Merge pull request #38252 from bharatnc/ncb/weighted-quantile-approx

add quantileInterpolatedWeighted function

docs/en/sql-reference/aggregate-functions/reference/quantileinterpolatedweighted.md

@@ -0,0 +1,68 @@
+---
+slug: /en/sql-reference/aggregate-functions/reference/quantileInterpolatedWeighted
+sidebar_position: 203
+---
+
+# quantileInterpolatedWeighted
+
+Computes [quantile](https://en.wikipedia.org/wiki/Quantile) of a numeric data sequence using linear interpolation, taking into account the weight of each element.
+
+To get the interpolated value, all the passed values are combined into an array, which are then sorted by their corresponding weights. Quantile interpolation is then performed using the [weighted percentile method](https://en.wikipedia.org/wiki/Percentile#The_weighted_percentile_method) by building a cumulative distribution based on weights and then a linear interpolation is performed using the weights and the values to compute the quantiles.
+
+When using multiple `quantile*` functions with different levels in a query, the internal states are not combined (that is, the query works less efficiently than it could). In this case, use the [quantiles](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles) function.
+
+**Syntax**
+
+``` sql
+quantileInterpolatedWeighted(level)(expr, weight)
+```
+
+Alias: `medianInterpolatedWeighted`.
+
+**Arguments**
+
+-   `level` — Level of quantile. Optional parameter. Constant floating-point number from 0 to 1. We recommend using a `level` value in the range of `[0.01, 0.99]`. Default value: 0.5. At `level=0.5` the function calculates [median](https://en.wikipedia.org/wiki/Median).
+-   `expr` — Expression over the column values resulting in numeric [data types](../../../sql-reference/data-types/index.md#data_types), [Date](../../../sql-reference/data-types/date.md) or [DateTime](../../../sql-reference/data-types/datetime.md).
+-   `weight` — Column with weights of sequence members. Weight is a number of value occurrences.
+
+**Returned value**
+
+-   Quantile of the specified level.
+
+Type:
+
+-   [Float64](../../../sql-reference/data-types/float.md) for numeric data type input.
+-   [Date](../../../sql-reference/data-types/date.md) if input values have the `Date` type.
+-   [DateTime](../../../sql-reference/data-types/datetime.md) if input values have the `DateTime` type.
+
+**Example**
+
+Input table:
+
+``` text
+┌─n─┬─val─┐
+│ 0 │   3 │
+│ 1 │   2 │
+│ 2 │   1 │
+│ 5 │   4 │
+└───┴─────┘
+```
+
+Query:
+
+``` sql
+SELECT quantileInterpolatedWeighted(n, val) FROM t
+```
+
+Result:
+
+``` text
+┌─quantileInterpolatedWeighted(n, val)─┐
+│                                    1 │
+└──────────────────────────────────────┘
+```
+
+**See Also**
+
+-   [median](../../../sql-reference/aggregate-functions/reference/median.md#median)
+-   [quantiles](../../../sql-reference/aggregate-functions/reference/quantiles.md#quantiles)

docs/en/sql-reference/aggregate-functions/reference/quantiles.md

@@ -9,7 +9,7 @@ sidebar_position: 201
 
 Syntax: `quantiles(level1, level2, …)(x)`
 
-All the quantile functions also have corresponding quantiles functions: `quantiles`, `quantilesDeterministic`, `quantilesTiming`, `quantilesTimingWeighted`, `quantilesExact`, `quantilesExactWeighted`, `quantilesTDigest`, `quantilesBFloat16`. These functions calculate all the quantiles of the listed levels in one pass, and return an array of the resulting values.
+All the quantile functions also have corresponding quantiles functions: `quantiles`, `quantilesDeterministic`, `quantilesTiming`, `quantilesTimingWeighted`, `quantilesExact`, `quantilesExactWeighted`, `quantileInterpolatedWeighted`, `quantilesTDigest`, `quantilesBFloat16`. These functions calculate all the quantiles of the listed levels in one pass, and return an array of the resulting values.
 
 ## quantilesExactExclusive
 

src/AggregateFunctions/AggregateFunctionQuantile.h

@@ -232,6 +232,9 @@ struct NameQuantilesExactInclusive { static constexpr auto name = "quantilesExac
 struct NameQuantileExactWeighted { static constexpr auto name = "quantileExactWeighted"; };
 struct NameQuantilesExactWeighted { static constexpr auto name = "quantilesExactWeighted"; };
 
+struct NameQuantileInterpolatedWeighted { static constexpr auto name = "quantileInterpolatedWeighted"; };
+struct NameQuantilesInterpolatedWeighted { static constexpr auto name = "quantilesInterpolatedWeighted"; };
+
 struct NameQuantileTiming { static constexpr auto name = "quantileTiming"; };
 struct NameQuantileTimingWeighted { static constexpr auto name = "quantileTimingWeighted"; };
 struct NameQuantilesTiming { static constexpr auto name = "quantilesTiming"; };

src/AggregateFunctions/AggregateFunctionQuantileInterpolatedWeighted.cpp

@@ -0,0 +1,70 @@
+#include <AggregateFunctions/AggregateFunctionQuantile.h>
+#include <AggregateFunctions/QuantileInterpolatedWeighted.h>
+#include <AggregateFunctions/AggregateFunctionFactory.h>
+#include <AggregateFunctions/Helpers.h>
+#include <DataTypes/DataTypeDate.h>
+#include <DataTypes/DataTypeDateTime.h>
+#include <Core/Field.h>
+
+
+namespace DB
+{
+struct Settings;
+
+namespace ErrorCodes
+{
+    extern const int ILLEGAL_TYPE_OF_ARGUMENT;
+}
+
+namespace
+{
+
+    template <typename Value, bool _> using FuncQuantileInterpolatedWeighted = AggregateFunctionQuantile<Value, QuantileInterpolatedWeighted<Value>, NameQuantileInterpolatedWeighted, true, void, false>;
+    template <typename Value, bool _> using FuncQuantilesInterpolatedWeighted = AggregateFunctionQuantile<Value, QuantileInterpolatedWeighted<Value>, NameQuantilesInterpolatedWeighted, true, void, true>;
+
+    template <template <typename, bool> class Function>
+    AggregateFunctionPtr createAggregateFunctionQuantile(
+        const std::string & name, const DataTypes & argument_types, const Array & params, const Settings *)
+    {
+        /// Second argument type check doesn't depend on the type of the first one.
+        Function<void, true>::assertSecondArg(argument_types);
+
+        const DataTypePtr & argument_type = argument_types[0];
+        WhichDataType which(argument_type);
+
+#define DISPATCH(TYPE) \
+    if (which.idx == TypeIndex::TYPE) return std::make_shared<Function<TYPE, true>>(argument_types, params);
+        FOR_BASIC_NUMERIC_TYPES(DISPATCH)
+#undef DISPATCH
+        if (which.idx == TypeIndex::Date) return std::make_shared<Function<DataTypeDate::FieldType, false>>(argument_types, params);
+        if (which.idx == TypeIndex::DateTime) return std::make_shared<Function<DataTypeDateTime::FieldType, false>>(argument_types, params);
+
+        if (which.idx == TypeIndex::Decimal32) return std::make_shared<Function<Decimal32, false>>(argument_types, params);
+        if (which.idx == TypeIndex::Decimal64) return std::make_shared<Function<Decimal64, false>>(argument_types, params);
+        if (which.idx == TypeIndex::Decimal128) return std::make_shared<Function<Decimal128, false>>(argument_types, params);
+        if (which.idx == TypeIndex::Decimal256) return std::make_shared<Function<Decimal256, false>>(argument_types, params);
+        if (which.idx == TypeIndex::DateTime64) return std::make_shared<Function<DateTime64, false>>(argument_types, params);
+
+        if (which.idx == TypeIndex::Int128) return std::make_shared<Function<Int128, true>>(argument_types, params);
+        if (which.idx == TypeIndex::UInt128) return std::make_shared<Function<UInt128, true>>(argument_types, params);
+        if (which.idx == TypeIndex::Int256) return std::make_shared<Function<Int256, true>>(argument_types, params);
+        if (which.idx == TypeIndex::UInt256) return std::make_shared<Function<UInt256, true>>(argument_types, params);
+
+        throw Exception("Illegal type " + argument_type->getName() + " of argument for aggregate function " + name,
+                        ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
+    }
+}
+
+void registerAggregateFunctionsQuantileInterpolatedWeighted(AggregateFunctionFactory & factory)
+{
+    /// For aggregate functions returning array we cannot return NULL on empty set.
+    AggregateFunctionProperties properties = { .returns_default_when_only_null = true };
+
+    factory.registerFunction(NameQuantileInterpolatedWeighted::name, createAggregateFunctionQuantile<FuncQuantileInterpolatedWeighted>);
+    factory.registerFunction(NameQuantilesInterpolatedWeighted::name, { createAggregateFunctionQuantile<FuncQuantilesInterpolatedWeighted>, properties });
+
+    /// 'median' is an alias for 'quantile'
+    factory.registerAlias("medianInterpolatedWeighted", NameQuantileInterpolatedWeighted::name);
+}
+
+}

src/AggregateFunctions/QuantileInterpolatedWeighted.h

@@ -0,0 +1,308 @@
+#pragma once
+
+#include <base/sort.h>
+
+#include <Common/HashTable/HashMap.h>
+#include <Common/NaNUtils.h>
+
+
+namespace DB
+{
+struct Settings;
+
+namespace ErrorCodes
+{
+    extern const int NOT_IMPLEMENTED;
+}
+
+/** Approximates Quantile by:
+  * - sorting input values and weights
+  * - building a cumulative distribution based on weights
+  * - performing linear interpolation between the weights and values
+  *
+  */
+template <typename Value>
+struct QuantileInterpolatedWeighted
+{
+    struct Int128Hash
+    {
+        size_t operator()(Int128 x) const
+        {
+            return CityHash_v1_0_2::Hash128to64({x >> 64, x & 0xffffffffffffffffll});
+        }
+    };
+
+    using Weight = UInt64;
+    using UnderlyingType = NativeType<Value>;
+    using Hasher = std::conditional_t<std::is_same_v<Value, Decimal128>, Int128Hash, HashCRC32<UnderlyingType>>;
+
+    /// When creating, the hash table must be small.
+    using Map = HashMapWithStackMemory<UnderlyingType, Weight, Hasher, 4>;
+
+    Map map;
+
+    void add(const Value & x)
+    {
+        /// We must skip NaNs as they are not compatible with comparison sorting.
+        if (!isNaN(x))
+            ++map[x];
+    }
+
+    void add(const Value & x, Weight weight)
+    {
+        if (!isNaN(x))
+            map[x] += weight;
+    }
+
+    void merge(const QuantileInterpolatedWeighted & rhs)
+    {
+        for (const auto & pair : rhs.map)
+            map[pair.getKey()] += pair.getMapped();
+    }
+
+    void serialize(WriteBuffer & buf) const
+    {
+        map.write(buf);
+    }
+
+    void deserialize(ReadBuffer & buf)
+    {
+        typename Map::Reader reader(buf);
+        while (reader.next())
+        {
+            const auto & pair = reader.get();
+            map[pair.first] = pair.second;
+        }
+    }
+
+    Value get(Float64 level) const
+    {
+        return getImpl<Value>(level);
+    }
+
+    void getMany(const Float64 * levels, const size_t * indices, size_t size, Value * result) const
+    {
+        getManyImpl<Value>(levels, indices, size, result);
+    }
+
+    /// The same, but in the case of an empty state, NaN is returned.
+    Float64 getFloat(Float64) const
+    {
+        throw Exception("Method getFloat is not implemented for QuantileInterpolatedWeighted", ErrorCodes::NOT_IMPLEMENTED);
+    }
+
+    void getManyFloat(const Float64 *, const size_t *, size_t, Float64 *) const
+    {
+        throw Exception("Method getManyFloat is not implemented for QuantileInterpolatedWeighted", ErrorCodes::NOT_IMPLEMENTED);
+    }
+
+private:
+    using Pair = typename std::pair<UnderlyingType, Float64>;
+
+    /// Get the value of the `level` quantile. The level must be between 0 and 1.
+    template <typename T>
+    T getImpl(Float64 level) const
+    {
+        size_t size = map.size();
+
+        if (0 == size)
+            return std::numeric_limits<Value>::quiet_NaN();
+
+        /// Maintain a vector of pair of values and weights for easier sorting and for building
+        /// a cumulative distribution using the provided weights.
+        std::vector<Pair> value_weight_pairs;
+        value_weight_pairs.reserve(size);
+
+        /// Note: weight provided must be a 64-bit integer
+        /// Float64 is used as accumulator here to get approximate results.
+        /// But weight used in the internal array is stored as Float64 as we
+        /// do some quantile estimation operation which involves division and
+        /// require Float64 level of precision.
+
+        Float64 sum_weight = 0;
+        for (const auto & pair : map)
+        {
+            sum_weight += pair.getMapped();
+            auto value = pair.getKey();
+            auto weight = pair.getMapped();
+            value_weight_pairs.push_back({value, weight});
+        }
+
+        ::sort(value_weight_pairs.begin(), value_weight_pairs.end(), [](const Pair & a, const Pair & b) { return a.first < b.first; });
+
+        Float64 accumulated = 0;
+
+        /// vector for populating and storing the cumulative sum using the provided weights.
+        /// example: [0,1,2,3,4,5] -> [0,1,3,6,10,15]
+        std::vector<Float64> weights_cum_sum;
+        weights_cum_sum.reserve(size);
+
+        for (size_t idx = 0; idx < size; ++idx)
+        {
+            accumulated += value_weight_pairs[idx].second;
+            weights_cum_sum.push_back(accumulated);
+        }
+
+        /// The following estimation of quantile is general and the idea is:
+        /// https://en.wikipedia.org/wiki/Percentile#The_weighted_percentile_method
+
+        /// calculates a simple cumulative distribution based on weights
+        if (sum_weight != 0)
+        {
+            for (size_t idx = 0; idx < size; ++idx)
+                value_weight_pairs[idx].second = (weights_cum_sum[idx] - 0.5 * value_weight_pairs[idx].second) / sum_weight;
+        }
+
+        /// perform linear interpolation
+        size_t idx = 0;
+        if (size >= 2)
+        {
+            if (level >= value_weight_pairs[size - 2].second)
+            {
+                idx = size - 2;
+            }
+            else
+            {
+                size_t start = 0, end = size - 1;
+                while (start <= end)
+                {
+                    size_t mid = start + (end - start) / 2;
+                    if (mid > size)
+                        break;
+                    if (level > value_weight_pairs[mid + 1].second)
+                        start = mid + 1;
+                    else
+                    {
+                        idx = mid;
+                        end = mid - 1;
+                    }
+                }
+            }
+        }
+
+        size_t l = idx;
+        size_t u = idx + 1 < size ? idx + 1 : idx;
+
+        Float64 xl = value_weight_pairs[l].second, xr = value_weight_pairs[u].second;
+        UnderlyingType yl = value_weight_pairs[l].first, yr = value_weight_pairs[u].first;
+
+        if (level < xl)
+            yr = yl;
+        if (level > xr)
+            yl = yr;
+
+        return static_cast<T>(interpolate(level, xl, xr, yl, yr));
+    }
+
+    /// 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 <typename T>
+    void getManyImpl(const Float64 * levels, const size_t * indices, size_t num_levels, Value * result) const
+    {
+        size_t size = map.size();
+
+        if (0 == size)
+        {
+            for (size_t i = 0; i < num_levels; ++i)
+                result[i] = Value();
+            return;
+        }
+
+        std::vector<Pair> value_weight_pairs;
+        value_weight_pairs.reserve(size);
+
+        Float64 sum_weight = 0;
+        for (const auto & pair : map)
+        {
+            sum_weight += pair.getMapped();
+            auto value = pair.getKey();
+            auto weight = pair.getMapped();
+            value_weight_pairs.push_back({value, weight});
+        }
+
+        ::sort(value_weight_pairs.begin(), value_weight_pairs.end(), [](const Pair & a, const Pair & b) { return a.first < b.first; });
+
+        Float64 accumulated = 0;
+
+        /// vector for populating and storing the cumulative sum using the provided weights.
+        /// example: [0,1,2,3,4,5] -> [0,1,3,6,10,15]
+        std::vector<Float64> weights_cum_sum;
+        weights_cum_sum.reserve(size);
+
+        for (size_t idx = 0; idx < size; ++idx)
+        {
+            accumulated += value_weight_pairs[idx].second;
+            weights_cum_sum.emplace_back(accumulated);
+        }
+
+
+        /// The following estimation of quantile is general and the idea is:
+        /// https://en.wikipedia.org/wiki/Percentile#The_weighted_percentile_method
+
+        /// calculates a simple cumulative distribution based on weights
+        if (sum_weight != 0)
+        {
+            for (size_t idx = 0; idx < size; ++idx)
+                value_weight_pairs[idx].second = (weights_cum_sum[idx] - 0.5 * value_weight_pairs[idx].second) / sum_weight;
+        }
+
+        for (size_t level_index = 0; level_index < num_levels; ++level_index)
+        {
+            /// perform linear interpolation for every level
+            auto level = levels[indices[level_index]];
+
+            size_t idx = 0;
+            if (size >= 2)
+            {
+                if (level >= value_weight_pairs[size - 2].second)
+                {
+                    idx = size - 2;
+                }
+                else
+                {
+                    size_t start = 0, end = size - 1;
+                    while (start <= end)
+                    {
+                        size_t mid = start + (end - start) / 2;
+                        if (mid > size)
+                            break;
+                        if (level > value_weight_pairs[mid + 1].second)
+                            start = mid + 1;
+                        else
+                        {
+                            idx = mid;
+                            end = mid - 1;
+                        }
+                    }
+                }
+            }
+
+            size_t l = idx;
+            size_t u = idx + 1 < size ? idx + 1 : idx;
+
+            Float64 xl = value_weight_pairs[l].second, xr = value_weight_pairs[u].second;
+            UnderlyingType yl = value_weight_pairs[l].first, yr = value_weight_pairs[u].first;
+
+            if (level < xl)
+                yr = yl;
+            if (level > xr)
+                yl = yr;
+
+            result[indices[level_index]] = static_cast<T>(interpolate(level, xl, xr, yl, yr));
+        }
+    }
+
+    /// This ignores overflows or NaN's that might arise during add, sub and mul operations and doesn't aim to provide exact
+    /// results since `the quantileInterpolatedWeighted` function itself relies mainly on approximation.
+    UnderlyingType NO_SANITIZE_UNDEFINED interpolate(Float64 level, Float64 xl, Float64 xr, UnderlyingType yl, UnderlyingType yr) const
+    {
+        UnderlyingType dy = yr - yl;
+        Float64 dx = xr - xl;
+        dx = dx == 0 ? 1 : dx; /// to handle NaN behavior that might arise during integer division below.
+
+        /// yl + (dy / dx) * (level - xl)
+        return static_cast<UnderlyingType>(yl + (dy / dx) * (level - xl));
+    }
+};
+
+}

src/AggregateFunctions/registerAggregateFunctions.cpp

@@ -21,6 +21,7 @@ void registerAggregateFunctionsQuantile(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileDeterministic(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileExact(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileExactWeighted(AggregateFunctionFactory &);
+void registerAggregateFunctionsQuantileInterpolatedWeighted(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileExactLow(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileExactHigh(AggregateFunctionFactory &);
 void registerAggregateFunctionsQuantileExactInclusive(AggregateFunctionFactory &);
@@ -106,6 +107,7 @@ void registerAggregateFunctions()
         registerAggregateFunctionsQuantileDeterministic(factory);
         registerAggregateFunctionsQuantileExact(factory);
         registerAggregateFunctionsQuantileExactWeighted(factory);
+        registerAggregateFunctionsQuantileInterpolatedWeighted(factory);
         registerAggregateFunctionsQuantileExactLow(factory);
         registerAggregateFunctionsQuantileExactHigh(factory);
         registerAggregateFunctionsQuantileExactInclusive(factory);

src/Interpreters/GatherFunctionQuantileVisitor.cpp

@@ -25,6 +25,7 @@ static const std::unordered_map<String, String> quantile_fuse_name_mapping = {
     {NameQuantileExactInclusive::name, NameQuantilesExactInclusive::name},
     {NameQuantileExactLow::name, NameQuantilesExactLow::name},
     {NameQuantileExactWeighted::name, NameQuantilesExactWeighted::name},
+    {NameQuantileInterpolatedWeighted::name, NameQuantilesInterpolatedWeighted::name},
     {NameQuantileTDigest::name, NameQuantilesTDigest::name},
     {NameQuantileTDigestWeighted::name, NameQuantilesTDigestWeighted::name},
     {NameQuantileTiming::name, NameQuantilesTiming::name},
@@ -61,9 +62,11 @@ void GatherFunctionQuantileData::FuseQuantileAggregatesData::addFuncNode(ASTPtr
 
     const auto & arguments = func->arguments->children;
 
+
     bool need_two_args = func->name == NameQuantileDeterministic::name || func->name == NameQuantileExactWeighted::name
-        || func->name == NameQuantileTimingWeighted::name || func->name == NameQuantileTDigestWeighted::name
-        || func->name == NameQuantileBFloat16Weighted::name;
+        || func->name == NameQuantileInterpolatedWeighted::name || func->name == NameQuantileTimingWeighted::name
+        || func->name == NameQuantileTDigestWeighted::name || func->name == NameQuantileBFloat16Weighted::name;
+
     if (arguments.size() != (need_two_args ? 2 : 1))
         return;
 

tests/queries/0_stateless/00315_quantile_off_by_one.reference

@@ -1,3 +1,4 @@
 10	[1,1,1,1,10,10,10,10,100,100,100]
+10	[1,1,2,4,7,10,35,61,87,100,100]
 100	100
 61	61

tests/queries/0_stateless/00315_quantile_off_by_one.sql

@@ -1,3 +1,4 @@
 SELECT quantileExactWeighted(0.5)(x, 1) AS q5, quantilesExactWeighted(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1)(x, 1) AS qs FROM (SELECT arrayJoin([1, 1, 1, 10, 10, 10, 10, 100, 100, 100]) AS x);
+SELECT quantileInterpolatedWeighted(0.5)(x, 1) AS q5, quantilesInterpolatedWeighted(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1)(x, 1) AS qs FROM (SELECT arrayJoin([1, 1, 1, 10, 10, 10, 10, 100, 100, 100]) AS x);
 SELECT quantileExact(0)(x), quantileTiming(0)(x) FROM (SELECT number + 100 AS x FROM system.numbers LIMIT 10000);
 SELECT quantileExact(x), quantileTiming(x) FROM (SELECT number % 123 AS x FROM system.numbers LIMIT 10000);

tests/queries/0_stateless/00753_quantile_format.reference

@@ -6,6 +6,8 @@
 ['2016-06-15 23:00:00']
 2016-06-15 23:00:00
 ['2016-06-15 23:00:00']
+2016-06-15 23:00:00
+['2016-06-15 23:00:00']
 30000
 [30000]
 30000

tests/queries/0_stateless/00753_quantile_format.sql

@@ -15,6 +15,9 @@ SELECT quantilesExact(0.2)(d) FROM datetime;
 SELECT quantileExactWeighted(0.2)(d, 1) FROM datetime;
 SELECT quantilesExactWeighted(0.2)(d, 1) FROM datetime;
 
+SELECT quantileInterpolatedWeighted(0.2)(d, 1) FROM datetime;
+SELECT quantilesInterpolatedWeighted(0.2)(d, 1) FROM datetime;
+
 SELECT quantileTiming(0.2)(d) FROM datetime;
 SELECT quantilesTiming(0.2)(d) FROM datetime;
 

tests/queries/0_stateless/02319_quantile_interpolated_weighted.reference

@@ -0,0 +1,12 @@
+quantileInterpolatedWeighted
+0	0	0	Decimal(38, 8)
+-25.5	-8.49999999	-5.1	Decimal(38, 8)
+0	0	0
+9.7	3.23333333	1.94
+19.9	6.63333332	3.98
+30.1	10.03333333	6.02
+40.3	13.43333332	8.06
+50	16.66666666	10
+[-50,-40.4,-30.3,-20.2,-10.1,0,10.1,20.2,30.3,40.4,50]
+[-16.66666666,-13.46666666,-10.09999999,-6.73333332,-3.36666666,0,3.36666666,6.73333332,10.09999999,13.46666666,16.66666666]
+[-10,-8.08,-6.06,-4.04,-2.02,0,2.02,4.04,6.06,8.08,10]

tests/queries/0_stateless/02319_quantile_interpolated_weighted.sql

@@ -0,0 +1,27 @@
+DROP TABLE IF EXISTS decimal;
+
+CREATE TABLE decimal
+(
+    a Decimal32(4),
+    b Decimal64(8),
+    c Decimal128(8)
+) ENGINE = Memory;
+
+INSERT INTO decimal (a, b, c)
+SELECT toDecimal32(number - 50, 4), toDecimal64(number - 50, 8) / 3, toDecimal128(number - 50, 8) / 5
+FROM system.numbers LIMIT 101;
+
+SELECT 'quantileInterpolatedWeighted';
+SELECT medianInterpolatedWeighted(a, 1), medianInterpolatedWeighted(b, 2), medianInterpolatedWeighted(c, 3) as x, toTypeName(x) FROM decimal;
+SELECT quantileInterpolatedWeighted(a, 1), quantileInterpolatedWeighted(b, 2), quantileInterpolatedWeighted(c, 3) as x, toTypeName(x) FROM decimal WHERE a < 0;
+SELECT quantileInterpolatedWeighted(0.0)(a, 1), quantileInterpolatedWeighted(0.0)(b, 2), quantileInterpolatedWeighted(0.0)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantileInterpolatedWeighted(0.2)(a, 1), quantileInterpolatedWeighted(0.2)(b, 2), quantileInterpolatedWeighted(0.2)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantileInterpolatedWeighted(0.4)(a, 1), quantileInterpolatedWeighted(0.4)(b, 2), quantileInterpolatedWeighted(0.4)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantileInterpolatedWeighted(0.6)(a, 1), quantileInterpolatedWeighted(0.6)(b, 2), quantileInterpolatedWeighted(0.6)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantileInterpolatedWeighted(0.8)(a, 1), quantileInterpolatedWeighted(0.8)(b, 2), quantileInterpolatedWeighted(0.8)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantileInterpolatedWeighted(1.0)(a, 1), quantileInterpolatedWeighted(1.0)(b, 2), quantileInterpolatedWeighted(1.0)(c, 3) FROM decimal WHERE a >= 0;
+SELECT quantilesInterpolatedWeighted(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)(a, 1) FROM decimal;
+SELECT quantilesInterpolatedWeighted(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)(b, 2) FROM decimal;
+SELECT quantilesInterpolatedWeighted(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)(c, 3) FROM decimal;
+
+DROP TABLE IF EXISTS decimal;