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