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