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