LCOV - code coverage report
Current view: top level - src/backend/lib - hyperloglog.c (source / functions) Hit Total Coverage
Test: PostgreSQL Lines: 35 57 61.4 %
Date: 2017-09-21 23:18:17 Functions: 4 6 66.7 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /*-------------------------------------------------------------------------
       2             :  *
       3             :  * hyperloglog.c
       4             :  *    HyperLogLog cardinality estimator
       5             :  *
       6             :  * Portions Copyright (c) 2014-2017, PostgreSQL Global Development Group
       7             :  *
       8             :  * Based on Hideaki Ohno's C++ implementation.  This is probably not ideally
       9             :  * suited to estimating the cardinality of very large sets;  in particular, we
      10             :  * have not attempted to further optimize the implementation as described in
      11             :  * the Heule, Nunkesser and Hall paper "HyperLogLog in Practice: Algorithmic
      12             :  * Engineering of a State of The Art Cardinality Estimation Algorithm".
      13             :  *
      14             :  * A sparse representation of HyperLogLog state is used, with fixed space
      15             :  * overhead.
      16             :  *
      17             :  * The copyright terms of Ohno's original version (the MIT license) follow.
      18             :  *
      19             :  * IDENTIFICATION
      20             :  *    src/backend/lib/hyperloglog.c
      21             :  *
      22             :  *-------------------------------------------------------------------------
      23             :  */
      24             : 
      25             : /*
      26             :  * Copyright (c) 2013 Hideaki Ohno <hide.o.j55{at}gmail.com>
      27             :  *
      28             :  * Permission is hereby granted, free of charge, to any person obtaining a copy
      29             :  * of this software and associated documentation files (the 'Software'), to
      30             :  * deal in the Software without restriction, including without limitation the
      31             :  * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
      32             :  * sell copies of the Software, and to permit persons to whom the Software is
      33             :  * furnished to do so, subject to the following conditions:
      34             :  *
      35             :  * The above copyright notice and this permission notice shall be included in
      36             :  * all copies or substantial portions of the Software.
      37             :  *
      38             :  * THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
      39             :  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
      40             :  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
      41             :  * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
      42             :  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
      43             :  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
      44             :  * IN THE SOFTWARE.
      45             :  */
      46             : 
      47             : #include "postgres.h"
      48             : 
      49             : #include <math.h>
      50             : 
      51             : #include "lib/hyperloglog.h"
      52             : 
      53             : #define POW_2_32            (4294967296.0)
      54             : #define NEG_POW_2_32        (-4294967296.0)
      55             : 
      56             : static inline uint8 rho(uint32 x, uint8 b);
      57             : 
      58             : /*
      59             :  * Initialize HyperLogLog track state, by bit width
      60             :  *
      61             :  * bwidth is bit width (so register size will be 2 to the power of bwidth).
      62             :  * Must be between 4 and 16 inclusive.
      63             :  */
      64             : void
      65        1030 : initHyperLogLog(hyperLogLogState *cState, uint8 bwidth)
      66             : {
      67             :     double      alpha;
      68             : 
      69        1030 :     if (bwidth < 4 || bwidth > 16)
      70           0 :         elog(ERROR, "bit width must be between 4 and 16 inclusive");
      71             : 
      72        1030 :     cState->registerWidth = bwidth;
      73        1030 :     cState->nRegisters = (Size) 1 << bwidth;
      74        1030 :     cState->arrSize = sizeof(uint8) * cState->nRegisters + 1;
      75             : 
      76             :     /*
      77             :      * Initialize hashes array to zero, not negative infinity, per discussion
      78             :      * of the coupon collector problem in the HyperLogLog paper
      79             :      */
      80        1030 :     cState->hashesArr = palloc0(cState->arrSize);
      81             : 
      82             :     /*
      83             :      * "alpha" is a value that for each possible number of registers (m) is
      84             :      * used to correct a systematic multiplicative bias present in m ^ 2 Z (Z
      85             :      * is "the indicator function" through which we finally compute E,
      86             :      * estimated cardinality).
      87             :      */
      88        1030 :     switch (cState->nRegisters)
      89             :     {
      90             :         case 16:
      91           0 :             alpha = 0.673;
      92           0 :             break;
      93             :         case 32:
      94           0 :             alpha = 0.697;
      95           0 :             break;
      96             :         case 64:
      97           0 :             alpha = 0.709;
      98           0 :             break;
      99             :         default:
     100        1030 :             alpha = 0.7213 / (1.0 + 1.079 / cState->nRegisters);
     101             :     }
     102             : 
     103             :     /*
     104             :      * Precalculate alpha m ^ 2, later used to generate "raw" HyperLogLog
     105             :      * estimate E
     106             :      */
     107        1030 :     cState->alphaMM = alpha * cState->nRegisters * cState->nRegisters;
     108        1030 : }
     109             : 
     110             : /*
     111             :  * Initialize HyperLogLog track state, by error rate
     112             :  *
     113             :  * Instead of specifying bwidth (number of bits used for addressing the
     114             :  * register), this method allows sizing the counter for particular error
     115             :  * rate using a simple formula from the paper:
     116             :  *
     117             :  *   e = 1.04 / sqrt(m)
     118             :  *
     119             :  * where 'm' is the number of registers, i.e. (2^bwidth). The method
     120             :  * finds the lowest bwidth with 'e' below the requested error rate, and
     121             :  * then uses it to initialize the counter.
     122             :  *
     123             :  * As bwidth has to be between 4 and 16, the worst possible error rate
     124             :  * is between ~25% (bwidth=4) and 0.4% (bwidth=16).
     125             :  */
     126             : void
     127           0 : initHyperLogLogError(hyperLogLogState *cState, double error)
     128             : {
     129           0 :     uint8       bwidth = 4;
     130             : 
     131           0 :     while (bwidth < 16)
     132             :     {
     133           0 :         double      m = (Size) 1 << bwidth;
     134             : 
     135           0 :         if (1.04 / sqrt(m) < error)
     136           0 :             break;
     137           0 :         bwidth++;
     138             :     }
     139             : 
     140           0 :     initHyperLogLog(cState, bwidth);
     141           0 : }
     142             : 
     143             : /*
     144             :  * Free HyperLogLog track state
     145             :  *
     146             :  * Releases allocated resources, but not the state itself (in case it's not
     147             :  * allocated by palloc).
     148             :  */
     149             : void
     150           0 : freeHyperLogLog(hyperLogLogState *cState)
     151             : {
     152           0 :     Assert(cState->hashesArr != NULL);
     153           0 :     pfree(cState->hashesArr);
     154           0 : }
     155             : 
     156             : /*
     157             :  * Adds element to the estimator, from caller-supplied hash.
     158             :  *
     159             :  * It is critical that the hash value passed be an actual hash value, typically
     160             :  * generated using hash_any().  The algorithm relies on a specific bit-pattern
     161             :  * observable in conjunction with stochastic averaging.  There must be a
     162             :  * uniform distribution of bits in hash values for each distinct original value
     163             :  * observed.
     164             :  */
     165             : void
     166       74609 : addHyperLogLog(hyperLogLogState *cState, uint32 hash)
     167             : {
     168             :     uint8       count;
     169             :     uint32      index;
     170             : 
     171             :     /* Use the first "k" (registerWidth) bits as a zero based index */
     172       74609 :     index = hash >> (BITS_PER_BYTE * sizeof(uint32) - cState->registerWidth);
     173             : 
     174             :     /* Compute the rank of the remaining 32 - "k" (registerWidth) bits */
     175       74609 :     count = rho(hash << cState->registerWidth,
     176       74609 :                 BITS_PER_BYTE * sizeof(uint32) - cState->registerWidth);
     177             : 
     178       74609 :     cState->hashesArr[index] = Max(count, cState->hashesArr[index]);
     179       74609 : }
     180             : 
     181             : /*
     182             :  * Estimates cardinality, based on elements added so far
     183             :  */
     184             : double
     185          66 : estimateHyperLogLog(hyperLogLogState *cState)
     186             : {
     187             :     double      result;
     188          66 :     double      sum = 0.0;
     189             :     int         i;
     190             : 
     191       67650 :     for (i = 0; i < cState->nRegisters; i++)
     192             :     {
     193       67584 :         sum += 1.0 / pow(2.0, cState->hashesArr[i]);
     194             :     }
     195             : 
     196             :     /* result set to "raw" HyperLogLog estimate (E in the HyperLogLog paper) */
     197          66 :     result = cState->alphaMM / sum;
     198             : 
     199          66 :     if (result <= (5.0 / 2.0) * cState->nRegisters)
     200             :     {
     201             :         /* Small range correction */
     202          66 :         int         zero_count = 0;
     203             : 
     204       67650 :         for (i = 0; i < cState->nRegisters; i++)
     205             :         {
     206       67584 :             if (cState->hashesArr[i] == 0)
     207       67478 :                 zero_count++;
     208             :         }
     209             : 
     210          66 :         if (zero_count != 0)
     211          66 :             result = cState->nRegisters * log((double) cState->nRegisters /
     212             :                                               zero_count);
     213             :     }
     214           0 :     else if (result > (1.0 / 30.0) * POW_2_32)
     215             :     {
     216             :         /* Large range correction */
     217           0 :         result = NEG_POW_2_32 * log(1.0 - (result / POW_2_32));
     218             :     }
     219             : 
     220          66 :     return result;
     221             : }
     222             : 
     223             : /*
     224             :  * Worker for addHyperLogLog().
     225             :  *
     226             :  * Calculates the position of the first set bit in first b bits of x argument
     227             :  * starting from the first, reading from most significant to least significant
     228             :  * bits.
     229             :  *
     230             :  * Example (when considering fist 10 bits of x):
     231             :  *
     232             :  * rho(x = 0b1000000000)   returns 1
     233             :  * rho(x = 0b0010000000)   returns 3
     234             :  * rho(x = 0b0000000000)   returns b + 1
     235             :  *
     236             :  * "The binary address determined by the first b bits of x"
     237             :  *
     238             :  * Return value "j" used to index bit pattern to watch.
     239             :  */
     240             : static inline uint8
     241       74609 : rho(uint32 x, uint8 b)
     242             : {
     243       74609 :     uint8       j = 1;
     244             : 
     245      176269 :     while (j <= b && !(x & 0x80000000))
     246             :     {
     247       27051 :         j++;
     248       27051 :         x <<= 1;
     249             :     }
     250             : 
     251       74609 :     return j;
     252             : }

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