f > ef->min_non_zero ? ef->m * f + ef->b : 1.0);
136 static double *solve_lgs(gs_matrix_t *mat, double *x, int size)
138 double init = 1.0 / size;
142 /* better convergence. */
143 for (i = 0; i < size; ++i)
146 stat_ev_dbl("execfreq_matrix_size", size);
150 dev = gs_matrix_gauss_seidel(mat, x, size);
151 } while (fabs(dev) > SEIDEL_TOLERANCE);
152 stat_ev_tim_pop("execfreq_seidel_time");
153 stat_ev_dbl("execfreq_seidel_iter", iter);
155 #ifdef COMPARE_AGAINST_GAUSSJORDAN
157 double *nw = XMALLOCN(double, size * size);
158 double *nx = XMALLOCNZ(double, size);
160 gs_matrix_export(mat, nw, size);
163 firm_gaussjordansolve(nw, nx, size);
164 stat_ev_tim_pop("execfreq_jordan_time");
175 * Determine probability that predecessor pos takes this cf edge.
177 static double get_cf_probability(ir_node *bb, int pos, double loop_weight)
181 double inv_loop_weight = 1./loop_weight;
182 const ir_node *pred = get_Block_cfgpred_block(bb, pos);
183 const ir_loop *pred_loop;
185 const ir_edge_t *edge;
193 loop = get_irn_loop(bb);
194 depth = get_loop_depth(loop);
195 pred_loop = get_irn_loop(pred);
196 pred_depth = get_loop_depth(pred_loop);
198 for (d = depth; d < pred_depth; ++d) {
199 cur *= inv_loop_weight;
202 foreach_block_succ(pred, edge) {
203 const ir_node *succ = get_edge_src_irn(edge);
204 const ir_loop *succ_loop = get_irn_loop(succ);
205 int succ_depth = get_loop_depth(succ_loop);
208 for (d = succ_depth; d < pred_depth; ++d) {
209 fac *= inv_loop_weight;
217 static void exec_freq_node_info(void *ctx, FILE *f, const ir_node *irn)
219 ir_exec_freq *ef = (ir_exec_freq*) ctx;
223 fprintf(f, "execution frequency: %g/%lu\n", get_block_execfreq(ef, irn), get_block_execfreq_ulong(ef, irn));
226 ir_exec_freq *create_execfreq(ir_graph *irg)
228 ir_exec_freq *execfreq = XMALLOCZ(ir_exec_freq);
229 execfreq->freqs = new_set(cmp_freq, 32);
231 memset(&execfreq->hook, 0, sizeof(execfreq->hook));
233 // set reasonable values to convert double execfreq to ulong execfreq
236 execfreq->hook.context = execfreq;
237 execfreq->hook.hook._hook_node_info = exec_freq_node_info;
238 register_hook(hook_node_info, &execfreq->hook);
244 void set_execfreq(ir_exec_freq *execfreq, const ir_node *block, double freq)
246 freq_t *f = set_insert_freq(execfreq->freqs, block);
250 static void collect_blocks(ir_node *bl, void *data)
252 set *freqs = (set*) data;
253 set_insert_freq(freqs, bl);
256 ir_exec_freq *compute_execfreq(ir_graph *irg, double loop_weight)
262 freq_t *freq, *s, *e;
264 ir_node *end = get_irg_end(irg);
272 * using a toposort on the CFG (without back edges) will propagate
273 * the values better for the gauss/seidel iteration.
274 * => they can "flow" from start to end.
276 dfs = dfs_new(&absgraph_irg_cfg_succ, irg);
277 ef = XMALLOCZ(ir_exec_freq);
278 ef->min_non_zero = HUGE_VAL; /* initialize with a reasonable large number. */
279 freqs = ef->freqs = new_set(cmp_freq, dfs_get_n_nodes(dfs));
282 * Populate the exec freq set.
283 * The DFS cannot be used alone, since the CFG might not be connected
284 * due to unreachable code.
286 irg_block_walk_graph(irg, collect_blocks, NULL, freqs);
288 construct_cf_backedges(irg);
291 size = dfs_get_n_nodes(dfs);
292 mat = gs_new_matrix(size, size);
293 x = XMALLOCN(double, size);
295 for (idx = dfs_get_n_nodes(dfs) - 1; idx >= 0; --idx) {
296 ir_node *bb = (ir_node *) dfs_get_post_num_node(dfs, size - idx - 1);
299 freq = set_insert_freq(freqs, bb);
302 /* Sum of (execution frequency of predecessor * probability of cf edge) ... */
303 for (i = get_Block_n_cfgpreds(bb) - 1; i >= 0; --i) {
304 ir_node *pred = get_Block_cfgpred_block(bb, i);
305 int pred_idx = size - dfs_get_post_num(dfs, pred) - 1;
307 gs_matrix_set(mat, idx, pred_idx, get_cf_probability(bb, i, loop_weight));
309 /* ... equals my execution frequency */
310 gs_matrix_set(mat, idx, idx, -1.0);
316 * Add an edge from end to start.
317 * The problem is then an eigenvalue problem:
318 * Solve A*x = 1*x => (A-I)x = 0
320 s = set_find_freq(freqs, get_irg_start_block(irg));
322 e = set_find_freq(freqs, get_irg_end_block(irg));
324 gs_matrix_set(mat, s->idx, e->idx, 1.0);
327 * Also add an edge for each kept block to start.
329 * This avoid strange results for e.g. an irg containing a exit()-call
330 * which block has no cfg successor.
332 n_keepalives = get_End_n_keepalives(end);
333 for (idx = n_keepalives - 1; idx >= 0; --idx) {
334 ir_node *keep = get_End_keepalive(end, idx);
336 if (is_Block(keep) && get_Block_n_cfg_outs(keep) == 0) {
337 freq_t *k = set_find_freq(freqs, keep);
339 gs_matrix_set(mat, s->idx, k->idx, 1.0);
343 /* solve the system and delete the matrix */
344 solve_lgs(mat, x, size);
345 gs_delete_matrix(mat);
348 * compute the normalization factor.
349 * 1.0 / exec freq of start block.
351 norm = x[s->idx] != 0.0 ? 1.0 / x[s->idx] : 1.0;
354 set_foreach(freqs, freq_t*, freq) {
357 /* take abs because it sometimes can be -0 in case of endless loops */
358 freq->freq = fabs(x[idx]) * norm;
360 /* get the maximum exec freq */
361 ef->max = MAX(ef->max, freq->freq);
363 /* Get the minimum non-zero execution frequency. */
364 if (freq->freq > 0.0)
365 ef->min_non_zero = MIN(ef->min_non_zero, freq->freq);
368 /* compute m and b of the transformation used to convert the doubles into scaled ints */
370 double smallest_diff = 1.0;
372 double l2 = ef->min_non_zero;
375 double h1 = MAX_INT_FREQ;
377 double *fs = (double*) malloc(set_count(freqs) * sizeof(fs[0]));
380 set_foreach(freqs, freq_t*, freq)
381 fs[n++] = freq->freq;
384 * find the smallest difference of the execution frequencies
385 * we try to ressolve it with 1 integer.
387 for (i = 0; i < n; ++i) {
391 for (j = i + 1; j < n; ++j) {
392 double diff = fabs(fs[i] - fs[j]);
395 smallest_diff = MIN(diff, smallest_diff);
399 /* according to that the slope of the translation function is 1.0 / smallest diff */
400 ef->m = 1.0 / smallest_diff;
402 /* the abscissa is then given by */
403 ef->b = l1 - ef->m * l2;
406 * if the slope is so high that the largest integer would be larger than MAX_INT_FREQ
407 * set the largest int freq to that upper limit and recompute the translation function
409 if (ef->m * h2 + ef->b > MAX_INT_FREQ) {
410 ef->m = (h1 - l1) / (h2 - l2);
411 ef->b = l1 - ef->m * l2;
417 memset(&ef->hook, 0, sizeof(ef->hook));
418 ef->hook.context = ef;
419 ef->hook.hook._hook_node_info = exec_freq_node_info;
420 register_hook(hook_node_info, &ef->hook);
427 void free_execfreq(ir_exec_freq *ef)
430 unregister_hook(hook_node_info, &ef->hook);