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         return ((num << bits) >> 1) != (num << (bits - 1));
  80 }
  81
  82 /* When min or max change, we may need to shuffle the frequency counts. */
  83 static void renormalize(struct tally *tally,
  84                         ssize_t new_min, ssize_t new_max)
  85 {
  86         size_t range, spill;
  87         unsigned int i, old_min;
  88
  89         /* Uninitialized?  Don't do anything... */
  90         if (tally->max < tally->min)
  91                 goto update;
  92
  93         /* If we don't have sufficient range, increase step bits until
  94          * buckets cover entire range of ssize_t anyway. */
  95         range = (new_max - new_min) + 1;
  96         while (!shift_overflows(tally->buckets, tally->step_bits)
  97                && range > ((size_t)tally->buckets << tally->step_bits)) {
  98                 /* Collapse down. */
  99                 for (i = 1; i < tally->buckets; i++) {
 100                         tally->counts[i/2] += tally->counts[i];
 101                         tally->counts[i] = 0;
 102                 }
 103                 tally->step_bits++;
 104         }
 105
 106         /* Now if minimum has dropped, move buckets up. */
 107         old_min = bucket_of(new_min, tally->step_bits, tally->min);
 108         memmove(tally->counts + old_min,
 109                 tally->counts,
 110                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
 111         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
 112
 113         /* If we moved boundaries, adjust buckets to that ratio. */
 114         spill = (tally->min - new_min) % (1 << tally->step_bits);
 115         for (i = 0; i < tally->buckets-1; i++) {
 116                 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
 117                 tally->counts[i] -= adjust;
 118                 tally->counts[i+1] += adjust;
 119         }
 120
 121 update:
 122         tally->min = new_min;
 123         tally->max = new_max;
 124 }
 125
 126 void tally_add(struct tally *tally, ssize_t val)
 127 {
 128         ssize_t new_min = tally->min, new_max = tally->max;
 129         bool need_renormalize = false;
 130
 131         if (val < tally->min) {
 132                 new_min = val;
 133                 need_renormalize = true;
 134         }
 135         if (val > tally->max) {
 136                 new_max = val;
 137                 need_renormalize = true;
 138         }
 139         if (need_renormalize)
 140                 renormalize(tally, new_min, new_max);
 141
 142         /* 128-bit arithmetic!  If we didn't want exact mean, we could just
 143          * pull it out of counts. */
 144         if (val > 0 && tally->total[0] + val < tally->total[0])
 145                 tally->total[1]++;
 146         else if (val < 0 && tally->total[0] + val > tally->total[0])
 147                 tally->total[1]--;
 148         tally->total[0] += val;
 149         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
 150 }
 151
 152 size_t tally_num(const struct tally *tally)
 153 {
 154         size_t i, num = 0;
 155         for (i = 0; i < tally->buckets; i++)
 156                 num += tally->counts[i];
 157         return num;
 158 }
 159
 160 ssize_t tally_min(const struct tally *tally)
 161 {
 162         return tally->min;
 163 }
 164
 165 ssize_t tally_max(const struct tally *tally)
 166 {
 167         return tally->max;
 168 }
 169
 170 /* FIXME: Own ccan module please! */
 171 static unsigned fls64(uint64_t val)
 172 {
 173 #if HAVE_BUILTIN_CLZL
 174         if (val <= ULONG_MAX) {
 175                 /* This is significantly faster! */
 176                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
 177         } else {
 178 #endif
 179         uint64_t r = 64;
 180
 181         if (!val)
 182                 return 0;
 183         if (!(val & 0xffffffff00000000ull)) {
 184                 val <<= 32;
 185                 r -= 32;
 186         }
 187         if (!(val & 0xffff000000000000ull)) {
 188                 val <<= 16;
 189                 r -= 16;
 190         }
 191         if (!(val & 0xff00000000000000ull)) {
 192                 val <<= 8;
 193                 r -= 8;
 194         }
 195         if (!(val & 0xf000000000000000ull)) {
 196                 val <<= 4;
 197                 r -= 4;
 198         }
 199         if (!(val & 0xc000000000000000ull)) {
 200                 val <<= 2;
 201                 r -= 2;
 202         }
 203         if (!(val & 0x8000000000000000ull)) {
 204                 val <<= 1;
 205                 r -= 1;
 206         }
 207         return r;
 208 #if HAVE_BUILTIN_CLZL
 209         }
 210 #endif
 211 }
 212
 213 /* This is stolen straight from Hacker's Delight. */
 214 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 215 {
 216         const uint64_t b = 4294967296ULL; // Number base (32 bits).
 217         uint32_t un[4],           // Dividend and divisor
 218                 vn[2];            // normalized and broken
 219                                   // up into halfwords.
 220         uint32_t q[2];            // Quotient as halfwords.
 221         uint64_t un1, un0,        // Dividend and divisor
 222                 vn0;              // as fullwords.
 223         uint64_t qhat;            // Estimated quotient digit.
 224         uint64_t rhat;            // A remainder.
 225         uint64_t p;               // Product of two digits.
 226         int64_t s, i, j, t, k;
 227
 228         if (u1 >= v)              // If overflow, return the largest
 229                 return (uint64_t)-1; // possible quotient.
 230
 231         s = 64 - fls64(v);                // 0 <= s <= 63.
 232         vn0 = v << s;             // Normalize divisor.
 233         vn[1] = vn0 >> 32;        // Break divisor up into
 234         vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
 235
 236         // Shift dividend left.
 237         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 238         un0 = u0 << s;
 239         un[3] = un1 >> 32;        // Break dividend up into
 240         un[2] = un1;              // four 32-bit halfwords
 241         un[1] = un0 >> 32;        // Note: storing into
 242         un[0] = un0;              // halfwords truncates.
 243
 244         for (j = 1; j >= 0; j--) {
 245                 // Compute estimate qhat of q[j].
 246                 qhat = (un[j+2]*b + un[j+1])/vn[1];
 247                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
 248         again:
 249                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 250                         qhat = qhat - 1;
 251                         rhat = rhat + vn[1];
 252                         if (rhat < b) goto again;
 253                 }
 254
 255                 // Multiply and subtract.
 256                 k = 0;
 257                 for (i = 0; i < 2; i++) {
 258                         p = qhat*vn[i];
 259                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 260                         un[i+j] = t;
 261                         k = (p >> 32) - (t >> 32);
 262                 }
 263                 t = un[j+2] - k;
 264                 un[j+2] = t;
 265
 266                 q[j] = qhat;              // Store quotient digit.
 267                 if (t < 0) {              // If we subtracted too
 268                         q[j] = q[j] - 1;  // much, add back.
 269                         k = 0;
 270                         for (i = 0; i < 2; i++) {
 271                                 t = un[i+j] + vn[i] + k;
 272                                 un[i+j] = t;
 273                                 k = t >> 32;
 274                         }
 275                         un[j+2] = un[j+2] + k;
 276                 }
 277         } // End j.
 278
 279         return q[1]*b + q[0];
 280 }
 281
 282 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 283 {
 284         int64_t q, uneg, vneg, diff, borrow;
 285
 286         uneg = u1 >> 63;          // -1 if u < 0.
 287         if (uneg) {               // Compute the absolute
 288                 u0 = -u0;         // value of the dividend u.
 289                 borrow = (u0 != 0);
 290                 u1 = -u1 - borrow;
 291         }
 292
 293         vneg = v >> 63;           // -1 if v < 0.
 294         v = (v ^ vneg) - vneg;    // Absolute value of v.
 295
 296         if ((uint64_t)u1 >= (uint64_t)v)
 297                 goto overflow;
 298
 299         q = divlu64(u1, u0, v);
 300
 301         diff = uneg ^ vneg;       // Negate q if signs of
 302         q = (q ^ diff) - diff;    // u and v differed.
 303
 304         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
 305         overflow:                          // possible neg. quotient.
 306                 q = 0x8000000000000000ULL;
 307         }
 308         return q;
 309 }
 310
 311 ssize_t tally_mean(const struct tally *tally)
 312 {
 313         size_t count = tally_num(tally);
 314         if (!count)
 315                 return 0;
 316
 317         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
 318                 /* Use standard 64-bit arithmetic. */
 319                 int64_t total = tally->total[0]
 320                         | (((uint64_t)tally->total[1]) << 32);
 321                 return total / count;
 322         }
 323         return divls64(tally->total[1], tally->total[0], count);
 324 }
 325
 326 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 327 {
 328         if (overflow) {
 329                 *overflow = tally->total[1];
 330                 return tally->total[0];
 331         }
 332
 333         /* If result is negative, make sure we can represent it. */
 334         if (tally->total[1] & ((size_t)1 << (SIZET_BITS-1))) {
 335                 /* Must have only underflowed once, and must be able to
 336                  * represent result at ssize_t. */
 337                 if ((~tally->total[1])+1 != 0
 338                     || (ssize_t)tally->total[0] >= 0) {
 339                         /* Underflow, return minimum. */
 340                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
 341                 }
 342         } else {
 343                 /* Result is positive, must not have overflowed, and must be
 344                  * able to represent as ssize_t. */
 345                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
 346                         /* Overflow.  Return maximum. */
 347                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
 348                 }
 349         }
 350         return tally->total[0];
 351 }
 352
 353 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 354 {
 355         ssize_t min, max;
 356
 357         min = bucket_min(tally->min, tally->step_bits, b);
 358         if (b == tally->buckets - 1)
 359                 max = tally->max;
 360         else
 361                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 362
 363         /* FIXME: Think harder about cumulative error; is this enough?. */
 364         *err = (max - min + 1) / 2;
 365         /* Avoid overflow. */
 366         return min + (max - min) / 2;
 367 }
 368
 369 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 370 {
 371         size_t count = tally_num(tally), total = 0;
 372         unsigned int i;
 373
 374         for (i = 0; i < tally->buckets; i++) {
 375                 total += tally->counts[i];
 376                 if (total * 2 >= count)
 377                         break;
 378         }
 379         return bucket_range(tally, i, err);
 380 }
 381
 382 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 383 {
 384         unsigned int i, min_best = 0, max_best = 0;
 385
 386         for (i = 0; i < tally->buckets; i++) {
 387                 if (tally->counts[i] > tally->counts[min_best]) {
 388                         min_best = max_best = i;
 389                 } else if (tally->counts[i] == tally->counts[min_best]) {
 390                         max_best = i;
 391                 }
 392         }
 393
 394         /* We can have more than one best, making our error huge. */
 395         if (min_best != max_best) {
 396                 ssize_t min, max;
 397                 min = bucket_range(tally, min_best, err);
 398                 max = bucket_range(tally, max_best, err);
 399                 max += *err;
 400                 *err += (size_t)(max - min);
 401                 return min + (max - min) / 2;
 402         }
 403
 404         return bucket_range(tally, min_best, err);
 405 }
 406
 407 static unsigned get_max_bucket(const struct tally *tally)
 408 {
 409         unsigned int i;
 410
 411         for (i = tally->buckets; i > 0; i--)
 412                 if (tally->counts[i-1])
 413                         break;
 414         return i;
 415 }
 416
 417 char *tally_histogram(const struct tally *tally,
 418                       unsigned width, unsigned height)
 419 {
 420         unsigned int i, count, max_bucket, largest_bucket;
 421         struct tally *tmp;
 422         char *graph, *p;
 423
 424         assert(width >= TALLY_MIN_HISTO_WIDTH);
 425         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 426
 427         /* Ignore unused buckets. */
 428         max_bucket = get_max_bucket(tally);
 429
 430         /* FIXME: It'd be nice to smooth here... */
 431         if (height >= max_bucket) {
 432                 height = max_bucket;
 433                 tmp = NULL;
 434         } else {
 435                 /* We create a temporary then renormalize so < height. */
 436                 /* FIXME: Antialias properly! */
 437                 tmp = tally_new(tally->buckets);
 438                 if (!tmp)
 439                         return NULL;
 440                 tmp->min = tally->min;
 441                 tmp->max = tally->max;
 442                 tmp->step_bits = tally->step_bits;
 443                 memcpy(tmp->counts, tally->counts,
 444                        sizeof(tally->counts[0]) * tmp->buckets);
 445                 while ((max_bucket = get_max_bucket(tmp)) >= height)
 446                         renormalize(tmp, tmp->min, tmp->max * 2);
 447                 /* Restore max */
 448                 tmp->max = tally->max;
 449                 tally = tmp;
 450                 height = max_bucket;
 451         }
 452
 453         /* Figure out longest line, for scale. */
 454         largest_bucket = 0;
 455         for (i = 0; i < tally->buckets; i++) {
 456                 if (tally->counts[i] > largest_bucket)
 457                         largest_bucket = tally->counts[i];
 458         }
 459
 460         p = graph = (char *)malloc(height * (width + 1) + 1);
 461         if (!graph) {
 462                 free(tmp);
 463                 return NULL;
 464         }
 465
 466         for (i = 0; i < height; i++) {
 467                 unsigned covered = 1, row;
 468
 469                 /* People expect minimum at the bottom. */
 470                 row = height - i - 1;
 471                 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
 472
 473                 if (row == 0)
 474                         covered = snprintf(p, width, "%zi", tally->min);
 475                 else if (row == height - 1)
 476                         covered = snprintf(p, width, "%zi", tally->max);
 477                 else if (row == bucket_of(tally->min, tally->step_bits, 0))
 478                         *p = '+';
 479                 else
 480                         *p = '|';
 481
 482                 if (covered > width)
 483                         covered = width;
 484                 p += covered;
 485
 486                 if (count > covered)
 487                         count -= covered;
 488                 else
 489                         count = 0;
 490
 491                 memset(p, '*', count);
 492                 p += count;
 493                 *p = '\n';
 494                 p++;
 495         }
 496         *p = '\0';
 497         free(tmp);
 498         return graph;
 499 }