28a66a9f7fa0ebf384c62d69de8b04b396f71cad
[ccan] / ccan / tally / tally.c
1 /* Licensed under LGPLv3+ - see LICENSE file for details */
2 #include <ccan/tally/tally.h>
3 #include <ccan/build_assert/build_assert.h>
4 #include <ccan/likely/likely.h>
5 #include <stdint.h>
6 #include <limits.h>
7 #include <string.h>
8 #include <stdio.h>
9 #include <assert.h>
10 #include <stdlib.h>
11
12 #define SIZET_BITS (sizeof(size_t)*CHAR_BIT)
13
14 /* We use power of 2 steps.  I tried being tricky, but it got buggy. */
15 struct tally {
16         ssize_t min, max;
17         size_t total[2];
18         /* This allows limited frequency analysis. */
19         unsigned buckets, step_bits;
20         size_t counts[1 /* Actually: [buckets] */ ];
21 };
22
23 struct tally *tally_new(unsigned buckets)
24 {
25         struct tally *tally;
26
27         /* There is always 1 bucket. */
28         if (buckets == 0) {
29                 buckets = 1;
30         }
31
32         /* Overly cautious check for overflow. */
33         if (sizeof(*tally) * buckets / sizeof(*tally) != buckets) {
34                 return NULL;
35         }
36
37         tally = (struct tally *)malloc(
38                 sizeof(*tally) + sizeof(tally->counts[0])*(buckets-1));
39         if (tally == NULL) {
40                 return NULL;
41         }
42
43         tally->max = ((size_t)1 << (SIZET_BITS - 1));
44         tally->min = ~tally->max;
45         tally->total[0] = tally->total[1] = 0;
46         tally->buckets = buckets;
47         tally->step_bits = 0;
48         memset(tally->counts, 0, sizeof(tally->counts[0])*buckets);
49         return tally;
50 }
51
52 static unsigned bucket_of(ssize_t min, unsigned step_bits, ssize_t val)
53 {
54         /* Don't over-shift. */
55         if (step_bits == SIZET_BITS) {
56                 return 0;
57         }
58         assert(step_bits < SIZET_BITS);
59         return (size_t)(val - min) >> step_bits;
60 }
61
62 /* Return the min value in bucket b. */
63 static ssize_t bucket_min(ssize_t min, unsigned step_bits, unsigned b)
64 {
65         /* Don't over-shift. */
66         if (step_bits == SIZET_BITS) {
67                 return min;
68         }
69         assert(step_bits < SIZET_BITS);
70         return min + ((ssize_t)b << step_bits);
71 }
72
73 /* Does shifting by this many bits truncate the number? */
74 static bool shift_overflows(size_t num, unsigned bits)
75 {
76         if (bits == 0) {
77                 return false;
78         }
79
80         return ((num << bits) >> 1) != (num << (bits - 1));
81 }
82
83 /* When min or max change, we may need to shuffle the frequency counts. */
84 static void renormalize(struct tally *tally,
85                         ssize_t new_min, ssize_t new_max)
86 {
87         size_t range, spill;
88         unsigned int i, old_min;
89
90         /* Uninitialized?  Don't do anything... */
91         if (tally->max < tally->min) {
92                 goto update;
93         }
94
95         /* If we don't have sufficient range, increase step bits until
96          * buckets cover entire range of ssize_t anyway. */
97         range = (new_max - new_min) + 1;
98         while (!shift_overflows(tally->buckets, tally->step_bits)
99                && range > ((size_t)tally->buckets << tally->step_bits)) {
100                 /* Collapse down. */
101                 for (i = 1; i < tally->buckets; i++) {
102                         tally->counts[i/2] += tally->counts[i];
103                         tally->counts[i] = 0;
104                 }
105                 tally->step_bits++;
106         }
107
108         /* Now if minimum has dropped, move buckets up. */
109         old_min = bucket_of(new_min, tally->step_bits, tally->min);
110         memmove(tally->counts + old_min,
111                 tally->counts,
112                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
113         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
114
115         /* If we moved boundaries, adjust buckets to that ratio. */
116         spill = (tally->min - new_min) % (1 << tally->step_bits);
117         for (i = 0; i < tally->buckets-1; i++) {
118                 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
119                 tally->counts[i] -= adjust;
120                 tally->counts[i+1] += adjust;
121         }
122
123 update:
124         tally->min = new_min;
125         tally->max = new_max;
126 }
127
128 void tally_add(struct tally *tally, ssize_t val)
129 {
130         ssize_t new_min = tally->min, new_max = tally->max;
131         bool need_renormalize = false;
132
133         if (val < tally->min) {
134                 new_min = val;
135                 need_renormalize = true;
136         }
137         if (val > tally->max) {
138                 new_max = val;
139                 need_renormalize = true;
140         }
141         if (need_renormalize) {
142                 renormalize(tally, new_min, new_max);
143         }
144
145         /* 128-bit arithmetic!  If we didn't want exact mean, we could just
146          * pull it out of counts. */
147         if (val > 0 && tally->total[0] + val < tally->total[0]) {
148                 tally->total[1]++;
149         } else if (val < 0 && tally->total[0] + val > tally->total[0]) {
150                 tally->total[1]--;
151         }
152         tally->total[0] += val;
153         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
154 }
155
156 size_t tally_num(const struct tally *tally)
157 {
158         size_t i, num = 0;
159         for (i = 0; i < tally->buckets; i++)
160                 num += tally->counts[i];
161         return num;
162 }
163
164 ssize_t tally_min(const struct tally *tally)
165 {
166         return tally->min;
167 }
168
169 ssize_t tally_max(const struct tally *tally)
170 {
171         return tally->max;
172 }
173
174 /* FIXME: Own ccan module please! */
175 static unsigned fls64(uint64_t val)
176 {
177 #if HAVE_BUILTIN_CLZL
178         if (val <= ULONG_MAX) {
179                 /* This is significantly faster! */
180                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
181         } else {
182 #endif
183         uint64_t r = 64;
184
185         if (!val)
186                 return 0;
187         if (!(val & 0xffffffff00000000ull)) {
188                 val <<= 32;
189                 r -= 32;
190         }
191         if (!(val & 0xffff000000000000ull)) {
192                 val <<= 16;
193                 r -= 16;
194         }
195         if (!(val & 0xff00000000000000ull)) {
196                 val <<= 8;
197                 r -= 8;
198         }
199         if (!(val & 0xf000000000000000ull)) {
200                 val <<= 4;
201                 r -= 4;
202         }
203         if (!(val & 0xc000000000000000ull)) {
204                 val <<= 2;
205                 r -= 2;
206         }
207         if (!(val & 0x8000000000000000ull)) {
208                 val <<= 1;
209                 r -= 1;
210         }
211         return r;
212 #if HAVE_BUILTIN_CLZL
213         }
214 #endif
215 }
216
217 /* This is stolen straight from Hacker's Delight. */
218 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
219 {
220         const uint64_t b = 4294967296ULL; // Number base (32 bits).
221         uint32_t un[4],           // Dividend and divisor
222                 vn[2];            // normalized and broken
223                                   // up into halfwords.
224         uint32_t q[2];            // Quotient as halfwords.
225         uint64_t un1, un0,        // Dividend and divisor
226                 vn0;              // as fullwords.
227         uint64_t qhat;            // Estimated quotient digit.
228         uint64_t rhat;            // A remainder.
229         uint64_t p;               // Product of two digits.
230         int64_t s, i, j, t, k;
231
232         if (u1 >= v)              // If overflow, return the largest
233                 return (uint64_t)-1; // possible quotient.
234
235         s = 64 - fls64(v);                // 0 <= s <= 63.
236         vn0 = v << s;             // Normalize divisor.
237         vn[1] = vn0 >> 32;        // Break divisor up into
238         vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
239
240         // Shift dividend left.
241         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
242         un0 = u0 << s;
243         un[3] = un1 >> 32;        // Break dividend up into
244         un[2] = un1;              // four 32-bit halfwords
245         un[1] = un0 >> 32;        // Note: storing into
246         un[0] = un0;              // halfwords truncates.
247
248         for (j = 1; j >= 0; j--) {
249                 // Compute estimate qhat of q[j].
250                 qhat = (un[j+2]*b + un[j+1])/vn[1];
251                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
252         again:
253                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
254                         qhat = qhat - 1;
255                         rhat = rhat + vn[1];
256                         if (rhat < b) goto again;
257                 }
258
259                 // Multiply and subtract.
260                 k = 0;
261                 for (i = 0; i < 2; i++) {
262                         p = qhat*vn[i];
263                         t = un[i+j] - k - (p & 0xFFFFFFFF);
264                         un[i+j] = t;
265                         k = (p >> 32) - (t >> 32);
266                 }
267                 t = un[j+2] - k;
268                 un[j+2] = t;
269
270                 q[j] = qhat;              // Store quotient digit.
271                 if (t < 0) {              // If we subtracted too
272                         q[j] = q[j] - 1;  // much, add back.
273                         k = 0;
274                         for (i = 0; i < 2; i++) {
275                                 t = un[i+j] + vn[i] + k;
276                                 un[i+j] = t;
277                                 k = t >> 32;
278                         }
279                         un[j+2] = un[j+2] + k;
280                 }
281         } // End j.
282
283         return q[1]*b + q[0];
284 }
285
286 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
287 {
288         int64_t q, uneg, vneg, diff, borrow;
289
290         uneg = u1 >> 63;          // -1 if u < 0.
291         if (uneg) {               // Compute the absolute
292                 u0 = -u0;         // value of the dividend u.
293                 borrow = (u0 != 0);
294                 u1 = -u1 - borrow;
295         }
296
297         vneg = v >> 63;           // -1 if v < 0.
298         v = (v ^ vneg) - vneg;    // Absolute value of v.
299
300         if ((uint64_t)u1 >= (uint64_t)v)
301                 goto overflow;
302
303         q = divlu64(u1, u0, v);
304
305         diff = uneg ^ vneg;       // Negate q if signs of
306         q = (q ^ diff) - diff;    // u and v differed.
307
308         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
309         overflow:                          // possible neg. quotient.
310                 q = 0x8000000000000000ULL;
311         }
312         return q;
313 }
314
315 ssize_t tally_mean(const struct tally *tally)
316 {
317         size_t count = tally_num(tally);
318         if (!count)
319                 return 0;
320
321         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
322                 /* Use standard 64-bit arithmetic. */
323                 int64_t total = tally->total[0]
324                         | (((uint64_t)tally->total[1]) << 32);
325                 return total / count;
326         }
327         return divls64(tally->total[1], tally->total[0], count);
328 }
329
330 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
331 {
332         if (overflow) {
333                 *overflow = tally->total[1];
334                 return tally->total[0];
335         }
336
337         /* If result is negative, make sure we can represent it. */
338         if (tally->total[1] & ((size_t)1 << (SIZET_BITS-1))) {
339                 /* Must have only underflowed once, and must be able to
340                  * represent result at ssize_t. */
341                 if ((~tally->total[1])+1 != 0
342                     || (ssize_t)tally->total[0] >= 0) {
343                         /* Underflow, return minimum. */
344                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
345                 }
346         } else {
347                 /* Result is positive, must not have overflowed, and must be
348                  * able to represent as ssize_t. */
349                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
350                         /* Overflow.  Return maximum. */
351                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
352                 }
353         }
354         return tally->total[0];
355 }
356
357 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
358 {
359         ssize_t min, max;
360
361         min = bucket_min(tally->min, tally->step_bits, b);
362         if (b == tally->buckets - 1)
363                 max = tally->max;
364         else
365                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
366
367         /* FIXME: Think harder about cumulative error; is this enough?. */
368         *err = (max - min + 1) / 2;
369         /* Avoid overflow. */
370         return min + (max - min) / 2;
371 }
372
373 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
374 {
375         size_t count = tally_num(tally), total = 0;
376         unsigned int i;
377
378         for (i = 0; i < tally->buckets; i++) {
379                 total += tally->counts[i];
380                 if (total * 2 >= count)
381                         break;
382         }
383         return bucket_range(tally, i, err);
384 }
385
386 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
387 {
388         unsigned int i, min_best = 0, max_best = 0;
389
390         for (i = 0; i < tally->buckets; i++) {
391                 if (tally->counts[i] > tally->counts[min_best]) {
392                         min_best = max_best = i;
393                 } else if (tally->counts[i] == tally->counts[min_best]) {
394                         max_best = i;
395                 }
396         }
397
398         /* We can have more than one best, making our error huge. */
399         if (min_best != max_best) {
400                 ssize_t min, max;
401                 min = bucket_range(tally, min_best, err);
402                 max = bucket_range(tally, max_best, err);
403                 max += *err;
404                 *err += (size_t)(max - min);
405                 return min + (max - min) / 2;
406         }
407
408         return bucket_range(tally, min_best, err);
409 }
410
411 static unsigned get_max_bucket(const struct tally *tally)
412 {
413         unsigned int i;
414
415         for (i = tally->buckets; i > 0; i--)
416                 if (tally->counts[i-1])
417                         break;
418         return i;
419 }
420
421 char *tally_histogram(const struct tally *tally,
422                       unsigned width, unsigned height)
423 {
424         unsigned int i, count, max_bucket, largest_bucket;
425         struct tally *tmp;
426         char *graph, *p;
427
428         assert(width >= TALLY_MIN_HISTO_WIDTH);
429         assert(height >= TALLY_MIN_HISTO_HEIGHT);
430
431         /* Ignore unused buckets. */
432         max_bucket = get_max_bucket(tally);
433
434         /* FIXME: It'd be nice to smooth here... */
435         if (height >= max_bucket) {
436                 height = max_bucket;
437                 tmp = NULL;
438         } else {
439                 /* We create a temporary then renormalize so < height. */
440                 /* FIXME: Antialias properly! */
441                 tmp = tally_new(tally->buckets);
442                 if (!tmp)
443                         return NULL;
444                 tmp->min = tally->min;
445                 tmp->max = tally->max;
446                 tmp->step_bits = tally->step_bits;
447                 memcpy(tmp->counts, tally->counts,
448                        sizeof(tally->counts[0]) * tmp->buckets);
449                 while ((max_bucket = get_max_bucket(tmp)) >= height)
450                         renormalize(tmp, tmp->min, tmp->max * 2);
451                 /* Restore max */
452                 tmp->max = tally->max;
453                 tally = tmp;
454                 height = max_bucket;
455         }
456
457         /* Figure out longest line, for scale. */
458         largest_bucket = 0;
459         for (i = 0; i < tally->buckets; i++) {
460                 if (tally->counts[i] > largest_bucket)
461                         largest_bucket = tally->counts[i];
462         }
463
464         p = graph = (char *)malloc(height * (width + 1) + 1);
465         if (!graph) {
466                 free(tmp);
467                 return NULL;
468         }
469
470         for (i = 0; i < height; i++) {
471                 unsigned covered = 1, row;
472
473                 /* People expect minimum at the bottom. */
474                 row = height - i - 1;
475                 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
476
477                 if (row == 0)
478                         covered = snprintf(p, width, "%zi", tally->min);
479                 else if (row == height - 1)
480                         covered = snprintf(p, width, "%zi", tally->max);
481                 else if (row == bucket_of(tally->min, tally->step_bits, 0))
482                         *p = '+';
483                 else
484                         *p = '|';
485
486                 if (covered > width)
487                         covered = width;
488                 p += covered;
489
490                 if (count > covered)
491                         count -= covered;
492                 else
493                         count = 0;
494
495                 memset(p, '*', count);
496                 p += count;
497                 *p = '\n';
498                 p++;
499         }
500         *p = '\0';
501         free(tmp);
502         return graph;
503 }