#pragma once #include #include #include #include #include #include #include #include #include #include #include #include #include namespace DB { /** Calculates quantile for time in milliseconds, less than 30 seconds. * If the value is greater than 30 seconds, the value is set to 30 seconds. * * If total values is not greater than about 5670, then the calculation is accurate. * * Otherwise * If time less that 1024 ms, than calculation is accurate. * Otherwise, the computation is rounded to a multiple of 16 ms. * * Three different data structures are used: * - flat array (of all met values) of fixed length, allocated inplace, size 64 bytes; Stores 0..31 values; * - flat array (of all values encountered), allocated separately, increasing length; * - a histogram (that is, value -> number), consisting of two parts * -- for values from 0 to 1023 - in increments of 1; * -- for values from 1024 to 30,000 - in increments of 16; */ #define TINY_MAX_ELEMS 31 #define BIG_THRESHOLD 30000 namespace detail { /** Helper structure for optimization in the case of a small number of values * - flat array of a fixed size "on the stack" in which all encountered values placed in succession. * Size - 64 bytes. Must be a POD-type (used in union). */ struct QuantileTimingTiny { mutable UInt16 elems[TINY_MAX_ELEMS]; /// mutable because array sorting is not considered a state change. /// 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. /// You must initialize it by zero itself. /// Why? `count` field is reused even in cases where the union contains other structures /// (the size of which falls short of this field.) UInt16 count; /// Can only be used while `count < TINY_MAX_ELEMS`. void insert(UInt64 x) { if (unlikely(x > BIG_THRESHOLD)) x = BIG_THRESHOLD; elems[count] = x; ++count; } /// Can only be used while `count + rhs.count <= TINY_MAX_ELEMS`. void merge(const QuantileTimingTiny & rhs) { for (size_t i = 0; i < rhs.count; ++i) { elems[count] = rhs.elems[i]; ++count; } } void serialize(WriteBuffer & buf) const { writeBinary(count, buf); buf.write(reinterpret_cast(elems), count * sizeof(elems[0])); } void deserialize(ReadBuffer & buf) { readBinary(count, buf); buf.readStrict(reinterpret_cast(elems), count * sizeof(elems[0])); } /** This function must be called before get-functions. */ void prepare() const { std::sort(elems, elems + count); } UInt16 get(double level) const { return level != 1 ? elems[static_cast(count * level)] : elems[count - 1]; } template void getMany(const double * levels, size_t size, ResultType * result) const { const double * levels_end = levels + size; while (levels != levels_end) { *result = get(*levels); ++levels; ++result; } } /// The same, but in the case of an empty state NaN is returned. float getFloat(double level) const { return count ? get(level) : std::numeric_limits::quiet_NaN(); } void getManyFloat(const double * levels, size_t size, float * result) const { if (count) getMany(levels, size, result); else for (size_t i = 0; i < size; ++i) result[i] = std::numeric_limits::quiet_NaN(); } }; /** Auxiliary structure for optimization in case of average number of values * - a flat array, allocated separately, into which all found values are put in succession. */ struct QuantileTimingMedium { /// sizeof - 24 bytes. using Array = PODArray; mutable Array elems; /// mutable because array sorting is not considered a state change. QuantileTimingMedium() {} QuantileTimingMedium(const UInt16 * begin, const UInt16 * end) : elems(begin, end) {} void insert(UInt64 x) { if (unlikely(x > BIG_THRESHOLD)) x = BIG_THRESHOLD; elems.emplace_back(x); } void merge(const QuantileTimingMedium & rhs) { elems.insert(rhs.elems.begin(), rhs.elems.end()); } void serialize(WriteBuffer & buf) const { writeBinary(elems.size(), buf); buf.write(reinterpret_cast(&elems[0]), elems.size() * sizeof(elems[0])); } void deserialize(ReadBuffer & buf) { size_t size = 0; readBinary(size, buf); elems.resize(size); buf.readStrict(reinterpret_cast(&elems[0]), size * sizeof(elems[0])); } UInt16 get(double level) const { UInt16 quantile = 0; if (!elems.empty()) { size_t n = level < 1 ? level * elems.size() : (elems.size() - 1); /// Sorting an array will not be considered a violation of constancy. auto & array = const_cast(elems); std::nth_element(array.begin(), array.begin() + n, array.end()); quantile = array[n]; } return quantile; } template void getMany(const double * levels, const size_t * levels_permutation, size_t size, ResultType * result) const { size_t prev_n = 0; auto & array = const_cast(elems); for (size_t i = 0; i < size; ++i) { auto level_index = levels_permutation[i]; auto level = levels[level_index]; size_t n = level < 1 ? level * elems.size() : (elems.size() - 1); std::nth_element(array.begin() + prev_n, array.begin() + n, array.end()); result[level_index] = array[n]; prev_n = n; } } /// Same, but in the case of an empty state, NaN is returned. float getFloat(double level) const { return !elems.empty() ? get(level) : std::numeric_limits::quiet_NaN(); } void getManyFloat(const double * levels, const size_t * levels_permutation, size_t size, float * result) const { if (!elems.empty()) getMany(levels, levels_permutation, size, result); else for (size_t i = 0; i < size; ++i) result[i] = std::numeric_limits::quiet_NaN(); } }; #define SMALL_THRESHOLD 1024 #define BIG_SIZE ((BIG_THRESHOLD - SMALL_THRESHOLD) / BIG_PRECISION) #define BIG_PRECISION 16 #define SIZE_OF_LARGE_WITHOUT_COUNT ((SMALL_THRESHOLD + BIG_SIZE) * sizeof(UInt64)) /** For a large number of values. The size is about 22 680 bytes. */ class QuantileTimingLarge { private: /// Total number of values. UInt64 count; /// Use of UInt64 is very wasteful. /// But UInt32 is definitely not enough, and it's too hard to invent 6-byte values. /// Number of values for each value is smaller than `small_threshold`. UInt64 count_small[SMALL_THRESHOLD]; /// The number of values for each value from `small_threshold` to `big_threshold`, rounded to `big_precision`. UInt64 count_big[BIG_SIZE]; /// Get value of quantile by index in array `count_big`. static inline UInt16 indexInBigToValue(size_t i) { return (i * BIG_PRECISION) + SMALL_THRESHOLD + (intHash32<0>(i) % BIG_PRECISION - (BIG_PRECISION / 2)); /// A small randomization so that it is not noticeable that all the values are even. } /// Lets you scroll through the histogram values, skipping zeros. class Iterator { private: const UInt64 * begin; const UInt64 * pos; const UInt64 * end; void adjust() { while (isValid() && 0 == *pos) ++pos; } public: Iterator(const QuantileTimingLarge & parent) : begin(parent.count_small), pos(begin), end(&parent.count_big[BIG_SIZE]) { adjust(); } bool isValid() const { return pos < end; } void next() { ++pos; adjust(); } UInt64 count() const { return *pos; } UInt16 key() const { return pos - begin < SMALL_THRESHOLD ? pos - begin : indexInBigToValue(pos - begin - SMALL_THRESHOLD); } }; public: QuantileTimingLarge() { memset(this, 0, sizeof(*this)); } void insert(UInt64 x) noexcept { insertWeighted(x, 1); } void insertWeighted(UInt64 x, size_t weight) noexcept { count += weight; if (x < SMALL_THRESHOLD) count_small[x] += weight; else if (x < BIG_THRESHOLD) count_big[(x - SMALL_THRESHOLD) / BIG_PRECISION] += weight; } void merge(const QuantileTimingLarge & rhs) noexcept { count += rhs.count; for (size_t i = 0; i < SMALL_THRESHOLD; ++i) count_small[i] += rhs.count_small[i]; for (size_t i = 0; i < BIG_SIZE; ++i) count_big[i] += rhs.count_big[i]; } void serialize(WriteBuffer & buf) const { writeBinary(count, buf); if (count * 2 > SMALL_THRESHOLD + BIG_SIZE) { /// Simple serialization for a heavily dense case. buf.write(reinterpret_cast(this) + sizeof(count), SIZE_OF_LARGE_WITHOUT_COUNT); } else { /// More compact serialization for a sparse case. for (size_t i = 0; i < SMALL_THRESHOLD; ++i) { if (count_small[i]) { writeBinary(UInt16(i), buf); writeBinary(count_small[i], buf); } } for (size_t i = 0; i < BIG_SIZE; ++i) { if (count_big[i]) { writeBinary(UInt16(i + SMALL_THRESHOLD), buf); writeBinary(count_big[i], buf); } } /// Symbolizes end of data. writeBinary(UInt16(BIG_THRESHOLD), buf); } } void deserialize(ReadBuffer & buf) { readBinary(count, buf); if (count * 2 > SMALL_THRESHOLD + BIG_SIZE) { buf.readStrict(reinterpret_cast(this) + sizeof(count), SIZE_OF_LARGE_WITHOUT_COUNT); } else { while (true) { UInt16 index = 0; readBinary(index, buf); if (index == BIG_THRESHOLD) break; UInt64 count = 0; readBinary(count, buf); if (index < SMALL_THRESHOLD) count_small[index] = count; else count_big[index - SMALL_THRESHOLD] = count; } } } /// Get the value of the `level` quantile. The level must be between 0 and 1. UInt16 get(double level) const { UInt64 pos = std::ceil(count * level); UInt64 accumulated = 0; Iterator it(*this); while (it.isValid()) { accumulated += it.count(); if (accumulated >= pos) break; it.next(); } return it.isValid() ? it.key() : BIG_THRESHOLD; } /// Get the `size` values of `levels` quantiles. Write `size` results starting with `result` address. /// indices - an array of index levels such that the corresponding elements will go in ascending order. template void getMany(const double * levels, const size_t * indices, size_t size, ResultType * result) const { const auto indices_end = indices + size; auto index = indices; UInt64 pos = std::ceil(count * levels[*index]); UInt64 accumulated = 0; Iterator it(*this); while (it.isValid()) { accumulated += it.count(); while (accumulated >= pos) { result[*index] = it.key(); ++index; if (index == indices_end) return; pos = std::ceil(count * levels[*index]); } it.next(); } while (index != indices_end) { result[*index] = BIG_THRESHOLD; ++index; } } /// The same, but in the case of an empty state, NaN is returned. float getFloat(double level) const { return count ? get(level) : std::numeric_limits::quiet_NaN(); } void getManyFloat(const double * levels, const size_t * levels_permutation, size_t size, float * result) const { if (count) getMany(levels, levels_permutation, size, result); else for (size_t i = 0; i < size; ++i) result[i] = std::numeric_limits::quiet_NaN(); } }; } /** sizeof - 64 bytes. * If there are not enough of them - allocates up to 20 KB of memory in addition. */ class QuantileTiming : private boost::noncopyable { private: union { detail::QuantileTimingTiny tiny; detail::QuantileTimingMedium medium; detail::QuantileTimingLarge * large; }; enum class Kind : UInt8 { Tiny = 1, Medium = 2, Large = 3 }; Kind which() const { if (tiny.count <= TINY_MAX_ELEMS) return Kind::Tiny; if (tiny.count == TINY_MAX_ELEMS + 1) return Kind::Medium; return Kind::Large; } void tinyToMedium() { detail::QuantileTimingTiny tiny_copy = tiny; new (&medium) detail::QuantileTimingMedium(tiny_copy.elems, tiny_copy.elems + tiny_copy.count); tiny.count = TINY_MAX_ELEMS + 1; } void mediumToLarge() { CurrentMemoryTracker::alloc(sizeof(detail::QuantileTimingLarge)); /// While the data is copied from medium, it is not possible to set `large` value (otherwise it will overwrite some data). detail::QuantileTimingLarge * tmp_large = new detail::QuantileTimingLarge; for (const auto & elem : medium.elems) tmp_large->insert(elem); /// Cannot throw, so don't worry about new. medium.~QuantileTimingMedium(); large = tmp_large; tiny.count = TINY_MAX_ELEMS + 2; /// large will be deleted in destructor. } void tinyToLarge() { CurrentMemoryTracker::alloc(sizeof(detail::QuantileTimingLarge)); /// While the data is copied from `medium` it is not possible to set `large` value (otherwise it will overwrite some data). detail::QuantileTimingLarge * tmp_large = new detail::QuantileTimingLarge; for (size_t i = 0; i < tiny.count; ++i) tmp_large->insert(tiny.elems[i]); /// Cannot throw, so don't worry about new. large = tmp_large; tiny.count = TINY_MAX_ELEMS + 2; /// large will be deleted in destructor. } bool mediumIsWorthToConvertToLarge() const { return medium.elems.size() >= sizeof(detail::QuantileTimingLarge) / sizeof(medium.elems[0]) / 2; } public: QuantileTiming() { tiny.count = 0; } ~QuantileTiming() { Kind kind = which(); if (kind == Kind::Medium) { medium.~QuantileTimingMedium(); } else if (kind == Kind::Large) { delete large; CurrentMemoryTracker::free(sizeof(detail::QuantileTimingLarge)); } } void insert(UInt64 x) { 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 insertWeighted(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 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::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::quiet_NaN(); } }; #undef SMALL_THRESHOLD #undef BIG_THRESHOLD #undef BIG_SIZE #undef BIG_PRECISION #undef TINY_MAX_ELEMS template class AggregateFunctionQuantileTiming final : public IUnaryAggregateFunction > { private: double level; public: AggregateFunctionQuantileTiming(double level_ = 0.5) : level(level_) {} String getName() const override { return "quantileTiming"; } DataTypePtr getReturnType() const override { return std::make_shared(); } void setArgument(const DataTypePtr & argument) { } void setParameters(const Array & params) override { if (params.size() != 1) throw Exception("Aggregate function " + getName() + " requires exactly one parameter.", ErrorCodes::NUMBER_OF_ARGUMENTS_DOESNT_MATCH); level = applyVisitor(FieldVisitorConvertToNumber(), params[0]); } void addImpl(AggregateDataPtr place, const IColumn & column, size_t row_num, Arena *) const { this->data(place).insert(static_cast &>(column).getData()[row_num]); } void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs, Arena * arena) const override { this->data(place).merge(this->data(rhs)); } void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override { this->data(place).serialize(buf); } void deserialize(AggregateDataPtr place, ReadBuffer & buf, Arena *) const override { this->data(place).deserialize(buf); } void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override { static_cast(to).getData().push_back(this->data(place).getFloat(level)); } }; /** Same, but with two arguments. The second argument is "weight" (integer) - how many times to consider the value. */ template class AggregateFunctionQuantileTimingWeighted final : public IBinaryAggregateFunction> { private: double level; public: AggregateFunctionQuantileTimingWeighted(double level_ = 0.5) : level(level_) {} String getName() const override { return "quantileTimingWeighted"; } DataTypePtr getReturnType() const override { return std::make_shared(); } void setArgumentsImpl(const DataTypes & arguments) { } void setParameters(const Array & params) override { if (params.size() != 1) throw Exception("Aggregate function " + getName() + " requires exactly one parameter.", ErrorCodes::NUMBER_OF_ARGUMENTS_DOESNT_MATCH); level = applyVisitor(FieldVisitorConvertToNumber(), params[0]); } void addImpl(AggregateDataPtr place, const IColumn & column_value, const IColumn & column_weight, size_t row_num, Arena *) const { this->data(place).insertWeighted( static_cast &>(column_value).getData()[row_num], static_cast &>(column_weight).getData()[row_num]); } void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs, Arena * arena) const override { this->data(place).merge(this->data(rhs)); } void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override { this->data(place).serialize(buf); } void deserialize(AggregateDataPtr place, ReadBuffer & buf, Arena *) const override { this->data(place).deserialize(buf); } void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override { static_cast(to).getData().push_back(this->data(place).getFloat(level)); } }; /** Same, but allows you to calculate several quantiles at once. * To do this, takes several levels as parameters. Example: quantilesTiming(0.5, 0.8, 0.9, 0.95)(ConnectTiming). * Returns an array of results. */ template class AggregateFunctionQuantilesTiming final : public IUnaryAggregateFunction > { private: QuantileLevels levels; public: String getName() const override { return "quantilesTiming"; } DataTypePtr getReturnType() const override { return std::make_shared(std::make_shared()); } void setArgument(const DataTypePtr & argument) { } void setParameters(const Array & params) override { levels.set(params); } void addImpl(AggregateDataPtr place, const IColumn & column, size_t row_num, Arena *) const { this->data(place).insert(static_cast &>(column).getData()[row_num]); } void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs, Arena * arena) const override { this->data(place).merge(this->data(rhs)); } void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override { this->data(place).serialize(buf); } void deserialize(AggregateDataPtr place, ReadBuffer & buf, Arena *) const override { this->data(place).deserialize(buf); } void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override { ColumnArray & arr_to = static_cast(to); ColumnArray::Offsets_t & offsets_to = arr_to.getOffsets(); size_t size = levels.size(); offsets_to.push_back((offsets_to.size() == 0 ? 0 : offsets_to.back()) + size); if (!size) return; typename ColumnFloat32::Container_t & data_to = static_cast(arr_to.getData()).getData(); size_t old_size = data_to.size(); data_to.resize(data_to.size() + size); this->data(place).getManyFloat(&levels.levels[0], &levels.permutation[0], size, &data_to[old_size]); } }; template class AggregateFunctionQuantilesTimingWeighted final : public IBinaryAggregateFunction> { private: QuantileLevels levels; public: String getName() const override { return "quantilesTimingWeighted"; } DataTypePtr getReturnType() const override { return std::make_shared(std::make_shared()); } void setArgumentsImpl(const DataTypes & arguments) { } void setParameters(const Array & params) override { levels.set(params); } void addImpl(AggregateDataPtr place, const IColumn & column_value, const IColumn & column_weight, size_t row_num, Arena *) const { this->data(place).insertWeighted( static_cast &>(column_value).getData()[row_num], static_cast &>(column_weight).getData()[row_num]); } void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs, Arena * arena) const override { this->data(place).merge(this->data(rhs)); } void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override { this->data(place).serialize(buf); } void deserialize(AggregateDataPtr place, ReadBuffer & buf, Arena *) const override { this->data(place).deserialize(buf); } void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override { ColumnArray & arr_to = static_cast(to); ColumnArray::Offsets_t & offsets_to = arr_to.getOffsets(); size_t size = levels.size(); offsets_to.push_back((offsets_to.size() == 0 ? 0 : offsets_to.back()) + size); if (!size) return; typename ColumnFloat32::Container_t & data_to = static_cast(arr_to.getData()).getData(); size_t old_size = data_to.size(); data_to.resize(data_to.size() + size); this->data(place).getManyFloat(&levels.levels[0], &levels.permutation[0], size, &data_to[old_size]); } }; }