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         unsigned buckets, step_bits;
  19         size_t counts[1 /* [buckets] */ ];
  20 };
  21
  22 struct tally *tally_new(unsigned buckets)
  23 {
  24         struct tally *tally;
  25
  26         /* Check for overflow. */
  27         if (buckets && SIZE_MAX / buckets < sizeof(tally->counts[0]))
  28                 return NULL;
  29         tally = malloc(sizeof(*tally) + sizeof(tally->counts[0])*buckets);
  30         if (tally) {
  31                 tally->max = ((size_t)1 << (SIZET_BITS - 1));
  32                 tally->min = ~tally->max;
  33                 tally->total[0] = tally->total[1] = 0;
  34                 /* There is always 1 bucket. */
  35                 tally->buckets = buckets+1;
  36                 tally->step_bits = 0;
  37                 memset(tally->counts, 0, sizeof(tally->counts[0])*(buckets+1));
  38         }
  39         return tally;
  40 }
  41
  42 static unsigned bucket_of(ssize_t min, unsigned step_bits, ssize_t val)
  43 {
  44         /* Don't over-shift. */
  45         if (step_bits == SIZET_BITS)
  46                 return 0;
  47         assert(step_bits < SIZET_BITS);
  48         return (size_t)(val - min) >> step_bits;
  49 }
  50
  51 /* Return the min value in bucket b. */
  52 static ssize_t bucket_min(ssize_t min, unsigned step_bits, unsigned b)
  53 {
  54         /* Don't over-shift. */
  55         if (step_bits == SIZET_BITS)
  56                 return min;
  57         assert(step_bits < SIZET_BITS);
  58         return min + ((ssize_t)b << step_bits);
  59 }
  60
  61 /* Does shifting by this many bits truncate the number? */
  62 static bool shift_overflows(size_t num, unsigned bits)
  63 {
  64         if (bits == 0)
  65                 return false;
  66
  67         return ((num << bits) >> 1) != (num << (bits - 1));
  68 }
  69
  70 /* When min or max change, we may need to shuffle the frequency counts. */
  71 static void renormalize(struct tally *tally,
  72                         ssize_t new_min, ssize_t new_max)
  73 {
  74         size_t range, spill;
  75         unsigned int i, old_min;
  76
  77         /* Uninitialized?  Don't do anything... */
  78         if (tally->max < tally->min)
  79                 goto update;
  80
  81         /* If we don't have sufficient range, increase step bits until
  82          * buckets cover entire range of ssize_t anyway. */
  83         range = (new_max - new_min) + 1;
  84         while (!shift_overflows(tally->buckets, tally->step_bits)
  85                && range > ((size_t)tally->buckets << tally->step_bits)) {
  86                 /* Collapse down. */
  87                 for (i = 1; i < tally->buckets; i++) {
  88                         tally->counts[i/2] += tally->counts[i];
  89                         tally->counts[i] = 0;
  90                 }
  91                 tally->step_bits++;
  92         }
  93
  94         /* Now if minimum has dropped, move buckets up. */
  95         old_min = bucket_of(new_min, tally->step_bits, tally->min);
  96         memmove(tally->counts + old_min,
  97                 tally->counts,
  98                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
  99         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
 100
 101         /* If we moved boundaries, adjust buckets to that ratio. */
 102         spill = (tally->min - new_min) % (1 << tally->step_bits);
 103         for (i = 0; i < tally->buckets-1; i++) {
 104                 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
 105                 tally->counts[i] -= adjust;
 106                 tally->counts[i+1] += adjust;
 107         }
 108
 109 update:
 110         tally->min = new_min;
 111         tally->max = new_max;
 112 }
 113
 114 void tally_add(struct tally *tally, ssize_t val)
 115 {
 116         ssize_t new_min = tally->min, new_max = tally->max;
 117         bool need_renormalize = false;
 118
 119         if (val < tally->min) {
 120                 new_min = val;
 121                 need_renormalize = true;
 122         }
 123         if (val > tally->max) {
 124                 new_max = val;
 125                 need_renormalize = true;
 126         }
 127         if (need_renormalize)
 128                 renormalize(tally, new_min, new_max);
 129
 130         /* 128-bit arithmetic!  If we didn't want exact mean, we could just
 131          * pull it out of counts. */
 132         if (val > 0 && tally->total[0] + val < tally->total[0])
 133                 tally->total[1]++;
 134         else if (val < 0 && tally->total[0] + val > tally->total[0])
 135                 tally->total[1]--;
 136         tally->total[0] += val;
 137         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
 138 }
 139
 140 size_t tally_num(const struct tally *tally)
 141 {
 142         size_t i, num = 0;
 143         for (i = 0; i < tally->buckets; i++)
 144                 num += tally->counts[i];
 145         return num;
 146 }
 147
 148 ssize_t tally_min(const struct tally *tally)
 149 {
 150         return tally->min;
 151 }
 152
 153 ssize_t tally_max(const struct tally *tally)
 154 {
 155         return tally->max;
 156 }
 157
 158 /* FIXME: Own ccan module please! */
 159 static unsigned fls64(uint64_t val)
 160 {
 161 #if HAVE_BUILTIN_CLZL
 162         if (val <= ULONG_MAX) {
 163                 /* This is significantly faster! */
 164                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
 165         } else {
 166 #endif
 167         uint64_t r = 64;
 168
 169         if (!val)
 170                 return 0;
 171         if (!(val & 0xffffffff00000000ull)) {
 172                 val <<= 32;
 173                 r -= 32;
 174         }
 175         if (!(val & 0xffff000000000000ull)) {
 176                 val <<= 16;
 177                 r -= 16;
 178         }
 179         if (!(val & 0xff00000000000000ull)) {
 180                 val <<= 8;
 181                 r -= 8;
 182         }
 183         if (!(val & 0xf000000000000000ull)) {
 184                 val <<= 4;
 185                 r -= 4;
 186         }
 187         if (!(val & 0xc000000000000000ull)) {
 188                 val <<= 2;
 189                 r -= 2;
 190         }
 191         if (!(val & 0x8000000000000000ull)) {
 192                 val <<= 1;
 193                 r -= 1;
 194         }
 195         return r;
 196 #if HAVE_BUILTIN_CLZL
 197         }
 198 #endif
 199 }
 200
 201 /* This is stolen straight from Hacker's Delight. */
 202 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 203 {
 204         const uint64_t b = 4294967296ULL; // Number base (32 bits).
 205         uint32_t un[4],           // Dividend and divisor
 206                 vn[2];            // normalized and broken
 207                                   // up into halfwords.
 208         uint32_t q[2];            // Quotient as halfwords.
 209         uint64_t un1, un0,        // Dividend and divisor
 210                 vn0;              // as fullwords.
 211         uint64_t qhat;            // Estimated quotient digit.
 212         uint64_t rhat;            // A remainder.
 213         uint64_t p;               // Product of two digits.
 214         int64_t s, i, j, t, k;
 215
 216         if (u1 >= v)              // If overflow, return the largest
 217                 return (uint64_t)-1; // possible quotient.
 218
 219         s = 64 - fls64(v);                // 0 <= s <= 63.
 220         vn0 = v << s;             // Normalize divisor.
 221         vn[1] = vn0 >> 32;        // Break divisor up into
 222         vn[0] = vn0 & 0xFFFFFFFF; // two 32-bit halves.
 223
 224         // Shift dividend left.
 225         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 226         un0 = u0 << s;
 227         un[3] = un1 >> 32;        // Break dividend up into
 228         un[2] = un1;              // four 32-bit halfwords
 229         un[1] = un0 >> 32;        // Note: storing into
 230         un[0] = un0;              // halfwords truncates.
 231
 232         for (j = 1; j >= 0; j--) {
 233                 // Compute estimate qhat of q[j].
 234                 qhat = (un[j+2]*b + un[j+1])/vn[1];
 235                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
 236         again:
 237                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 238                         qhat = qhat - 1;
 239                         rhat = rhat + vn[1];
 240                         if (rhat < b) goto again;
 241                 }
 242
 243                 // Multiply and subtract.
 244                 k = 0;
 245                 for (i = 0; i < 2; i++) {
 246                         p = qhat*vn[i];
 247                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 248                         un[i+j] = t;
 249                         k = (p >> 32) - (t >> 32);
 250                 }
 251                 t = un[j+2] - k;
 252                 un[j+2] = t;
 253
 254                 q[j] = qhat;              // Store quotient digit.
 255                 if (t < 0) {              // If we subtracted too
 256                         q[j] = q[j] - 1;  // much, add back.
 257                         k = 0;
 258                         for (i = 0; i < 2; i++) {
 259                                 t = un[i+j] + vn[i] + k;
 260                                 un[i+j] = t;
 261                                 k = t >> 32;
 262                         }
 263                         un[j+2] = un[j+2] + k;
 264                 }
 265         } // End j.
 266
 267         return q[1]*b + q[0];
 268 }
 269
 270 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 271 {
 272         int64_t q, uneg, vneg, diff, borrow;
 273
 274         uneg = u1 >> 63;          // -1 if u < 0.
 275         if (uneg) {               // Compute the absolute
 276                 u0 = -u0;         // value of the dividend u.
 277                 borrow = (u0 != 0);
 278                 u1 = -u1 - borrow;
 279         }
 280
 281         vneg = v >> 63;           // -1 if v < 0.
 282         v = (v ^ vneg) - vneg;    // Absolute value of v.
 283
 284         if ((uint64_t)u1 >= (uint64_t)v)
 285                 goto overflow;
 286
 287         q = divlu64(u1, u0, v);
 288
 289         diff = uneg ^ vneg;       // Negate q if signs of
 290         q = (q ^ diff) - diff;    // u and v differed.
 291
 292         if ((diff ^ q) < 0 && q != 0) {    // If overflow, return the largest
 293         overflow:                          // possible neg. quotient.
 294                 q = 0x8000000000000000ULL;
 295         }
 296         return q;
 297 }
 298
 299 ssize_t tally_mean(const struct tally *tally)
 300 {
 301         size_t count = tally_num(tally);
 302         if (!count)
 303                 return 0;
 304
 305         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
 306                 /* Use standard 64-bit arithmetic. */
 307                 int64_t total = tally->total[0]
 308                         | (((uint64_t)tally->total[1]) << 32);
 309                 return total / count;
 310         }
 311         return divls64(tally->total[1], tally->total[0], count);
 312 }
 313
 314 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 315 {
 316         if (overflow) {
 317                 *overflow = tally->total[1];
 318                 return tally->total[0];
 319         }
 320
 321         /* If result is negative, make sure we can represent it. */
 322         if (tally->total[1] & (1 << (SIZET_BITS-1))) {
 323                 /* Must have only underflowed once, and must be able to
 324                  * represent result at ssize_t. */
 325                 if ((~tally->total[1])+1 != 0
 326                     || (ssize_t)tally->total[0] >= 0) {
 327                         /* Underflow, return minimum. */
 328                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
 329                 }
 330         } else {
 331                 /* Result is positive, must not have overflowed, and must be
 332                  * able to represent as ssize_t. */
 333                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
 334                         /* Overflow.  Return maximum. */
 335                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
 336                 }
 337         }
 338         return tally->total[0];
 339 }
 340
 341 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 342 {
 343         ssize_t min, max;
 344
 345         min = bucket_min(tally->min, tally->step_bits, b);
 346         if (b == tally->buckets - 1)
 347                 max = tally->max;
 348         else
 349                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 350
 351         /* FIXME: Think harder about cumulative error; is this enough?. */
 352         *err = (max - min + 1) / 2;
 353         /* Avoid overflow. */
 354         return min + (max - min) / 2;
 355 }
 356
 357 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 358 {
 359         size_t count = tally_num(tally), total = 0;
 360         unsigned int i;
 361
 362         for (i = 0; i < tally->buckets; i++) {
 363                 total += tally->counts[i];
 364                 if (total * 2 >= count)
 365                         break;
 366         }
 367         return bucket_range(tally, i, err);
 368 }
 369
 370 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 371 {
 372         unsigned int i, min_best = 0, max_best = 0;
 373
 374         for (i = 0; i < tally->buckets; i++) {
 375                 if (tally->counts[i] > tally->counts[min_best]) {
 376                         min_best = max_best = i;
 377                 } else if (tally->counts[i] == tally->counts[min_best]) {
 378                         max_best = i;
 379                 }
 380         }
 381
 382         /* We can have more than one best, making our error huge. */
 383         if (min_best != max_best) {
 384                 ssize_t min, max;
 385                 min = bucket_range(tally, min_best, err);
 386                 max = bucket_range(tally, max_best, err);
 387                 max += *err;
 388                 *err += (size_t)(max - min);
 389                 return min + (max - min) / 2;
 390         }
 391
 392         return bucket_range(tally, min_best, err);
 393 }
 394
 395 static unsigned get_max_bucket(const struct tally *tally)
 396 {
 397         unsigned int i;
 398
 399         for (i = tally->buckets; i > 0; i--)
 400                 if (tally->counts[i-1])
 401                         break;
 402         return i;
 403 }
 404
 405 char *tally_histogram(const struct tally *tally,
 406                       unsigned width, unsigned height)
 407 {
 408         unsigned int i, count, max_bucket, largest_bucket;
 409         struct tally *tmp;
 410         char *graph, *p;
 411
 412         assert(width >= TALLY_MIN_HISTO_WIDTH);
 413         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 414
 415         /* Ignore unused buckets. */
 416         max_bucket = get_max_bucket(tally);
 417
 418         /* FIXME: It'd be nice to smooth here... */
 419         if (height >= max_bucket) {
 420                 height = max_bucket;
 421                 tmp = NULL;
 422         } else {
 423                 /* We create a temporary then renormalize so < height. */
 424                 /* FIXME: Antialias properly! */
 425                 tmp = tally_new(tally->buckets-1);
 426                 if (!tmp)
 427                         return NULL;
 428                 tmp->min = tally->min;
 429                 tmp->max = tally->max;
 430                 tmp->step_bits = tally->step_bits;
 431                 memcpy(tmp->counts, tally->counts,
 432                        sizeof(tally->counts[0]) * tmp->buckets);
 433                 while ((max_bucket = get_max_bucket(tmp)) >= height)
 434                         renormalize(tmp, tmp->min, tmp->max * 2);
 435                 /* Restore max */
 436                 tmp->max = tally->max;
 437                 tally = tmp;
 438                 height = max_bucket;
 439         }
 440
 441         /* Figure out longest line, for scale. */
 442         largest_bucket = 0;
 443         for (i = 0; i < tally->buckets; i++) {
 444                 if (tally->counts[i] > largest_bucket)
 445                         largest_bucket = tally->counts[i];
 446         }
 447
 448         p = graph = malloc(height * (width + 1) + 1);
 449         if (!graph) {
 450                 free(tmp);
 451                 return NULL;
 452         }
 453
 454         for (i = 0; i < height; i++) {
 455                 unsigned covered = 1;
 456                 count = (double)tally->counts[i] / largest_bucket * (width-1)+1;
 457
 458                 if (i == 0)
 459                         covered = snprintf(p, width, "%zi", tally->min);
 460                 else if (i == height - 1)
 461                         covered = snprintf(p, width, "%zi", tally->max);
 462                 else if (i == bucket_of(tally->min, tally->step_bits, 0))
 463                         *p = '+';
 464                 else
 465                         *p = '|';
 466
 467                 if (covered > width)
 468                         covered = width;
 469                 p += covered;
 470
 471                 if (count > covered)
 472                         count -= covered;
 473                 else
 474                         count = 0;
 475
 476                 memset(p, '*', count);
 477                 p += count;
 478                 *p = '\n';
 479                 p++;
 480         }
 481         *p = '\0';
 482         free(tmp);
 483         return graph;
 484 }