#include "cache.h" #include "commit.h" #include "diff.h" #include "revision.h" #include "refs.h" #include "list-objects.h" #include "quote.h" #include "sha1-lookup.h" #include "run-command.h" #include "log-tree.h" #include "bisect.h" #include "sha1-array.h" #include "argv-array.h" static struct sha1_array good_revs; static struct sha1_array skipped_revs; static struct object_id *current_bad_oid; static const char *argv_checkout[] = {"checkout", "-q", NULL, "--", NULL}; static const char *argv_show_branch[] = {"show-branch", NULL, NULL}; static const char *term_bad; static const char *term_good; /* Remember to update object flag allocation in object.h */ #define COUNTED (1u<<16) /* * This is a truly stupid algorithm, but it's only * used for bisection, and we just don't care enough. * * We care just barely enough to avoid recursing for * non-merge entries. */ static int count_distance(struct commit_list *entry) { int nr = 0; while (entry) { struct commit *commit = entry->item; struct commit_list *p; if (commit->object.flags & (UNINTERESTING | COUNTED)) break; if (!(commit->object.flags & TREESAME)) nr++; commit->object.flags |= COUNTED; p = commit->parents; entry = p; if (p) { p = p->next; while (p) { nr += count_distance(p); p = p->next; } } } return nr; } static void clear_distance(struct commit_list *list) { while (list) { struct commit *commit = list->item; commit->object.flags &= ~COUNTED; list = list->next; } } #define DEBUG_BISECT 0 static inline int weight(struct commit_list *elem) { return *((int*)(elem->item->util)); } static inline void weight_set(struct commit_list *elem, int weight) { *((int*)(elem->item->util)) = weight; } static int count_interesting_parents(struct commit *commit) { struct commit_list *p; int count; for (count = 0, p = commit->parents; p; p = p->next) { if (p->item->object.flags & UNINTERESTING) continue; count++; } return count; } static inline int halfway(struct commit_list *p, int nr) { /* * Don't short-cut something we are not going to return! */ if (p->item->object.flags & TREESAME) return 0; if (DEBUG_BISECT) return 0; /* * 2 and 3 are halfway of 5. * 3 is halfway of 6 but 2 and 4 are not. */ switch (2 * weight(p) - nr) { case -1: case 0: case 1: return 1; default: return 0; } } #if !DEBUG_BISECT #define show_list(a,b,c,d) do { ; } while (0) #else static void show_list(const char *debug, int counted, int nr, struct commit_list *list) { struct commit_list *p; fprintf(stderr, "%s (%d/%d)\n", debug, counted, nr); for (p = list; p; p = p->next) { struct commit_list *pp; struct commit *commit = p->item; unsigned flags = commit->object.flags; enum object_type type; unsigned long size; char *buf = read_sha1_file(commit->object.oid.hash, &type, &size); const char *subject_start; int subject_len; fprintf(stderr, "%c%c%c ", (flags & TREESAME) ? ' ' : 'T', (flags & UNINTERESTING) ? 'U' : ' ', (flags & COUNTED) ? 'C' : ' '); if (commit->util) fprintf(stderr, "%3d", weight(p)); else fprintf(stderr, "---"); fprintf(stderr, " %.*s", 8, oid_to_hex(&commit->object.oid)); for (pp = commit->parents; pp; pp = pp->next) fprintf(stderr, " %.*s", 8, oid_to_hex(&pp->item->object.oid)); subject_len = find_commit_subject(buf, &subject_start); if (subject_len) fprintf(stderr, " %.*s", subject_len, subject_start); fprintf(stderr, "\n"); } } #endif /* DEBUG_BISECT */ static struct commit_list *best_bisection(struct commit_list *list, int nr) { struct commit_list *p, *best; int best_distance = -1; best = list; for (p = list; p; p = p->next) { int distance; unsigned flags = p->item->object.flags; if (flags & TREESAME) continue; distance = weight(p); if (nr - distance < distance) distance = nr - distance; if (distance > best_distance) { best = p; best_distance = distance; } } return best; } struct commit_dist { struct commit *commit; int distance; }; static int compare_commit_dist(const void *a_, const void *b_) { struct commit_dist *a, *b; a = (struct commit_dist *)a_; b = (struct commit_dist *)b_; if (a->distance != b->distance) return b->distance - a->distance; /* desc sort */ return oidcmp(&a->commit->object.oid, &b->commit->object.oid); } static struct commit_list *best_bisection_sorted(struct commit_list *list, int nr) { struct commit_list *p; struct commit_dist *array = xcalloc(nr, sizeof(*array)); int cnt, i; for (p = list, cnt = 0; p; p = p->next) { int distance; unsigned flags = p->item->object.flags; if (flags & TREESAME) continue; distance = weight(p); if (nr - distance < distance) distance = nr - distance; array[cnt].commit = p->item; array[cnt].distance = distance; cnt++; } QSORT(array, cnt, compare_commit_dist); for (p = list, i = 0; i < cnt; i++) { char buf[100]; /* enough for dist=%d */ struct object *obj = &(array[i].commit->object); snprintf(buf, sizeof(buf), "dist=%d", array[i].distance); add_name_decoration(DECORATION_NONE, buf, obj); p->item = array[i].commit; p = p->next; } if (p) p->next = NULL; free(array); return list; } /* * zero or positive weight is the number of interesting commits it can * reach, including itself. Especially, weight = 0 means it does not * reach any tree-changing commits (e.g. just above uninteresting one * but traversal is with pathspec). * * weight = -1 means it has one parent and its distance is yet to * be computed. * * weight = -2 means it has more than one parent and its distance is * unknown. After running count_distance() first, they will get zero * or positive distance. */ static struct commit_list *do_find_bisection(struct commit_list *list, int nr, int *weights, int find_all) { int n, counted; struct commit_list *p; counted = 0; for (n = 0, p = list; p; p = p->next) { struct commit *commit = p->item; unsigned flags = commit->object.flags; p->item->util = &weights[n++]; switch (count_interesting_parents(commit)) { case 0: if (!(flags & TREESAME)) { weight_set(p, 1); counted++; show_list("bisection 2 count one", counted, nr, list); } /* * otherwise, it is known not to reach any * tree-changing commit and gets weight 0. */ break; case 1: weight_set(p, -1); break; default: weight_set(p, -2); break; } } show_list("bisection 2 initialize", counted, nr, list); /* * If you have only one parent in the resulting set * then you can reach one commit more than that parent * can reach. So we do not have to run the expensive * count_distance() for single strand of pearls. * * However, if you have more than one parents, you cannot * just add their distance and one for yourself, since * they usually reach the same ancestor and you would * end up counting them twice that way. * * So we will first count distance of merges the usual * way, and then fill the blanks using cheaper algorithm. */ for (p = list; p; p = p->next) { if (p->item->object.flags & UNINTERESTING) continue; if (weight(p) != -2) continue; weight_set(p, count_distance(p)); clear_distance(list); /* Does it happen to be at exactly half-way? */ if (!find_all && halfway(p, nr)) return p; counted++; } show_list("bisection 2 count_distance", counted, nr, list); while (counted < nr) { for (p = list; p; p = p->next) { struct commit_list *q; unsigned flags = p->item->object.flags; if (0 <= weight(p)) continue; for (q = p->item->parents; q; q = q->next) { if (q->item->object.flags & UNINTERESTING) continue; if (0 <= weight(q)) break; } if (!q) continue; /* * weight for p is unknown but q is known. * add one for p itself if p is to be counted, * otherwise inherit it from q directly. */ if (!(flags & TREESAME)) { weight_set(p, weight(q)+1); counted++; show_list("bisection 2 count one", counted, nr, list); } else weight_set(p, weight(q)); /* Does it happen to be at exactly half-way? */ if (!find_all && halfway(p, nr)) return p; } } show_list("bisection 2 counted all", counted, nr, list); if (!find_all) return best_bisection(list, nr); else return best_bisection_sorted(list, nr); } struct commit_list *find_bisection(struct commit_list *list, int *reaches, int *all, int find_all) { int nr, on_list; struct commit_list *p, *best, *next, *last; int *weights; show_list("bisection 2 entry", 0, 0, list); /* * Count the number of total and tree-changing items on the * list, while reversing the list. */ for (nr = on_list = 0, last = NULL, p = list; p; p = next) { unsigned flags = p->item->object.flags; next = p->next; if (flags & UNINTERESTING) continue; p->next = last; last = p; if (!(flags & TREESAME)) nr++; on_list++; } list = last; show_list("bisection 2 sorted", 0, nr, list); *all = nr; weights = xcalloc(on_list, sizeof(*weights)); /* Do the real work of finding bisection commit. */ best = do_find_bisection(list, nr, weights, find_all); if (best) { if (!find_all) best->next = NULL; *reaches = weight(best); } free(weights); return best; } static int register_ref(const char *refname, const struct object_id *oid, int flags, void *cb_data) { struct strbuf good_prefix = STRBUF_INIT; strbuf_addstr(&good_prefix, term_good); strbuf_addstr(&good_prefix, "-"); if (!strcmp(refname, term_bad)) { current_bad_oid = xmalloc(sizeof(*current_bad_oid)); oidcpy(current_bad_oid, oid); } else if (starts_with(refname, good_prefix.buf)) { sha1_array_append(&good_revs, oid->hash); } else if (starts_with(refname, "skip-")) { sha1_array_append(&skipped_revs, oid->hash); } strbuf_release(&good_prefix); return 0; } static int read_bisect_refs(void) { return for_each_ref_in("refs/bisect/", register_ref, NULL); } static GIT_PATH_FUNC(git_path_bisect_names, "BISECT_NAMES") static GIT_PATH_FUNC(git_path_bisect_expected_rev, "BISECT_EXPECTED_REV") static void read_bisect_paths(struct argv_array *array) { struct strbuf str = STRBUF_INIT; const char *filename = git_path_bisect_names(); FILE *fp = fopen(filename, "r"); if (!fp) die_errno(_("Could not open file '%s'"), filename); while (strbuf_getline_lf(&str, fp) != EOF) { strbuf_trim(&str); if (sq_dequote_to_argv_array(str.buf, array)) die(_("Badly quoted content in file '%s': %s"), filename, str.buf); } strbuf_release(&str); fclose(fp); } static char *join_sha1_array_hex(struct sha1_array *array, char delim) { struct strbuf joined_hexs = STRBUF_INIT; int i; for (i = 0; i < array->nr; i++) { strbuf_addstr(&joined_hexs, sha1_to_hex(array->sha1[i])); if (i + 1 < array->nr) strbuf_addch(&joined_hexs, delim); } return strbuf_detach(&joined_hexs, NULL); } /* * In this function, passing a not NULL skipped_first is very special. * It means that we want to know if the first commit in the list is * skipped because we will want to test a commit away from it if it is * indeed skipped. * So if the first commit is skipped, we cannot take the shortcut to * just "return list" when we find the first non skipped commit, we * have to return a fully filtered list. * * We use (*skipped_first == -1) to mean "it has been found that the * first commit is not skipped". In this case *skipped_first is set back * to 0 just before the function returns. */ struct commit_list *filter_skipped(struct commit_list *list, struct commit_list **tried, int show_all, int *count, int *skipped_first) { struct commit_list *filtered = NULL, **f = &filtered; *tried = NULL; if (skipped_first) *skipped_first = 0; if (count) *count = 0; if (!skipped_revs.nr) return list; while (list) { struct commit_list *next = list->next; list->next = NULL; if (0 <= sha1_array_lookup(&skipped_revs, list->item->object.oid.hash)) { if (skipped_first && !*skipped_first) *skipped_first = 1; /* Move current to tried list */ *tried = list; tried = &list->next; } else { if (!show_all) { if (!skipped_first || !*skipped_first) return list; } else if (skipped_first && !*skipped_first) { /* This means we know it's not skipped */ *skipped_first = -1; } /* Move current to filtered list */ *f = list; f = &list->next; if (count) (*count)++; } list = next; } if (skipped_first && *skipped_first == -1) *skipped_first = 0; return filtered; } #define PRN_MODULO 32768 /* * This is a pseudo random number generator based on "man 3 rand". * It is not used properly because the seed is the argument and it * is increased by one between each call, but that should not matter * for this application. */ static unsigned get_prn(unsigned count) { count = count * 1103515245 + 12345; return (count/65536) % PRN_MODULO; } /* * Custom integer square root from * http://en.wikipedia.org/wiki/Integer_square_root */ static int sqrti(int val) { float d, x = val; if (val == 0) return 0; do { float y = (x + (float)val / x) / 2; d = (y > x) ? y - x : x - y; x = y; } while (d >= 0.5); return (int)x; } static struct commit_list *skip_away(struct commit_list *list, int count) { struct commit_list *cur, *previous; int prn, index, i; prn = get_prn(count); index = (count * prn / PRN_MODULO) * sqrti(prn) / sqrti(PRN_MODULO); cur = list; previous = NULL; for (i = 0; cur; cur = cur->next, i++) { if (i == index) { if (oidcmp(&cur->item->object.oid, current_bad_oid)) return cur; if (previous) return previous; return list; } previous = cur; } return list; } static struct commit_list *managed_skipped(struct commit_list *list, struct commit_list **tried) { int count, skipped_first; *tried = NULL; if (!skipped_revs.nr) return list; list = filter_skipped(list, tried, 0, &count, &skipped_first); if (!skipped_first) return list; return skip_away(list, count); } static void bisect_rev_setup(struct rev_info *revs, const char *prefix, const char *bad_format, const char *good_format, int read_paths) { struct argv_array rev_argv = ARGV_ARRAY_INIT; int i; init_revisions(revs, prefix); revs->abbrev = 0; revs->commit_format = CMIT_FMT_UNSPECIFIED; /* rev_argv.argv[0] will be ignored by setup_revisions */ argv_array_push(&rev_argv, "bisect_rev_setup"); argv_array_pushf(&rev_argv, bad_format, oid_to_hex(current_bad_oid)); for (i = 0; i < good_revs.nr; i++) argv_array_pushf(&rev_argv, good_format, sha1_to_hex(good_revs.sha1[i])); argv_array_push(&rev_argv, "--"); if (read_paths) read_bisect_paths(&rev_argv); setup_revisions(rev_argv.argc, rev_argv.argv, revs, NULL); /* XXX leak rev_argv, as "revs" may still be pointing to it */ } static void bisect_common(struct rev_info *revs) { if (prepare_revision_walk(revs)) die("revision walk setup failed"); if (revs->tree_objects) mark_edges_uninteresting(revs, NULL); } static void exit_if_skipped_commits(struct commit_list *tried, const struct object_id *bad) { if (!tried) return; printf("There are only 'skip'ped commits left to test.\n" "The first %s commit could be any of:\n", term_bad); for ( ; tried; tried = tried->next) printf("%s\n", oid_to_hex(&tried->item->object.oid)); if (bad) printf("%s\n", oid_to_hex(bad)); printf(_("We cannot bisect more!\n")); exit(2); } static int is_expected_rev(const struct object_id *oid) { const char *filename = git_path_bisect_expected_rev(); struct stat st; struct strbuf str = STRBUF_INIT; FILE *fp; int res = 0; if (stat(filename, &st) || !S_ISREG(st.st_mode)) return 0; fp = fopen(filename, "r"); if (!fp) return 0; if (strbuf_getline_lf(&str, fp) != EOF) res = !strcmp(str.buf, oid_to_hex(oid)); strbuf_release(&str); fclose(fp); return res; } static int bisect_checkout(const unsigned char *bisect_rev, int no_checkout) { char bisect_rev_hex[GIT_SHA1_HEXSZ + 1]; memcpy(bisect_rev_hex, sha1_to_hex(bisect_rev), GIT_SHA1_HEXSZ + 1); update_ref(NULL, "BISECT_EXPECTED_REV", bisect_rev, NULL, 0, UPDATE_REFS_DIE_ON_ERR); argv_checkout[2] = bisect_rev_hex; if (no_checkout) { update_ref(NULL, "BISECT_HEAD", bisect_rev, NULL, 0, UPDATE_REFS_DIE_ON_ERR); } else { int res; res = run_command_v_opt(argv_checkout, RUN_GIT_CMD); if (res) exit(res); } argv_show_branch[1] = bisect_rev_hex; return run_command_v_opt(argv_show_branch, RUN_GIT_CMD); } static struct commit *get_commit_reference(const unsigned char *sha1) { struct commit *r = lookup_commit_reference(sha1); if (!r) die(_("Not a valid commit name %s"), sha1_to_hex(sha1)); return r; } static struct commit **get_bad_and_good_commits(int *rev_nr) { struct commit **rev; int i, n = 0; ALLOC_ARRAY(rev, 1 + good_revs.nr); rev[n++] = get_commit_reference(current_bad_oid->hash); for (i = 0; i < good_revs.nr; i++) rev[n++] = get_commit_reference(good_revs.sha1[i]); *rev_nr = n; return rev; } static void handle_bad_merge_base(void) { if (is_expected_rev(current_bad_oid)) { char *bad_hex = oid_to_hex(current_bad_oid); char *good_hex = join_sha1_array_hex(&good_revs, ' '); if (!strcmp(term_bad, "bad") && !strcmp(term_good, "good")) { fprintf(stderr, _("The merge base %s is bad.\n" "This means the bug has been fixed " "between %s and [%s].\n"), bad_hex, bad_hex, good_hex); } else if (!strcmp(term_bad, "new") && !strcmp(term_good, "old")) { fprintf(stderr, _("The merge base %s is new.\n" "The property has changed " "between %s and [%s].\n"), bad_hex, bad_hex, good_hex); } else { fprintf(stderr, _("The merge base %s is %s.\n" "This means the first '%s' commit is " "between %s and [%s].\n"), bad_hex, term_bad, term_good, bad_hex, good_hex); } exit(3); } fprintf(stderr, _("Some %s revs are not ancestors of the %s rev.\n" "git bisect cannot work properly in this case.\n" "Maybe you mistook %s and %s revs?\n"), term_good, term_bad, term_good, term_bad); exit(1); } static void handle_skipped_merge_base(const unsigned char *mb) { char *mb_hex = sha1_to_hex(mb); char *bad_hex = oid_to_hex(current_bad_oid); char *good_hex = join_sha1_array_hex(&good_revs, ' '); warning(_("the merge base between %s and [%s] " "must be skipped.\n" "So we cannot be sure the first %s commit is " "between %s and %s.\n" "We continue anyway."), bad_hex, good_hex, term_bad, mb_hex, bad_hex); free(good_hex); } /* * "check_merge_bases" checks that merge bases are not "bad" (or "new"). * * - If one is "bad" (or "new"), it means the user assumed something wrong * and we must exit with a non 0 error code. * - If one is "good" (or "old"), that's good, we have nothing to do. * - If one is "skipped", we can't know but we should warn. * - If we don't know, we should check it out and ask the user to test. */ static void check_merge_bases(int no_checkout) { struct commit_list *result; int rev_nr; struct commit **rev = get_bad_and_good_commits(&rev_nr); result = get_merge_bases_many(rev[0], rev_nr - 1, rev + 1); for (; result; result = result->next) { const unsigned char *mb = result->item->object.oid.hash; if (!hashcmp(mb, current_bad_oid->hash)) { handle_bad_merge_base(); } else if (0 <= sha1_array_lookup(&good_revs, mb)) { continue; } else if (0 <= sha1_array_lookup(&skipped_revs, mb)) { handle_skipped_merge_base(mb); } else { printf(_("Bisecting: a merge base must be tested\n")); exit(bisect_checkout(mb, no_checkout)); } } free(rev); free_commit_list(result); } static int check_ancestors(const char *prefix) { struct rev_info revs; struct object_array pending_copy; int res; bisect_rev_setup(&revs, prefix, "^%s", "%s", 0); /* Save pending objects, so they can be cleaned up later. */ pending_copy = revs.pending; revs.leak_pending = 1; /* * bisect_common calls prepare_revision_walk right away, which * (together with .leak_pending = 1) makes us the sole owner of * the list of pending objects. */ bisect_common(&revs); res = (revs.commits != NULL); /* Clean up objects used, as they will be reused. */ clear_commit_marks_for_object_array(&pending_copy, ALL_REV_FLAGS); free(pending_copy.objects); return res; } /* * "check_good_are_ancestors_of_bad" checks that all "good" revs are * ancestor of the "bad" rev. * * If that's not the case, we need to check the merge bases. * If a merge base must be tested by the user, its source code will be * checked out to be tested by the user and we will exit. */ static void check_good_are_ancestors_of_bad(const char *prefix, int no_checkout) { char *filename = git_pathdup("BISECT_ANCESTORS_OK"); struct stat st; int fd; if (!current_bad_oid) die(_("a %s revision is needed"), term_bad); /* Check if file BISECT_ANCESTORS_OK exists. */ if (!stat(filename, &st) && S_ISREG(st.st_mode)) goto done; /* Bisecting with no good rev is ok. */ if (good_revs.nr == 0) goto done; /* Check if all good revs are ancestor of the bad rev. */ if (check_ancestors(prefix)) check_merge_bases(no_checkout); /* Create file BISECT_ANCESTORS_OK. */ fd = open(filename, O_CREAT | O_TRUNC | O_WRONLY, 0600); if (fd < 0) warning_errno(_("could not create file '%s'"), filename); else close(fd); done: free(filename); } /* * This does "git diff-tree --pretty COMMIT" without one fork+exec. */ static void show_diff_tree(const char *prefix, struct commit *commit) { struct rev_info opt; /* diff-tree init */ init_revisions(&opt, prefix); git_config(git_diff_basic_config, NULL); /* no "diff" UI options */ opt.abbrev = 0; opt.diff = 1; /* This is what "--pretty" does */ opt.verbose_header = 1; opt.use_terminator = 0; opt.commit_format = CMIT_FMT_DEFAULT; /* diff-tree init */ if (!opt.diffopt.output_format) opt.diffopt.output_format = DIFF_FORMAT_RAW; setup_revisions(0, NULL, &opt, NULL); log_tree_commit(&opt, commit); } /* * The terms used for this bisect session are stored in BISECT_TERMS. * We read them and store them to adapt the messages accordingly. * Default is bad/good. */ void read_bisect_terms(const char **read_bad, const char **read_good) { struct strbuf str = STRBUF_INIT; const char *filename = git_path("BISECT_TERMS"); FILE *fp = fopen(filename, "r"); if (!fp) { if (errno == ENOENT) { *read_bad = "bad"; *read_good = "good"; return; } else { die_errno(_("could not read file '%s'"), filename); } } else { strbuf_getline_lf(&str, fp); *read_bad = strbuf_detach(&str, NULL); strbuf_getline_lf(&str, fp); *read_good = strbuf_detach(&str, NULL); } strbuf_release(&str); fclose(fp); } /* * We use the convention that exiting with an exit code 10 means that * the bisection process finished successfully. * In this case the calling shell script should exit 0. * * If no_checkout is non-zero, the bisection process does not * checkout the trial commit but instead simply updates BISECT_HEAD. */ int bisect_next_all(const char *prefix, int no_checkout) { struct rev_info revs; struct commit_list *tried; int reaches = 0, all = 0, nr, steps; const unsigned char *bisect_rev; char *steps_msg; read_bisect_terms(&term_bad, &term_good); if (read_bisect_refs()) die(_("reading bisect refs failed")); check_good_are_ancestors_of_bad(prefix, no_checkout); bisect_rev_setup(&revs, prefix, "%s", "^%s", 1); revs.limited = 1; bisect_common(&revs); revs.commits = find_bisection(revs.commits, &reaches, &all, !!skipped_revs.nr); revs.commits = managed_skipped(revs.commits, &tried); if (!revs.commits) { /* * We should exit here only if the "bad" * commit is also a "skip" commit. */ exit_if_skipped_commits(tried, NULL); printf(_("%s was both %s and %s\n"), oid_to_hex(current_bad_oid), term_good, term_bad); exit(1); } if (!all) { fprintf(stderr, _("No testable commit found.\n" "Maybe you started with bad path parameters?\n")); exit(4); } bisect_rev = revs.commits->item->object.oid.hash; if (!hashcmp(bisect_rev, current_bad_oid->hash)) { exit_if_skipped_commits(tried, current_bad_oid); printf("%s is the first %s commit\n", sha1_to_hex(bisect_rev), term_bad); show_diff_tree(prefix, revs.commits->item); /* This means the bisection process succeeded. */ exit(10); } nr = all - reaches - 1; steps = estimate_bisect_steps(all); steps_msg = xstrfmt(Q_("(roughly %d step)", "(roughly %d steps)", steps), steps); /* TRANSLATORS: the last %s will be replaced with "(roughly %d steps)" translation */ printf(Q_("Bisecting: %d revision left to test after this %s\n", "Bisecting: %d revisions left to test after this %s\n", nr), nr, steps_msg); free(steps_msg); return bisect_checkout(bisect_rev, no_checkout); } static inline int log2i(int n) { int log2 = 0; for (; n > 1; n >>= 1) log2++; return log2; } static inline int exp2i(int n) { return 1 << n; } /* * Estimate the number of bisect steps left (after the current step) * * For any x between 0 included and 2^n excluded, the probability for * n - 1 steps left looks like: * * P(2^n + x) == (2^n - x) / (2^n + x) * * and P(2^n + x) < 0.5 means 2^n < 3x */ int estimate_bisect_steps(int all) { int n, x, e; if (all < 3) return 0; n = log2i(all); e = exp2i(n); x = all - e; return (e < 3 * x) ? n : n - 1; }