git.ozlabs.org Git - ccan/blob - ccan/tally/tally.c

   1 #include "config.h"
   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
  11 #define SIZET_BITS (sizeof(size_t)*CHAR_BIT)
  12
  13 /* We use power of 2 steps.  I tried being tricky, but it got buggy. */
  14 struct tally {
  15         ssize_t min, max;
  16         size_t total[2];
  17         /* This allows limited frequency analysis. */
  18         size_t buckets;
  19         size_t step_bits;
  20         size_t counts[1 /* [buckets] */ ];
  21 };
  22
  23 struct tally *tally_new(size_t buckets)
  24 {
  25         struct tally *tally;
  26
  27         /* Check for overflow. */
  28         if (buckets && SIZE_MAX / buckets < sizeof(tally->counts[0]))
  29                 return NULL;
  30         tally = malloc(sizeof(*tally) + sizeof(tally->counts[0])*buckets);
  31         if (tally) {
  32                 /* SSIZE_MAX isn't portable, so make it one of these types. */
  33                 BUILD_ASSERT(sizeof(tally->min) == sizeof(int)
  34                              || sizeof(tally->min) == sizeof(long)
  35                              || sizeof(tally->min) == sizeof(long long));
  36                 if (sizeof(tally->min) == sizeof(int)) {
  37                         tally->min = INT_MAX;
  38                         tally->max = INT_MIN;
  39                 } else if (sizeof(tally->min) == sizeof(long)) {
  40                         tally->min = LONG_MAX;
  41                         tally->max = LONG_MIN;
  42                 } else if (sizeof(tally->min) == sizeof(long long)) {
  43                         tally->min = (ssize_t)LLONG_MAX;
  44                         tally->max = (ssize_t)LLONG_MIN;
  45                 }
  46                 tally->total[0] = tally->total[1] = 0;
  47                 /* There is always 1 bucket. */
  48                 tally->buckets = buckets+1;
  49                 tally->step_bits = 0;
  50                 memset(tally->counts, 0, sizeof(tally->counts[0])*(buckets+1));
  51         }
  52         return tally;
  53 }
  54
  55 static unsigned bucket_of(ssize_t min, unsigned step_bits, ssize_t val)
  56 {
  57         /* Don't over-shift. */
  58         if (step_bits == SIZET_BITS)
  59                 return 0;
  60         assert(step_bits < SIZET_BITS);
  61         return (size_t)(val - min) >> step_bits;
  62 }
  63
  64 /* Return the min value in bucket b. */
  65 static ssize_t bucket_min(ssize_t min, unsigned step_bits, unsigned b)
  66 {
  67         /* Don't over-shift. */
  68         if (step_bits == SIZET_BITS)
  69                 return min;
  70         assert(step_bits < SIZET_BITS);
  71         return min + ((ssize_t)b << step_bits);
  72 }
  73
  74 /* Does shifting by this many bits truncate the number? */
  75 static bool shift_overflows(size_t num, unsigned bits)
  76 {
  77         if (bits == 0)
  78                 return false;
  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         /* If we don't have sufficient range, increase step bits until
  95          * buckets cover entire range of ssize_t anyway. */
  96         range = (new_max - new_min) + 1;
  97         while (!shift_overflows(tally->buckets, tally->step_bits)
  98                && range > ((size_t)tally->buckets << tally->step_bits)) {
  99                 /* Collapse down. */
 100                 for (i = 1; i < tally->buckets; i++) {
 101                         tally->counts[i/2] += tally->counts[i];
 102                         tally->counts[i] = 0;
 103                 }
 104                 tally->step_bits++;
 105         }
 106
 107         /* Now if minimum has dropped, move buckets up. */
 108         old_min = bucket_of(new_min, tally->step_bits, tally->min);
 109         memmove(tally->counts + old_min,
 110                 tally->counts,
 111                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
 112         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
 113
 114         /* If we moved boundaries, adjust buckets to that ratio. */
 115         spill = (tally->min - new_min) % (1 << tally->step_bits);
 116         for (i = 0; i < tally->buckets-1; i++) {
 117                 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
 118                 tally->counts[i] -= adjust;
 119                 tally->counts[i+1] += adjust;
 120         }
 121
 122 update:
 123         tally->min = new_min;
 124         tally->max = new_max;
 125 }
 126
 127 void tally_add(struct tally *tally, ssize_t val)
 128 {
 129         ssize_t new_min = tally->min, new_max = tally->max;
 130         bool need_renormalize = false;
 131
 132         if (val < tally->min) {
 133                 new_min = val;
 134                 need_renormalize = true;
 135         }
 136         if (val > tally->max) {
 137                 new_max = val;
 138                 need_renormalize = true;
 139         }
 140         if (need_renormalize)
 141                 renormalize(tally, new_min, new_max);
 142
 143         /* 128-bit arithmetic!  If we didn't want exact mean, we could just
 144          * pull it out of counts. */
 145         if (val > 0 && tally->total[0] + val < tally->total[0])
 146                 tally->total[1]++;
 147         else if (val < 0 && tally->total[0] + val > tally->total[0])
 148                 tally->total[1]--;
 149         tally->total[0] += val;
 150         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
 151 }
 152
 153 size_t tally_num(const struct tally *tally)
 154 {
 155         size_t i, num = 0;
 156         for (i = 0; i < tally->buckets; i++)
 157                 num += tally->counts[i];
 158         return num;
 159 }
 160
 161 ssize_t tally_min(const struct tally *tally)
 162 {
 163         return tally->min;
 164 }
 165
 166 ssize_t tally_max(const struct tally *tally)
 167 {
 168         return tally->max;
 169 }
 170
 171 /* FIXME: Own ccan module please! */
 172 static unsigned fls64(uint64_t val)
 173 {
 174 #if HAVE_BUILTIN_CLZL
 175         if (val <= ULONG_MAX) {
 176                 /* This is significantly faster! */
 177                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
 178         } else {
 179 #endif
 180         uint64_t r = 64;
 181
 182         if (!val)
 183                 return 0;
 184         if (!(val & 0xffffffff00000000ull)) {
 185                 val <<= 32;
 186                 r -= 32;
 187         }
 188         if (!(val & 0xffff000000000000ull)) {
 189                 val <<= 16;
 190                 r -= 16;
 191         }
 192         if (!(val & 0xff00000000000000ull)) {
 193                 val <<= 8;
 194                 r -= 8;
 195         }
 196         if (!(val & 0xf000000000000000ull)) {
 197                 val <<= 4;
 198                 r -= 4;
 199         }
 200         if (!(val & 0xc000000000000000ull)) {
 201                 val <<= 2;
 202                 r -= 2;
 203         }
 204         if (!(val & 0x8000000000000000ull)) {
 205                 val <<= 1;
 206                 r -= 1;
 207         }
 208         return r;
 209 #if HAVE_BUILTIN_CLZL
 210         }
 211 #endif
 212 }
 213
 214 /* This is stolen straight from Hacker's Delight. */
 215 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 216 {
 217         const uint64_t b = 4294967296ULL; // Number base (32 bits).
 218         uint32_t un[4],           // Dividend and divisor
 219                 vn[2];            // normalized and broken
 220                                   // up into halfwords.
 221         uint32_t q[2];            // Quotient as halfwords.
 222         uint64_t un1, un0,        // Dividend and divisor
 223                 vn0;              // as fullwords.
 224         uint64_t qhat;            // Estimated quotient digit.
 225         uint64_t rhat;            // A remainder.
 226         uint64_t p;               // Product of two digits.
 227         int64_t s, i, j, t, k;
 228
 229         if (u1 >= v)              // If overflow, return the largest
 230                 return (uint64_t)-1; // possible quotient.
 231
 232         s = 64 - fls64(v);                // 0 <= s <= 63.
 233         vn0 = v << s;             // Normalize divisor.
 234         vn[1] = vn0 >> 32;        // Break divisor up into
 235         vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
 236
 237         // Shift dividend left.
 238         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 239         un0 = u0 << s;
 240         un[3] = un1 >> 32;        // Break dividend up into
 241         un[2] = un1;              // four 32-bit halfwords
 242         un[1] = un0 >> 32;        // Note: storing into
 243         un[0] = un0;              // halfwords truncates.
 244
 245         for (j = 1; j >= 0; j--) {
 246                 // Compute estimate qhat of q[j].
 247                 qhat = (un[j+2]*b + un[j+1])/vn[1];
 248                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
 249         again:
 250                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 251                         qhat = qhat - 1;
 252                         rhat = rhat + vn[1];
 253                         if (rhat < b) goto again;
 254                 }
 255
 256                 // Multiply and subtract.
 257                 k = 0;
 258                 for (i = 0; i < 2; i++) {
 259                         p = qhat*vn[i];
 260                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 261                         un[i+j] = t;
 262                         k = (p >> 32) - (t >> 32);
 263                 }
 264                 t = un[j+2] - k;
 265                 un[j+2] = t;
 266
 267                 q[j] = qhat;              // Store quotient digit.
 268                 if (t < 0) {              // If we subtracted too
 269                         q[j] = q[j] - 1;  // much, add back.
 270                         k = 0;
 271                         for (i = 0; i < 2; i++) {
 272                                 t = un[i+j] + vn[i] + k;
 273                                 un[i+j] = t;
 274                                 k = t >> 32;
 275                         }
 276                         un[j+2] = un[j+2] + k;
 277                 }
 278         } // End j.
 279
 280         return q[1]*b + q[0];
 281 }
 282
 283 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 284 {
 285         int64_t q, uneg, vneg, diff, borrow;
 286
 287         uneg = u1 >> 63;          // -1 if u < 0.
 288         if (uneg) {               // Compute the absolute
 289                 u0 = -u0;         // value of the dividend u.
 290                 borrow = (u0 != 0);
 291                 u1 = -u1 - borrow;
 292         }
 293
 294         vneg = v >> 63;           // -1 if v < 0.
 295         v = (v ^ vneg) - vneg;    // Absolute value of v.
 296
 297         if ((uint64_t)u1 >= (uint64_t)v)
 298                 goto overflow;
 299
 300         q = divlu64(u1, u0, v);
 301
 302         diff = uneg ^ vneg;       // Negate q if signs of
 303         q = (q ^ diff) - diff;    // u and v differed.
 304
 305         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
 306         overflow:                          // possible neg. quotient.
 307                 q = 0x8000000000000000ULL;
 308         }
 309         return q;
 310 }
 311
 312 ssize_t tally_mean(const struct tally *tally)
 313 {
 314         size_t count = tally_num(tally);
 315         if (!count)
 316                 return 0;
 317
 318         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
 319                 /* Use standard 64-bit arithmetic. */
 320                 int64_t total = tally->total[0]
 321                         | (((uint64_t)tally->total[1]) << 32);
 322                 return total / count;
 323         }
 324         return divls64(tally->total[1], tally->total[0], count);
 325 }
 326
 327 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 328 {
 329         if (overflow) {
 330                 *overflow = tally->total[1];
 331                 return tally->total[0];
 332         }
 333
 334         /* If result is negative, make sure we can represent it. */
 335         if (tally->total[1] & (1 << (SIZET_BITS-1))) {
 336                 /* Must have only underflowed once, and must be able to
 337                  * represent result at ssize_t. */
 338                 if ((~tally->total[1])+1 != 0
 339                     || (ssize_t)tally->total[0] >= 0) {
 340                         /* Underflow, return minimum. */
 341                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
 342                 }
 343         } else {
 344                 /* Result is positive, must not have overflowed, and must be
 345                  * able to represent as ssize_t. */
 346                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
 347                         /* Overflow.  Return maximum. */
 348                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
 349                 }
 350         }
 351         return tally->total[0];
 352 }
 353
 354 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 355 {
 356         ssize_t min, max;
 357
 358         min = bucket_min(tally->min, tally->step_bits, b);
 359         if (b == tally->buckets - 1)
 360                 max = tally->max;
 361         else
 362                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 363
 364         /* FIXME: Think harder about cumulative error; is this enough?. */
 365         *err = (max - min + 1) / 2;
 366         /* Avoid overflow. */
 367         return min + (max - min) / 2;
 368 }
 369
 370 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 371 {
 372         size_t count = tally_num(tally), total = 0;
 373         unsigned int i;
 374
 375         for (i = 0; i < tally->buckets; i++) {
 376                 total += tally->counts[i];
 377                 if (total * 2 >= count)
 378                         break;
 379         }
 380         return bucket_range(tally, i, err);
 381 }
 382
 383 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 384 {
 385         unsigned int i, min_best = 0, max_best = 0;
 386
 387         for (i = 0; i < tally->buckets; i++) {
 388                 if (tally->counts[i] > tally->counts[min_best]) {
 389                         min_best = max_best = i;
 390                 } else if (tally->counts[i] == tally->counts[min_best]) {
 391                         max_best = i;
 392                 }
 393         }
 394
 395         /* We can have more than one best, making our error huge. */
 396         if (min_best != max_best) {
 397                 ssize_t min, max;
 398                 min = bucket_range(tally, min_best, err);
 399                 max = bucket_range(tally, max_best, err);
 400                 max += *err;
 401                 *err += (size_t)(max - min);
 402                 return min + (max - min) / 2;
 403         }
 404
 405         return bucket_range(tally, min_best, err);
 406 }
 407
 408 static unsigned get_max_bucket(const struct tally *tally)
 409 {
 410         unsigned int i;
 411
 412         for (i = tally->buckets; i > 0; i--)
 413                 if (tally->counts[i-1])
 414                         break;
 415         return i;
 416 }
 417
 418 char *tally_histogram(const struct tally *tally,
 419                       unsigned width, unsigned height)
 420 {
 421         unsigned int i, count, max_bucket, largest_bucket;
 422         struct tally *tmp;
 423         char *graph, *p;
 424
 425         assert(width >= TALLY_MIN_HISTO_WIDTH);
 426         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 427
 428         /* Ignore unused buckets. */
 429         max_bucket = get_max_bucket(tally);
 430
 431         /* FIXME: It'd be nice to smooth here... */
 432         if (height >= max_bucket) {
 433                 height = max_bucket;
 434                 tmp = NULL;
 435         } else {
 436                 /* We create a temporary then renormalize so < height. */
 437                 /* FIXME: Antialias properly! */
 438                 tmp = tally_new(tally->buckets-1);
 439                 if (!tmp)
 440                         return NULL;
 441                 tmp->min = tally->min;
 442                 tmp->max = tally->max;
 443                 tmp->step_bits = tally->step_bits;
 444                 memcpy(tmp->counts, tally->counts,
 445                        sizeof(tally->counts[0]) * tmp->buckets);
 446                 while ((max_bucket = get_max_bucket(tmp)) >= height)
 447                         renormalize(tmp, tmp->min, tmp->max *= 2);
 448                 /* Restore max */
 449                 tmp->max = tally->max;
 450                 tally = tmp;
 451                 height = max_bucket;
 452         }
 453
 454         /* Figure out longest line, for scale. */
 455         largest_bucket = 0;
 456         for (i = 0; i < tally->buckets; i++) {
 457                 if (tally->counts[i] > largest_bucket)
 458                         largest_bucket = tally->counts[i];
 459         }
 460
 461         p = graph = malloc(height * (width + 1) + 1);
 462         if (!graph) {
 463                 free(tmp);
 464                 return NULL;
 465         }
 466         for (i = 0; i < height; i++) {
 467                 unsigned covered = 0;
 468                 count = (double)tally->counts[i] / largest_bucket * width;
 469
 470                 if (i == 0)
 471                         covered = snprintf(p, width, "%zi", tally->min);
 472                 else if (i == height - 1)
 473                         covered = snprintf(p, width, "%zi", tally->max);
 474                 if (covered) {
 475                         if (covered > width)
 476                                 covered = width;
 477                         p += covered;
 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 }