/*
* This file is part of DisOrder
* Copyright (C) 2008 Richard Kettlewell
+ * Copyright (C) 2008 Mark Wooding
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
xfclose(stdout);
exit(0);
}
-
-/** @brief Weighted track record */
-struct weighted_track {
- /** @brief Next track in the list */
- struct weighted_track *next;
- /** @brief Track name */
- const char *track;
- /** @brief Weight for this track (always positive) */
- unsigned long weight;
-};
-
-/** @brief List of tracks with nonzero weight */
-static struct weighted_track *tracks;
-
/** @brief Sum of all weights */
static unsigned long long total_weight;
+/** @brief The winning track */
+static const char *winning = 0;
+
/** @brief Count of tracks */
static long ntracks;
return 90000;
}
+static unsigned char random_buffer[4096];
+static size_t random_left;
+
+/** @brief Fill [buf, buf+n) with random bytes */
+static void random_bytes(unsigned char *buf, size_t n) {
+ while(n > 0) {
+ if(random_left > 0) {
+ const size_t this_time = n > random_left ? random_left : n;
+
+ memcpy(buf, random_buffer + random_left - this_time, this_time);
+ n -= this_time;
+ random_left -= this_time;
+ } else {
+ static int fd = -1;
+ int r;
+
+ if(fd < 0) {
+ if((fd = open("/dev/urandom", O_RDONLY)) < 0)
+ fatal(errno, "opening /dev/urandom");
+ }
+ if((r = read(fd, random_buffer, sizeof random_buffer)) < 0)
+ fatal(errno, "reading /dev/urandom");
+ if((size_t)r < sizeof random_buffer)
+ fatal(0, "short read from /dev/urandom");
+ random_left = sizeof random_buffer;
+ }
+ }
+}
+
+/** @brief Pick a random integer uniformly from [0, limit) */
+static unsigned long long pick_weight(unsigned long long limit) {
+ unsigned char buf[(sizeof(unsigned long long) * CHAR_BIT + 7)/8], m;
+ unsigned long long t, r, slop;
+ int i, nby, nbi;
+
+ //info("pick_weight: limit = %llu", limit);
+
+ /* First, decide how many bits of output we actually need; do bytes first
+ * (they're quicker) and then bits.
+ *
+ * To speed this up, we could use a binary search if we knew where to
+ * start. (Note that shifting by ULLONG_BITS or more (if such a constant
+ * existed) is undefined behaviour, so we mustn't do that.) Figuring out a
+ * start point involves preprocessor and/or autoconf magic.
+ */
+ for (nby = 1, t = (limit - 1) >> 8; t; nby++, t >>= 8)
+ ;
+ nbi = (nby - 1) << 3; t = limit >> nbi;
+ if (t >> 4) { t >>= 4; nbi += 4; }
+ if (t >> 2) { t >>= 2; nbi += 2; }
+ if (t >> 1) { t >>= 1; nbi += 1; }
+ nbi++;
+ //info("nby = %d; nbi = %d", nby, nbi);
+
+ /* Main randomness collection loop. We read a number of bytes from the
+ * randomness source, and glue them together into an integer (dropping
+ * bits off the top byte as necessary). Call the result r; we have
+ * 2^{nbi - 1) <= limit < 2^nbi and r < 2^nbi. If r < limit then we win;
+ * otherwise we try again. Given the above bounds, we expect fewer than 2
+ * iterations.
+ *
+ * Unfortunately there are subtleties. In particular, 2^nbi may in fact be
+ * zero due to overflow. So in fact what we do is compute slop = 2^nbi -
+ * limit > 0; if r < slop then we try again, otherwise r - slop is our
+ * winner.
+ */
+ slop = (2 << (nbi - 1)) - limit;
+ m = nbi & 7 ? (1 << (nbi & 7)) - 1 : 0xff;
+ //info("slop = %llu", slop);
+ //info("m = 0x%02x", m);
+
+ do {
+ /* Actually get some random data. */
+ random_bytes(buf, nby);
+
+ /* Clobber the top byte. */
+ buf[0] &= m;
+
+ /* Turn it into an integer. */
+ for (r = 0, i = 0; i < nby; i++)
+ r = (r << 8) | buf[i];
+ //info("r = %llu", r);
+ } while (r < slop);
+
+ return r - slop;
+}
+
/** @brief Called for each track */
static int collect_tracks_callback(const char *track,
struct kvp *data,
DB_TXN attribute((unused)) *tid) {
unsigned long weight = compute_weight(track, data, prefs);
+ /* Decide whether this is the winning track.
+ *
+ * Suppose that we have n things, and thing i, for 0 <= i < n, has weight
+ * w_i. Let c_i = w_0 + ... + w_{i-1} be the cumulative weight of the
+ * things previous to thing i, and let W = c_n = w_0 + ... + w_{i-1} be the
+ * total weight. We can clearly choose a random thing with the correct
+ * weightings by picking a random number r in [0, W) and chooeing thing i
+ * where c_i <= r < c_i + w_i. But this involves having an enormous list
+ * and taking two passes over it (which has bad locality and is ugly).
+ *
+ * Here's another way. Initialize v = -1. Examine the things in order;
+ * for thing i, choose a random number r_i in [0, c_i + w_i). If r_i < w_i
+ * then set v <- i.
+ *
+ * Claim. For all 0 <= i < n, the above algorithm chooses thing i with
+ * probability w_i/W.
+ *
+ * Proof. Induction on n. The claim is clear for n = 1. Suppose it's
+ * true for n - 1. Let L be the event that we choose thing n - 1. Clearly
+ * Pr[L] = w_{n-1}/W. Condition on not-L: then the probabilty that we
+ * choose thing i, for 0 <= i < n - 1, is w_i/c_{n-1} (induction
+ * hypothesis); undoing the conditioning gives the desired result.
+ */
if(weight) {
- struct weighted_track *const t = xmalloc(sizeof *t);
-
- /* Clamp weight so that we can fit in billions of tracks when we do
- * arithmetic in long long */
- if(weight > 0x7fffffff)
- weight = 0x7fffffff;
- t->next = tracks;
- t->track = track;
- t->weight = weight;
- tracks = t;
total_weight += weight;
- ++ntracks;
+ if (pick_weight(total_weight) < weight)
+ winning = track;
}
+ ntracks++;
return 0;
}
-/** @brief Pick a random integer uniformly from [0, limit) */
-static unsigned long long pick_weight(unsigned long long limit) {
- unsigned long long n;
- static int fd = -1;
- int r;
-
- if(fd < 0) {
- if((fd = open("/dev/urandom", O_RDONLY)) < 0)
- fatal(errno, "opening /dev/urandom");
- }
- if((r = read(fd, &n, sizeof n)) < 0)
- fatal(errno, "reading /dev/urandom");
- if((size_t)r < sizeof n)
- fatal(0, "short read from /dev/urandom");
- return n % limit;
-}
-
-/** @brief Pick a track at random and write it to stdout */
-static void pick_track(void) {
- long long w;
- struct weighted_track *t;
-
- w = pick_weight(total_weight);
- t = tracks;
- while(t && w >= t->weight) {
- w -= t->weight;
- t = t->next;
- }
- if(!t)
- fatal(0, "ran out of tracks but %lld weighting left", w);
- xprintf("%s", t->track);
-}
-
int main(int argc, char **argv) {
int n, logsyslog = !isatty(2), err;
const char *tags;
//info("ntracks=%ld total_weight=%lld", ntracks, total_weight);
if(!total_weight)
fatal(0, "no tracks match random choice criteria");
+ if(!winning)
+ fatal(0, "internal: failed to pick a track");
/* Pick a track */
- pick_track();
+ xprintf("%s", winning);
xfclose(stdout);
return 0;
}