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
  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         }
 162         return num;
 163 }
 164
 165 ssize_t tally_min(const struct tally *tally)
 166 {
 167         return tally->min;
 168 }
 169
 170 ssize_t tally_max(const struct tally *tally)
 171 {
 172         return tally->max;
 173 }
 174
 175 /* FIXME: Own ccan module please! */
 176 static unsigned fls64(uint64_t val)
 177 {
 178 #if HAVE_BUILTIN_CLZL
 179         if (val <= ULONG_MAX) {
 180                 /* This is significantly faster! */
 181                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
 182         } else {
 183 #endif
 184         uint64_t r = 64;
 185
 186         if (!val) {
 187                 return 0;
 188         }
 189         if (!(val & 0xffffffff00000000ull)) {
 190                 val <<= 32;
 191                 r -= 32;
 192         }
 193         if (!(val & 0xffff000000000000ull)) {
 194                 val <<= 16;
 195                 r -= 16;
 196         }
 197         if (!(val & 0xff00000000000000ull)) {
 198                 val <<= 8;
 199                 r -= 8;
 200         }
 201         if (!(val & 0xf000000000000000ull)) {
 202                 val <<= 4;
 203                 r -= 4;
 204         }
 205         if (!(val & 0xc000000000000000ull)) {
 206                 val <<= 2;
 207                 r -= 2;
 208         }
 209         if (!(val & 0x8000000000000000ull)) {
 210                 val <<= 1;
 211                 r -= 1;
 212         }
 213         return r;
 214 #if HAVE_BUILTIN_CLZL
 215         }
 216 #endif
 217 }
 218
 219 /* This is stolen straight from Hacker's Delight. */
 220 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 221 {
 222         const uint64_t b = 4294967296ULL; // Number base (32 bits).
 223         uint32_t un[4],           // Dividend and divisor
 224                 vn[2];            // normalized and broken
 225                                   // up into halfwords.
 226         uint32_t q[2];            // Quotient as halfwords.
 227         uint64_t un1, un0,        // Dividend and divisor
 228                 vn0;              // as fullwords.
 229         uint64_t qhat;            // Estimated quotient digit.
 230         uint64_t rhat;            // A remainder.
 231         uint64_t p;               // Product of two digits.
 232         int64_t s, i, j, t, k;
 233
 234         if (u1 >= v)              // If overflow, return the largest
 235                 return (uint64_t)-1; // possible quotient.
 236
 237         s = 64 - fls64(v);                // 0 <= s <= 63.
 238         vn0 = v << s;             // Normalize divisor.
 239         vn[1] = vn0 >> 32;        // Break divisor up into
 240         vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
 241
 242         // Shift dividend left.
 243         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 244         un0 = u0 << s;
 245         un[3] = un1 >> 32;        // Break dividend up into
 246         un[2] = un1;              // four 32-bit halfwords
 247         un[1] = un0 >> 32;        // Note: storing into
 248         un[0] = un0;              // halfwords truncates.
 249
 250         for (j = 1; j >= 0; j--) {
 251                 // Compute estimate qhat of q[j].
 252                 qhat = (un[j+2]*b + un[j+1])/vn[1];
 253                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
 254         again:
 255                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 256                         qhat = qhat - 1;
 257                         rhat = rhat + vn[1];
 258                         if (rhat < b) goto again;
 259                 }
 260
 261                 // Multiply and subtract.
 262                 k = 0;
 263                 for (i = 0; i < 2; i++) {
 264                         p = qhat*vn[i];
 265                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 266                         un[i+j] = t;
 267                         k = (p >> 32) - (t >> 32);
 268                 }
 269                 t = un[j+2] - k;
 270                 un[j+2] = t;
 271
 272                 q[j] = qhat;              // Store quotient digit.
 273                 if (t < 0) {              // If we subtracted too
 274                         q[j] = q[j] - 1;  // much, add back.
 275                         k = 0;
 276                         for (i = 0; i < 2; i++) {
 277                                 t = un[i+j] + vn[i] + k;
 278                                 un[i+j] = t;
 279                                 k = t >> 32;
 280                         }
 281                         un[j+2] = un[j+2] + k;
 282                 }
 283         } // End j.
 284
 285         return q[1]*b + q[0];
 286 }
 287
 288 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 289 {
 290         int64_t q, uneg, vneg, diff, borrow;
 291
 292         uneg = u1 >> 63;          // -1 if u < 0.
 293         if (uneg) {               // Compute the absolute
 294                 u0 = -u0;         // value of the dividend u.
 295                 borrow = (u0 != 0);
 296                 u1 = -u1 - borrow;
 297         }
 298
 299         vneg = v >> 63;           // -1 if v < 0.
 300         v = (v ^ vneg) - vneg;    // Absolute value of v.
 301
 302         if ((uint64_t)u1 >= (uint64_t)v)
 303                 goto overflow;
 304
 305         q = divlu64(u1, u0, v);
 306
 307         diff = uneg ^ vneg;       // Negate q if signs of
 308         q = (q ^ diff) - diff;    // u and v differed.
 309
 310         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
 311         overflow:                          // possible neg. quotient.
 312                 q = 0x8000000000000000ULL;
 313         }
 314         return q;
 315 }
 316
 317 ssize_t tally_mean(const struct tally *tally)
 318 {
 319         size_t count = tally_num(tally);
 320         if (!count)
 321                 return 0;
 322
 323         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
 324                 /* Use standard 64-bit arithmetic. */
 325                 int64_t total = tally->total[0]
 326                         | (((uint64_t)tally->total[1]) << 32);
 327                 return total / count;
 328         }
 329         return divls64(tally->total[1], tally->total[0], count);
 330 }
 331
 332 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 333 {
 334         if (overflow) {
 335                 *overflow = tally->total[1];
 336                 return tally->total[0];
 337         }
 338
 339         /* If result is negative, make sure we can represent it. */
 340         if (tally->total[1] & ((size_t)1 << (SIZET_BITS-1))) {
 341                 /* Must have only underflowed once, and must be able to
 342                  * represent result at ssize_t. */
 343                 if ((~tally->total[1])+1 != 0
 344                     || (ssize_t)tally->total[0] >= 0) {
 345                         /* Underflow, return minimum. */
 346                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
 347                 }
 348         } else {
 349                 /* Result is positive, must not have overflowed, and must be
 350                  * able to represent as ssize_t. */
 351                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
 352                         /* Overflow.  Return maximum. */
 353                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
 354                 }
 355         }
 356         return tally->total[0];
 357 }
 358
 359 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 360 {
 361         ssize_t min, max;
 362
 363         min = bucket_min(tally->min, tally->step_bits, b);
 364         if (b == tally->buckets - 1)
 365                 max = tally->max;
 366         else
 367                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 368
 369         /* FIXME: Think harder about cumulative error; is this enough?. */
 370         *err = (max - min + 1) / 2;
 371         /* Avoid overflow. */
 372         return min + (max - min) / 2;
 373 }
 374
 375 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 376 {
 377         size_t count = tally_num(tally), total = 0;
 378         unsigned int i;
 379
 380         for (i = 0; i < tally->buckets; i++) {
 381                 total += tally->counts[i];
 382                 if (total * 2 >= count)
 383                         break;
 384         }
 385         return bucket_range(tally, i, err);
 386 }
 387
 388 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 389 {
 390         unsigned int i, min_best = 0, max_best = 0;
 391
 392         for (i = 0; i < tally->buckets; i++) {
 393                 if (tally->counts[i] > tally->counts[min_best]) {
 394                         min_best = max_best = i;
 395                 } else if (tally->counts[i] == tally->counts[min_best]) {
 396                         max_best = i;
 397                 }
 398         }
 399
 400         /* We can have more than one best, making our error huge. */
 401         if (min_best != max_best) {
 402                 ssize_t min, max;
 403                 min = bucket_range(tally, min_best, err);
 404                 max = bucket_range(tally, max_best, err);
 405                 max += *err;
 406                 *err += (size_t)(max - min);
 407                 return min + (max - min) / 2;
 408         }
 409
 410         return bucket_range(tally, min_best, err);
 411 }
 412
 413 static unsigned get_max_bucket(const struct tally *tally)
 414 {
 415         unsigned int i;
 416
 417         for (i = tally->buckets; i > 0; i--)
 418                 if (tally->counts[i-1])
 419                         break;
 420         return i;
 421 }
 422
 423 char *tally_histogram(const struct tally *tally,
 424                       unsigned width, unsigned height)
 425 {
 426         unsigned int i, count, max_bucket, largest_bucket;
 427         struct tally *tmp;
 428         char *graph, *p;
 429
 430         assert(width >= TALLY_MIN_HISTO_WIDTH);
 431         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 432
 433         /* Ignore unused buckets. */
 434         max_bucket = get_max_bucket(tally);
 435
 436         /* FIXME: It'd be nice to smooth here... */
 437         if (height >= max_bucket) {
 438                 height = max_bucket;
 439                 tmp = NULL;
 440         } else {
 441                 /* We create a temporary then renormalize so < height. */
 442                 /* FIXME: Antialias properly! */
 443                 tmp = tally_new(tally->buckets);
 444                 if (!tmp)
 445                         return NULL;
 446                 tmp->min = tally->min;
 447                 tmp->max = tally->max;
 448                 tmp->step_bits = tally->step_bits;
 449                 memcpy(tmp->counts, tally->counts,
 450                        sizeof(tally->counts[0]) * tmp->buckets);
 451                 while ((max_bucket = get_max_bucket(tmp)) >= height)
 452                         renormalize(tmp, tmp->min, tmp->max * 2);
 453                 /* Restore max */
 454                 tmp->max = tally->max;
 455                 tally = tmp;
 456                 height = max_bucket;
 457         }
 458
 459         /* Figure out longest line, for scale. */
 460         largest_bucket = 0;
 461         for (i = 0; i < tally->buckets; i++) {
 462                 if (tally->counts[i] > largest_bucket)
 463                         largest_bucket = tally->counts[i];
 464         }
 465
 466         p = graph = (char *)malloc(height * (width + 1) + 1);
 467         if (!graph) {
 468                 free(tmp);
 469                 return NULL;
 470         }
 471
 472         for (i = 0; i < height; i++) {
 473                 unsigned covered = 1, row;
 474
 475                 /* People expect minimum at the bottom. */
 476                 row = height - i - 1;
 477                 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
 478
 479                 if (row == 0)
 480                         covered = snprintf(p, width, "%zi", tally->min);
 481                 else if (row == height - 1)
 482                         covered = snprintf(p, width, "%zi", tally->max);
 483                 else if (row == bucket_of(tally->min, tally->step_bits, 0))
 484                         *p = '+';
 485                 else
 486                         *p = '|';
 487
 488                 if (covered > width)
 489                         covered = width;
 490                 p += covered;
 491
 492                 if (count > covered)
 493                         count -= covered;
 494                 else
 495                         count = 0;
 496
 497                 memset(p, '*', count);
 498                 p += count;
 499                 *p = '\n';
 500                 p++;
 501         }
 502         *p = '\0';
 503         free(tmp);
 504         return graph;
 505 }