2 #include <ccan/tally/tally.h>
3 #include <ccan/build_assert/build_assert.h>
4 #include <ccan/likely/likely.h>
11 #define SIZET_BITS (sizeof(size_t)*CHAR_BIT)
13 /* We use power of 2 steps. I tried being tricky, but it got buggy. */
17 /* This allows limited frequency analysis. */
18 unsigned buckets, step_bits;
19 size_t counts[1 /* Actually: [buckets] */ ];
22 struct tally *tally_new(unsigned buckets)
26 /* There is always 1 bucket. */
30 /* Check for overflow. */
31 if (buckets && SIZE_MAX / buckets < sizeof(tally->counts[0]))
33 tally = malloc(sizeof(*tally) + sizeof(tally->counts[0])*(buckets-1));
35 tally->max = ((size_t)1 << (SIZET_BITS - 1));
36 tally->min = ~tally->max;
37 tally->total[0] = tally->total[1] = 0;
38 tally->buckets = buckets;
40 memset(tally->counts, 0, sizeof(tally->counts[0])*buckets);
45 static unsigned bucket_of(ssize_t min, unsigned step_bits, ssize_t val)
47 /* Don't over-shift. */
48 if (step_bits == SIZET_BITS)
50 assert(step_bits < SIZET_BITS);
51 return (size_t)(val - min) >> step_bits;
54 /* Return the min value in bucket b. */
55 static ssize_t bucket_min(ssize_t min, unsigned step_bits, unsigned b)
57 /* Don't over-shift. */
58 if (step_bits == SIZET_BITS)
60 assert(step_bits < SIZET_BITS);
61 return min + ((ssize_t)b << step_bits);
64 /* Does shifting by this many bits truncate the number? */
65 static bool shift_overflows(size_t num, unsigned bits)
70 return ((num << bits) >> 1) != (num << (bits - 1));
73 /* When min or max change, we may need to shuffle the frequency counts. */
74 static void renormalize(struct tally *tally,
75 ssize_t new_min, ssize_t new_max)
78 unsigned int i, old_min;
80 /* Uninitialized? Don't do anything... */
81 if (tally->max < tally->min)
84 /* If we don't have sufficient range, increase step bits until
85 * buckets cover entire range of ssize_t anyway. */
86 range = (new_max - new_min) + 1;
87 while (!shift_overflows(tally->buckets, tally->step_bits)
88 && range > ((size_t)tally->buckets << tally->step_bits)) {
90 for (i = 1; i < tally->buckets; i++) {
91 tally->counts[i/2] += tally->counts[i];
97 /* Now if minimum has dropped, move buckets up. */
98 old_min = bucket_of(new_min, tally->step_bits, tally->min);
99 memmove(tally->counts + old_min,
101 sizeof(tally->counts[0]) * (tally->buckets - old_min));
102 memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
104 /* If we moved boundaries, adjust buckets to that ratio. */
105 spill = (tally->min - new_min) % (1 << tally->step_bits);
106 for (i = 0; i < tally->buckets-1; i++) {
107 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
108 tally->counts[i] -= adjust;
109 tally->counts[i+1] += adjust;
113 tally->min = new_min;
114 tally->max = new_max;
117 void tally_add(struct tally *tally, ssize_t val)
119 ssize_t new_min = tally->min, new_max = tally->max;
120 bool need_renormalize = false;
122 if (val < tally->min) {
124 need_renormalize = true;
126 if (val > tally->max) {
128 need_renormalize = true;
130 if (need_renormalize)
131 renormalize(tally, new_min, new_max);
133 /* 128-bit arithmetic! If we didn't want exact mean, we could just
134 * pull it out of counts. */
135 if (val > 0 && tally->total[0] + val < tally->total[0])
137 else if (val < 0 && tally->total[0] + val > tally->total[0])
139 tally->total[0] += val;
140 tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
143 size_t tally_num(const struct tally *tally)
146 for (i = 0; i < tally->buckets; i++)
147 num += tally->counts[i];
151 ssize_t tally_min(const struct tally *tally)
156 ssize_t tally_max(const struct tally *tally)
161 /* FIXME: Own ccan module please! */
162 static unsigned fls64(uint64_t val)
164 #if HAVE_BUILTIN_CLZL
165 if (val <= ULONG_MAX) {
166 /* This is significantly faster! */
167 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
174 if (!(val & 0xffffffff00000000ull)) {
178 if (!(val & 0xffff000000000000ull)) {
182 if (!(val & 0xff00000000000000ull)) {
186 if (!(val & 0xf000000000000000ull)) {
190 if (!(val & 0xc000000000000000ull)) {
194 if (!(val & 0x8000000000000000ull)) {
199 #if HAVE_BUILTIN_CLZL
204 /* This is stolen straight from Hacker's Delight. */
205 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
207 const uint64_t b = 4294967296ULL; // Number base (32 bits).
208 uint32_t un[4], // Dividend and divisor
209 vn[2]; // normalized and broken
210 // up into halfwords.
211 uint32_t q[2]; // Quotient as halfwords.
212 uint64_t un1, un0, // Dividend and divisor
213 vn0; // as fullwords.
214 uint64_t qhat; // Estimated quotient digit.
215 uint64_t rhat; // A remainder.
216 uint64_t p; // Product of two digits.
217 int64_t s, i, j, t, k;
219 if (u1 >= v) // If overflow, return the largest
220 return (uint64_t)-1; // possible quotient.
222 s = 64 - fls64(v); // 0 <= s <= 63.
223 vn0 = v << s; // Normalize divisor.
224 vn[1] = vn0 >> 32; // Break divisor up into
225 vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
227 // Shift dividend left.
228 un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
230 un[3] = un1 >> 32; // Break dividend up into
231 un[2] = un1; // four 32-bit halfwords
232 un[1] = un0 >> 32; // Note: storing into
233 un[0] = un0; // halfwords truncates.
235 for (j = 1; j >= 0; j--) {
236 // Compute estimate qhat of q[j].
237 qhat = (un[j+2]*b + un[j+1])/vn[1];
238 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
240 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
243 if (rhat < b) goto again;
246 // Multiply and subtract.
248 for (i = 0; i < 2; i++) {
250 t = un[i+j] - k - (p & 0xFFFFFFFF);
252 k = (p >> 32) - (t >> 32);
257 q[j] = qhat; // Store quotient digit.
258 if (t < 0) { // If we subtracted too
259 q[j] = q[j] - 1; // much, add back.
261 for (i = 0; i < 2; i++) {
262 t = un[i+j] + vn[i] + k;
266 un[j+2] = un[j+2] + k;
270 return q[1]*b + q[0];
273 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
275 int64_t q, uneg, vneg, diff, borrow;
277 uneg = u1 >> 63; // -1 if u < 0.
278 if (uneg) { // Compute the absolute
279 u0 = -u0; // value of the dividend u.
284 vneg = v >> 63; // -1 if v < 0.
285 v = (v ^ vneg) - vneg; // Absolute value of v.
287 if ((uint64_t)u1 >= (uint64_t)v)
290 q = divlu64(u1, u0, v);
292 diff = uneg ^ vneg; // Negate q if signs of
293 q = (q ^ diff) - diff; // u and v differed.
295 if ((diff ^ q) < 0 && q != 0) { // If overflow, return the largest
296 overflow: // possible neg. quotient.
297 q = 0x8000000000000000ULL;
302 ssize_t tally_mean(const struct tally *tally)
304 size_t count = tally_num(tally);
308 if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
309 /* Use standard 64-bit arithmetic. */
310 int64_t total = tally->total[0]
311 | (((uint64_t)tally->total[1]) << 32);
312 return total / count;
314 return divls64(tally->total[1], tally->total[0], count);
317 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
320 *overflow = tally->total[1];
321 return tally->total[0];
324 /* If result is negative, make sure we can represent it. */
325 if (tally->total[1] & ((size_t)1 << (SIZET_BITS-1))) {
326 /* Must have only underflowed once, and must be able to
327 * represent result at ssize_t. */
328 if ((~tally->total[1])+1 != 0
329 || (ssize_t)tally->total[0] >= 0) {
330 /* Underflow, return minimum. */
331 return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
334 /* Result is positive, must not have overflowed, and must be
335 * able to represent as ssize_t. */
336 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
337 /* Overflow. Return maximum. */
338 return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
341 return tally->total[0];
344 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
348 min = bucket_min(tally->min, tally->step_bits, b);
349 if (b == tally->buckets - 1)
352 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
354 /* FIXME: Think harder about cumulative error; is this enough?. */
355 *err = (max - min + 1) / 2;
356 /* Avoid overflow. */
357 return min + (max - min) / 2;
360 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
362 size_t count = tally_num(tally), total = 0;
365 for (i = 0; i < tally->buckets; i++) {
366 total += tally->counts[i];
367 if (total * 2 >= count)
370 return bucket_range(tally, i, err);
373 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
375 unsigned int i, min_best = 0, max_best = 0;
377 for (i = 0; i < tally->buckets; i++) {
378 if (tally->counts[i] > tally->counts[min_best]) {
379 min_best = max_best = i;
380 } else if (tally->counts[i] == tally->counts[min_best]) {
385 /* We can have more than one best, making our error huge. */
386 if (min_best != max_best) {
388 min = bucket_range(tally, min_best, err);
389 max = bucket_range(tally, max_best, err);
391 *err += (size_t)(max - min);
392 return min + (max - min) / 2;
395 return bucket_range(tally, min_best, err);
398 static unsigned get_max_bucket(const struct tally *tally)
402 for (i = tally->buckets; i > 0; i--)
403 if (tally->counts[i-1])
408 char *tally_histogram(const struct tally *tally,
409 unsigned width, unsigned height)
411 unsigned int i, count, max_bucket, largest_bucket;
415 assert(width >= TALLY_MIN_HISTO_WIDTH);
416 assert(height >= TALLY_MIN_HISTO_HEIGHT);
418 /* Ignore unused buckets. */
419 max_bucket = get_max_bucket(tally);
421 /* FIXME: It'd be nice to smooth here... */
422 if (height >= max_bucket) {
426 /* We create a temporary then renormalize so < height. */
427 /* FIXME: Antialias properly! */
428 tmp = tally_new(tally->buckets);
431 tmp->min = tally->min;
432 tmp->max = tally->max;
433 tmp->step_bits = tally->step_bits;
434 memcpy(tmp->counts, tally->counts,
435 sizeof(tally->counts[0]) * tmp->buckets);
436 while ((max_bucket = get_max_bucket(tmp)) >= height)
437 renormalize(tmp, tmp->min, tmp->max * 2);
439 tmp->max = tally->max;
444 /* Figure out longest line, for scale. */
446 for (i = 0; i < tally->buckets; i++) {
447 if (tally->counts[i] > largest_bucket)
448 largest_bucket = tally->counts[i];
451 p = graph = malloc(height * (width + 1) + 1);
457 for (i = 0; i < height; i++) {
458 unsigned covered = 1, row;
460 /* People expect minimum at the bottom. */
461 row = height - i - 1;
462 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
465 covered = snprintf(p, width, "%zi", tally->min);
466 else if (row == height - 1)
467 covered = snprintf(p, width, "%zi", tally->max);
468 else if (row == bucket_of(tally->min, tally->step_bits, 0))
482 memset(p, '*', count);