#include "hyperloglog.h"
#include <util/generic/bitops.h>
#include <util/generic/yexception.h>
#include <util/stream/output.h>
#include <algorithm>
#include <array>
#include <cmath>
#include <functional>
namespace {
using TLookup = std::array<double, 256>;
struct TCorrection {
TLookup Estimations;
TLookup Biases;
double GetBias(double e) const {
for (size_t idx = 0;; ++idx) {
const auto estr = Estimations[idx];
if (estr >= e) {
if (idx == 0) {
return Biases[0];
}
const auto estl = Estimations[idx - 1];
const auto biasl = Biases[idx - 1];
const auto biasr = Biases[idx];
const auto de = estr - estl;
const auto db = biasr - biasl;
const auto scale = e - estl;
return biasl + scale * db / de;
} else if (std::fabs(estr) < 1e-4) {
//limiter
return Biases[idx - 1];
}
}
}
};
double EstimateBias(double e, unsigned precision) {
static const TCorrection CORRECTIONS[1 + THyperLogLog::PRECISION_MAX - THyperLogLog::PRECISION_MIN] = {
#include "hyperloglog_corrections.inc"
};
if (precision < THyperLogLog::PRECISION_MIN || precision > THyperLogLog::PRECISION_MAX) {
return 0.;
}
return CORRECTIONS[precision - THyperLogLog::PRECISION_MIN].GetBias(e);
}
double GetThreshold(unsigned precision) {
static const double THRESHOLD_DATA[1 + THyperLogLog::PRECISION_MAX - THyperLogLog::PRECISION_MIN] = {
10, // Precision 4
20, // Precision 5
40, // Precision 6
80, // Precision 7
220, // Precision 8
400, // Precision 9
900, // Precision 10
1800, // Precision 11
3100, // Precision 12
6500, // Precision 13
11500, // Precision 14
20000, // Precision 15
50000, // Precision 16
120000, // Precision 17
350000 // Precision 18
};
if (precision < THyperLogLog::PRECISION_MIN || precision > THyperLogLog::PRECISION_MAX) {
return 0.;
}
return THRESHOLD_DATA[precision - THyperLogLog::PRECISION_MIN];
}
double EmpiricAlpha(size_t m) {
switch (m) {
case 16:
return 0.673;
case 32:
return 0.697;
case 64:
return 0.709;
default:
return 0.7213 / (1.0 + 1.079 / m);
}
}
double RawEstimate(const ui8* counts, size_t size) {
double sum = {};
for (size_t i = 0; i < size; ++i) {
sum += std::pow(2.0, -counts[i]);
}
return EmpiricAlpha(size) * size * size / sum;
}
double LinearCounting(size_t registers, size_t zeroed) {
return std::log(double(registers) / zeroed) * registers;
}
}
THyperLogLogBase::THyperLogLogBase(unsigned precision)
: Precision(precision) {
Y_ENSURE(precision >= PRECISION_MIN && precision <= PRECISION_MAX);
}
void THyperLogLogBase::Update(ui64 hash) {
const unsigned subHashBits = 8 * sizeof(hash) - Precision;
const auto subHash = hash & MaskLowerBits(subHashBits);
const auto leadingZeroes = subHash ? (subHashBits - GetValueBitCount(subHash)) : subHashBits;
const ui8 weight = static_cast<ui8>(leadingZeroes + 1);
const size_t reg = static_cast<size_t>(hash >> subHashBits);
RegistersRef[reg] = std::max(RegistersRef[reg], weight);
}
void THyperLogLogBase::Merge(const THyperLogLogBase& rh) {
Y_ENSURE(Precision == rh.Precision);
std::transform(RegistersRef.begin(), RegistersRef.end(), rh.RegistersRef.begin(), RegistersRef.begin(), [](ui8 l, ui8 r) { return std::max(l, r); });
}
ui64 THyperLogLogBase::Estimate() const {
const auto m = RegistersRef.size();
const auto e = RawEstimate(RegistersRef.data(), m);
const auto e_ = e <= 5 * m ? (e - EstimateBias(e, Precision)) : e;
const auto v = std::count(RegistersRef.begin(), RegistersRef.end(), ui8(0));
const auto h = v != 0 ? LinearCounting(m, v) : e_;
return h <= GetThreshold(Precision) ? h : e_;
}
void THyperLogLogBase::Save(IOutputStream& out) const {
out.Write(static_cast<char>(Precision));
out.Write(RegistersRef.data(), RegistersRef.size() * sizeof(RegistersRef.front()));
}