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https://github.com/ClickHouse/ClickHouse.git
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775 lines
23 KiB
C++
775 lines
23 KiB
C++
#pragma once
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#include <Common/HashTable/Hash.h>
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#include <Common/PODArray.h>
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#include <IO/ReadBuffer.h>
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#include <IO/WriteBuffer.h>
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#include <IO/ReadHelpers.h>
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#include <IO/WriteHelpers.h>
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namespace DB
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{
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namespace ErrorCodes
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{
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extern const int LOGICAL_ERROR;
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}
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/** Calculates quantile for time in milliseconds, less than 30 seconds.
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* If the value is greater than 30 seconds, the value is set to 30 seconds.
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*
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* If total values is not greater than about 5670, then the calculation is accurate.
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*
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* Otherwise
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* If time less that 1024 ms, than calculation is accurate.
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* Otherwise, the computation is rounded to a multiple of 16 ms.
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*
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* Three different data structures are used:
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* - flat array (of all met values) of fixed length, allocated inplace, size 64 bytes; Stores 0..31 values;
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* - flat array (of all values encountered), allocated separately, increasing length;
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* - a histogram (that is, value -> number), consisting of two parts
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* -- for values from 0 to 1023 - in increments of 1;
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* -- for values from 1024 to 30,000 - in increments of 16;
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*/
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#define TINY_MAX_ELEMS 31
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#define BIG_THRESHOLD 30000
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namespace detail
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{
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/** Helper structure for optimization in the case of a small number of values
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* - flat array of a fixed size "on the stack" in which all encountered values placed in succession.
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* Size - 64 bytes. Must be a POD-type (used in union).
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*/
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struct QuantileTimingTiny
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{
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mutable UInt16 elems[TINY_MAX_ELEMS]; /// mutable because array sorting is not considered a state change.
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/// It's important that `count` be at the end of the structure, since the beginning of the structure will be subsequently rewritten by other objects.
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/// You must initialize it by zero itself.
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/// Why? `count` field is reused even in cases where the union contains other structures
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/// (the size of which falls short of this field.)
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UInt16 count;
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/// Can only be used while `count < TINY_MAX_ELEMS`.
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void insert(UInt64 x)
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{
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if (unlikely(x > BIG_THRESHOLD))
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x = BIG_THRESHOLD;
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elems[count] = x;
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++count;
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}
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/// Can only be used while `count + rhs.count <= TINY_MAX_ELEMS`.
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void merge(const QuantileTimingTiny & rhs)
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{
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for (size_t i = 0; i < rhs.count; ++i)
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{
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elems[count] = rhs.elems[i];
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++count;
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}
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}
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void serialize(WriteBuffer & buf) const
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{
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writeBinary(count, buf);
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buf.write(reinterpret_cast<const char *>(elems), count * sizeof(elems[0]));
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}
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void deserialize(ReadBuffer & buf)
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{
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readBinary(count, buf);
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buf.readStrict(reinterpret_cast<char *>(elems), count * sizeof(elems[0]));
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}
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/** This function must be called before get-functions. */
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void prepare() const
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{
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std::sort(elems, elems + count);
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}
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UInt16 get(double level) const
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{
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return level != 1
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? elems[static_cast<size_t>(count * level)]
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: elems[count - 1];
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}
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template <typename ResultType>
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void getMany(const double * levels, size_t size, ResultType * result) const
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{
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const double * levels_end = levels + size;
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while (levels != levels_end)
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{
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*result = get(*levels);
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++levels;
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++result;
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}
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}
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/// The same, but in the case of an empty state NaN is returned.
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float getFloat(double level) const
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{
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return count
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? get(level)
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: std::numeric_limits<float>::quiet_NaN();
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}
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void getManyFloat(const double * levels, size_t size, float * result) const
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{
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if (count)
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getMany(levels, size, result);
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else
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for (size_t i = 0; i < size; ++i)
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result[i] = std::numeric_limits<float>::quiet_NaN();
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}
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};
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/** Auxiliary structure for optimization in case of average number of values
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* - a flat array, allocated separately, into which all found values are put in succession.
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*/
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struct QuantileTimingMedium
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{
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/// sizeof - 24 bytes.
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using Array = PODArray<UInt16, 128>;
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mutable Array elems; /// mutable because array sorting is not considered a state change.
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QuantileTimingMedium() {}
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QuantileTimingMedium(const UInt16 * begin, const UInt16 * end) : elems(begin, end) {}
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void insert(UInt64 x)
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{
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if (unlikely(x > BIG_THRESHOLD))
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x = BIG_THRESHOLD;
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elems.emplace_back(x);
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}
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void merge(const QuantileTimingMedium & rhs)
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{
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elems.insert(rhs.elems.begin(), rhs.elems.end());
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}
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void serialize(WriteBuffer & buf) const
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{
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writeBinary(elems.size(), buf);
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buf.write(reinterpret_cast<const char *>(elems.data()), elems.size() * sizeof(elems[0]));
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}
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void deserialize(ReadBuffer & buf)
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{
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size_t size = 0;
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readBinary(size, buf);
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elems.resize(size);
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buf.readStrict(reinterpret_cast<char *>(elems.data()), size * sizeof(elems[0]));
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}
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UInt16 get(double level) const
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{
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UInt16 quantile = 0;
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if (!elems.empty())
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{
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size_t n = level < 1
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? level * elems.size()
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: (elems.size() - 1);
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/// Sorting an array will not be considered a violation of constancy.
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auto & array = const_cast<Array &>(elems);
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std::nth_element(array.begin(), array.begin() + n, array.end());
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quantile = array[n];
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}
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return quantile;
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}
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template <typename ResultType>
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void getMany(const double * levels, const size_t * levels_permutation, size_t size, ResultType * result) const
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{
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size_t prev_n = 0;
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auto & array = const_cast<Array &>(elems);
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for (size_t i = 0; i < size; ++i)
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{
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auto level_index = levels_permutation[i];
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auto level = levels[level_index];
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size_t n = level < 1
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? level * elems.size()
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: (elems.size() - 1);
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std::nth_element(array.begin() + prev_n, array.begin() + n, array.end());
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result[level_index] = array[n];
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prev_n = n;
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}
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}
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/// Same, but in the case of an empty state, NaN is returned.
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float getFloat(double level) const
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{
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return !elems.empty()
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? get(level)
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: std::numeric_limits<float>::quiet_NaN();
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}
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void getManyFloat(const double * levels, const size_t * levels_permutation, size_t size, float * result) const
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{
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if (!elems.empty())
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getMany(levels, levels_permutation, size, result);
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else
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for (size_t i = 0; i < size; ++i)
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result[i] = std::numeric_limits<float>::quiet_NaN();
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}
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};
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#define SMALL_THRESHOLD 1024
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#define BIG_SIZE ((BIG_THRESHOLD - SMALL_THRESHOLD) / BIG_PRECISION)
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#define BIG_PRECISION 16
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#define SIZE_OF_LARGE_WITHOUT_COUNT ((SMALL_THRESHOLD + BIG_SIZE) * sizeof(UInt64))
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/** For a large number of values. The size is about 22 680 bytes.
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*/
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class QuantileTimingLarge
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{
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private:
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/// Total number of values.
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UInt64 count;
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/// Use of UInt64 is very wasteful.
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/// But UInt32 is definitely not enough, and it's too hard to invent 6-byte values.
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/// Number of values for each value is smaller than `small_threshold`.
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UInt64 count_small[SMALL_THRESHOLD];
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/// The number of values for each value from `small_threshold` to `big_threshold`, rounded to `big_precision`.
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UInt64 count_big[BIG_SIZE];
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/// Get value of quantile by index in array `count_big`.
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static inline UInt16 indexInBigToValue(size_t i)
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{
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return (i * BIG_PRECISION) + SMALL_THRESHOLD
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+ (intHash32<0>(i) % BIG_PRECISION - (BIG_PRECISION / 2)); /// A small randomization so that it is not noticeable that all the values are even.
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}
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/// Lets you scroll through the histogram values, skipping zeros.
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class Iterator
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{
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private:
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const UInt64 * begin;
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const UInt64 * pos;
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const UInt64 * end;
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void adjust()
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{
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while (isValid() && 0 == *pos)
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++pos;
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}
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public:
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Iterator(const QuantileTimingLarge & parent)
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: begin(parent.count_small), pos(begin), end(&parent.count_big[BIG_SIZE])
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{
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adjust();
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}
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bool isValid() const { return pos < end; }
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void next()
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{
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++pos;
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adjust();
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}
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UInt64 count() const { return *pos; }
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UInt16 key() const
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{
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return pos - begin < SMALL_THRESHOLD
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? pos - begin
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: indexInBigToValue(pos - begin - SMALL_THRESHOLD);
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}
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};
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public:
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QuantileTimingLarge()
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{
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memset(this, 0, sizeof(*this));
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}
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void insert(UInt64 x) noexcept
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{
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insertWeighted(x, 1);
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}
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void insertWeighted(UInt64 x, size_t weight) noexcept
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{
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count += weight;
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if (x < SMALL_THRESHOLD)
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count_small[x] += weight;
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else if (x < BIG_THRESHOLD)
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count_big[(x - SMALL_THRESHOLD) / BIG_PRECISION] += weight;
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}
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void merge(const QuantileTimingLarge & rhs) noexcept
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{
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count += rhs.count;
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for (size_t i = 0; i < SMALL_THRESHOLD; ++i)
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count_small[i] += rhs.count_small[i];
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for (size_t i = 0; i < BIG_SIZE; ++i)
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count_big[i] += rhs.count_big[i];
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}
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void serialize(WriteBuffer & buf) const
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{
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writeBinary(count, buf);
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if (count * 2 > SMALL_THRESHOLD + BIG_SIZE)
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{
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/// Simple serialization for a heavily dense case.
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buf.write(reinterpret_cast<const char *>(this) + sizeof(count), SIZE_OF_LARGE_WITHOUT_COUNT);
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}
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else
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{
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/// More compact serialization for a sparse case.
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for (size_t i = 0; i < SMALL_THRESHOLD; ++i)
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{
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if (count_small[i])
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{
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writeBinary(UInt16(i), buf);
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writeBinary(count_small[i], buf);
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}
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}
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for (size_t i = 0; i < BIG_SIZE; ++i)
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{
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if (count_big[i])
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{
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writeBinary(UInt16(i + SMALL_THRESHOLD), buf);
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writeBinary(count_big[i], buf);
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}
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}
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/// Symbolizes end of data.
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writeBinary(UInt16(BIG_THRESHOLD), buf);
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}
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}
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void deserialize(ReadBuffer & buf)
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{
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readBinary(count, buf);
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if (count * 2 > SMALL_THRESHOLD + BIG_SIZE)
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{
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buf.readStrict(reinterpret_cast<char *>(this) + sizeof(count), SIZE_OF_LARGE_WITHOUT_COUNT);
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}
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else
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{
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while (true)
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{
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UInt16 index = 0;
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readBinary(index, buf);
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if (index == BIG_THRESHOLD)
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break;
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UInt64 elem_count = 0;
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readBinary(elem_count, buf);
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if (index < SMALL_THRESHOLD)
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count_small[index] = elem_count;
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else
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count_big[index - SMALL_THRESHOLD] = elem_count;
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}
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}
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}
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/// Get the value of the `level` quantile. The level must be between 0 and 1.
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UInt16 get(double level) const
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{
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UInt64 pos = std::ceil(count * level);
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UInt64 accumulated = 0;
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Iterator it(*this);
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while (it.isValid())
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{
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accumulated += it.count();
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if (accumulated >= pos)
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break;
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it.next();
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}
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return it.isValid() ? it.key() : BIG_THRESHOLD;
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}
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/// Get the `size` values of `levels` quantiles. Write `size` results starting with `result` address.
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/// indices - an array of index levels such that the corresponding elements will go in ascending order.
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template <typename ResultType>
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void getMany(const double * levels, const size_t * indices, size_t size, ResultType * result) const
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{
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const auto indices_end = indices + size;
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auto index = indices;
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UInt64 pos = std::ceil(count * levels[*index]);
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UInt64 accumulated = 0;
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Iterator it(*this);
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while (it.isValid())
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{
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accumulated += it.count();
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while (accumulated >= pos)
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{
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result[*index] = it.key();
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++index;
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if (index == indices_end)
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return;
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pos = std::ceil(count * levels[*index]);
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}
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it.next();
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}
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while (index != indices_end)
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{
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result[*index] = std::numeric_limits<ResultType>::max() < BIG_THRESHOLD
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? std::numeric_limits<ResultType>::max() : BIG_THRESHOLD;
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++index;
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}
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}
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/// The same, but in the case of an empty state, NaN is returned.
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float getFloat(double level) const
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{
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return count
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? get(level)
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: std::numeric_limits<float>::quiet_NaN();
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}
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void getManyFloat(const double * levels, const size_t * levels_permutation, size_t size, float * result) const
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{
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if (count)
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getMany(levels, levels_permutation, size, result);
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else
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for (size_t i = 0; i < size; ++i)
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result[i] = std::numeric_limits<float>::quiet_NaN();
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}
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};
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}
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/** sizeof - 64 bytes.
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* If there are not enough of them - allocates up to 20 KB of memory in addition.
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*/
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template <typename> /// Unused template parameter is for AggregateFunctionQuantile.
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class QuantileTiming : private boost::noncopyable
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{
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private:
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union
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{
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detail::QuantileTimingTiny tiny;
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detail::QuantileTimingMedium medium;
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detail::QuantileTimingLarge * large;
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};
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enum class Kind : uint8_t
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{
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Tiny = 1,
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Medium = 2,
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Large = 3
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};
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Kind which() const
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{
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if (tiny.count <= TINY_MAX_ELEMS)
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return Kind::Tiny;
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if (tiny.count == TINY_MAX_ELEMS + 1)
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return Kind::Medium;
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return Kind::Large;
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}
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void tinyToMedium()
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{
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detail::QuantileTimingTiny tiny_copy = tiny;
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new (&medium) detail::QuantileTimingMedium(tiny_copy.elems, tiny_copy.elems + tiny_copy.count);
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tiny.count = TINY_MAX_ELEMS + 1;
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}
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void mediumToLarge()
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{
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/// While the data is copied from medium, it is not possible to set `large` value (otherwise it will overwrite some data).
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detail::QuantileTimingLarge * tmp_large = new detail::QuantileTimingLarge;
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for (const auto & elem : medium.elems)
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tmp_large->insert(elem); /// Cannot throw, so don't worry about new.
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medium.~QuantileTimingMedium();
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large = tmp_large;
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tiny.count = TINY_MAX_ELEMS + 2; /// large will be deleted in destructor.
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}
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void tinyToLarge()
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{
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/// While the data is copied from `medium` it is not possible to set `large` value (otherwise it will overwrite some data).
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detail::QuantileTimingLarge * tmp_large = new detail::QuantileTimingLarge;
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for (size_t i = 0; i < tiny.count; ++i)
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tmp_large->insert(tiny.elems[i]); /// Cannot throw, so don't worry about new.
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large = tmp_large;
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tiny.count = TINY_MAX_ELEMS + 2; /// large will be deleted in destructor.
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}
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bool mediumIsWorthToConvertToLarge() const
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{
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return medium.elems.size() >= sizeof(detail::QuantileTimingLarge) / sizeof(medium.elems[0]) / 2;
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}
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public:
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QuantileTiming()
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{
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tiny.count = 0;
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}
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~QuantileTiming()
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{
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Kind kind = which();
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if (kind == Kind::Medium)
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{
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medium.~QuantileTimingMedium();
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}
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else if (kind == Kind::Large)
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{
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delete large;
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}
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}
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void add(UInt64 x)
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{
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if (tiny.count < TINY_MAX_ELEMS)
|
|
{
|
|
tiny.insert(x);
|
|
}
|
|
else
|
|
{
|
|
if (unlikely(tiny.count == TINY_MAX_ELEMS))
|
|
tinyToMedium();
|
|
|
|
if (which() == Kind::Medium)
|
|
{
|
|
if (unlikely(mediumIsWorthToConvertToLarge()))
|
|
{
|
|
mediumToLarge();
|
|
large->insert(x);
|
|
}
|
|
else
|
|
medium.insert(x);
|
|
}
|
|
else
|
|
large->insert(x);
|
|
}
|
|
}
|
|
|
|
void add(UInt64 x, size_t weight)
|
|
{
|
|
/// NOTE: First condition is to avoid overflow.
|
|
if (weight < TINY_MAX_ELEMS && tiny.count + weight <= TINY_MAX_ELEMS)
|
|
{
|
|
for (size_t i = 0; i < weight; ++i)
|
|
tiny.insert(x);
|
|
}
|
|
else
|
|
{
|
|
if (unlikely(tiny.count <= TINY_MAX_ELEMS))
|
|
tinyToLarge(); /// For the weighted variant we do not use `medium` - presumably, it is impractical.
|
|
|
|
large->insertWeighted(x, weight);
|
|
}
|
|
}
|
|
|
|
/// NOTE Too complicated.
|
|
void merge(const QuantileTiming & rhs)
|
|
{
|
|
if (tiny.count + rhs.tiny.count <= TINY_MAX_ELEMS)
|
|
{
|
|
tiny.merge(rhs.tiny);
|
|
}
|
|
else
|
|
{
|
|
auto kind = which();
|
|
auto rhs_kind = rhs.which();
|
|
|
|
/// If one with which we merge has a larger data structure, then we bring the current structure to the same one.
|
|
if (kind == Kind::Tiny && rhs_kind == Kind::Medium)
|
|
{
|
|
tinyToMedium();
|
|
kind = Kind::Medium;
|
|
}
|
|
else if (kind == Kind::Tiny && rhs_kind == Kind::Large)
|
|
{
|
|
tinyToLarge();
|
|
kind = Kind::Large;
|
|
}
|
|
else if (kind == Kind::Medium && rhs_kind == Kind::Large)
|
|
{
|
|
mediumToLarge();
|
|
kind = Kind::Large;
|
|
}
|
|
/// Case when two states are small, but when merged, they will turn into average.
|
|
else if (kind == Kind::Tiny && rhs_kind == Kind::Tiny)
|
|
{
|
|
tinyToMedium();
|
|
kind = Kind::Medium;
|
|
}
|
|
|
|
if (kind == Kind::Medium && rhs_kind == Kind::Medium)
|
|
{
|
|
medium.merge(rhs.medium);
|
|
}
|
|
else if (kind == Kind::Large && rhs_kind == Kind::Large)
|
|
{
|
|
large->merge(*rhs.large);
|
|
}
|
|
else if (kind == Kind::Medium && rhs_kind == Kind::Tiny)
|
|
{
|
|
medium.elems.insert(rhs.tiny.elems, rhs.tiny.elems + rhs.tiny.count);
|
|
}
|
|
else if (kind == Kind::Large && rhs_kind == Kind::Tiny)
|
|
{
|
|
for (size_t i = 0; i < rhs.tiny.count; ++i)
|
|
large->insert(rhs.tiny.elems[i]);
|
|
}
|
|
else if (kind == Kind::Large && rhs_kind == Kind::Medium)
|
|
{
|
|
for (const auto & elem : rhs.medium.elems)
|
|
large->insert(elem);
|
|
}
|
|
else
|
|
throw Exception("Logical error in QuantileTiming::merge function: not all cases are covered", ErrorCodes::LOGICAL_ERROR);
|
|
|
|
/// For determinism, we should always convert to `large` when size condition is reached
|
|
/// - regardless of merge order.
|
|
if (kind == Kind::Medium && unlikely(mediumIsWorthToConvertToLarge()))
|
|
{
|
|
mediumToLarge();
|
|
}
|
|
}
|
|
}
|
|
|
|
void serialize(WriteBuffer & buf) const
|
|
{
|
|
auto kind = which();
|
|
DB::writePODBinary(kind, buf);
|
|
|
|
if (kind == Kind::Tiny)
|
|
tiny.serialize(buf);
|
|
else if (kind == Kind::Medium)
|
|
medium.serialize(buf);
|
|
else
|
|
large->serialize(buf);
|
|
}
|
|
|
|
/// Called for an empty object.
|
|
void deserialize(ReadBuffer & buf)
|
|
{
|
|
Kind kind;
|
|
DB::readPODBinary(kind, buf);
|
|
|
|
if (kind == Kind::Tiny)
|
|
{
|
|
tiny.deserialize(buf);
|
|
}
|
|
else if (kind == Kind::Medium)
|
|
{
|
|
tinyToMedium();
|
|
medium.deserialize(buf);
|
|
}
|
|
else if (kind == Kind::Large)
|
|
{
|
|
tinyToLarge();
|
|
large->deserialize(buf);
|
|
}
|
|
}
|
|
|
|
/// Get the value of the `level` quantile. The level must be between 0 and 1.
|
|
UInt16 get(double level) const
|
|
{
|
|
Kind kind = which();
|
|
|
|
if (kind == Kind::Tiny)
|
|
{
|
|
tiny.prepare();
|
|
return tiny.get(level);
|
|
}
|
|
else if (kind == Kind::Medium)
|
|
{
|
|
return medium.get(level);
|
|
}
|
|
else
|
|
{
|
|
return large->get(level);
|
|
}
|
|
}
|
|
|
|
/// Get the size values of the quantiles of the `levels` levels. Record `size` results starting with `result` address.
|
|
template <typename ResultType>
|
|
void getMany(const double * levels, const size_t * levels_permutation, size_t size, ResultType * result) const
|
|
{
|
|
Kind kind = which();
|
|
|
|
if (kind == Kind::Tiny)
|
|
{
|
|
tiny.prepare();
|
|
tiny.getMany(levels, size, result);
|
|
}
|
|
else if (kind == Kind::Medium)
|
|
{
|
|
medium.getMany(levels, levels_permutation, size, result);
|
|
}
|
|
else /*if (kind == Kind::Large)*/
|
|
{
|
|
large->getMany(levels, levels_permutation, size, result);
|
|
}
|
|
}
|
|
|
|
/// The same, but in the case of an empty state, NaN is returned.
|
|
float getFloat(double level) const
|
|
{
|
|
return tiny.count
|
|
? get(level)
|
|
: std::numeric_limits<float>::quiet_NaN();
|
|
}
|
|
|
|
void getManyFloat(const double * levels, const size_t * levels_permutation, size_t size, float * result) const
|
|
{
|
|
if (tiny.count)
|
|
getMany(levels, levels_permutation, size, result);
|
|
else
|
|
for (size_t i = 0; i < size; ++i)
|
|
result[i] = std::numeric_limits<float>::quiet_NaN();
|
|
}
|
|
};
|
|
|
|
#undef SMALL_THRESHOLD
|
|
#undef BIG_THRESHOLD
|
|
#undef BIG_SIZE
|
|
#undef BIG_PRECISION
|
|
#undef TINY_MAX_ELEMS
|
|
|
|
}
|