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