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
  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
  95         /* If we don't have sufficient range, increase step bits until
  96          * buckets cover entire range of ssize_t anyway. */
  97         range = (new_max - new_min) + 1;
  98         while (!shift_overflows(tally->buckets, tally->step_bits)
  99                && range > ((size_t)tally->buckets << tally->step_bits)) {
 100                 /* Collapse down. */
 101                 for (i = 1; i < tally->buckets; i++) {
 102                         tally->counts[i/2] += tally->counts[i];
 103                         tally->counts[i] = 0;
 104                 }
 105                 tally->step_bits++;
 106         }
 107
 108         /* Now if minimum has dropped, move buckets up. */
 109         old_min = bucket_of(new_min, tally->step_bits, tally->min);
 110         memmove(tally->counts + old_min,
 111                 tally->counts,
 112                 sizeof(tally->counts[0]) * (tally->buckets - old_min));
 113         memset(tally->counts, 0, sizeof(tally->counts[0]) * old_min);
 114
 115         /* If we moved boundaries, adjust buckets to that ratio. */
 116         spill = (tally->min - new_min) % (1 << tally->step_bits);
 117         for (i = 0; i < tally->buckets-1; i++) {
 118                 size_t adjust = (tally->counts[i] >> tally->step_bits) * spill;
 119                 tally->counts[i] -= adjust;
 120                 tally->counts[i+1] += adjust;
 121         }
 122
 123 update:
 124         tally->min = new_min;
 125         tally->max = new_max;
 126 }
 127
 128 void tally_add(struct tally *tally, ssize_t val)
 129 {
 130         ssize_t new_min = tally->min, new_max = tally->max;
 131         bool need_renormalize = false;
 132
 133         if (val < tally->min) {
 134                 new_min = val;
 135                 need_renormalize = true;
 136         }
 137         if (val > tally->max) {
 138                 new_max = val;
 139                 need_renormalize = true;
 140         }
 141         if (need_renormalize) {
 142                 renormalize(tally, new_min, new_max);
 143         }
 144
 145         /* 128-bit arithmetic!  If we didn't want exact mean, we could just
 146          * pull it out of counts. */
 147         if (val > 0 && tally->total[0] + val < tally->total[0]) {
 148                 tally->total[1]++;
 149         } else if (val < 0 && tally->total[0] + val > tally->total[0]) {
 150                 tally->total[1]--;
 151         }
 152         tally->total[0] += val;
 153         tally->counts[bucket_of(tally->min, tally->step_bits, val)]++;
 154 }
 155
 156 size_t tally_num(const struct tally *tally)
 157 {
 158         size_t i, num = 0;
 159         for (i = 0; i < tally->buckets; i++) {
 160                 num += tally->counts[i];
 161         }
 162         return num;
 163 }
 164
 165 ssize_t tally_min(const struct tally *tally)
 166 {
 167         return tally->min;
 168 }
 169
 170 ssize_t tally_max(const struct tally *tally)
 171 {
 172         return tally->max;
 173 }
 174
 175 /* FIXME: Own ccan module please! */
 176 static unsigned fls64(uint64_t val)
 177 {
 178 #if HAVE_BUILTIN_CLZL
 179         if (val <= ULONG_MAX) {
 180                 /* This is significantly faster! */
 181                 return val ? sizeof(long) * CHAR_BIT - __builtin_clzl(val) : 0;
 182         } else {
 183 #endif
 184         uint64_t r = 64;
 185
 186         if (!val) {
 187                 return 0;
 188         }
 189         if (!(val & 0xffffffff00000000ull)) {
 190                 val <<= 32;
 191                 r -= 32;
 192         }
 193         if (!(val & 0xffff000000000000ull)) {
 194                 val <<= 16;
 195                 r -= 16;
 196         }
 197         if (!(val & 0xff00000000000000ull)) {
 198                 val <<= 8;
 199                 r -= 8;
 200         }
 201         if (!(val & 0xf000000000000000ull)) {
 202                 val <<= 4;
 203                 r -= 4;
 204         }
 205         if (!(val & 0xc000000000000000ull)) {
 206                 val <<= 2;
 207                 r -= 2;
 208         }
 209         if (!(val & 0x8000000000000000ull)) {
 210                 val <<= 1;
 211                 r -= 1;
 212         }
 213         return r;
 214 #if HAVE_BUILTIN_CLZL
 215         }
 216 #endif
 217 }
 218
 219 /* This is stolen straight from Hacker's Delight. */
 220 static uint64_t divlu64(uint64_t u1, uint64_t u0, uint64_t v)
 221 {
 222         const uint64_t b = 4294967296ULL; /* Number base (32 bits). */
 223         uint32_t un[4],           /* Dividend and divisor */
 224                 vn[2];            /* normalized and broken */
 225                                   /* up into halfwords. */
 226         uint32_t q[2];            /* Quotient as halfwords. */
 227         uint64_t un1, un0,        /* Dividend and divisor */
 228                 vn0;              /* as fullwords. */
 229         uint64_t qhat;            /* Estimated quotient digit. */
 230         uint64_t rhat;            /* A remainder. */
 231         uint64_t p;               /* Product of two digits. */
 232         int64_t s, i, j, t, k;
 233
 234         if (u1 >= v) {            /* If overflow, return the largest */
 235                 return (uint64_t)-1; /* possible quotient. */
 236         }
 237
 238         s = 64 - fls64(v);                /* 0 <= s <= 63. */
 239         vn0 = v << s;             /* Normalize divisor. */
 240         vn[1] = vn0 >> 32;        /* Break divisor up into */
 241         vn[0] = vn0 & 0xFFFFFFFF; /* two 32-bit halves. */
 242
 243         // Shift dividend left.
 244         un1 = ((u1 << s) | (u0 >> (64 - s))) & (-s >> 63);
 245         un0 = u0 << s;
 246         un[3] = un1 >> 32;        /* Break dividend up into */
 247         un[2] = un1;              /* four 32-bit halfwords */
 248         un[1] = un0 >> 32;        /* Note: storing into */
 249         un[0] = un0;              /* halfwords truncates. */
 250
 251         for (j = 1; j >= 0; j--) {
 252                 /* Compute estimate qhat of q[j]. */
 253                 qhat = (un[j+2]*b + un[j+1])/vn[1];
 254                 rhat = (un[j+2]*b + un[j+1]) - qhat*vn[1];
 255         again:
 256                 if (qhat >= b || qhat*vn[0] > b*rhat + un[j]) {
 257                         qhat = qhat - 1;
 258                         rhat = rhat + vn[1];
 259                         if (rhat < b) {
 260                                 goto again;
 261                         }
 262                 }
 263
 264                 /* Multiply and subtract. */
 265                 k = 0;
 266                 for (i = 0; i < 2; i++) {
 267                         p = qhat*vn[i];
 268                         t = un[i+j] - k - (p & 0xFFFFFFFF);
 269                         un[i+j] = t;
 270                         k = (p >> 32) - (t >> 32);
 271                 }
 272                 t = un[j+2] - k;
 273                 un[j+2] = t;
 274
 275                 q[j] = qhat;              /* Store quotient digit. */
 276                 if (t < 0) {              /* If we subtracted too */
 277                         q[j] = q[j] - 1;  /* much, add back. */
 278                         k = 0;
 279                         for (i = 0; i < 2; i++) {
 280                                 t = un[i+j] + vn[i] + k;
 281                                 un[i+j] = t;
 282                                 k = t >> 32;
 283                         }
 284                         un[j+2] = un[j+2] + k;
 285                 }
 286         } /* End j. */
 287
 288         return q[1]*b + q[0];
 289 }
 290
 291 static int64_t divls64(int64_t u1, uint64_t u0, int64_t v)
 292 {
 293         int64_t q, uneg, vneg, diff, borrow;
 294
 295         uneg = u1 >> 63;          /* -1 if u < 0. */
 296         if (uneg) {               /* Compute the absolute */
 297                 u0 = -u0;         /* value of the dividend u. */
 298                 borrow = (u0 != 0);
 299                 u1 = -u1 - borrow;
 300         }
 301
 302         vneg = v >> 63;           /* -1 if v < 0. */
 303         v = (v ^ vneg) - vneg;    /* Absolute value of v. */
 304
 305         if ((uint64_t)u1 >= (uint64_t)v) {
 306                 goto overflow;
 307         }
 308
 309         q = divlu64(u1, u0, v);
 310
 311         diff = uneg ^ vneg;       /* Negate q if signs of */
 312         q = (q ^ diff) - diff;    /* u and v differed. */
 313
 314         if ((diff ^ q) < 0 && q != 0) {    /* If overflow, return the
 315                                               largest */
 316         overflow:                          /* possible neg. quotient. */
 317                 q = 0x8000000000000000ULL;
 318         }
 319         return q;
 320 }
 321
 322 ssize_t tally_mean(const struct tally *tally)
 323 {
 324         size_t count = tally_num(tally);
 325         if (!count) {
 326                 return 0;
 327         }
 328
 329         if (sizeof(tally->total[0]) == sizeof(uint32_t)) {
 330                 /* Use standard 64-bit arithmetic. */
 331                 int64_t total = tally->total[0]
 332                         | (((uint64_t)tally->total[1]) << 32);
 333                 return total / count;
 334         }
 335         return divls64(tally->total[1], tally->total[0], count);
 336 }
 337
 338 ssize_t tally_total(const struct tally *tally, ssize_t *overflow)
 339 {
 340         if (overflow) {
 341                 *overflow = tally->total[1];
 342                 return tally->total[0];
 343         }
 344
 345         /* If result is negative, make sure we can represent it. */
 346         if (tally->total[1] & ((size_t)1 << (SIZET_BITS-1))) {
 347                 /* Must have only underflowed once, and must be able to
 348                  * represent result at ssize_t. */
 349                 if ((~tally->total[1])+1 != 0
 350                     || (ssize_t)tally->total[0] >= 0) {
 351                         /* Underflow, return minimum. */
 352                         return (ssize_t)((size_t)1 << (SIZET_BITS - 1));
 353                 }
 354         } else {
 355                 /* Result is positive, must not have overflowed, and must be
 356                  * able to represent as ssize_t. */
 357                 if (tally->total[1] || (ssize_t)tally->total[0] < 0) {
 358                         /* Overflow.  Return maximum. */
 359                         return (ssize_t)~((size_t)1 << (SIZET_BITS - 1));
 360                 }
 361         }
 362         return tally->total[0];
 363 }
 364
 365 static ssize_t bucket_range(const struct tally *tally, unsigned b, size_t *err)
 366 {
 367         ssize_t min, max;
 368
 369         min = bucket_min(tally->min, tally->step_bits, b);
 370         if (b == tally->buckets - 1) {
 371                 max = tally->max;
 372         } else {
 373                 max = bucket_min(tally->min, tally->step_bits, b+1) - 1;
 374         }
 375
 376         /* FIXME: Think harder about cumulative error; is this enough?. */
 377         *err = (max - min + 1) / 2;
 378         /* Avoid overflow. */
 379         return min + (max - min) / 2;
 380 }
 381
 382 ssize_t tally_approx_median(const struct tally *tally, size_t *err)
 383 {
 384         size_t count = tally_num(tally), total = 0;
 385         unsigned int i;
 386
 387         for (i = 0; i < tally->buckets; i++) {
 388                 total += tally->counts[i];
 389                 if (total * 2 >= count) {
 390                         break;
 391                 }
 392         }
 393         return bucket_range(tally, i, err);
 394 }
 395
 396 ssize_t tally_approx_mode(const struct tally *tally, size_t *err)
 397 {
 398         unsigned int i, min_best = 0, max_best = 0;
 399
 400         for (i = 0; i < tally->buckets; i++) {
 401                 if (tally->counts[i] > tally->counts[min_best]) {
 402                         min_best = max_best = i;
 403                 } else if (tally->counts[i] == tally->counts[min_best]) {
 404                         max_best = i;
 405                 }
 406         }
 407
 408         /* We can have more than one best, making our error huge. */
 409         if (min_best != max_best) {
 410                 ssize_t min, max;
 411                 min = bucket_range(tally, min_best, err);
 412                 max = bucket_range(tally, max_best, err);
 413                 max += *err;
 414                 *err += (size_t)(max - min);
 415                 return min + (max - min) / 2;
 416         }
 417
 418         return bucket_range(tally, min_best, err);
 419 }
 420
 421 static unsigned get_max_bucket(const struct tally *tally)
 422 {
 423         unsigned int i;
 424
 425         for (i = tally->buckets; i > 0; i--) {
 426                 if (tally->counts[i-1]) {
 427                         break;
 428                 }
 429         }
 430         return i;
 431 }
 432
 433 char *tally_histogram(const struct tally *tally,
 434                       unsigned width, unsigned height)
 435 {
 436         unsigned int i, count, max_bucket, largest_bucket;
 437         struct tally *tmp;
 438         char *graph, *p;
 439
 440         assert(width >= TALLY_MIN_HISTO_WIDTH);
 441         assert(height >= TALLY_MIN_HISTO_HEIGHT);
 442
 443         /* Ignore unused buckets. */
 444         max_bucket = get_max_bucket(tally);
 445
 446         /* FIXME: It'd be nice to smooth here... */
 447         if (height >= max_bucket) {
 448                 height = max_bucket;
 449                 tmp = NULL;
 450         } else {
 451                 /* We create a temporary then renormalize so < height. */
 452                 /* FIXME: Antialias properly! */
 453                 tmp = tally_new(tally->buckets);
 454                 if (!tmp) {
 455                         return NULL;
 456                 }
 457                 tmp->min = tally->min;
 458                 tmp->max = tally->max;
 459                 tmp->step_bits = tally->step_bits;
 460                 memcpy(tmp->counts, tally->counts,
 461                        sizeof(tally->counts[0]) * tmp->buckets);
 462                 while ((max_bucket = get_max_bucket(tmp)) >= height) {
 463                         renormalize(tmp, tmp->min, tmp->max * 2);
 464                 }
 465                 /* Restore max */
 466                 tmp->max = tally->max;
 467                 tally = tmp;
 468                 height = max_bucket;
 469         }
 470
 471         /* Figure out longest line, for scale. */
 472         largest_bucket = 0;
 473         for (i = 0; i < tally->buckets; i++) {
 474                 if (tally->counts[i] > largest_bucket) {
 475                         largest_bucket = tally->counts[i];
 476                 }
 477         }
 478
 479         p = graph = (char *)malloc(height * (width + 1) + 1);
 480         if (!graph) {
 481                 free(tmp);
 482                 return NULL;
 483         }
 484
 485         for (i = 0; i < height; i++) {
 486                 unsigned covered = 1, row;
 487
 488                 /* People expect minimum at the bottom. */
 489                 row = height - i - 1;
 490                 count = (double)tally->counts[row] / largest_bucket * (width-1)+1;
 491
 492                 if (row == 0) {
 493                         covered = snprintf(p, width, "%zi", tally->min);
 494                 } else if (row == height - 1) {
 495                         covered = snprintf(p, width, "%zi", tally->max);
 496                 } else if (row == bucket_of(tally->min, tally->step_bits, 0)) {
 497                         *p = '+';
 498                 } else {
 499                         *p = '|';
 500                 }
 501
 502                 if (covered > width) {
 503                         covered = width;
 504                 }
 505                 p += covered;
 506
 507                 if (count > covered) {
 508                         count -= covered;
 509                         memset(p, '*', count);
 510                 } else {
 511                         count = 0;
 512                 }
 513
 514                 p += count;
 515                 *p = '\n';
 516                 p++;
 517         }
 518         *p = '\0';
 519         free(tmp);
 520         return graph;
 521 }