git.ozlabs.org Git - ccan/blob - ccan/tally/tally.c

   1 #include "config.h"
   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
  11 #define SIZET_BITS (sizeof(size_t)*CHAR_BIT)
  12
  13 /* We use power of 2 steps.  I tried being tricky, but it got buggy. */
  14 struct tally {
  15         ssize_t min, max;
  16         size_t total[2];
  17         /* This allows limited frequency analysis. */
  18         unsigned buckets, step_bits;
  19         size_t counts[1 /* Actually: [buckets] */ ];
  20 };
  21
  22 struct tally *tally_new(unsigned buckets)
  23 {
  24         struct tally *tally;
  25
  26         /* There is always 1 bucket. */
  27         if (buckets == 0)
  28                 buckets = 1;
  29
  30         /* Check for overflow. */
  31         if (buckets && SIZE_MAX / buckets < sizeof(tally->counts[0]))
  32                 return NULL;
  33         tally = malloc(sizeof(*tally) + sizeof(tally->counts[0])*(buckets-1));
  34         if (tally) {
  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;
  39                 tally->step_bits = 0;
  40                 memset(tally->counts, 0, sizeof(tally->counts[0])*buckets);
  41         }
  42         return tally;
  43 }
  44
  45 static unsigned bucket_of(ssize_t min, unsigned step_bits, ssize_t val)
  46 {
  47         /* Don't over-shift. */
  48         if (step_bits == SIZET_BITS)
  49                 return 0;
  50         assert(step_bits < SIZET_BITS);
  51         return (size_t)(val - min) >> step_bits;
  52 }
  53
  54 /* Return the min value in bucket b. */
  55 static ssize_t bucket_min(ssize_t min, unsigned step_bits, unsigned b)
  56 {
  57         /* Don't over-shift. */
  58         if (step_bits == SIZET_BITS)
  59                 return min;
  60         assert(step_bits < SIZET_BITS);
  61         return min + ((ssize_t)b << step_bits);
  62 }
  63
  64 /* Does shifting by this many bits truncate the number? */
  65 static bool shift_overflows(size_t num, unsigned bits)
  66 {
  67         if (bits == 0)
  68                 return false;
  69
  70         return ((num << bits) >> 1) != (num << (bits - 1));
  71 }
  72
  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)
  76 {
  77         size_t range, spill;
  78         unsigned int i, old_min;
  79
  80         /* Uninitialized?  Don't do anything... */
  81         if (tally->max < tally->min)
  82                 goto update;
  83
  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)) {
  89                 /* Collapse down. */
  90                 for (i = 1; i < tally->buckets; i++) {
  91                         tally->counts[i/2] += tally->counts[i];
  92                         tally->counts[i] = 0;
  93                 }
  94                 tally->step_bits++;
  95         }
  96
  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,
 100                 tally->counts,
 101                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
 102         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
 103
 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;
 110         }
 111
 112 update:
 113         tally->min = new_min;
 114         tally->max = new_max;
 115 }
 116
 117 void tally_add(struct tally *tally, ssize_t val)
 118 {
 119         ssize_t new_min = tally->min, new_max = tally->max;
 120         bool need_renormalize = false;
 121
 122         if (val < tally->min) {
 123                 new_min = val;
 124                 need_renormalize = true;
 125         }
 126         if (val > tally->max) {
 127                 new_max = val;
 128                 need_renormalize = true;
 129         }
 130         if (need_renormalize)
 131                 renormalize(tally, new_min, new_max);
 132
 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])
 136                 tally->total[1]++;
 137         else if (val < 0 && tally->total[0] + val > tally->total[0])
 138                 tally->total[1]--;
 139         tally->total[0] += val;
 140         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
 141 }
 142
 143 size_t tally_num(const struct tally *tally)
 144 {
 145         size_t i, num = 0;
 146         for (i = 0; i < tally->buckets; i++)
 147                 num += tally->counts[i];
 148         return num;
 149 }
 150
 151 ssize_t tally_min(const struct tally *tally)
 152 {
 153         return tally->min;
 154 }
 155
 156 ssize_t tally_max(const struct tally *tally)
 157 {
 158         return tally->max;
 159 }
 160
 161 /* FIXME: Own ccan module please! */
 162 static unsigned fls64(uint64_t val)
 163 {
 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;
 168         } else {
 169 #endif
 170         uint64_t r = 64;
 171
 172         if (!val)
 173                 return 0;
 174         if (!(val & 0xffffffff00000000ull)) {
 175                 val <<= 32;
 176                 r -= 32;
 177         }
 178         if (!(val & 0xffff000000000000ull)) {
 179                 val <<= 16;
 180                 r -= 16;
 181         }
 182         if (!(val & 0xff00000000000000ull)) {
 183                 val <<= 8;
 184                 r -= 8;
 185         }
 186         if (!(val & 0xf000000000000000ull)) {
 187                 val <<= 4;
 188                 r -= 4;
 189         }
 190         if (!(val & 0xc000000000000000ull)) {
 191                 val <<= 2;
 192                 r -= 2;
 193         }
 194         if (!(val & 0x8000000000000000ull)) {
 195                 val <<= 1;
 196                 r -= 1;
 197         }
 198         return r;
 199 #if HAVE_BUILTIN_CLZL
 200         }
 201 #endif
 202 }
 203
 204 /* This is stolen straight from Hacker's Delight. */
 205 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 206 {
 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;
 218
 219         if (u1 >= v)              // If overflow, return the largest
 220                 return (uint64_t)-1; // possible quotient.
 221
 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.
 226
 227         // Shift dividend left.
 228         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 229         un0 = u0 << s;
 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.
 234
 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];
 239         again:
 240                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 241                         qhat = qhat - 1;
 242                         rhat = rhat + vn[1];
 243                         if (rhat < b) goto again;
 244                 }
 245
 246                 // Multiply and subtract.
 247                 k = 0;
 248                 for (i = 0; i < 2; i++) {
 249                         p = qhat*vn[i];
 250                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 251                         un[i+j] = t;
 252                         k = (p >> 32) - (t >> 32);
 253                 }
 254                 t = un[j+2] - k;
 255                 un[j+2] = t;
 256
 257                 q[j] = qhat;              // Store quotient digit.
 258                 if (t < 0) {              // If we subtracted too
 259                         q[j] = q[j] - 1;  // much, add back.
 260                         k = 0;
 261                         for (i = 0; i < 2; i++) {
 262                                 t = un[i+j] + vn[i] + k;
 263                                 un[i+j] = t;
 264                                 k = t >> 32;
 265                         }
 266                         un[j+2] = un[j+2] + k;
 267                 }
 268         } // End j.
 269
 270         return q[1]*b + q[0];
 271 }
 272
 273 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 274 {
 275         int64_t q, uneg, vneg, diff, borrow;
 276
 277         uneg = u1 >> 63;          // -1 if u < 0.
 278         if (uneg) {               // Compute the absolute
 279                 u0 = -u0;         // value of the dividend u.
 280                 borrow = (u0 != 0);
 281                 u1 = -u1 - borrow;
 282         }
 283
 284         vneg = v >> 63;           // -1 if v < 0.
 285         v = (v ^ vneg) - vneg;    // Absolute value of v.
 286
 287         if ((uint64_t)u1 >= (uint64_t)v)
 288                 goto overflow;
 289
 290         q = divlu64(u1, u0, v);
 291
 292         diff = uneg ^ vneg;       // Negate q if signs of
 293         q = (q ^ diff) - diff;    // u and v differed.
 294
 295         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
 296         overflow:                          // possible neg. quotient.
 297                 q = 0x8000000000000000ULL;
 298         }
 299         return q;
 300 }
 301
 302 ssize_t tally_mean(const struct tally *tally)
 303 {
 304         size_t count = tally_num(tally);
 305         if (!count)
 306                 return 0;
 307
 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;
 313         }
 314         return divls64(tally->total[1], tally->total[0], count);
 315 }
 316
 317 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 318 {
 319         if (overflow) {
 320                 *overflow = tally->total[1];
 321                 return tally->total[0];
 322         }
 323
 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));
 332                 }
 333         } else {
 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));
 339                 }
 340         }
 341         return tally->total[0];
 342 }
 343
 344 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 345 {
 346         ssize_t min, max;
 347
 348         min = bucket_min(tally->min, tally->step_bits, b);
 349         if (b == tally->buckets - 1)
 350                 max = tally->max;
 351         else
 352                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 353
 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;
 358 }
 359
 360 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 361 {
 362         size_t count = tally_num(tally), total = 0;
 363         unsigned int i;
 364
 365         for (i = 0; i < tally->buckets; i++) {
 366                 total += tally->counts[i];
 367                 if (total * 2 >= count)
 368                         break;
 369         }
 370         return bucket_range(tally, i, err);
 371 }
 372
 373 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 374 {
 375         unsigned int i, min_best = 0, max_best = 0;
 376
 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]) {
 381                         max_best = i;
 382                 }
 383         }
 384
 385         /* We can have more than one best, making our error huge. */
 386         if (min_best != max_best) {
 387                 ssize_t min, max;
 388                 min = bucket_range(tally, min_best, err);
 389                 max = bucket_range(tally, max_best, err);
 390                 max += *err;
 391                 *err += (size_t)(max - min);
 392                 return min + (max - min) / 2;
 393         }
 394
 395         return bucket_range(tally, min_best, err);
 396 }
 397
 398 static unsigned get_max_bucket(const struct tally *tally)
 399 {
 400         unsigned int i;
 401
 402         for (i = tally->buckets; i > 0; i--)
 403                 if (tally->counts[i-1])
 404                         break;
 405         return i;
 406 }
 407
 408 char *tally_histogram(const struct tally *tally,
 409                       unsigned width, unsigned height)
 410 {
 411         unsigned int i, count, max_bucket, largest_bucket;
 412         struct tally *tmp;
 413         char *graph, *p;
 414
 415         assert(width >= TALLY_MIN_HISTO_WIDTH);
 416         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 417
 418         /* Ignore unused buckets. */
 419         max_bucket = get_max_bucket(tally);
 420
 421         /* FIXME: It'd be nice to smooth here... */
 422         if (height >= max_bucket) {
 423                 height = max_bucket;
 424                 tmp = NULL;
 425         } else {
 426                 /* We create a temporary then renormalize so < height. */
 427                 /* FIXME: Antialias properly! */
 428                 tmp = tally_new(tally->buckets);
 429                 if (!tmp)
 430                         return NULL;
 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);
 438                 /* Restore max */
 439                 tmp->max = tally->max;
 440                 tally = tmp;
 441                 height = max_bucket;
 442         }
 443
 444         /* Figure out longest line, for scale. */
 445         largest_bucket = 0;
 446         for (i = 0; i < tally->buckets; i++) {
 447                 if (tally->counts[i] > largest_bucket)
 448                         largest_bucket = tally->counts[i];
 449         }
 450
 451         p = graph = malloc(height * (width + 1) + 1);
 452         if (!graph) {
 453                 free(tmp);
 454                 return NULL;
 455         }
 456
 457         for (i = 0; i < height; i++) {
 458                 unsigned covered = 1, row;
 459
 460                 /* People expect minimum at the bottom. */
 461                 row = height - i - 1;
 462                 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
 463
 464                 if (row == 0)
 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))
 469                         *p = '+';
 470                 else
 471                         *p = '|';
 472
 473                 if (covered > width)
 474                         covered = width;
 475                 p += covered;
 476
 477                 if (count > covered)
 478                         count -= covered;
 479                 else
 480                         count = 0;
 481
 482                 memset(p, '*', count);
 483                 p += count;
 484                 *p = '\n';
 485                 p++;
 486         }
 487         *p = '\0';
 488         free(tmp);
 489         return graph;
 490 }