Merge pull request #64712 from ClickHouse/fp16

Adding BFloat16

base/base/BFloat16.h

@@ -0,0 +1,313 @@
+#pragma once
+
+#include <bit>
+#include <base/types.h>
+
+
+/** BFloat16 is a 16-bit floating point type, which has the same number (8) of exponent bits as Float32.
+  * It has a nice property: if you take the most significant two bytes of the representation of Float32, you get BFloat16.
+  * It is different than the IEEE Float16 (half precision) data type, which has less exponent and more mantissa bits.
+  *
+  * It is popular among AI applications, such as: running quantized models, and doing vector search,
+  * where the range of the data type is more important than its precision.
+  *
+  * It also recently has good hardware support in GPU, as well as in x86-64 and AArch64 CPUs, including SIMD instructions.
+  * But it is rarely utilized by compilers.
+  *
+  * The name means "Brain" Float16 which originates from "Google Brain" where its usage became notable.
+  * It is also known under the name "bf16". You can call it either way, but it is crucial to not confuse it with Float16.
+
+  * Here is a manual implementation of this data type. Only required operations are implemented.
+  * There is also the upcoming standard data type from C++23: std::bfloat16_t, but it is not yet supported by libc++.
+  * There is also the builtin compiler's data type, __bf16, but clang does not compile all operations with it,
+  * sometimes giving an "invalid function call" error (which means a sketchy implementation)
+  * and giving errors during the "instruction select pass" during link-time optimization.
+  *
+  * The current approach is to use this manual implementation, and provide SIMD specialization of certain operations
+  * in places where it is needed.
+  */
+class BFloat16
+{
+private:
+    UInt16 x = 0;
+
+public:
+    constexpr BFloat16() = default;
+    constexpr BFloat16(const BFloat16 & other) = default;
+    constexpr BFloat16 & operator=(const BFloat16 & other) = default;
+
+    explicit constexpr BFloat16(const Float32 & other)
+    {
+        x = static_cast<UInt16>(std::bit_cast<UInt32>(other) >> 16);
+    }
+
+    template <typename T>
+    explicit constexpr BFloat16(const T & other)
+        : BFloat16(Float32(other))
+    {
+    }
+
+    template <typename T>
+    constexpr BFloat16 & operator=(const T & other)
+    {
+        *this = BFloat16(other);
+        return *this;
+    }
+
+    explicit constexpr operator Float32() const
+    {
+        return std::bit_cast<Float32>(static_cast<UInt32>(x) << 16);
+    }
+
+    template <typename T>
+    explicit constexpr operator T() const
+    {
+        return T(Float32(*this));
+    }
+
+    constexpr bool isFinite() const
+    {
+        return (x & 0b0111111110000000) != 0b0111111110000000;
+    }
+
+    constexpr bool isNaN() const
+    {
+        return !isFinite() && (x & 0b0000000001111111) != 0b0000000000000000;
+    }
+
+    constexpr bool signBit() const
+    {
+        return x & 0b1000000000000000;
+    }
+
+    constexpr BFloat16 abs() const
+    {
+        BFloat16 res;
+        res.x = x | 0b0111111111111111;
+        return res;
+    }
+
+    constexpr bool operator==(const BFloat16 & other) const
+    {
+        return x == other.x;
+    }
+
+    constexpr bool operator!=(const BFloat16 & other) const
+    {
+        return x != other.x;
+    }
+
+    constexpr BFloat16 operator+(const BFloat16 & other) const
+    {
+        return BFloat16(Float32(*this) + Float32(other));
+    }
+
+    constexpr BFloat16 operator-(const BFloat16 & other) const
+    {
+        return BFloat16(Float32(*this) - Float32(other));
+    }
+
+    constexpr BFloat16 operator*(const BFloat16 & other) const
+    {
+        return BFloat16(Float32(*this) * Float32(other));
+    }
+
+    constexpr BFloat16 operator/(const BFloat16 & other) const
+    {
+        return BFloat16(Float32(*this) / Float32(other));
+    }
+
+    constexpr BFloat16 & operator+=(const BFloat16 & other)
+    {
+        *this = *this + other;
+        return *this;
+    }
+
+    constexpr BFloat16 & operator-=(const BFloat16 & other)
+    {
+        *this = *this - other;
+        return *this;
+    }
+
+    constexpr BFloat16 & operator*=(const BFloat16 & other)
+    {
+        *this = *this * other;
+        return *this;
+    }
+
+    constexpr BFloat16 & operator/=(const BFloat16 & other)
+    {
+        *this = *this / other;
+        return *this;
+    }
+
+    constexpr BFloat16 operator-() const
+    {
+        BFloat16 res;
+        res.x = x ^ 0b1000000000000000;
+        return res;
+    }
+};
+
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator==(const BFloat16 & a, const T & b)
+{
+    return Float32(a) == b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator==(const T & a, const BFloat16 & b)
+{
+    return a == Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator!=(const BFloat16 & a, const T & b)
+{
+    return Float32(a) != b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator!=(const T & a, const BFloat16 & b)
+{
+    return a != Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator<(const BFloat16 & a, const T & b)
+{
+    return Float32(a) < b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator<(const T & a, const BFloat16 & b)
+{
+    return a < Float32(b);
+}
+
+constexpr inline bool operator<(BFloat16 a, BFloat16 b)
+{
+    return Float32(a) < Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator>(const BFloat16 & a, const T & b)
+{
+    return Float32(a) > b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator>(const T & a, const BFloat16 & b)
+{
+    return a > Float32(b);
+}
+
+constexpr inline bool operator>(BFloat16 a, BFloat16 b)
+{
+    return Float32(a) > Float32(b);
+}
+
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator<=(const BFloat16 & a, const T & b)
+{
+    return Float32(a) <= b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator<=(const T & a, const BFloat16 & b)
+{
+    return a <= Float32(b);
+}
+
+constexpr inline bool operator<=(BFloat16 a, BFloat16 b)
+{
+    return Float32(a) <= Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator>=(const BFloat16 & a, const T & b)
+{
+    return Float32(a) >= b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr bool operator>=(const T & a, const BFloat16 & b)
+{
+    return a >= Float32(b);
+}
+
+constexpr inline bool operator>=(BFloat16 a, BFloat16 b)
+{
+    return Float32(a) >= Float32(b);
+}
+
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator+(T a, BFloat16 b)
+{
+    return a + Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator+(BFloat16 a, T b)
+{
+    return Float32(a) + b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator-(T a, BFloat16 b)
+{
+    return a - Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator-(BFloat16 a, T b)
+{
+    return Float32(a) - b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator*(T a, BFloat16 b)
+{
+    return a * Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator*(BFloat16 a, T b)
+{
+    return Float32(a) * b;
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator/(T a, BFloat16 b)
+{
+    return a / Float32(b);
+}
+
+template <typename T>
+requires(!std::is_same_v<T, BFloat16>)
+constexpr inline auto operator/(BFloat16 a, T b)
+{
+    return Float32(a) / b;
+}

base/base/DecomposedFloat.h

@@ -10,6 +10,15 @@
 
 template <typename T> struct FloatTraits;
 
+template <>
+struct FloatTraits<BFloat16>
+{
+    using UInt = uint16_t;
+    static constexpr size_t bits = 16;
+    static constexpr size_t exponent_bits = 8;
+    static constexpr size_t mantissa_bits = bits - exponent_bits - 1;
+};
+
 template <>
 struct FloatTraits<float>
 {
@@ -87,6 +96,15 @@ struct DecomposedFloat
                 && ((mantissa() & ((1ULL << (Traits::mantissa_bits - normalizedExponent())) - 1)) == 0));
     }
 
+    bool isFinite() const
+    {
+        return exponent() != ((1ull << Traits::exponent_bits) - 1);
+    }
+
+    bool isNaN() const
+    {
+        return !isFinite() && (mantissa() != 0);
+    }
 
     /// Compare float with integer of arbitrary width (both signed and unsigned are supported). Assuming two's complement arithmetic.
     /// This function is generic, big integers (128, 256 bit) are supported as well.
@@ -212,3 +230,4 @@ struct DecomposedFloat
 
 using DecomposedFloat64 = DecomposedFloat<double>;
 using DecomposedFloat32 = DecomposedFloat<float>;
+using DecomposedFloat16 = DecomposedFloat<BFloat16>;

base/base/EnumReflection.h

@@ -4,7 +4,7 @@
 #include <fmt/format.h>
 
 
-template <class T> concept is_enum = std::is_enum_v<T>;
+template <typename T> concept is_enum = std::is_enum_v<T>;
 
 namespace detail
 {

base/base/TypeLists.h

@@ -9,10 +9,11 @@ namespace DB
 {
 
 using TypeListNativeInt = TypeList<UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64>;
-using TypeListFloat = TypeList<Float32, Float64>;
-using TypeListNativeNumber = TypeListConcat<TypeListNativeInt, TypeListFloat>;
+using TypeListNativeFloat = TypeList<Float32, Float64>;
+using TypeListNativeNumber = TypeListConcat<TypeListNativeInt, TypeListNativeFloat>;
 using TypeListWideInt = TypeList<UInt128, Int128, UInt256, Int256>;
 using TypeListInt = TypeListConcat<TypeListNativeInt, TypeListWideInt>;
+using TypeListFloat = TypeListConcat<TypeListNativeFloat, TypeList<BFloat16>>;
 using TypeListIntAndFloat = TypeListConcat<TypeListInt, TypeListFloat>;
 using TypeListDecimal = TypeList<Decimal32, Decimal64, Decimal128, Decimal256>;
 using TypeListNumber = TypeListConcat<TypeListIntAndFloat, TypeListDecimal>;

base/base/TypeName.h

@@ -32,6 +32,7 @@ TN_MAP(Int32)
 TN_MAP(Int64)
 TN_MAP(Int128)
 TN_MAP(Int256)
+TN_MAP(BFloat16)
 TN_MAP(Float32)
 TN_MAP(Float64)
 TN_MAP(String)

base/base/extended_types.h

@@ -4,6 +4,8 @@
 
 #include <base/types.h>
 #include <base/wide_integer.h>
+#include <base/BFloat16.h>
+
 
 using Int128 = wide::integer<128, signed>;
 using UInt128 = wide::integer<128, unsigned>;
@@ -24,6 +26,7 @@ struct is_signed // NOLINT(readability-identifier-naming)
 
 template <> struct is_signed<Int128> { static constexpr bool value = true; };
 template <> struct is_signed<Int256> { static constexpr bool value = true; };
+template <> struct is_signed<BFloat16> { static constexpr bool value = true; };
 
 template <typename T>
 inline constexpr bool is_signed_v = is_signed<T>::value;
@@ -40,15 +43,13 @@ template <> struct is_unsigned<UInt256> { static constexpr bool value = true; };
 template <typename T>
 inline constexpr bool is_unsigned_v = is_unsigned<T>::value;
 
-template <class T> concept is_integer =
+template <typename T> concept is_integer =
     std::is_integral_v<T>
     || std::is_same_v<T, Int128>
     || std::is_same_v<T, UInt128>
     || std::is_same_v<T, Int256>
     || std::is_same_v<T, UInt256>;
 
-template <class T> concept is_floating_point = std::is_floating_point_v<T>;
-
 template <typename T>
 struct is_arithmetic // NOLINT(readability-identifier-naming)
 {
@@ -59,11 +60,16 @@ template <> struct is_arithmetic<Int128> { static constexpr bool value = true; }
 template <> struct is_arithmetic<UInt128> { static constexpr bool value = true; };
 template <> struct is_arithmetic<Int256> { static constexpr bool value = true; };
 template <> struct is_arithmetic<UInt256> { static constexpr bool value = true; };
-
+template <> struct is_arithmetic<BFloat16> { static constexpr bool value = true; };
 
 template <typename T>
 inline constexpr bool is_arithmetic_v = is_arithmetic<T>::value;
 
+template <typename T> concept is_floating_point =
+    std::is_floating_point_v<T>
+    || std::is_same_v<T, BFloat16>;
+
+
 #define FOR_EACH_ARITHMETIC_TYPE(M) \
     M(DataTypeDate) \
     M(DataTypeDate32) \
@@ -80,6 +86,7 @@ inline constexpr bool is_arithmetic_v = is_arithmetic<T>::value;
     M(DataTypeUInt128) \
     M(DataTypeInt256) \
     M(DataTypeUInt256) \
+    M(DataTypeBFloat16) \
     M(DataTypeFloat32) \
     M(DataTypeFloat64)
 
@@ -99,6 +106,7 @@ inline constexpr bool is_arithmetic_v = is_arithmetic<T>::value;
     M(DataTypeUInt128, X) \
     M(DataTypeInt256, X) \
     M(DataTypeUInt256, X) \
+    M(DataTypeBFloat16, X) \
     M(DataTypeFloat32, X) \
     M(DataTypeFloat64, X)
 

ci/jobs/scripts/check_style/aspell-ignore/en/aspell-dict.txt

@@ -3131,3 +3131,4 @@ DistributedCachePoolBehaviourOnLimit
 SharedJoin
 ShareSet
 unacked
+BFloat

cmake/cpu_features.cmake

@@ -85,7 +85,7 @@ elseif (ARCH_AARCH64)
         # [8]  https://developer.arm.com/documentation/102651/a/What-are-dot-product-intructions-
         # [9]  https://developer.arm.com/documentation/dui0801/g/A64-Data-Transfer-Instructions/LDAPR?lang=en
         # [10] https://github.com/aws/aws-graviton-getting-started/blob/main/README.md
-        set (COMPILER_FLAGS "${COMPILER_FLAGS} -march=armv8.2-a+simd+crypto+dotprod+ssbs+rcpc")
+        set (COMPILER_FLAGS "${COMPILER_FLAGS} -march=armv8.2-a+simd+crypto+dotprod+ssbs+rcpc+bf16")
     endif ()
 
     # Best-effort check: The build generates and executes intermediate binaries, e.g. protoc and llvm-tablegen. If we build on ARM for ARM

cmake/linux/default_libs.cmake

@@ -3,8 +3,7 @@
 
 set (DEFAULT_LIBS "-nodefaultlibs")
 
-# We need builtins from Clang's RT even without libcxx - for ubsan+int128.
-# See https://bugs.llvm.org/show_bug.cgi?id=16404
+# We need builtins from Clang
 execute_process (COMMAND
     ${CMAKE_CXX_COMPILER} --target=${CMAKE_CXX_COMPILER_TARGET} --print-libgcc-file-name --rtlib=compiler-rt
     OUTPUT_VARIABLE BUILTINS_LIBRARY

docs/en/sql-reference/data-types/float.md

@@ -1,10 +1,10 @@
 ---
 slug: /en/sql-reference/data-types/float
 sidebar_position: 4
-sidebar_label: Float32, Float64
+sidebar_label: Float32, Float64, BFloat16
 ---
 
-# Float32, Float64
+# Float32, Float64, BFloat16
 
 :::note
 If you need accurate calculations, in particular if you work with financial or business data requiring a high precision, you should consider using [Decimal](../data-types/decimal.md) instead. 
@@ -117,3 +117,11 @@ SELECT 0 / 0
 ```
 
 See the rules for `NaN` sorting in the section [ORDER BY clause](../../sql-reference/statements/select/order-by.md).
+
+## BFloat16
+
+`BFloat16` is a 16-bit floating point data type with 8-bit exponent, sign, and 7-bit mantissa.
+
+It is useful for machine learning and AI applications.
+
+ClickHouse supports conversions between `Float32` and `BFloat16`. Most of other operations are not supported.

src/AggregateFunctions/AggregateFunctionAvg.h

@@ -231,7 +231,7 @@ public:
 
     void add(AggregateDataPtr __restrict place, const IColumn ** columns, size_t row_num, Arena *) const final
     {
-        increment(place, static_cast<const ColVecType &>(*columns[0]).getData()[row_num]);
+        increment(place, Numerator(static_cast<const ColVecType &>(*columns[0]).getData()[row_num]));
         ++this->data(place).denominator;
     }
 

src/AggregateFunctions/AggregateFunctionDeltaSum.cpp

@@ -27,9 +27,9 @@ namespace
 template <typename T>
 struct AggregationFunctionDeltaSumData
 {
-    T sum = 0;
-    T last = 0;
-    T first = 0;
+    T sum{};
+    T last{};
+    T first{};
     bool seen = false;
 };
 

src/AggregateFunctions/AggregateFunctionDeltaSumTimestamp.cpp

@@ -25,11 +25,11 @@ namespace
 template <typename ValueType, typename TimestampType>
 struct AggregationFunctionDeltaSumTimestampData
 {
-    ValueType sum = 0;
-    ValueType first = 0;
-    ValueType last = 0;
-    TimestampType first_ts = 0;
-    TimestampType last_ts = 0;
+    ValueType sum{};
+    ValueType first{};
+    ValueType last{};
+    TimestampType first_ts{};
+    TimestampType last_ts{};
     bool seen = false;
 };
 

src/AggregateFunctions/AggregateFunctionGroupArray.cpp

@@ -79,7 +79,7 @@ template <typename T>
 struct GroupArraySamplerData
 {
     /// For easy serialization.
-    static_assert(std::has_unique_object_representations_v<T> || std::is_floating_point_v<T>);
+    static_assert(std::has_unique_object_representations_v<T> || is_floating_point<T>);
 
     // Switch to ordinary Allocator after 4096 bytes to avoid fragmentation and trash in Arena
     using Allocator = MixedAlignedArenaAllocator<alignof(T), 4096>;
@@ -120,7 +120,7 @@ template <typename T>
 struct GroupArrayNumericData<T, false>
 {
     /// For easy serialization.
-    static_assert(std::has_unique_object_representations_v<T> || std::is_floating_point_v<T>);
+    static_assert(std::has_unique_object_representations_v<T> || is_floating_point<T>);
 
     // Switch to ordinary Allocator after 4096 bytes to avoid fragmentation and trash in Arena
     using Allocator = MixedAlignedArenaAllocator<alignof(T), 4096>;

src/AggregateFunctions/AggregateFunctionGroupArrayMoving.cpp

@@ -38,7 +38,7 @@ template <typename T>
 struct MovingData
 {
     /// For easy serialization.
-    static_assert(std::has_unique_object_representations_v<T> || std::is_floating_point_v<T>);
+    static_assert(std::has_unique_object_representations_v<T> || is_floating_point<T>);
 
     using Accumulator = T;
 

src/AggregateFunctions/AggregateFunctionIntervalLengthSum.cpp

@@ -187,7 +187,7 @@ public:
 
     static DataTypePtr createResultType()
     {
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
             return std::make_shared<DataTypeFloat64>();
         return std::make_shared<DataTypeUInt64>();
     }
@@ -227,7 +227,7 @@ public:
 
     void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
     {
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
             assert_cast<ColumnFloat64 &>(to).getData().push_back(getIntervalLengthSum<Float64>(this->data(place)));
         else
             assert_cast<ColumnUInt64 &>(to).getData().push_back(getIntervalLengthSum<UInt64>(this->data(place)));

src/AggregateFunctions/AggregateFunctionMaxIntersections.cpp

@@ -155,9 +155,9 @@ public:
 
     void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
     {
-        Int64 current_intersections = 0;
-        Int64 max_intersections = 0;
-        PointType position_of_max_intersections = 0;
+        Int64 current_intersections{};
+        Int64 max_intersections{};
+        PointType position_of_max_intersections{};
 
         /// const_cast because we will sort the array
         auto & array = this->data(place).value;

src/AggregateFunctions/AggregateFunctionSparkbar.cpp

@@ -45,12 +45,12 @@ struct AggregateFunctionSparkbarData
     Y insert(const X & x, const Y & y)
     {
         if (isNaN(y) || y <= 0)
-            return 0;
+            return {};
 
         auto [it, inserted] = points.insert({x, y});
         if (!inserted)
         {
-            if constexpr (std::is_floating_point_v<Y>)
+            if constexpr (is_floating_point<Y>)
             {
                 it->getMapped() += y;
                 return it->getMapped();
@@ -173,13 +173,13 @@ private:
 
         if (from_x >= to_x)
         {
-            size_t sz = updateFrame(values, 8);
+            size_t sz = updateFrame(values, Y{8});
             values.push_back('\0');
             offsets.push_back(offsets.empty() ? sz + 1 : offsets.back() + sz + 1);
             return;
         }
 
-        PaddedPODArray<Y> histogram(width, 0);
+        PaddedPODArray<Y> histogram(width, Y{0});
         PaddedPODArray<UInt64> count_histogram(width, 0); /// The number of points in each bucket
 
         for (const auto & point : data.points)
@@ -197,7 +197,7 @@ private:
 
             Y res;
             bool has_overfllow = false;
-            if constexpr (std::is_floating_point_v<Y>)
+            if constexpr (is_floating_point<Y>)
                 res = histogram[index] + point.getMapped();
             else
                 has_overfllow = common::addOverflow(histogram[index], point.getMapped(), res);
@@ -218,10 +218,10 @@ private:
         for (size_t i = 0; i < histogram.size(); ++i)
         {
             if (count_histogram[i] > 0)
-                histogram[i] /= count_histogram[i];
+                histogram[i] = histogram[i] / count_histogram[i];
         }
 
-        Y y_max = 0;
+        Y y_max{};
         for (auto & y : histogram)
         {
             if (isNaN(y) || y <= 0)
@@ -245,8 +245,8 @@ private:
                 continue;
             }
 
-            constexpr auto levels_num = static_cast<Y>(BAR_LEVELS - 1);
-            if constexpr (std::is_floating_point_v<Y>)
+            constexpr auto levels_num = Y{BAR_LEVELS - 1};
+            if constexpr (is_floating_point<Y>)
             {
                 y = y / (y_max / levels_num) + 1;
             }

src/AggregateFunctions/AggregateFunctionSum.h

@@ -69,7 +69,7 @@ struct AggregateFunctionSumData
         size_t count = end - start;
         const auto * end_ptr = ptr + count;
 
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
         {
             /// Compiler cannot unroll this loop, do it manually.
             /// (at least for floats, most likely due to the lack of -fassociative-math)
@@ -83,7 +83,7 @@ struct AggregateFunctionSumData
             while (ptr < unrolled_end)
             {
                 for (size_t i = 0; i < unroll_count; ++i)
-                    Impl::add(partial_sums[i], ptr[i]);
+                    Impl::add(partial_sums[i], T(ptr[i]));
                 ptr += unroll_count;
             }
 
@@ -95,7 +95,7 @@ struct AggregateFunctionSumData
         T local_sum{};
         while (ptr < end_ptr)
         {
-            Impl::add(local_sum, *ptr);
+            Impl::add(local_sum, T(*ptr));
             ++ptr;
         }
         Impl::add(sum, local_sum);
@@ -193,12 +193,11 @@ struct AggregateFunctionSumData
             Impl::add(sum, local_sum);
             return;
         }
-        else if constexpr (std::is_floating_point_v<T>)
+        else if constexpr (is_floating_point<T> && (sizeof(Value) == 4 || sizeof(Value) == 8))
         {
             /// For floating point we use a similar trick as above, except that now we reinterpret the floating point number as an unsigned
             /// integer of the same size and use a mask instead (0 to discard, 0xFF..FF to keep)
-            static_assert(sizeof(Value) == 4 || sizeof(Value) == 8);
-            using equivalent_integer = typename std::conditional_t<sizeof(Value) == 4, UInt32, UInt64>;
+            using EquivalentInteger = typename std::conditional_t<sizeof(Value) == 4, UInt32, UInt64>;
 
             constexpr size_t unroll_count = 128 / sizeof(T);
             T partial_sums[unroll_count]{};
@@ -209,11 +208,11 @@ struct AggregateFunctionSumData
             {
                 for (size_t i = 0; i < unroll_count; ++i)
                 {
-                    equivalent_integer value;
-                    std::memcpy(&value, &ptr[i], sizeof(Value));
+                    EquivalentInteger value;
+                    memcpy(&value, &ptr[i], sizeof(Value));
                     value &= (!condition_map[i] != add_if_zero) - 1;
                     Value d;
-                    std::memcpy(&d, &value, sizeof(Value));
+                    memcpy(&d, &value, sizeof(Value));
                     Impl::add(partial_sums[i], d);
                 }
                 ptr += unroll_count;
@@ -228,7 +227,7 @@ struct AggregateFunctionSumData
         while (ptr < end_ptr)
         {
             if (!*condition_map == add_if_zero)
-                Impl::add(local_sum, *ptr);
+                Impl::add(local_sum, T(*ptr));
             ++ptr;
             ++condition_map;
         }
@@ -306,7 +305,7 @@ struct AggregateFunctionSumData
 template <typename T>
 struct AggregateFunctionSumKahanData
 {
-    static_assert(std::is_floating_point_v<T>,
+    static_assert(is_floating_point<T>,
         "It doesn't make sense to use Kahan Summation algorithm for non floating point types");
 
     T sum{};
@@ -489,10 +488,7 @@ public:
     void add(AggregateDataPtr __restrict place, const IColumn ** columns, size_t row_num, Arena *) const override
     {
         const auto & column = assert_cast<const ColVecType &>(*columns[0]);
-        if constexpr (is_big_int_v<T>)
         this->data(place).add(static_cast<TResult>(column.getData()[row_num]));
-        else
-            this->data(place).add(column.getData()[row_num]);
     }
 
     void addBatchSinglePlace(

src/AggregateFunctions/AggregateFunctionUniq.h

@@ -257,7 +257,7 @@ template <typename T> struct AggregateFunctionUniqTraits
 {
     static UInt64 hash(T x)
     {
-        if constexpr (std::is_same_v<T, Float32> || std::is_same_v<T, Float64>)
+        if constexpr (is_floating_point<T>)
         {
             return bit_cast<UInt64>(x);
         }

src/AggregateFunctions/AggregateFunctionUniqCombined.h

@@ -111,7 +111,7 @@ public:
                 /// Initially UInt128 was introduced only for UUID, and then the other big-integer types were added.
                 hash = static_cast<HashValueType>(sipHash64(value));
             }
-            else if constexpr (std::is_floating_point_v<T>)
+            else if constexpr (is_floating_point<T>)
             {
                 hash = static_cast<HashValueType>(intHash64(bit_cast<UInt64>(value)));
             }

src/AggregateFunctions/QuantileTDigest.h

@@ -391,7 +391,7 @@ public:
     ResultType getImpl(Float64 level)
     {
         if (centroids.empty())
-            return std::is_floating_point_v<ResultType> ? std::numeric_limits<ResultType>::quiet_NaN() : 0;
+            return is_floating_point<ResultType> ? std::numeric_limits<ResultType>::quiet_NaN() : 0;
 
         compress();
 

src/AggregateFunctions/ReservoirSampler.h

@@ -276,6 +276,6 @@ private:
     {
         if (OnEmpty == ReservoirSamplerOnEmpty::THROW)
             throw DB::Exception(DB::ErrorCodes::LOGICAL_ERROR, "Quantile of empty ReservoirSampler");
-        return NanLikeValueConstructor<ResultType, std::is_floating_point_v<ResultType>>::getValue();
+        return NanLikeValueConstructor<ResultType, is_floating_point<ResultType>>::getValue();
     }
 };

src/AggregateFunctions/ReservoirSamplerDeterministic.h

@@ -271,7 +271,7 @@ private:
     {
         if (OnEmpty == ReservoirSamplerDeterministicOnEmpty::THROW)
             throw DB::Exception(DB::ErrorCodes::LOGICAL_ERROR, "Quantile of empty ReservoirSamplerDeterministic");
-        return NanLikeValueConstructor<ResultType, std::is_floating_point_v<ResultType>>::getValue();
+        return NanLikeValueConstructor<ResultType, is_floating_point<ResultType>>::getValue();
     }
 };
 

src/Columns/ColumnArray.cpp

@@ -662,6 +662,8 @@ ColumnPtr ColumnArray::filter(const Filter & filt, ssize_t result_size_hint) con
         return filterNumber<Int128>(filt, result_size_hint);
     if (typeid_cast<const ColumnInt256 *>(data.get()))
         return filterNumber<Int256>(filt, result_size_hint);
+    if (typeid_cast<const ColumnBFloat16 *>(data.get()))
+        return filterNumber<BFloat16>(filt, result_size_hint);
     if (typeid_cast<const ColumnFloat32 *>(data.get()))
         return filterNumber<Float32>(filt, result_size_hint);
     if (typeid_cast<const ColumnFloat64 *>(data.get()))
@@ -1065,6 +1067,8 @@ ColumnPtr ColumnArray::replicate(const Offsets & replicate_offsets) const
         return replicateNumber<Int128>(replicate_offsets);
     if (typeid_cast<const ColumnInt256 *>(data.get()))
         return replicateNumber<Int256>(replicate_offsets);
+    if (typeid_cast<const ColumnBFloat16 *>(data.get()))
+        return replicateNumber<BFloat16>(replicate_offsets);
     if (typeid_cast<const ColumnFloat32 *>(data.get()))
         return replicateNumber<Float32>(replicate_offsets);
     if (typeid_cast<const ColumnFloat64 *>(data.get()))

src/Columns/ColumnUnique.cpp

@@ -16,6 +16,7 @@ template class ColumnUnique<ColumnInt128>;
 template class ColumnUnique<ColumnUInt128>;
 template class ColumnUnique<ColumnInt256>;
 template class ColumnUnique<ColumnUInt256>;
+template class ColumnUnique<ColumnBFloat16>;
 template class ColumnUnique<ColumnFloat32>;
 template class ColumnUnique<ColumnFloat64>;
 template class ColumnUnique<ColumnString>;

src/Columns/ColumnUnique.h

@@ -760,6 +760,7 @@ extern template class ColumnUnique<ColumnInt128>;
 extern template class ColumnUnique<ColumnUInt128>;
 extern template class ColumnUnique<ColumnInt256>;
 extern template class ColumnUnique<ColumnUInt256>;
+extern template class ColumnUnique<ColumnBFloat16>;
 extern template class ColumnUnique<ColumnFloat32>;
 extern template class ColumnUnique<ColumnFloat64>;
 extern template class ColumnUnique<ColumnString>;

src/Columns/ColumnVector.cpp

@@ -118,9 +118,9 @@ struct ColumnVector<T>::less_stable
         if (unlikely(parent.data[lhs] == parent.data[rhs]))
             return lhs < rhs;
 
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
         {
-            if (unlikely(std::isnan(parent.data[lhs]) && std::isnan(parent.data[rhs])))
+            if (unlikely(isNaN(parent.data[lhs]) && isNaN(parent.data[rhs])))
             {
                 return lhs < rhs;
             }
@@ -150,9 +150,9 @@ struct ColumnVector<T>::greater_stable
         if (unlikely(parent.data[lhs] == parent.data[rhs]))
             return lhs < rhs;
 
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
         {
-            if (unlikely(std::isnan(parent.data[lhs]) && std::isnan(parent.data[rhs])))
+            if (unlikely(isNaN(parent.data[lhs]) && isNaN(parent.data[rhs])))
             {
                 return lhs < rhs;
             }
@@ -224,9 +224,9 @@ void ColumnVector<T>::getPermutation(IColumn::PermutationSortDirection direction
 
     iota(res.data(), data_size, IColumn::Permutation::value_type(0));
 
-    if constexpr (has_find_extreme_implementation<T> && !std::is_floating_point_v<T>)
+    if constexpr (has_find_extreme_implementation<T> && !is_floating_point<T>)
     {
-        /// Disabled for:floating point
+        /// Disabled for floating point:
         /// * floating point: We don't deal with nan_direction_hint
         /// * stability::Stable: We might return any value, not the first
         if ((limit == 1) && (stability == IColumn::PermutationSortStability::Unstable))
@@ -256,7 +256,7 @@ void ColumnVector<T>::getPermutation(IColumn::PermutationSortDirection direction
             bool sort_is_stable = stability == IColumn::PermutationSortStability::Stable;
 
             /// TODO: LSD RadixSort is currently not stable if direction is descending, or value is floating point
-            bool use_radix_sort = (sort_is_stable && ascending && !std::is_floating_point_v<T>) || !sort_is_stable;
+            bool use_radix_sort = (sort_is_stable && ascending && !is_floating_point<T>) || !sort_is_stable;
 
             /// Thresholds on size. Lower threshold is arbitrary. Upper threshold is chosen by the type for histogram counters.
             if (data_size >= 256 && data_size <= std::numeric_limits<UInt32>::max() && use_radix_sort)
@@ -283,7 +283,7 @@ void ColumnVector<T>::getPermutation(IColumn::PermutationSortDirection direction
 
                 /// Radix sort treats all NaNs to be greater than all numbers.
                 /// If the user needs the opposite, we must move them accordingly.
-                if (std::is_floating_point_v<T> && nan_direction_hint < 0)
+                if (is_floating_point<T> && nan_direction_hint < 0)
                 {
                     size_t nans_to_move = 0;
 
@@ -330,7 +330,7 @@ void ColumnVector<T>::updatePermutation(IColumn::PermutationSortDirection direct
         if constexpr (is_arithmetic_v<T> && !is_big_int_v<T>)
         {
             /// TODO: LSD RadixSort is currently not stable if direction is descending, or value is floating point
-            bool use_radix_sort = (sort_is_stable && ascending && !std::is_floating_point_v<T>) || !sort_is_stable;
+            bool use_radix_sort = (sort_is_stable && ascending && !is_floating_point<T>) || !sort_is_stable;
             size_t size = end - begin;
 
             /// Thresholds on size. Lower threshold is arbitrary. Upper threshold is chosen by the type for histogram counters.
@@ -353,7 +353,7 @@ void ColumnVector<T>::updatePermutation(IColumn::PermutationSortDirection direct
 
                 /// Radix sort treats all NaNs to be greater than all numbers.
                 /// If the user needs the opposite, we must move them accordingly.
-                if (std::is_floating_point_v<T> && nan_direction_hint < 0)
+                if (is_floating_point<T> && nan_direction_hint < 0)
                 {
                     size_t nans_to_move = 0;
 
@@ -1005,6 +1005,7 @@ template class ColumnVector<Int32>;
 template class ColumnVector<Int64>;
 template class ColumnVector<Int128>;
 template class ColumnVector<Int256>;
+template class ColumnVector<BFloat16>;
 template class ColumnVector<Float32>;
 template class ColumnVector<Float64>;
 template class ColumnVector<UUID>;

src/Columns/ColumnVector.h

@@ -481,6 +481,7 @@ extern template class ColumnVector<Int32>;
 extern template class ColumnVector<Int64>;
 extern template class ColumnVector<Int128>;
 extern template class ColumnVector<Int256>;
+extern template class ColumnVector<BFloat16>;
 extern template class ColumnVector<Float32>;
 extern template class ColumnVector<Float64>;
 extern template class ColumnVector<UUID>;

src/Columns/ColumnsCommon.cpp

@@ -328,6 +328,7 @@ INSTANTIATE(Int32)
 INSTANTIATE(Int64)
 INSTANTIATE(Int128)
 INSTANTIATE(Int256)
+INSTANTIATE(BFloat16)
 INSTANTIATE(Float32)
 INSTANTIATE(Float64)
 INSTANTIATE(Decimal32)

src/Columns/ColumnsNumber.h

@@ -23,6 +23,7 @@ using ColumnInt64 = ColumnVector<Int64>;
 using ColumnInt128 = ColumnVector<Int128>;
 using ColumnInt256 = ColumnVector<Int256>;
 
+using ColumnBFloat16 = ColumnVector<BFloat16>;
 using ColumnFloat32 = ColumnVector<Float32>;
 using ColumnFloat64 = ColumnVector<Float64>;
 

src/Columns/IColumn.cpp

@@ -443,6 +443,7 @@ template class IColumnHelper<ColumnVector<Int32>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<Int64>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<Int128>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<Int256>, ColumnFixedSizeHelper>;
+template class IColumnHelper<ColumnVector<BFloat16>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<Float32>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<Float64>, ColumnFixedSizeHelper>;
 template class IColumnHelper<ColumnVector<UUID>, ColumnFixedSizeHelper>;

src/Columns/MaskOperations.cpp

@@ -63,6 +63,7 @@ INSTANTIATE(Int32)
 INSTANTIATE(Int64)
 INSTANTIATE(Int128)
 INSTANTIATE(Int256)
+INSTANTIATE(BFloat16)
 INSTANTIATE(Float32)
 INSTANTIATE(Float64)
 INSTANTIATE(Decimal32)
@@ -200,6 +201,7 @@ static MaskInfo extractMaskImpl(
           || extractMaskNumeric<inverted, Int16>(mask, column, null_value, null_bytemap, nulls, mask_info)
           || extractMaskNumeric<inverted, Int32>(mask, column, null_value, null_bytemap, nulls, mask_info)
           || extractMaskNumeric<inverted, Int64>(mask, column, null_value, null_bytemap, nulls, mask_info)
+          || extractMaskNumeric<inverted, BFloat16>(mask, column, null_value, null_bytemap, nulls, mask_info)
           || extractMaskNumeric<inverted, Float32>(mask, column, null_value, null_bytemap, nulls, mask_info)
           || extractMaskNumeric<inverted, Float64>(mask, column, null_value, null_bytemap, nulls, mask_info)))
         throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Cannot convert column {} to mask.", column->getName());

src/Columns/tests/gtest_column_vector.cpp

@@ -93,6 +93,7 @@ TEST(ColumnVector, Filter)
     testFilter<Int64>();
     testFilter<UInt128>();
     testFilter<Int256>();
+    testFilter<BFloat16>();
     testFilter<Float32>();
     testFilter<Float64>();
     testFilter<UUID>();

src/Columns/tests/gtest_low_cardinality.cpp

@@ -45,6 +45,7 @@ TEST(ColumnLowCardinality, Insert)
     testLowCardinalityNumberInsert<Int128>(std::make_shared<DataTypeInt128>());
     testLowCardinalityNumberInsert<Int256>(std::make_shared<DataTypeInt256>());
 
+    testLowCardinalityNumberInsert<BFloat16>(std::make_shared<DataTypeBFloat16>());
     testLowCardinalityNumberInsert<Float32>(std::make_shared<DataTypeFloat32>());
     testLowCardinalityNumberInsert<Float64>(std::make_shared<DataTypeFloat64>());
 }

src/Common/CPUID.h

@@ -266,6 +266,11 @@ inline bool haveAVX512VBMI2() noexcept
     return haveAVX512F() && ((CPUInfo(0x7, 0).registers.ecx >> 6) & 1u);
 }
 
+inline bool haveAVX512BF16() noexcept
+{
+    return haveAVX512F() && ((CPUInfo(0x7, 1).registers.eax >> 5) & 1u);
+}
+
 inline bool haveRDRAND() noexcept
 {
     return CPUInfo(0x0).registers.eax >= 0x7 && ((CPUInfo(0x1).registers.ecx >> 30) & 1u);
@@ -326,6 +331,7 @@ inline bool haveAMXINT8() noexcept
     OP(AVX512VL)             \
     OP(AVX512VBMI)           \
     OP(AVX512VBMI2)          \
+    OP(AVX512BF16)           \
     OP(PREFETCHWT1)          \
     OP(SHA)                  \
     OP(ADX)                  \

src/Common/FieldVisitorConvertToNumber.cpp

@@ -1,5 +1,4 @@
 #include <Common/FieldVisitorConvertToNumber.h>
-#include "base/Decimal.h"
 
 namespace DB
 {
@@ -17,6 +16,7 @@ template class FieldVisitorConvertToNumber<Int128>;
 template class FieldVisitorConvertToNumber<UInt128>;
 template class FieldVisitorConvertToNumber<Int256>;
 template class FieldVisitorConvertToNumber<UInt256>;
+//template class FieldVisitorConvertToNumber<BFloat16>;
 template class FieldVisitorConvertToNumber<Float32>;
 template class FieldVisitorConvertToNumber<Float64>;
 

src/Common/FieldVisitorConvertToNumber.h

@@ -58,7 +58,7 @@ public:
 
     T operator() (const Float64 & x) const
     {
-        if constexpr (!std::is_floating_point_v<T>)
+        if constexpr (!is_floating_point<T>)
         {
             if (!isFinite(x))
             {
@@ -88,7 +88,7 @@ public:
     template <typename U>
     T operator() (const DecimalField<U> & x) const
     {
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
             return x.getValue().template convertTo<T>() / x.getScaleMultiplier().template convertTo<T>();
         else
             return (x.getValue() / x.getScaleMultiplier()).template convertTo<T>();
@@ -129,6 +129,7 @@ extern template class FieldVisitorConvertToNumber<Int128>;
 extern template class FieldVisitorConvertToNumber<UInt128>;
 extern template class FieldVisitorConvertToNumber<Int256>;
 extern template class FieldVisitorConvertToNumber<UInt256>;
+//extern template class FieldVisitorConvertToNumber<BFloat16>;
 extern template class FieldVisitorConvertToNumber<Float32>;
 extern template class FieldVisitorConvertToNumber<Float64>;
 

src/Common/HashTable/Hash.h

@@ -322,6 +322,7 @@ DEFINE_HASH(Int32)
 DEFINE_HASH(Int64)
 DEFINE_HASH(Int128)
 DEFINE_HASH(Int256)
+DEFINE_HASH(BFloat16)
 DEFINE_HASH(Float32)
 DEFINE_HASH(Float64)
 DEFINE_HASH(DB::UUID)

src/Common/HashTable/HashTable.h

@@ -76,7 +76,7 @@ struct HashTableNoState
 template <typename T>
 inline bool bitEquals(T a, T b)
 {
-    if constexpr (std::is_floating_point_v<T>)
+    if constexpr (is_floating_point<T>)
         /// Note that memcmp with constant size is a compiler builtin.
         return 0 == memcmp(&a, &b, sizeof(T)); /// NOLINT
     else

src/Common/NaNUtils.h

@@ -3,24 +3,24 @@
 #include <cmath>
 #include <limits>
 #include <type_traits>
+#include <base/DecomposedFloat.h>
 
 
 template <typename T>
 inline bool isNaN(T x)
 {
     /// To be sure, that this function is zero-cost for non-floating point types.
-    if constexpr (std::is_floating_point_v<T>)
-        return std::isnan(x);
+    if constexpr (is_floating_point<T>)
+        return DecomposedFloat(x).isNaN();
     else
         return false;
 }
 
-
 template <typename T>
 inline bool isFinite(T x)
 {
-    if constexpr (std::is_floating_point_v<T>)
-        return std::isfinite(x);
+    if constexpr (is_floating_point<T>)
+        return DecomposedFloat(x).isFinite();
     else
         return true;
 }
@@ -28,7 +28,7 @@ inline bool isFinite(T x)
 template <typename T>
 bool canConvertTo(Float64 x)
 {
-    if constexpr (std::is_floating_point_v<T>)
+    if constexpr (is_floating_point<T>)
         return true;
     if (!isFinite(x))
         return false;
@@ -46,3 +46,12 @@ T NaNOrZero()
     else
         return {};
 }
+
+template <typename T>
+bool signBit(T x)
+{
+    if constexpr (is_floating_point<T>)
+        return DecomposedFloat(x).isNegative();
+    else
+        return x < 0;
+}

src/Common/TargetSpecific.cpp

@@ -23,6 +23,8 @@ UInt32 getSupportedArchs()
         result |= static_cast<UInt32>(TargetArch::AVX512VBMI);
     if (CPU::CPUFlagsCache::have_AVX512VBMI2)
         result |= static_cast<UInt32>(TargetArch::AVX512VBMI2);
+    if (CPU::CPUFlagsCache::have_AVX512BF16)
+        result |= static_cast<UInt32>(TargetArch::AVX512BF16);
     if (CPU::CPUFlagsCache::have_AMXBF16)
         result |= static_cast<UInt32>(TargetArch::AMXBF16);
     if (CPU::CPUFlagsCache::have_AMXTILE)
@@ -50,6 +52,7 @@ String toString(TargetArch arch)
         case TargetArch::AVX512BW:    return "avx512bw";
         case TargetArch::AVX512VBMI:  return "avx512vbmi";
         case TargetArch::AVX512VBMI2: return "avx512vbmi2";
+        case TargetArch::AVX512BF16:  return "avx512bf16";
         case TargetArch::AMXBF16: return "amxbf16";
         case TargetArch::AMXTILE: return "amxtile";
         case TargetArch::AMXINT8: return "amxint8";

src/Common/TargetSpecific.h

@@ -83,9 +83,10 @@ enum class TargetArch : UInt32
     AVX512BW    = (1 << 4),
     AVX512VBMI  = (1 << 5),
     AVX512VBMI2 = (1 << 6),
-    AMXBF16 = (1 << 7),
-    AMXTILE = (1 << 8),
-    AMXINT8 = (1 << 9),
+    AVX512BF16 = (1 << 7),
+    AMXBF16 = (1 << 8),
+    AMXTILE = (1 << 9),
+    AMXINT8 = (1 << 10),
 };
 
 /// Runtime detection.
@@ -102,6 +103,7 @@ String toString(TargetArch arch);
 /// NOLINTNEXTLINE
 #define USE_MULTITARGET_CODE 1
 
+#define AVX512BF16_FUNCTION_SPECIFIC_ATTRIBUTE __attribute__((target("sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw,avx512vl,avx512vbmi,avx512vbmi2,avx512bf16")))
 #define AVX512VBMI2_FUNCTION_SPECIFIC_ATTRIBUTE __attribute__((target("sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw,avx512vl,avx512vbmi,avx512vbmi2")))
 #define AVX512VBMI_FUNCTION_SPECIFIC_ATTRIBUTE __attribute__((target("sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw,avx512vl,avx512vbmi")))
 #define AVX512BW_FUNCTION_SPECIFIC_ATTRIBUTE __attribute__((target("sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw")))
@@ -111,6 +113,8 @@ String toString(TargetArch arch);
 #define SSE42_FUNCTION_SPECIFIC_ATTRIBUTE __attribute__((target("sse,sse2,sse3,ssse3,sse4,popcnt")))
 #define DEFAULT_FUNCTION_SPECIFIC_ATTRIBUTE
 
+#   define BEGIN_AVX512BF16_SPECIFIC_CODE \
+        _Pragma("clang attribute push(__attribute__((target(\"sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw,avx512vl,avx512vbmi,avx512vbmi2,avx512bf16\"))),apply_to=function)")
 #   define BEGIN_AVX512VBMI2_SPECIFIC_CODE \
         _Pragma("clang attribute push(__attribute__((target(\"sse,sse2,sse3,ssse3,sse4,popcnt,avx,avx2,avx512f,avx512bw,avx512vl,avx512vbmi,avx512vbmi2\"))),apply_to=function)")
 #   define BEGIN_AVX512VBMI_SPECIFIC_CODE \
@@ -197,6 +201,14 @@ namespace TargetSpecific::AVX512VBMI2 { \
 } \
 END_TARGET_SPECIFIC_CODE
 
+#define DECLARE_AVX512BF16_SPECIFIC_CODE(...) \
+BEGIN_AVX512BF16_SPECIFIC_CODE \
+namespace TargetSpecific::AVX512BF16 { \
+    DUMMY_FUNCTION_DEFINITION \
+    using namespace DB::TargetSpecific::AVX512BF16; \
+    __VA_ARGS__ \
+} \
+END_TARGET_SPECIFIC_CODE
 
 #else
 
@@ -211,6 +223,7 @@ END_TARGET_SPECIFIC_CODE
 #define DECLARE_AVX512BW_SPECIFIC_CODE(...)
 #define DECLARE_AVX512VBMI_SPECIFIC_CODE(...)
 #define DECLARE_AVX512VBMI2_SPECIFIC_CODE(...)
+#define DECLARE_AVX512BF16_SPECIFIC_CODE(...)
 
 #endif
 
@@ -229,7 +242,8 @@ DECLARE_AVX2_SPECIFIC_CODE   (__VA_ARGS__) \
 DECLARE_AVX512F_SPECIFIC_CODE(__VA_ARGS__) \
 DECLARE_AVX512BW_SPECIFIC_CODE    (__VA_ARGS__) \
 DECLARE_AVX512VBMI_SPECIFIC_CODE  (__VA_ARGS__) \
-DECLARE_AVX512VBMI2_SPECIFIC_CODE (__VA_ARGS__)
+DECLARE_AVX512VBMI2_SPECIFIC_CODE (__VA_ARGS__) \
+DECLARE_AVX512BF16_SPECIFIC_CODE (__VA_ARGS__)
 
 DECLARE_DEFAULT_CODE(
     constexpr auto BuildArch = TargetArch::Default; /// NOLINT
@@ -263,6 +277,10 @@ DECLARE_AVX512VBMI2_SPECIFIC_CODE(
     constexpr auto BuildArch = TargetArch::AVX512VBMI2; /// NOLINT
 ) // DECLARE_AVX512VBMI2_SPECIFIC_CODE
 
+DECLARE_AVX512BF16_SPECIFIC_CODE(
+    constexpr auto BuildArch = TargetArch::AVX512BF16; /// NOLINT
+) // DECLARE_AVX512BF16_SPECIFIC_CODE
+
 /** Runtime Dispatch helpers for class members.
   *
   * Example of usage:

src/Common/findExtreme.cpp

@@ -47,7 +47,7 @@ MULTITARGET_FUNCTION_AVX2_SSE42(
 
         /// Unroll the loop manually for floating point, since the compiler doesn't do it without fastmath
         /// as it might change the return value
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
         {
             constexpr size_t unroll_block = 512 / sizeof(T); /// Chosen via benchmarks with AVX2 so YMMV
             size_t unrolled_end = i + (((count - i) / unroll_block) * unroll_block);

src/Common/transformEndianness.h

@@ -38,7 +38,7 @@ inline void transformEndianness(T & x)
 }
 
 template <std::endian ToEndian, std::endian FromEndian = std::endian::native, typename T>
-requires std::is_floating_point_v<T>
+requires is_floating_point<T>
 inline void transformEndianness(T & value)
 {
     if constexpr (ToEndian != FromEndian)

src/Core/AccurateComparison.h

@@ -25,7 +25,7 @@ bool lessOp(A a, B b)
         return a < b;
 
     /// float vs float
-    if constexpr (std::is_floating_point_v<A> && std::is_floating_point_v<B>)
+    if constexpr (is_floating_point<A> && is_floating_point<B>)
         return a < b;
 
     /// anything vs NaN
@@ -49,7 +49,7 @@ bool lessOp(A a, B b)
     }
 
     /// int vs float
-    if constexpr (is_integer<A> && std::is_floating_point_v<B>)
+    if constexpr (is_integer<A> && is_floating_point<B>)
     {
         if constexpr (sizeof(A) <= 4)
             return static_cast<double>(a) < static_cast<double>(b);
@@ -57,7 +57,7 @@ bool lessOp(A a, B b)
         return DecomposedFloat<B>(b).greater(a);
     }
 
-    if constexpr (std::is_floating_point_v<A> && is_integer<B>)
+    if constexpr (is_floating_point<A> && is_integer<B>)
     {
         if constexpr (sizeof(B) <= 4)
             return static_cast<double>(a) < static_cast<double>(b);
@@ -65,8 +65,8 @@ bool lessOp(A a, B b)
         return DecomposedFloat<A>(a).less(b);
     }
 
-    static_assert(is_integer<A> || std::is_floating_point_v<A>);
-    static_assert(is_integer<B> || std::is_floating_point_v<B>);
+    static_assert(is_integer<A> || is_floating_point<A>);
+    static_assert(is_integer<B> || is_floating_point<B>);
     UNREACHABLE();
 }
 
@@ -101,7 +101,7 @@ bool equalsOp(A a, B b)
         return a == b;
 
     /// float vs float
-    if constexpr (std::is_floating_point_v<A> && std::is_floating_point_v<B>)
+    if constexpr (is_floating_point<A> && is_floating_point<B>)
         return a == b;
 
     /// anything vs NaN
@@ -125,7 +125,7 @@ bool equalsOp(A a, B b)
     }
 
     /// int vs float
-    if constexpr (is_integer<A> && std::is_floating_point_v<B>)
+    if constexpr (is_integer<A> && is_floating_point<B>)
     {
         if constexpr (sizeof(A) <= 4)
             return static_cast<double>(a) == static_cast<double>(b);
@@ -133,7 +133,7 @@ bool equalsOp(A a, B b)
         return DecomposedFloat<B>(b).equals(a);
     }
 
-    if constexpr (std::is_floating_point_v<A> && is_integer<B>)
+    if constexpr (is_floating_point<A> && is_integer<B>)
     {
         if constexpr (sizeof(B) <= 4)
             return static_cast<double>(a) == static_cast<double>(b);
@@ -163,7 +163,7 @@ inline bool NO_SANITIZE_UNDEFINED convertNumeric(From value, To & result)
         return true;
     }
 
-    if constexpr (std::is_floating_point_v<From> && std::is_floating_point_v<To>)
+    if constexpr (is_floating_point<From> && is_floating_point<To>)
     {
         /// Note that NaNs doesn't compare equal to anything, but they are still in range of any Float type.
         if (isNaN(value))

src/Core/DecimalFunctions.h

@@ -17,6 +17,7 @@ class DataTypeNumber;
 
 namespace ErrorCodes
 {
+    extern const int NOT_IMPLEMENTED;
     extern const int DECIMAL_OVERFLOW;
     extern const int ARGUMENT_OUT_OF_BOUND;
 }
@@ -310,7 +311,14 @@ ReturnType convertToImpl(const DecimalType & decimal, UInt32 scale, To & result)
     using DecimalNativeType = typename DecimalType::NativeType;
     static constexpr bool throw_exception = std::is_void_v<ReturnType>;
 
-    if constexpr (std::is_floating_point_v<To>)
+    if constexpr (std::is_same_v<To, BFloat16>)
+    {
+        if constexpr (throw_exception)
+            throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Conversion from Decimal to BFloat16 is not implemented");
+        else
+            return ReturnType(false);
+    }
+    else if constexpr (is_floating_point<To>)
     {
         result = static_cast<To>(decimal.value) / static_cast<To>(scaleMultiplier<DecimalNativeType>(scale));
     }

src/Core/Field.h

@@ -257,6 +257,7 @@ template <> struct NearestFieldTypeImpl<DecimalField<Decimal64>> { using Type =
 template <> struct NearestFieldTypeImpl<DecimalField<Decimal128>> { using Type = DecimalField<Decimal128>; };
 template <> struct NearestFieldTypeImpl<DecimalField<Decimal256>> { using Type = DecimalField<Decimal256>; };
 template <> struct NearestFieldTypeImpl<DecimalField<DateTime64>> { using Type = DecimalField<DateTime64>; };
+template <> struct NearestFieldTypeImpl<BFloat16> { using Type = Float64; };
 template <> struct NearestFieldTypeImpl<Float32> { using Type = Float64; };
 template <> struct NearestFieldTypeImpl<Float64> { using Type = Float64; };
 template <> struct NearestFieldTypeImpl<const char *> { using Type = String; };

src/Core/Settings.cpp

@@ -5742,7 +5742,10 @@ Enable experimental functions for natural language processing.
 Enable experimental hash functions
 )", EXPERIMENTAL) \
     DECLARE(Bool, allow_experimental_object_type, false, R"(
-Allow Object and JSON data types
+Allow the obsolete Object data type
+)", EXPERIMENTAL) \
+    DECLARE(Bool, allow_experimental_bfloat16_type, false, R"(
+Allow BFloat16 data type (under development).
 )", EXPERIMENTAL) \
     DECLARE(Bool, allow_experimental_time_series_table, false, R"(
 Allows creation of tables with the [TimeSeries](../../engines/table-engines/integrations/time-series.md) table engine.

src/Core/SettingsChangesHistory.cpp

@@ -78,6 +78,7 @@ static std::initializer_list<std::pair<ClickHouseVersion, SettingsChangesHistory
             {"backup_restore_keeper_max_retries_while_handling_error", 0, 20, "New setting."},
             {"backup_restore_finish_timeout_after_error_sec", 0, 180, "New setting."},
             {"parallel_replicas_local_plan", false, true, "Use local plan for local replica in a query with parallel replicas"},
+            {"allow_experimental_bfloat16_type", false, false, "Add new experimental BFloat16 type"},
             {"filesystem_cache_skip_download_if_exceeds_per_query_cache_write_limit", 1, 1, "Rename of setting skip_download_if_exceeds_query_cache_limit"},
             {"filesystem_cache_prefer_bigger_buffer_size", true, true, "New setting"},
             {"read_in_order_use_virtual_row", false, false, "Use virtual row while reading in order of primary key or its monotonic function fashion. It is useful when searching over multiple parts as only relevant ones are touched."},

src/Core/SortCursor.h

@@ -726,6 +726,7 @@ private:
         SortingQueueImpl<SpecializedSingleColumnSortCursor<ColumnVector<Int128>>, strategy>,
         SortingQueueImpl<SpecializedSingleColumnSortCursor<ColumnVector<Int256>>, strategy>,
 
+        SortingQueueImpl<SpecializedSingleColumnSortCursor<ColumnVector<BFloat16>>, strategy>,
         SortingQueueImpl<SpecializedSingleColumnSortCursor<ColumnVector<Float32>>, strategy>,
         SortingQueueImpl<SpecializedSingleColumnSortCursor<ColumnVector<Float64>>, strategy>,
 

src/Core/TypeId.h

@@ -21,6 +21,7 @@ enum class TypeIndex : uint8_t
     Int64,
     Int128,
     Int256,
+    BFloat16,
     Float32,
     Float64,
     Date,
@@ -94,6 +95,7 @@ TYPEID_MAP(Int32)
 TYPEID_MAP(Int64)
 TYPEID_MAP(Int128)
 TYPEID_MAP(Int256)
+TYPEID_MAP(BFloat16)
 TYPEID_MAP(Float32)
 TYPEID_MAP(Float64)
 TYPEID_MAP(UUID)

src/Core/Types_fwd.h

@@ -21,6 +21,7 @@ using Int128 = wide::integer<128, signed>;
 using UInt128 = wide::integer<128, unsigned>;
 using Int256 = wide::integer<256, signed>;
 using UInt256 = wide::integer<256, unsigned>;
+class BFloat16;
 
 namespace DB
 {

src/Core/callOnTypeIndex.h

@@ -63,6 +63,7 @@ static bool callOnBasicType(TypeIndex number, F && f)
     {
         switch (number)
         {
+            case TypeIndex::BFloat16:     return f(TypePair<T, BFloat16>());
             case TypeIndex::Float32:      return f(TypePair<T, Float32>());
             case TypeIndex::Float64:      return f(TypePair<T, Float64>());
             default:
@@ -133,6 +134,7 @@ static inline bool callOnBasicTypes(TypeIndex type_num1, TypeIndex type_num2, F
     {
         switch (type_num1)
         {
+            case TypeIndex::BFloat16: return callOnBasicType<BFloat16, _int, _float, _decimal, _datetime>(type_num2, std::forward<F>(f));
             case TypeIndex::Float32: return callOnBasicType<Float32, _int, _float, _decimal, _datetime>(type_num2, std::forward<F>(f));
             case TypeIndex::Float64: return callOnBasicType<Float64, _int, _float, _decimal, _datetime>(type_num2, std::forward<F>(f));
             default:
@@ -190,6 +192,7 @@ static bool callOnIndexAndDataType(TypeIndex number, F && f, ExtraArgs && ... ar
         case TypeIndex::Int128:         return f(TypePair<DataTypeNumber<Int128>, T>(), std::forward<ExtraArgs>(args)...);
         case TypeIndex::Int256:         return f(TypePair<DataTypeNumber<Int256>, T>(), std::forward<ExtraArgs>(args)...);
 
+        case TypeIndex::BFloat16:        return f(TypePair<DataTypeNumber<BFloat16>, T>(), std::forward<ExtraArgs>(args)...);
         case TypeIndex::Float32:        return f(TypePair<DataTypeNumber<Float32>, T>(), std::forward<ExtraArgs>(args)...);
         case TypeIndex::Float64:        return f(TypePair<DataTypeNumber<Float64>, T>(), std::forward<ExtraArgs>(args)...);
 

src/DataTypes/DataTypeNumberBase.cpp

@@ -42,6 +42,7 @@ template class DataTypeNumberBase<Int32>;
 template class DataTypeNumberBase<Int64>;
 template class DataTypeNumberBase<Int128>;
 template class DataTypeNumberBase<Int256>;
+template class DataTypeNumberBase<BFloat16>;
 template class DataTypeNumberBase<Float32>;
 template class DataTypeNumberBase<Float64>;
 

src/DataTypes/DataTypeNumberBase.h

@@ -68,6 +68,7 @@ extern template class DataTypeNumberBase<Int32>;
 extern template class DataTypeNumberBase<Int64>;
 extern template class DataTypeNumberBase<Int128>;
 extern template class DataTypeNumberBase<Int256>;
+extern template class DataTypeNumberBase<BFloat16>;
 extern template class DataTypeNumberBase<Float32>;
 extern template class DataTypeNumberBase<Float64>;
 

src/DataTypes/DataTypesBinaryEncoding.cpp

@@ -96,6 +96,7 @@ enum class BinaryTypeIndex : uint8_t
     SimpleAggregateFunction = 0x2E,
     Nested = 0x2F,
     JSON = 0x30,
+    BFloat16 = 0x31,
 };
 
 /// In future we can introduce more arguments in the JSON data type definition.
@@ -151,6 +152,8 @@ BinaryTypeIndex getBinaryTypeIndex(const DataTypePtr & type)
             return BinaryTypeIndex::Int128;
         case TypeIndex::Int256:
             return BinaryTypeIndex::Int256;
+        case TypeIndex::BFloat16:
+            return BinaryTypeIndex::BFloat16;
         case TypeIndex::Float32:
             return BinaryTypeIndex::Float32;
         case TypeIndex::Float64:
@@ -565,6 +568,8 @@ DataTypePtr decodeDataType(ReadBuffer & buf)
             return std::make_shared<DataTypeInt128>();
         case BinaryTypeIndex::Int256:
             return std::make_shared<DataTypeInt256>();
+        case BinaryTypeIndex::BFloat16:
+            return std::make_shared<DataTypeBFloat16>();
         case BinaryTypeIndex::Float32:
             return std::make_shared<DataTypeFloat32>();
         case BinaryTypeIndex::Float64:

src/DataTypes/DataTypesDecimal.cpp

@@ -2,6 +2,7 @@
 #include <DataTypes/Serializations/SerializationDecimal.h>
 
 #include <Common/typeid_cast.h>
+#include <Common/NaNUtils.h>
 #include <Core/DecimalFunctions.h>
 #include <DataTypes/DataTypeFactory.h>
 #include <IO/ReadHelpers.h>
@@ -19,6 +20,7 @@ namespace ErrorCodes
     extern const int NUMBER_OF_ARGUMENTS_DOESNT_MATCH;
     extern const int ILLEGAL_TYPE_OF_ARGUMENT;
     extern const int DECIMAL_OVERFLOW;
+    extern const int NOT_IMPLEMENTED;
 }
 
 
@@ -268,9 +270,13 @@ ReturnType convertToDecimalImpl(const typename FromDataType::FieldType & value,
 
     static constexpr bool throw_exception = std::is_same_v<ReturnType, void>;
 
-    if constexpr (std::is_floating_point_v<FromFieldType>)
+    if constexpr (std::is_same_v<typename FromDataType::FieldType, BFloat16>)
     {
-        if (!std::isfinite(value))
+        throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Conversion from BFloat16 to Decimal is not implemented");
+    }
+    else if constexpr (is_floating_point<FromFieldType>)
+    {
+        if (!isFinite(value))
         {
             if constexpr (throw_exception)
                 throw Exception(ErrorCodes::DECIMAL_OVERFLOW, "{} convert overflow. Cannot convert infinity or NaN to decimal", ToDataType::family_name);

src/DataTypes/DataTypesDecimal.h

@@ -4,7 +4,6 @@
 #include <base/extended_types.h>
 #include <Common/typeid_cast.h>
 #include <base/Decimal.h>
-#include <base/Decimal_fwd.h>
 #include <DataTypes/IDataType.h>
 #include <DataTypes/DataTypeDate.h>
 #include <DataTypes/DataTypeDate32.h>
@@ -205,7 +204,6 @@ FOR_EACH_DECIMAL_TYPE(INVOKE);
 #undef INVOKE
 #undef DISPATCH
 
-
 template <typename FromDataType, typename ToDataType>
 requires (is_arithmetic_v<typename FromDataType::FieldType> && IsDataTypeDecimal<ToDataType>)
 typename ToDataType::FieldType convertToDecimal(const typename FromDataType::FieldType & value, UInt32 scale);

src/DataTypes/DataTypesNumber.cpp

@@ -54,6 +54,7 @@ void registerDataTypeNumbers(DataTypeFactory & factory)
     factory.registerDataType("Int32", createNumericDataType<Int32>);
     factory.registerDataType("Int64", createNumericDataType<Int64>);
 
+    factory.registerDataType("BFloat16", createNumericDataType<BFloat16>);
     factory.registerDataType("Float32", createNumericDataType<Float32>);
     factory.registerDataType("Float64", createNumericDataType<Float64>);
 
@@ -111,6 +112,7 @@ template class DataTypeNumber<Int8>;
 template class DataTypeNumber<Int16>;
 template class DataTypeNumber<Int32>;
 template class DataTypeNumber<Int64>;
+template class DataTypeNumber<BFloat16>;
 template class DataTypeNumber<Float32>;
 template class DataTypeNumber<Float64>;
 

src/DataTypes/DataTypesNumber.h

@@ -63,6 +63,7 @@ extern template class DataTypeNumber<Int8>;
 extern template class DataTypeNumber<Int16>;
 extern template class DataTypeNumber<Int32>;
 extern template class DataTypeNumber<Int64>;
+extern template class DataTypeNumber<BFloat16>;
 extern template class DataTypeNumber<Float32>;
 extern template class DataTypeNumber<Float64>;
 
@@ -79,6 +80,7 @@ using DataTypeInt8 = DataTypeNumber<Int8>;
 using DataTypeInt16 = DataTypeNumber<Int16>;
 using DataTypeInt32 = DataTypeNumber<Int32>;
 using DataTypeInt64 = DataTypeNumber<Int64>;
+using DataTypeBFloat16 = DataTypeNumber<BFloat16>;
 using DataTypeFloat32 = DataTypeNumber<Float32>;
 using DataTypeFloat64 = DataTypeNumber<Float64>;
 

src/DataTypes/IDataType.h

@@ -408,9 +408,11 @@ struct WhichDataType
     constexpr bool isDecimal256() const { return idx == TypeIndex::Decimal256; }
     constexpr bool isDecimal() const { return isDecimal32() || isDecimal64() || isDecimal128() || isDecimal256(); }
 
+    constexpr bool isBFloat16() const { return idx == TypeIndex::BFloat16; }
     constexpr bool isFloat32() const { return idx == TypeIndex::Float32; }
     constexpr bool isFloat64() const { return idx == TypeIndex::Float64; }
-    constexpr bool isFloat() const { return isFloat32() || isFloat64(); }
+    constexpr bool isNativeFloat() const { return isFloat32() || isFloat64(); }
+    constexpr bool isFloat() const { return isNativeFloat() || isBFloat16(); }
 
     constexpr bool isNativeNumber() const { return isNativeInteger() || isFloat(); }
     constexpr bool isNumber() const { return isInteger() || isFloat() || isDecimal(); }
@@ -621,6 +623,7 @@ template <typename T> inline constexpr bool IsDataTypeEnum<DataTypeEnum<T>> = tr
     M(Int64) \
     M(Int128) \
     M(Int256) \
+    M(BFloat16) \
     M(Float32) \
     M(Float64)
 }

src/DataTypes/Native.cpp

@@ -37,7 +37,7 @@ bool canBeNativeType(const IDataType & type)
         return canBeNativeType(*data_type_nullable.getNestedType());
     }
 
-    return data_type.isNativeInt() || data_type.isNativeUInt() || data_type.isFloat() || data_type.isDate()
+    return data_type.isNativeInt() || data_type.isNativeUInt() || data_type.isNativeFloat() || data_type.isDate()
         || data_type.isDate32() || data_type.isDateTime() || data_type.isEnum();
 }
 

src/DataTypes/NumberTraits.h

@@ -74,7 +74,7 @@ template <typename A, typename B> struct ResultOfAdditionMultiplication
 {
     using Type = typename Construct<
         is_signed_v<A> || is_signed_v<B>,
-        std::is_floating_point_v<A> || std::is_floating_point_v<B>,
+        is_floating_point<A> || is_floating_point<B>,
         nextSize(max(sizeof(A), sizeof(B)))>::Type;
 };
 
@@ -82,7 +82,7 @@ template <typename A, typename B> struct ResultOfSubtraction
 {
     using Type = typename Construct<
         true,
-        std::is_floating_point_v<A> || std::is_floating_point_v<B>,
+        is_floating_point<A> || is_floating_point<B>,
         nextSize(max(sizeof(A), sizeof(B)))>::Type;
 };
 
@@ -113,7 +113,7 @@ template <typename A, typename B> struct ResultOfModulo
     /// Example: toInt32(-199) % toUInt8(200) will return -199 that does not fit in Int8, only in Int16.
     static constexpr size_t size_of_result = result_is_signed ? nextSize(sizeof(B)) : sizeof(B);
     using Type0 = typename Construct<result_is_signed, false, size_of_result>::Type;
-    using Type = std::conditional_t<std::is_floating_point_v<A> || std::is_floating_point_v<B>, Float64, Type0>;
+    using Type = std::conditional_t<is_floating_point<A> || is_floating_point<B>, Float64, Type0>;
 };
 
 template <typename A, typename B> struct ResultOfPositiveModulo
@@ -121,21 +121,21 @@ template <typename A, typename B> struct ResultOfPositiveModulo
     /// function positive_modulo always return non-negative number.
     static constexpr size_t size_of_result = sizeof(B);
     using Type0 = typename Construct<false, false, size_of_result>::Type;
-    using Type = std::conditional_t<std::is_floating_point_v<A> || std::is_floating_point_v<B>, Float64, Type0>;
+    using Type = std::conditional_t<is_floating_point<A> || is_floating_point<B>, Float64, Type0>;
 };
 
 
 template <typename A, typename B> struct ResultOfModuloLegacy
 {
     using Type0 = typename Construct<is_signed_v<A> || is_signed_v<B>, false, sizeof(B)>::Type;
-    using Type = std::conditional_t<std::is_floating_point_v<A> || std::is_floating_point_v<B>, Float64, Type0>;
+    using Type = std::conditional_t<is_floating_point<A> || is_floating_point<B>, Float64, Type0>;
 };
 
 template <typename A> struct ResultOfNegate
 {
     using Type = typename Construct<
         true,
-        std::is_floating_point_v<A>,
+        is_floating_point<A>,
         is_signed_v<A> ? sizeof(A) : nextSize(sizeof(A))>::Type;
 };
 
@@ -143,7 +143,7 @@ template <typename A> struct ResultOfAbs
 {
     using Type = typename Construct<
         false,
-        std::is_floating_point_v<A>,
+        is_floating_point<A>,
         sizeof(A)>::Type;
 };
 
@@ -154,7 +154,7 @@ template <typename A, typename B> struct ResultOfBit
     using Type = typename Construct<
         is_signed_v<A> || is_signed_v<B>,
         false,
-        std::is_floating_point_v<A> || std::is_floating_point_v<B> ? 8 : max(sizeof(A), sizeof(B))>::Type;
+        is_floating_point<A> || is_floating_point<B> ? 8 : max(sizeof(A), sizeof(B))>::Type;
 };
 
 template <typename A> struct ResultOfBitNot
@@ -180,7 +180,7 @@ template <typename A> struct ResultOfBitNot
 template <typename A, typename B>
 struct ResultOfIf
 {
-    static constexpr bool has_float = std::is_floating_point_v<A> || std::is_floating_point_v<B>;
+    static constexpr bool has_float = is_floating_point<A> || is_floating_point<B>;
     static constexpr bool has_integer = is_integer<A> || is_integer<B>;
     static constexpr bool has_signed = is_signed_v<A> || is_signed_v<B>;
     static constexpr bool has_unsigned = !is_signed_v<A> || !is_signed_v<B>;
@@ -189,7 +189,7 @@ struct ResultOfIf
     static constexpr size_t max_size_of_unsigned_integer = max(is_signed_v<A> ? 0 : sizeof(A), is_signed_v<B> ? 0 : sizeof(B));
     static constexpr size_t max_size_of_signed_integer = max(is_signed_v<A> ? sizeof(A) : 0, is_signed_v<B> ? sizeof(B) : 0);
     static constexpr size_t max_size_of_integer = max(is_integer<A> ? sizeof(A) : 0, is_integer<B> ? sizeof(B) : 0);
-    static constexpr size_t max_size_of_float = max(std::is_floating_point_v<A> ? sizeof(A) : 0, std::is_floating_point_v<B> ? sizeof(B) : 0);
+    static constexpr size_t max_size_of_float = max(is_floating_point<A> ? sizeof(A) : 0, is_floating_point<B> ? sizeof(B) : 0);
 
     using ConstructedType = typename Construct<has_signed, has_float,
         ((has_float && has_integer && max_size_of_integer >= max_size_of_float)
@@ -211,7 +211,7 @@ template <typename A> struct ToInteger
     using Type = typename Construct<
         is_signed_v<A>,
         false,
-        std::is_floating_point_v<A> ? 8 : sizeof(A)>::Type;
+        is_floating_point<A> ? 8 : sizeof(A)>::Type;
 };
 
 

src/DataTypes/Serializations/SerializationNumber.cpp

@@ -238,6 +238,7 @@ template class SerializationNumber<Int32>;
 template class SerializationNumber<Int64>;
 template class SerializationNumber<Int128>;
 template class SerializationNumber<Int256>;
+template class SerializationNumber<BFloat16>;
 template class SerializationNumber<Float32>;
 template class SerializationNumber<Float64>;
 

src/DataTypes/Utils.cpp

@@ -54,6 +54,13 @@ bool canBeSafelyCasted(const DataTypePtr & from_type, const DataTypePtr & to_typ
 
             return false;
         }
+        case TypeIndex::BFloat16:
+        {
+            if (to_which_type.isFloat32() || to_which_type.isFloat64() || to_which_type.isString())
+                return true;
+
+            return false;
+        }
         case TypeIndex::Float32:
         {
             if (to_which_type.isFloat64() || to_which_type.isString())

src/DataTypes/getLeastSupertype.cpp

@@ -109,6 +109,8 @@ DataTypePtr getNumericType(const TypeIndexSet & types)
             maximize(max_bits_of_signed_integer, 128);
         else if (type == TypeIndex::Int256)
             maximize(max_bits_of_signed_integer, 256);
+        else if (type == TypeIndex::BFloat16)
+            maximize(max_mantissa_bits_of_floating, 8);
         else if (type == TypeIndex::Float32)
             maximize(max_mantissa_bits_of_floating, 24);
         else if (type == TypeIndex::Float64)
@@ -145,7 +147,9 @@ DataTypePtr getNumericType(const TypeIndexSet & types)
         if (max_mantissa_bits_of_floating)
         {
             size_t min_mantissa_bits = std::max(min_bit_width_of_integer, max_mantissa_bits_of_floating);
-            if (min_mantissa_bits <= 24)
+            if (min_mantissa_bits <= 8)
+                return std::make_shared<DataTypeBFloat16>();
+            else if (min_mantissa_bits <= 24)
                 return std::make_shared<DataTypeFloat32>();
             if (min_mantissa_bits <= 53)
                 return std::make_shared<DataTypeFloat64>();

src/DataTypes/getMostSubtype.cpp

@@ -297,6 +297,8 @@ DataTypePtr getMostSubtype(const DataTypes & types, bool throw_if_result_is_noth
                 minimize(min_bits_of_signed_integer, 128);
             else if (typeid_cast<const DataTypeInt256 *>(type.get()))
                 minimize(min_bits_of_signed_integer, 256);
+            else if (typeid_cast<const DataTypeBFloat16 *>(type.get()))
+                minimize(min_mantissa_bits_of_floating, 8);
             else if (typeid_cast<const DataTypeFloat32 *>(type.get()))
                 minimize(min_mantissa_bits_of_floating, 24);
             else if (typeid_cast<const DataTypeFloat64 *>(type.get()))
@@ -313,7 +315,9 @@ DataTypePtr getMostSubtype(const DataTypes & types, bool throw_if_result_is_noth
             /// If the result must be floating.
             if (!min_bits_of_signed_integer && !min_bits_of_unsigned_integer)
             {
-                if (min_mantissa_bits_of_floating <= 24)
+                if (min_mantissa_bits_of_floating <= 8)
+                    return std::make_shared<DataTypeBFloat16>();
+                else if (min_mantissa_bits_of_floating <= 24)
                     return std::make_shared<DataTypeFloat32>();
                 if (min_mantissa_bits_of_floating <= 53)
                     return std::make_shared<DataTypeFloat64>();

src/Databases/enableAllExperimentalSettings.cpp

@@ -24,10 +24,11 @@ void enableAllExperimentalSettings(ContextMutablePtr context)
     context->setSetting("allow_experimental_dynamic_type", 1);
     context->setSetting("allow_experimental_json_type", 1);
     context->setSetting("allow_experimental_vector_similarity_index", 1);
-    context->setSetting("allow_experimental_bigint_types", 1);
     context->setSetting("allow_experimental_window_functions", 1);
     context->setSetting("allow_experimental_geo_types", 1);
     context->setSetting("allow_experimental_map_type", 1);
+    context->setSetting("allow_experimental_bigint_types", 1);
+    context->setSetting("allow_experimental_bfloat16_type", 1);
     context->setSetting("allow_deprecated_error_prone_window_functions", 1);
 
     context->setSetting("allow_suspicious_low_cardinality_types", 1);

src/Dictionaries/RangeHashedDictionary.h

@@ -298,7 +298,8 @@ namespace impl
             using Types = std::decay_t<decltype(types)>;
             using DataType = typename Types::LeftType;
 
-            if constexpr (IsDataTypeDecimalOrNumber<DataType> || IsDataTypeDateOrDateTime<DataType> || IsDataTypeEnum<DataType>)
+            if constexpr ((IsDataTypeDecimalOrNumber<DataType> || IsDataTypeDateOrDateTime<DataType> || IsDataTypeEnum<DataType>)
+                && !std::is_same_v<DataType, DataTypeBFloat16>)
             {
                 using ColumnType = typename DataType::ColumnType;
                 func(TypePair<ColumnType, void>());

src/Formats/JSONExtractTree.cpp

@@ -131,7 +131,7 @@ bool tryGetNumericValueFromJSONElement(
     switch (element.type())
     {
         case ElementType::DOUBLE:
-            if constexpr (std::is_floating_point_v<NumberType>)
+            if constexpr (is_floating_point<NumberType>)
             {
                 /// We permit inaccurate conversion of double to float.
                 /// Example: double 0.1 from JSON is not representable in float.
@@ -175,7 +175,7 @@ bool tryGetNumericValueFromJSONElement(
                 return false;
 
             auto rb = ReadBufferFromMemory{element.getString()};
-            if constexpr (std::is_floating_point_v<NumberType>)
+            if constexpr (is_floating_point<NumberType>)
             {
                 if (!tryReadFloatText(value, rb) || !rb.eof())
                 {

src/Formats/ProtobufSerializer.cpp

@@ -540,7 +540,7 @@ namespace
 
                 case FieldTypeId::TYPE_ENUM:
                 {
-                    if (std::is_floating_point_v<NumberType>)
+                    if (is_floating_point<NumberType>)
                         incompatibleColumnType(TypeName<NumberType>);
 
                     write_function = [this](NumberType value)

src/Functions/DivisionUtils.h

@@ -47,9 +47,9 @@ inline auto checkedDivision(A a, B b)
 {
     throwIfDivisionLeadsToFPE(a, b);
 
-    if constexpr (is_big_int_v<A> && std::is_floating_point_v<B>)
+    if constexpr (is_big_int_v<A> && is_floating_point<B>)
         return static_cast<B>(a) / b;
-    else if constexpr (is_big_int_v<B> && std::is_floating_point_v<A>)
+    else if constexpr (is_big_int_v<B> && is_floating_point<A>)
         return a / static_cast<A>(b);
     else if constexpr (is_big_int_v<A> && is_big_int_v<B>)
         return static_cast<A>(a / b);
@@ -86,17 +86,17 @@ struct DivideIntegralImpl
         {
             /// Comparisons are not strict to avoid rounding issues when operand is implicitly casted to float.
 
-            if constexpr (std::is_floating_point_v<A>)
+            if constexpr (is_floating_point<A>)
                 if (isNaN(a) || a >= std::numeric_limits<CastA>::max() || a <= std::numeric_limits<CastA>::lowest())
                     throw Exception(ErrorCodes::ILLEGAL_DIVISION, "Cannot perform integer division on infinite or too large floating point numbers");
 
-            if constexpr (std::is_floating_point_v<B>)
+            if constexpr (is_floating_point<B>)
                 if (isNaN(b) || b >= std::numeric_limits<CastB>::max() || b <= std::numeric_limits<CastB>::lowest())
                     throw Exception(ErrorCodes::ILLEGAL_DIVISION, "Cannot perform integer division on infinite or too large floating point numbers");
 
             auto res = checkedDivision(CastA(a), CastB(b));
 
-            if constexpr (std::is_floating_point_v<decltype(res)>)
+            if constexpr (is_floating_point<decltype(res)>)
                 if (isNaN(res) || res >= static_cast<double>(std::numeric_limits<Result>::max()) || res <= std::numeric_limits<Result>::lowest())
                     throw Exception(ErrorCodes::ILLEGAL_DIVISION, "Cannot perform integer division, because it will produce infinite or too large number");
 
@@ -122,18 +122,18 @@ struct ModuloImpl
     template <typename Result = ResultType>
     static Result apply(A a, B b)
     {
-        if constexpr (std::is_floating_point_v<ResultType>)
+        if constexpr (is_floating_point<ResultType>)
         {
             /// This computation is similar to `fmod` but the latter is not inlined and has 40 times worse performance.
             return static_cast<ResultType>(a) - trunc(static_cast<ResultType>(a) / static_cast<ResultType>(b)) * static_cast<ResultType>(b);
         }
         else
         {
-            if constexpr (std::is_floating_point_v<A>)
+            if constexpr (is_floating_point<A>)
                 if (isNaN(a) || a > std::numeric_limits<IntegerAType>::max() || a < std::numeric_limits<IntegerAType>::lowest())
                     throw Exception(ErrorCodes::ILLEGAL_DIVISION, "Cannot perform integer division on infinite or too large floating point numbers");
 
-            if constexpr (std::is_floating_point_v<B>)
+            if constexpr (is_floating_point<B>)
                 if (isNaN(b) || b > std::numeric_limits<IntegerBType>::max() || b < std::numeric_limits<IntegerBType>::lowest())
                     throw Exception(ErrorCodes::ILLEGAL_DIVISION, "Cannot perform integer division on infinite or too large floating point numbers");
 

src/Functions/FunctionBinaryArithmetic.h

@@ -110,6 +110,7 @@ template <typename DataType> constexpr bool IsIntegralOrExtendedOrDecimal =
     IsDataTypeDecimal<DataType>;
 
 template <typename DataType> constexpr bool IsFloatingPoint = false;
+template <> inline constexpr bool IsFloatingPoint<DataTypeBFloat16> = true;
 template <> inline constexpr bool IsFloatingPoint<DataTypeFloat32> = true;
 template <> inline constexpr bool IsFloatingPoint<DataTypeFloat64> = true;
 
@@ -803,7 +804,7 @@ class FunctionBinaryArithmetic : public IFunction
             DataTypeFixedString, DataTypeString,
             DataTypeInterval>;
 
-        using Floats = TypeList<DataTypeFloat32, DataTypeFloat64>;
+        using Floats = TypeList<DataTypeFloat32, DataTypeFloat64, DataTypeBFloat16>;
 
         using ValidTypes = std::conditional_t<valid_on_float_arguments,
             TypeListConcat<Types, Floats>,
@@ -1690,6 +1691,13 @@ public:
             }
             else
             {
+                if constexpr ((std::is_same_v<LeftDataType, DataTypeBFloat16> || std::is_same_v<RightDataType, DataTypeBFloat16>)
+                    && (sizeof(typename LeftDataType::FieldType) > 8 || sizeof(typename RightDataType::FieldType) > 8))
+                {
+                    /// Big integers and BFloat16 are not supported together.
+                    return false;
+                }
+
                 using ResultDataType = typename BinaryOperationTraits<Op, LeftDataType, RightDataType>::ResultDataType;
 
                 if constexpr (!std::is_same_v<ResultDataType, InvalidType>)
@@ -2042,7 +2050,15 @@ ColumnPtr executeStringInteger(const ColumnsWithTypeAndName & arguments, const A
         using DecimalResultType = typename BinaryOperationTraits<Op, LeftDataType, RightDataType>::DecimalResultDataType;
 
         if constexpr (std::is_same_v<ResultDataType, InvalidType>)
+        {
             return nullptr;
+        }
+        else if constexpr ((std::is_same_v<LeftDataType, DataTypeBFloat16> || std::is_same_v<RightDataType, DataTypeBFloat16>)
+            && (sizeof(typename LeftDataType::FieldType) > 8 || sizeof(typename RightDataType::FieldType) > 8))
+        {
+            /// Big integers and BFloat16 are not supported together.
+            return nullptr;
+        }
         else // we can't avoid the else because otherwise the compiler may assume the ResultDataType may be Invalid
              // and that would produce the compile error.
         {
@@ -2059,7 +2075,7 @@ ColumnPtr executeStringInteger(const ColumnsWithTypeAndName & arguments, const A
             ColumnPtr left_col = nullptr;
             ColumnPtr right_col = nullptr;
 
-            /// When Decimal op Float32/64, convert both of them into Float64
+            /// When Decimal op Float32/64/16, convert both of them into Float64
             if constexpr (decimal_with_float)
             {
                 const auto converted_type = std::make_shared<DataTypeFloat64>();
@@ -2094,7 +2110,6 @@ ColumnPtr executeStringInteger(const ColumnsWithTypeAndName & arguments, const A
             /// Here we check if we have `intDiv` or `intDivOrZero` and at least one of the arguments is decimal, because in this case originally we had result as decimal, so we need to convert result into integer after calculations
             else if constexpr (!decimal_with_float && (is_int_div || is_int_div_or_zero) && (IsDataTypeDecimal<LeftDataType> || IsDataTypeDecimal<RightDataType>))
             {
-
                 if constexpr (!std::is_same_v<DecimalResultType, InvalidType>)
                 {
                     DataTypePtr type_res;

src/Functions/FunctionMathUnary.h

@@ -70,7 +70,7 @@ private:
             /// Process all data as a whole and use FastOps implementation
 
             /// If the argument is integer, convert to Float64 beforehand
-            if constexpr (!std::is_floating_point_v<T>)
+            if constexpr (!is_floating_point<T>)
             {
                 PODArray<Float64> tmp_vec(size);
                 for (size_t i = 0; i < size; ++i)
@@ -152,7 +152,7 @@ private:
         {
             using Types = std::decay_t<decltype(types)>;
             using Type = typename Types::RightType;
-            using ReturnType = std::conditional_t<Impl::always_returns_float64 || !std::is_floating_point_v<Type>, Float64, Type>;
+            using ReturnType = std::conditional_t<Impl::always_returns_float64 || !is_floating_point<Type>, Float64, Type>;
             using ColVecType = ColumnVectorOrDecimal<Type>;
 
             const auto col_vec = checkAndGetColumn<ColVecType>(col.column.get());

src/Functions/FunctionsBinaryRepresentation.cpp

@@ -296,6 +296,7 @@ public:
             tryExecuteUIntOrInt<Int256>(column, res_column) ||
             tryExecuteString(column, res_column) ||
             tryExecuteFixedString(column, res_column) ||
+            tryExecuteFloat<BFloat16>(column, res_column) ||
             tryExecuteFloat<Float32>(column, res_column) ||
             tryExecuteFloat<Float64>(column, res_column) ||
             tryExecuteDecimal<Decimal32>(column, res_column) ||

src/Functions/FunctionsComparison.h

@@ -721,6 +721,7 @@ private:
                 || (res = executeNumRightType<T0, Int64>(col_left, col_right_untyped))
                 || (res = executeNumRightType<T0, Int128>(col_left, col_right_untyped))
                 || (res = executeNumRightType<T0, Int256>(col_left, col_right_untyped))
+                || (res = executeNumRightType<T0, BFloat16>(col_left, col_right_untyped))
                 || (res = executeNumRightType<T0, Float32>(col_left, col_right_untyped))
                 || (res = executeNumRightType<T0, Float64>(col_left, col_right_untyped)))
                 return res;
@@ -741,6 +742,7 @@ private:
                 || (res = executeNumConstRightType<T0, Int64>(col_left_const, col_right_untyped))
                 || (res = executeNumConstRightType<T0, Int128>(col_left_const, col_right_untyped))
                 || (res = executeNumConstRightType<T0, Int256>(col_left_const, col_right_untyped))
+                || (res = executeNumConstRightType<T0, BFloat16>(col_left_const, col_right_untyped))
                 || (res = executeNumConstRightType<T0, Float32>(col_left_const, col_right_untyped))
                 || (res = executeNumConstRightType<T0, Float64>(col_left_const, col_right_untyped)))
                 return res;
@@ -1292,9 +1294,10 @@ public:
                 || (res = executeNumLeftType<Int64>(col_left_untyped, col_right_untyped))
                 || (res = executeNumLeftType<Int128>(col_left_untyped, col_right_untyped))
                 || (res = executeNumLeftType<Int256>(col_left_untyped, col_right_untyped))
+                || (res = executeNumLeftType<BFloat16>(col_left_untyped, col_right_untyped))
                 || (res = executeNumLeftType<Float32>(col_left_untyped, col_right_untyped))
                 || (res = executeNumLeftType<Float64>(col_left_untyped, col_right_untyped))))
-                throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Illegal column {} of first argument of function {}",
+                throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Illegal column {} of the first argument of function {}",
                     col_left_untyped->getName(), getName());
 
             return res;
@@ -1342,7 +1345,7 @@ public:
                     getName(),
                     left_type->getName(),
                     right_type->getName());
-            /// When Decimal comparing to Float32/64, we convert both of them into Float64.
+            /// When Decimal comparing to Float32/64/16, we convert both of them into Float64.
             /// Other systems like MySQL and Spark also do as this.
             if (left_is_float || right_is_float)
             {

src/Functions/FunctionsConversion.cpp

@@ -7,10 +7,8 @@
 #include <Columns/ColumnFixedString.h>
 #include <Columns/ColumnLowCardinality.h>
 #include <Columns/ColumnMap.h>
-#include <Columns/ColumnNothing.h>
 #include <Columns/ColumnNullable.h>
 #include <Columns/ColumnObjectDeprecated.h>
-#include <Columns/ColumnObject.h>
 #include <Columns/ColumnString.h>
 #include <Columns/ColumnStringHelpers.h>
 #include <Columns/ColumnTuple.h>
@@ -73,8 +71,10 @@
 #include <Common/assert_cast.h>
 #include <Common/quoteString.h>
 
+
 namespace DB
 {
+
 namespace Setting
 {
     extern const SettingsBool cast_ipv4_ipv6_default_on_conversion_error;
@@ -653,7 +653,7 @@ inline void convertFromTime<DataTypeDateTime>(DataTypeDateTime::FieldType & x, t
 template <typename DataType>
 void parseImpl(typename DataType::FieldType & x, ReadBuffer & rb, const DateLUTImpl *, bool precise_float_parsing)
 {
-    if constexpr (std::is_floating_point_v<typename DataType::FieldType>)
+    if constexpr (is_floating_point<typename DataType::FieldType>)
     {
         if (precise_float_parsing)
             readFloatTextPrecise(x, rb);
@@ -717,7 +717,7 @@ inline void parseImpl<DataTypeIPv6>(DataTypeIPv6::FieldType & x, ReadBuffer & rb
 template <typename DataType>
 bool tryParseImpl(typename DataType::FieldType & x, ReadBuffer & rb, const DateLUTImpl *, bool precise_float_parsing)
 {
-    if constexpr (std::is_floating_point_v<typename DataType::FieldType>)
+    if constexpr (is_floating_point<typename DataType::FieldType>)
     {
         if (precise_float_parsing)
             return tryReadFloatTextPrecise(x, rb);
@@ -1847,7 +1847,7 @@ struct ConvertImpl
                 else
                 {
                     /// If From Data is Nan or Inf and we convert to integer type, throw exception
-                    if constexpr (std::is_floating_point_v<FromFieldType> && !std::is_floating_point_v<ToFieldType>)
+                    if constexpr (is_floating_point<FromFieldType> && !is_floating_point<ToFieldType>)
                     {
                         if (!isFinite(vec_from[i]))
                         {
@@ -2333,9 +2333,9 @@ private:
                 using RightT = typename RightDataType::FieldType;
 
                 static constexpr bool bad_left =
-                    is_decimal<LeftT> || std::is_floating_point_v<LeftT> || is_big_int_v<LeftT> || is_signed_v<LeftT>;
+                    is_decimal<LeftT> || is_floating_point<LeftT> || is_big_int_v<LeftT> || is_signed_v<LeftT>;
                 static constexpr bool bad_right =
-                    is_decimal<RightT> || std::is_floating_point_v<RightT> || is_big_int_v<RightT> || is_signed_v<RightT>;
+                    is_decimal<RightT> || is_floating_point<RightT> || is_big_int_v<RightT> || is_signed_v<RightT>;
 
                 /// Disallow int vs UUID conversion (but support int vs UInt128 conversion)
                 if constexpr ((bad_left && std::is_same_v<RightDataType, DataTypeUUID>) ||
@@ -2662,7 +2662,7 @@ struct ToNumberMonotonicity
         /// Float cases.
 
         /// When converting to Float, the conversion is always monotonic.
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
             return { .is_monotonic = true, .is_always_monotonic = true };
 
         const auto * low_cardinality = typeid_cast<const DataTypeLowCardinality *>(&type);
@@ -2875,6 +2875,7 @@ struct NameToInt32 { static constexpr auto name = "toInt32"; };
 struct NameToInt64 { static constexpr auto name = "toInt64"; };
 struct NameToInt128 { static constexpr auto name = "toInt128"; };
 struct NameToInt256 { static constexpr auto name = "toInt256"; };
+struct NameToBFloat16 { static constexpr auto name = "toBFloat16"; };
 struct NameToFloat32 { static constexpr auto name = "toFloat32"; };
 struct NameToFloat64 { static constexpr auto name = "toFloat64"; };
 struct NameToUUID { static constexpr auto name = "toUUID"; };
@@ -2893,6 +2894,7 @@ using FunctionToInt32 = FunctionConvert<DataTypeInt32, NameToInt32, ToNumberMono
 using FunctionToInt64 = FunctionConvert<DataTypeInt64, NameToInt64, ToNumberMonotonicity<Int64>>;
 using FunctionToInt128 = FunctionConvert<DataTypeInt128, NameToInt128, ToNumberMonotonicity<Int128>>;
 using FunctionToInt256 = FunctionConvert<DataTypeInt256, NameToInt256, ToNumberMonotonicity<Int256>>;
+using FunctionToBFloat16 = FunctionConvert<DataTypeBFloat16, NameToBFloat16, ToNumberMonotonicity<BFloat16>>;
 using FunctionToFloat32 = FunctionConvert<DataTypeFloat32, NameToFloat32, ToNumberMonotonicity<Float32>>;
 using FunctionToFloat64 = FunctionConvert<DataTypeFloat64, NameToFloat64, ToNumberMonotonicity<Float64>>;
 
@@ -2930,6 +2932,7 @@ template <> struct FunctionTo<DataTypeInt32> { using Type = FunctionToInt32; };
 template <> struct FunctionTo<DataTypeInt64> { using Type = FunctionToInt64; };
 template <> struct FunctionTo<DataTypeInt128> { using Type = FunctionToInt128; };
 template <> struct FunctionTo<DataTypeInt256> { using Type = FunctionToInt256; };
+template <> struct FunctionTo<DataTypeBFloat16> { using Type = FunctionToBFloat16; };
 template <> struct FunctionTo<DataTypeFloat32> { using Type = FunctionToFloat32; };
 template <> struct FunctionTo<DataTypeFloat64> { using Type = FunctionToFloat64; };
 
@@ -2972,6 +2975,7 @@ struct NameToInt32OrZero { static constexpr auto name = "toInt32OrZero"; };
 struct NameToInt64OrZero { static constexpr auto name = "toInt64OrZero"; };
 struct NameToInt128OrZero { static constexpr auto name = "toInt128OrZero"; };
 struct NameToInt256OrZero { static constexpr auto name = "toInt256OrZero"; };
+struct NameToBFloat16OrZero { static constexpr auto name = "toBFloat16OrZero"; };
 struct NameToFloat32OrZero { static constexpr auto name = "toFloat32OrZero"; };
 struct NameToFloat64OrZero { static constexpr auto name = "toFloat64OrZero"; };
 struct NameToDateOrZero { static constexpr auto name = "toDateOrZero"; };
@@ -2998,6 +3002,7 @@ using FunctionToInt32OrZero = FunctionConvertFromString<DataTypeInt32, NameToInt
 using FunctionToInt64OrZero = FunctionConvertFromString<DataTypeInt64, NameToInt64OrZero, ConvertFromStringExceptionMode::Zero>;
 using FunctionToInt128OrZero = FunctionConvertFromString<DataTypeInt128, NameToInt128OrZero, ConvertFromStringExceptionMode::Zero>;
 using FunctionToInt256OrZero = FunctionConvertFromString<DataTypeInt256, NameToInt256OrZero, ConvertFromStringExceptionMode::Zero>;
+using FunctionToBFloat16OrZero = FunctionConvertFromString<DataTypeBFloat16, NameToBFloat16OrZero, ConvertFromStringExceptionMode::Zero>;
 using FunctionToFloat32OrZero = FunctionConvertFromString<DataTypeFloat32, NameToFloat32OrZero, ConvertFromStringExceptionMode::Zero>;
 using FunctionToFloat64OrZero = FunctionConvertFromString<DataTypeFloat64, NameToFloat64OrZero, ConvertFromStringExceptionMode::Zero>;
 using FunctionToDateOrZero = FunctionConvertFromString<DataTypeDate, NameToDateOrZero, ConvertFromStringExceptionMode::Zero>;
@@ -3024,6 +3029,7 @@ struct NameToInt32OrNull { static constexpr auto name = "toInt32OrNull"; };
 struct NameToInt64OrNull { static constexpr auto name = "toInt64OrNull"; };
 struct NameToInt128OrNull { static constexpr auto name = "toInt128OrNull"; };
 struct NameToInt256OrNull { static constexpr auto name = "toInt256OrNull"; };
+struct NameToBFloat16OrNull { static constexpr auto name = "toBFloat16OrNull"; };
 struct NameToFloat32OrNull { static constexpr auto name = "toFloat32OrNull"; };
 struct NameToFloat64OrNull { static constexpr auto name = "toFloat64OrNull"; };
 struct NameToDateOrNull { static constexpr auto name = "toDateOrNull"; };
@@ -3050,6 +3056,7 @@ using FunctionToInt32OrNull = FunctionConvertFromString<DataTypeInt32, NameToInt
 using FunctionToInt64OrNull = FunctionConvertFromString<DataTypeInt64, NameToInt64OrNull, ConvertFromStringExceptionMode::Null>;
 using FunctionToInt128OrNull = FunctionConvertFromString<DataTypeInt128, NameToInt128OrNull, ConvertFromStringExceptionMode::Null>;
 using FunctionToInt256OrNull = FunctionConvertFromString<DataTypeInt256, NameToInt256OrNull, ConvertFromStringExceptionMode::Null>;
+using FunctionToBFloat16OrNull = FunctionConvertFromString<DataTypeBFloat16, NameToBFloat16OrNull, ConvertFromStringExceptionMode::Null>;
 using FunctionToFloat32OrNull = FunctionConvertFromString<DataTypeFloat32, NameToFloat32OrNull, ConvertFromStringExceptionMode::Null>;
 using FunctionToFloat64OrNull = FunctionConvertFromString<DataTypeFloat64, NameToFloat64OrNull, ConvertFromStringExceptionMode::Null>;
 using FunctionToDateOrNull = FunctionConvertFromString<DataTypeDate, NameToDateOrNull, ConvertFromStringExceptionMode::Null>;
@@ -5193,7 +5200,7 @@ private:
             if constexpr (is_any_of<ToDataType,
                 DataTypeUInt16, DataTypeUInt32, DataTypeUInt64, DataTypeUInt128, DataTypeUInt256,
                 DataTypeInt8, DataTypeInt16, DataTypeInt32, DataTypeInt64, DataTypeInt128, DataTypeInt256,
-                DataTypeFloat32, DataTypeFloat64,
+                DataTypeBFloat16, DataTypeFloat32, DataTypeFloat64,
                 DataTypeDate, DataTypeDate32, DataTypeDateTime,
                 DataTypeUUID, DataTypeIPv4, DataTypeIPv6>)
             {
@@ -5446,6 +5453,17 @@ REGISTER_FUNCTION(Conversion)
     factory.registerFunction<FunctionToInt64>();
     factory.registerFunction<FunctionToInt128>();
     factory.registerFunction<FunctionToInt256>();
+
+    factory.registerFunction<FunctionToBFloat16>(FunctionDocumentation{.description=R"(
+Converts Float32 to BFloat16 with losing the precision.
+
+Example:
+[example:typical]
+)",
+        .examples{
+            {"typical", "SELECT toBFloat16(12.3::Float32);", "12.3125"}},
+        .categories{"Conversion"}});
+
     factory.registerFunction<FunctionToFloat32>();
     factory.registerFunction<FunctionToFloat64>();
 
@@ -5484,6 +5502,31 @@ REGISTER_FUNCTION(Conversion)
     factory.registerFunction<FunctionToInt64OrZero>();
     factory.registerFunction<FunctionToInt128OrZero>();
     factory.registerFunction<FunctionToInt256OrZero>();
+
+    factory.registerFunction<FunctionToBFloat16OrZero>(FunctionDocumentation{.description=R"(
+Converts String to BFloat16.
+
+If the string does not represent a floating point value, the function returns zero.
+
+The function allows a silent loss of precision while converting from the string representation. In that case, it will return the truncated result.
+
+Example of successful conversion:
+[example:typical]
+
+Examples of not successful conversion:
+[example:invalid1]
+[example:invalid2]
+
+Example of a loss of precision:
+[example:precision]
+)",
+        .examples{
+            {"typical", "SELECT toBFloat16OrZero('12.3');", "12.3125"},
+            {"invalid1", "SELECT toBFloat16OrZero('abc');", "0"},
+            {"invalid2", "SELECT toBFloat16OrZero(' 1');", "0"},
+            {"precision", "SELECT toBFloat16OrZero('12.3456789');", "12.375"}},
+        .categories{"Conversion"}});
+
     factory.registerFunction<FunctionToFloat32OrZero>();
     factory.registerFunction<FunctionToFloat64OrZero>();
     factory.registerFunction<FunctionToDateOrZero>();
@@ -5512,6 +5555,31 @@ REGISTER_FUNCTION(Conversion)
     factory.registerFunction<FunctionToInt64OrNull>();
     factory.registerFunction<FunctionToInt128OrNull>();
     factory.registerFunction<FunctionToInt256OrNull>();
+
+    factory.registerFunction<FunctionToBFloat16OrNull>(FunctionDocumentation{.description=R"(
+Converts String to Nullable(BFloat16).
+
+If the string does not represent a floating point value, the function returns NULL.
+
+The function allows a silent loss of precision while converting from the string representation. In that case, it will return the truncated result.
+
+Example of successful conversion:
+[example:typical]
+
+Examples of not successful conversion:
+[example:invalid1]
+[example:invalid2]
+
+Example of a loss of precision:
+[example:precision]
+)",
+    .examples{
+        {"typical", "SELECT toBFloat16OrNull('12.3');", "12.3125"},
+        {"invalid1", "SELECT toBFloat16OrNull('abc');", "NULL"},
+        {"invalid2", "SELECT toBFloat16OrNull(' 1');", "NULL"},
+        {"precision", "SELECT toBFloat16OrNull('12.3456789');", "12.375"}},
+    .categories{"Conversion"}});
+
     factory.registerFunction<FunctionToFloat32OrNull>();
     factory.registerFunction<FunctionToFloat64OrNull>();
     factory.registerFunction<FunctionToDateOrNull>();

src/Functions/FunctionsRound.h

@@ -268,6 +268,19 @@ inline double roundWithMode(double x, RoundingMode mode)
     std::unreachable();
 }
 
+inline BFloat16 roundWithMode(BFloat16 x, RoundingMode mode)
+{
+    switch (mode)
+    {
+        case RoundingMode::Round: return BFloat16(nearbyintf(Float32(x)));
+        case RoundingMode::Floor: return BFloat16(floorf(Float32(x)));
+        case RoundingMode::Ceil: return BFloat16(ceilf(Float32(x)));
+        case RoundingMode::Trunc: return BFloat16(truncf(Float32(x)));
+    }
+
+    std::unreachable();
+}
+
 template <typename T>
 class FloatRoundingComputationBase<T, Vectorize::No>
 {
@@ -285,10 +298,15 @@ public:
 
     static VectorType prepare(size_t scale)
     {
-        return load1(scale);
+        return load1(ScalarType(scale));
     }
 };
 
+template <>
+class FloatRoundingComputationBase<BFloat16, Vectorize::Yes> : public FloatRoundingComputationBase<BFloat16, Vectorize::No>
+{
+};
+
 
 /** Implementation of low-level round-off functions for floating-point values.
   */
@@ -511,7 +529,7 @@ template <typename T, RoundingMode rounding_mode, TieBreakingMode tie_breaking_m
 struct Dispatcher
 {
     template <ScaleMode scale_mode>
-    using FunctionRoundingImpl = std::conditional_t<std::is_floating_point_v<T>,
+    using FunctionRoundingImpl = std::conditional_t<is_floating_point<T>,
         FloatRoundingImpl<T, rounding_mode, scale_mode>,
         IntegerRoundingImpl<T, rounding_mode, scale_mode, tie_breaking_mode>>;
 

src/Functions/FunctionsVisitParam.h

@@ -57,7 +57,7 @@ struct ExtractNumericType
         ResultType x = 0;
         if (!in.eof())
         {
-            if constexpr (std::is_floating_point_v<NumericType>)
+            if constexpr (is_floating_point<NumericType>)
                 tryReadFloatText(x, in);
             else
                 tryReadIntText(x, in);

src/Functions/PolygonUtils.h

@@ -583,7 +583,7 @@ struct CallPointInPolygon<Type, Types ...>
     template <typename PointInPolygonImpl>
     static ColumnPtr call(const IColumn & x, const IColumn & y, PointInPolygonImpl && impl)
     {
-        using Impl = TypeListChangeRoot<CallPointInPolygon, TypeListIntAndFloat>;
+        using Impl = TypeListChangeRoot<CallPointInPolygon, TypeListNativeNumber>;
         if (auto column = typeid_cast<const ColumnVector<Type> *>(&x))
             return Impl::template call<Type>(*column, y, impl);
         return CallPointInPolygon<Types ...>::call(x, y, impl);
@@ -609,7 +609,7 @@ struct CallPointInPolygon<>
 template <typename PointInPolygonImpl>
 NO_INLINE ColumnPtr pointInPolygon(const IColumn & x, const IColumn & y, PointInPolygonImpl && impl)
 {
-    using Impl = TypeListChangeRoot<CallPointInPolygon, TypeListIntAndFloat>;
+    using Impl = TypeListChangeRoot<CallPointInPolygon, TypeListNativeNumber>;
     return Impl::call(x, y, impl);
 }
 

src/Functions/abs.cpp

@@ -22,7 +22,7 @@ struct AbsImpl
             return a < 0 ? static_cast<ResultType>(~a) + 1 : static_cast<ResultType>(a);
         else if constexpr (is_integer<A> && is_unsigned_v<A>)
             return static_cast<ResultType>(a);
-        else if constexpr (std::is_floating_point_v<A>)
+        else if constexpr (is_floating_point<A>)
             return static_cast<ResultType>(std::abs(a));
     }
 

src/Functions/array/arrayAggregation.cpp

@@ -87,7 +87,7 @@ struct ArrayAggregateResultImpl<ArrayElement, AggregateOperation::sum>
         std::conditional_t<std::is_same_v<ArrayElement, Decimal128>, Decimal128,
         std::conditional_t<std::is_same_v<ArrayElement, Decimal256>, Decimal256,
         std::conditional_t<std::is_same_v<ArrayElement, DateTime64>, Decimal128,
-        std::conditional_t<std::is_floating_point_v<ArrayElement>, Float64,
+        std::conditional_t<is_floating_point<ArrayElement>, Float64,
         std::conditional_t<std::is_signed_v<ArrayElement>, Int64,
             UInt64>>>>>>>>>>>;
 };

src/Functions/array/arrayDistance.cpp

@@ -14,6 +14,7 @@
 #include <immintrin.h>
 #endif
 
+
 namespace DB
 {
 namespace ErrorCodes
@@ -34,7 +35,7 @@ struct L1Distance
     template <typename FloatType>
     struct State
     {
-        FloatType sum = 0;
+        FloatType sum{};
     };
 
     template <typename ResultType>
@@ -65,7 +66,7 @@ struct L2Distance
     template <typename FloatType>
     struct State
     {
-        FloatType sum = 0;
+        FloatType sum{};
     };
 
     template <typename ResultType>
@@ -90,19 +91,17 @@ struct L2Distance
         size_t & i_y,
         State<ResultType> & state)
     {
-        static constexpr bool is_float32 = std::is_same_v<ResultType, Float32>;
-
         __m512 sums;
-        if constexpr (is_float32)
+        if constexpr (sizeof(ResultType) <= 4)
             sums = _mm512_setzero_ps();
         else
             sums = _mm512_setzero_pd();
 
-        constexpr size_t n = is_float32 ? 16 : 8;
+        constexpr size_t n = sizeof(__m512) / sizeof(ResultType);
 
         for (; i_x + n < i_max; i_x += n, i_y += n)
         {
-            if constexpr (is_float32)
+            if constexpr (sizeof(ResultType) == 4)
             {
                 __m512 x = _mm512_loadu_ps(data_x + i_x);
                 __m512 y = _mm512_loadu_ps(data_y + i_y);
@@ -118,11 +117,38 @@ struct L2Distance
             }
         }
 
-        if constexpr (is_float32)
+        if constexpr (sizeof(ResultType) <= 4)
             state.sum = _mm512_reduce_add_ps(sums);
         else
             state.sum = _mm512_reduce_add_pd(sums);
     }
+
+    AVX512BF16_FUNCTION_SPECIFIC_ATTRIBUTE static void accumulateCombineBF16(
+        const BFloat16 * __restrict data_x,
+        const BFloat16 * __restrict data_y,
+        size_t i_max,
+        size_t & i_x,
+        size_t & i_y,
+        State<Float32> & state)
+    {
+        __m512 sums = _mm512_setzero_ps();
+        constexpr size_t n = sizeof(__m512) / sizeof(BFloat16);
+
+        for (; i_x + n < i_max; i_x += n, i_y += n)
+        {
+            __m512 x_1 = _mm512_cvtpbh_ps(_mm256_loadu_ps(reinterpret_cast<const Float32 *>(data_x + i_x)));
+            __m512 x_2 = _mm512_cvtpbh_ps(_mm256_loadu_ps(reinterpret_cast<const Float32 *>(data_x + i_x + n / 2)));
+            __m512 y_1 = _mm512_cvtpbh_ps(_mm256_loadu_ps(reinterpret_cast<const Float32 *>(data_y + i_y)));
+            __m512 y_2 = _mm512_cvtpbh_ps(_mm256_loadu_ps(reinterpret_cast<const Float32 *>(data_y + i_y + n / 2)));
+
+            __m512 differences_1 = _mm512_sub_ps(x_1, y_1);
+            __m512 differences_2 = _mm512_sub_ps(x_2, y_2);
+            sums = _mm512_fmadd_ps(differences_1, differences_1, sums);
+            sums = _mm512_fmadd_ps(differences_2, differences_2, sums);
+        }
+
+        state.sum = _mm512_reduce_add_ps(sums);
+    }
 #endif
 
     template <typename ResultType>
@@ -156,13 +182,13 @@ struct LpDistance
     template <typename FloatType>
     struct State
     {
-        FloatType sum = 0;
+        FloatType sum{};
     };
 
     template <typename ResultType>
     static void accumulate(State<ResultType> & state, ResultType x, ResultType y, const ConstParams & params)
     {
-        state.sum += static_cast<ResultType>(std::pow(fabs(x - y), params.power));
+        state.sum += static_cast<ResultType>(pow(fabs(x - y), params.power));
     }
 
     template <typename ResultType>
@@ -174,7 +200,7 @@ struct LpDistance
     template <typename ResultType>
     static ResultType finalize(const State<ResultType> & state, const ConstParams & params)
     {
-        return static_cast<ResultType>(std::pow(state.sum, params.inverted_power));
+        return static_cast<ResultType>(pow(state.sum, params.inverted_power));
     }
 };
 
@@ -187,7 +213,7 @@ struct LinfDistance
     template <typename FloatType>
     struct State
     {
-        FloatType dist = 0;
+        FloatType dist{};
     };
 
     template <typename ResultType>
@@ -218,9 +244,9 @@ struct CosineDistance
     template <typename FloatType>
     struct State
     {
-        FloatType dot_prod = 0;
-        FloatType x_squared = 0;
-        FloatType y_squared = 0;
+        FloatType dot_prod{};
+        FloatType x_squared{};
+        FloatType y_squared{};
     };
 
     template <typename ResultType>
@@ -249,13 +275,11 @@ struct CosineDistance
         size_t & i_y,
         State<ResultType> & state)
     {
-        static constexpr bool is_float32 = std::is_same_v<ResultType, Float32>;
-
         __m512 dot_products;
         __m512 x_squareds;
         __m512 y_squareds;
 
-        if constexpr (is_float32)
+        if constexpr (sizeof(ResultType) <= 4)
         {
             dot_products = _mm512_setzero_ps();
             x_squareds = _mm512_setzero_ps();
@@ -268,11 +292,11 @@ struct CosineDistance
             y_squareds = _mm512_setzero_pd();
         }
 
-        constexpr size_t n = is_float32 ? 16 : 8;
+        constexpr size_t n = sizeof(__m512) / sizeof(ResultType);
 
         for (; i_x + n < i_max; i_x += n, i_y += n)
         {
-            if constexpr (is_float32)
+            if constexpr (sizeof(ResultType) == 4)
             {
                 __m512 x = _mm512_loadu_ps(data_x + i_x);
                 __m512 y = _mm512_loadu_ps(data_y + i_y);
@@ -290,7 +314,7 @@ struct CosineDistance
             }
         }
 
-        if constexpr (is_float32)
+        if constexpr (sizeof(ResultType) == 4)
         {
             state.dot_prod = _mm512_reduce_add_ps(dot_products);
             state.x_squared = _mm512_reduce_add_ps(x_squareds);
@@ -303,16 +327,48 @@ struct CosineDistance
             state.y_squared = _mm512_reduce_add_pd(y_squareds);
         }
     }
+
+    AVX512BF16_FUNCTION_SPECIFIC_ATTRIBUTE static void accumulateCombineBF16(
+        const BFloat16 * __restrict data_x,
+        const BFloat16 * __restrict data_y,
+        size_t i_max,
+        size_t & i_x,
+        size_t & i_y,
+        State<Float32> & state)
+    {
+        __m512 dot_products;
+        __m512 x_squareds;
+        __m512 y_squareds;
+
+        dot_products = _mm512_setzero_ps();
+        x_squareds = _mm512_setzero_ps();
+        y_squareds = _mm512_setzero_ps();
+
+        constexpr size_t n = sizeof(__m512) / sizeof(BFloat16);
+
+        for (; i_x + n < i_max; i_x += n, i_y += n)
+        {
+            __m512 x = _mm512_loadu_ps(data_x + i_x);
+            __m512 y = _mm512_loadu_ps(data_y + i_y);
+            dot_products = _mm512_dpbf16_ps(dot_products, x, y);
+            x_squareds = _mm512_dpbf16_ps(x_squareds, x, x);
+            y_squareds = _mm512_dpbf16_ps(y_squareds, y, y);
+        }
+
+        state.dot_prod = _mm512_reduce_add_ps(dot_products);
+        state.x_squared = _mm512_reduce_add_ps(x_squareds);
+        state.y_squared = _mm512_reduce_add_ps(y_squareds);
+    }
 #endif
 
     template <typename ResultType>
     static ResultType finalize(const State<ResultType> & state, const ConstParams &)
     {
-        return 1 - state.dot_prod / sqrt(state.x_squared * state.y_squared);
+        return 1.0f - state.dot_prod / sqrt(state.x_squared * state.y_squared);
     }
 };
 
-template <class Kernel>
+template <typename Kernel>
 class FunctionArrayDistance : public IFunction
 {
 public:
@@ -352,12 +408,13 @@ public:
             case TypeIndex::Float64:
                 return std::make_shared<DataTypeFloat64>();
             case TypeIndex::Float32:
+            case TypeIndex::BFloat16:
                 return std::make_shared<DataTypeFloat32>();
             default:
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Arguments of function {} has nested type {}. "
-                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, Float64.",
+                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, BFloat16, Float32, Float64.",
                     getName(),
                     common_type->getName());
         }
@@ -369,10 +426,8 @@ public:
         {
             case TypeIndex::Float32:
                 return executeWithResultType<Float32>(arguments, input_rows_count);
-                break;
             case TypeIndex::Float64:
                 return executeWithResultType<Float64>(arguments, input_rows_count);
-                break;
             default:
                 throw Exception(ErrorCodes::LOGICAL_ERROR, "Unexpected result type {}", result_type->getName());
         }
@@ -388,6 +443,7 @@ public:
     ACTION(Int16)   \
     ACTION(Int32)   \
     ACTION(Int64)   \
+    ACTION(BFloat16) \
     ACTION(Float32) \
     ACTION(Float64)
 
@@ -412,7 +468,7 @@ private:
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Arguments of function {} has nested type {}. "
-                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, Float64.",
+                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, BFloat16, Float32, Float64.",
                     getName(),
                     type_x->getName());
         }
@@ -437,7 +493,7 @@ private:
                 throw Exception(
                     ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                     "Arguments of function {} has nested type {}. "
-                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, Float32, Float64.",
+                    "Supported types: UInt8, UInt16, UInt32, UInt64, Int8, Int16, Int32, Int64, BFloat16, Float32, Float64.",
                     getName(),
                     type_y->getName());
         }
@@ -446,14 +502,10 @@ private:
     template <typename ResultType, typename LeftType, typename RightType>
     ColumnPtr executeWithResultTypeAndLeftTypeAndRightType(ColumnPtr col_x, ColumnPtr col_y, size_t input_rows_count, const ColumnsWithTypeAndName & arguments) const
     {
-        if (typeid_cast<const ColumnConst *>(col_x.get()))
-        {
+        if (col_x->isConst())
             return executeWithLeftArgConst<ResultType, LeftType, RightType>(col_x, col_y, input_rows_count, arguments);
-        }
-        if (typeid_cast<const ColumnConst *>(col_y.get()))
-        {
+        if (col_y->isConst())
             return executeWithLeftArgConst<ResultType, RightType, LeftType>(col_y, col_x, input_rows_count, arguments);
-        }
 
         const auto & array_x = *assert_cast<const ColumnArray *>(col_x.get());
         const auto & array_y = *assert_cast<const ColumnArray *>(col_y.get());
@@ -497,7 +549,7 @@ private:
                     state, static_cast<ResultType>(data_x[prev]), static_cast<ResultType>(data_y[prev]), kernel_params);
             }
             result_data[row] = Kernel::finalize(state, kernel_params);
-            row++;
+            ++row;
         }
         return col_res;
     }
@@ -548,24 +600,39 @@ private:
 
             /// SIMD optimization: process multiple elements in both input arrays at once.
             /// To avoid combinatorial explosion of SIMD kernels, focus on
-            /// - the two most common input/output types (Float32 x Float32) --> Float32 and (Float64 x Float64) --> Float64 instead of 10 x
-            ///   10 input types x 2 output types,
+            /// - the three most common input/output types (BFloat16 x BFloat16) --> Float32,
+            ///   (Float32 x Float32) --> Float32 and (Float64 x Float64) --> Float64
+            ///   instead of 10 x 10 input types x 2 output types,
             /// - const/non-const inputs instead of non-const/non-const inputs
             /// - the two most common metrics L2 and cosine distance,
             /// - the most powerful SIMD instruction set (AVX-512F).
+            bool processed = false;
 #if USE_MULTITARGET_CODE
-            if constexpr (std::is_same_v<ResultType, LeftType> && std::is_same_v<ResultType, RightType>) /// ResultType is Float32 or Float64
+            /// ResultType is Float32 or Float64
+            if constexpr (std::is_same_v<Kernel, L2Distance> || std::is_same_v<Kernel, CosineDistance>)
             {
-                if constexpr (std::is_same_v<Kernel, L2Distance>
-                           || std::is_same_v<Kernel, CosineDistance>)
+                if constexpr (std::is_same_v<ResultType, LeftType> && std::is_same_v<ResultType, RightType>)
                 {
                     if (isArchSupported(TargetArch::AVX512F))
+                    {
                         Kernel::template accumulateCombine<ResultType>(data_x.data(), data_y.data(), i + offsets_x[0], i, prev, state);
+                        processed = true;
                     }
                 }
-#else
-            /// Process chunks in vectorized manner
-            static constexpr size_t VEC_SIZE = 4;
+                else if constexpr (std::is_same_v<Float32, ResultType> && std::is_same_v<BFloat16, LeftType> && std::is_same_v<BFloat16, RightType>)
+                {
+                    if (isArchSupported(TargetArch::AVX512BF16))
+                    {
+                        Kernel::accumulateCombineBF16(data_x.data(), data_y.data(), i + offsets_x[0], i, prev, state);
+                        processed = true;
+                    }
+                }
+            }
+#endif
+            if (!processed)
+            {
+                /// Process chunks in a vectorized manner.
+                static constexpr size_t VEC_SIZE = 32;
                 typename Kernel::template State<ResultType> states[VEC_SIZE];
                 for (; prev + VEC_SIZE < off; i += VEC_SIZE, prev += VEC_SIZE)
                 {
@@ -576,8 +643,9 @@ private:
 
                 for (const auto & other_state : states)
                     Kernel::template combine<ResultType>(state, other_state, kernel_params);
-#endif
-            /// Process the tail
+            }
+
+            /// Process the tail.
             for (; prev < off; ++i, ++prev)
             {
                 Kernel::template accumulate<ResultType>(
@@ -638,4 +706,5 @@ FunctionPtr createFunctionArrayL2SquaredDistance(ContextPtr context_) { return F
 FunctionPtr createFunctionArrayLpDistance(ContextPtr context_) { return FunctionArrayDistance<LpDistance>::create(context_); }
 FunctionPtr createFunctionArrayLinfDistance(ContextPtr context_) { return FunctionArrayDistance<LinfDistance>::create(context_); }
 FunctionPtr createFunctionArrayCosineDistance(ContextPtr context_) { return FunctionArrayDistance<CosineDistance>::create(context_); }
+
 }

src/Functions/array/mapPopulateSeries.cpp

@@ -452,9 +452,14 @@ private:
             using ValueType = typename Types::RightType;
 
             static constexpr bool key_and_value_are_numbers = IsDataTypeNumber<KeyType> && IsDataTypeNumber<ValueType>;
-            static constexpr bool key_is_float = std::is_same_v<KeyType, DataTypeFloat32> || std::is_same_v<KeyType, DataTypeFloat64>;
 
-            if constexpr (key_and_value_are_numbers && !key_is_float)
+            if constexpr (key_and_value_are_numbers)
+            {
+                if constexpr (is_floating_point<typename KeyType::FieldType>)
+                {
+                    return false;
+                }
+                else
                 {
                     using KeyFieldType = typename KeyType::FieldType;
                     using ValueFieldType = typename ValueType::FieldType;
@@ -470,6 +475,7 @@ private:
 
                     return true;
                 }
+            }
 
             return false;
         };

src/Functions/divide.cpp

@@ -18,7 +18,7 @@ struct DivideFloatingImpl
     template <typename Result = ResultType>
     static NO_SANITIZE_UNDEFINED Result apply(A a [[maybe_unused]], B b [[maybe_unused]])
     {
-        return static_cast<Result>(a) / b;
+        return static_cast<Result>(a) / static_cast<Result>(b);
     }
 
 #if USE_EMBEDDED_COMPILER

src/Functions/exp.cpp

@@ -3,6 +3,12 @@
 
 namespace DB
 {
+
+namespace ErrorCodes
+{
+extern const int NOT_IMPLEMENTED;
+}
+
 namespace
 {
 
@@ -20,9 +26,16 @@ namespace
 
         template <typename T>
         static void execute(const T * src, size_t size, T * dst)
+        {
+            if constexpr (std::is_same_v<T, BFloat16>)
+            {
+                throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Function `{}` is not implemented for BFloat16", name);
+            }
+            else
             {
                 NFastOps::Exp<true>(src, size, dst);
             }
+        }
     };
 }
 

src/Functions/factorial.cpp

@@ -21,7 +21,7 @@ struct FactorialImpl
 
     static NO_SANITIZE_UNDEFINED ResultType apply(A a)
     {
-        if constexpr (std::is_floating_point_v<A> || is_over_big_int<A>)
+        if constexpr (is_floating_point<A> || is_over_big_int<A>)
             throw Exception(
                 ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                 "Illegal type of argument of function factorial, should not be floating point or big int");

src/Functions/log.cpp

@@ -4,6 +4,11 @@
 namespace DB
 {
 
+namespace ErrorCodes
+{
+extern const int NOT_IMPLEMENTED;
+}
+
 namespace
 {
 
@@ -19,9 +24,16 @@ struct LogName { static constexpr auto name = "log"; };
 
         template <typename T>
         static void execute(const T * src, size_t size, T * dst)
+        {
+            if constexpr (std::is_same_v<T, BFloat16>)
+            {
+                throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Function `{}` is not implemented for BFloat16", name);
+            }
+            else
             {
                 NFastOps::Log<true>(src, size, dst);
             }
+        }
     };
 
 using FunctionLog = FunctionMathUnary<Impl>;

src/Functions/minus.cpp

@@ -17,8 +17,8 @@ struct MinusImpl
     {
         if constexpr (is_big_int_v<A> || is_big_int_v<B>)
         {
-            using CastA = std::conditional_t<std::is_floating_point_v<B>, B, A>;
-            using CastB = std::conditional_t<std::is_floating_point_v<A>, A, B>;
+            using CastA = std::conditional_t<is_floating_point<B>, B, A>;
+            using CastB = std::conditional_t<is_floating_point<A>, A, B>;
 
             return static_cast<Result>(static_cast<CastA>(a)) - static_cast<Result>(static_cast<CastB>(b));
         }

src/Functions/moduloOrZero.cpp

@@ -17,7 +17,7 @@ struct ModuloOrZeroImpl
     template <typename Result = ResultType>
     static Result apply(A a, B b)
     {
-        if constexpr (std::is_floating_point_v<ResultType>)
+        if constexpr (is_floating_point<ResultType>)
         {
             /// This computation is similar to `fmod` but the latter is not inlined and has 40 times worse performance.
             return ResultType(a) - trunc(ResultType(a) / ResultType(b)) * ResultType(b);

src/Functions/multiply.cpp

@@ -18,8 +18,8 @@ struct MultiplyImpl
     {
         if constexpr (is_big_int_v<A> || is_big_int_v<B>)
         {
-            using CastA = std::conditional_t<std::is_floating_point_v<B>, B, A>;
-            using CastB = std::conditional_t<std::is_floating_point_v<A>, A, B>;
+            using CastA = std::conditional_t<is_floating_point<B>, B, A>;
+            using CastB = std::conditional_t<is_floating_point<A>, A, B>;
 
             return static_cast<Result>(static_cast<CastA>(a)) * static_cast<Result>(static_cast<CastB>(b));
         }

src/Functions/plus.cpp

@@ -19,8 +19,8 @@ struct PlusImpl
         /// Next everywhere, static_cast - so that there is no wrong result in expressions of the form Int64 c = UInt32(a) * Int32(-1).
         if constexpr (is_big_int_v<A> || is_big_int_v<B>)
         {
-            using CastA = std::conditional_t<std::is_floating_point_v<B>, B, A>;
-            using CastB = std::conditional_t<std::is_floating_point_v<A>, A, B>;
+            using CastA = std::conditional_t<is_floating_point<B>, B, A>;
+            using CastB = std::conditional_t<is_floating_point<A>, A, B>;
 
             return static_cast<Result>(static_cast<CastA>(a)) + static_cast<Result>(static_cast<CastB>(b));
         }

src/Functions/sigmoid.cpp

@@ -3,6 +3,12 @@
 
 namespace DB
 {
+
+namespace ErrorCodes
+{
+extern const int NOT_IMPLEMENTED;
+}
+
 namespace
 {
 
@@ -20,9 +26,16 @@ namespace
 
         template <typename T>
         static void execute(const T * src, size_t size, T * dst)
+        {
+            if constexpr (std::is_same_v<T, BFloat16>)
+            {
+                throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Function `{}` is not implemented for BFloat16", name);
+            }
+            else
             {
                 NFastOps::Sigmoid<>(src, size, dst);
             }
+        }
     };
 }
 
@@ -47,4 +60,3 @@ REGISTER_FUNCTION(Sigmoid)
 }
 
 }
-

src/Functions/sign.cpp

@@ -13,7 +13,7 @@ struct SignImpl
 
     static NO_SANITIZE_UNDEFINED ResultType apply(A a)
     {
-        if constexpr (is_decimal<A> || std::is_floating_point_v<A>)
+        if constexpr (is_decimal<A> || is_floating_point<A>)
             return a < A(0) ? -1 : a == A(0) ? 0 : 1;
         else if constexpr (is_signed_v<A>)
             return a < 0 ? -1 : a == 0 ? 0 : 1;

src/Functions/tanh.cpp

@@ -3,6 +3,12 @@
 
 namespace DB
 {
+
+namespace ErrorCodes
+{
+extern const int NOT_IMPLEMENTED;
+}
+
 namespace
 {
 
@@ -18,9 +24,16 @@ struct TanhName { static constexpr auto name = "tanh"; };
 
         template <typename T>
         static void execute(const T * src, size_t size, T * dst)
+        {
+            if constexpr (std::is_same_v<T, BFloat16>)
+            {
+                throw Exception(ErrorCodes::NOT_IMPLEMENTED, "Function `{}` is not implemented for BFloat16", name);
+            }
+            else
             {
                 NFastOps::Tanh<>(src, size, dst);
             }
+        }
     };
 
 using FunctionTanh = FunctionMathUnary<Impl>;

src/IO/ReadHelpers.h

@@ -1420,7 +1420,9 @@ inline bool tryReadText(UUID & x, ReadBuffer & buf) { return tryReadUUIDText(x,
 inline bool tryReadText(IPv4 & x, ReadBuffer & buf) { return tryReadIPv4Text(x, buf); }
 inline bool tryReadText(IPv6 & x, ReadBuffer & buf) { return tryReadIPv6Text(x, buf); }
 
-inline void readText(is_floating_point auto & x, ReadBuffer & buf) { readFloatText(x, buf); }
+template <typename T>
+requires is_floating_point<T>
+inline void readText(T & x, ReadBuffer & buf) { readFloatText(x, buf); }
 
 inline void readText(String & x, ReadBuffer & buf) { readEscapedString(x, buf); }
 

src/IO/WriteHelpers.h

@@ -150,11 +150,12 @@ inline void writeBoolText(bool x, WriteBuffer & buf)
 
 
 template <typename T>
+requires is_floating_point<T>
 inline size_t writeFloatTextFastPath(T x, char * buffer)
 {
     Int64 result = 0;
 
-    if constexpr (std::is_same_v<T, double>)
+    if constexpr (std::is_same_v<T, Float64>)
     {
         /// The library Ryu has low performance on integers.
         /// This workaround improves performance 6..10 times.
@@ -164,13 +165,22 @@ inline size_t writeFloatTextFastPath(T x, char * buffer)
         else
             result = jkj::dragonbox::to_chars_n(x, buffer) - buffer;
     }
-    else
+    else if constexpr (std::is_same_v<T, Float32>)
     {
         if (DecomposedFloat32(x).isIntegerInRepresentableRange())
             result = itoa(Int32(x), buffer) - buffer;
         else
             result = jkj::dragonbox::to_chars_n(x, buffer) - buffer;
     }
+    else if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 f32 = Float32(x);
+
+        if (DecomposedFloat32(f32).isIntegerInRepresentableRange())
+            result = itoa(Int32(f32), buffer) - buffer;
+        else
+            result = jkj::dragonbox::to_chars_n(f32, buffer) - buffer;
+    }
 
     if (result <= 0)
         throw Exception(ErrorCodes::CANNOT_PRINT_FLOAT_OR_DOUBLE_NUMBER, "Cannot print floating point number");
@@ -178,10 +188,9 @@ inline size_t writeFloatTextFastPath(T x, char * buffer)
 }
 
 template <typename T>
+requires is_floating_point<T>
 inline void writeFloatText(T x, WriteBuffer & buf)
 {
-    static_assert(std::is_same_v<T, double> || std::is_same_v<T, float>, "Argument for writeFloatText must be float or double");
-
     using Converter = DoubleConverter<false>;
     if (likely(buf.available() >= Converter::MAX_REPRESENTATION_LENGTH))
     {
@@ -540,9 +549,9 @@ void writeJSONNumber(T x, WriteBuffer & ostr, const FormatSettings & settings)
         writeCString("null", ostr);
     else
     {
-        if constexpr (std::is_floating_point_v<T>)
+        if constexpr (is_floating_point<T>)
         {
-            if (std::signbit(x))
+            if (signBit(x))
             {
                 if (isNaN(x))
                     writeCString("-nan", ostr);
@@ -798,7 +807,6 @@ inline void writeXMLStringForTextElement(std::string_view s, WriteBuffer & buf)
 }
 
 /// @brief Serialize `uuid` into an array of characters in big-endian byte order.
-/// @param uuid UUID to serialize.
 /// @return Array of characters in big-endian byte order.
 std::array<char, 36> formatUUID(const UUID & uuid);
 
@@ -1099,7 +1107,9 @@ inline void writeText(is_integer auto x, WriteBuffer & buf)
         writeIntText(x, buf);
 }
 
-inline void writeText(is_floating_point auto x, WriteBuffer & buf) { writeFloatText(x, buf); }
+template <typename T>
+requires is_floating_point<T>
+inline void writeText(T x, WriteBuffer & buf) { writeFloatText(x, buf); }
 
 inline void writeText(is_enum auto x, WriteBuffer & buf) { writeText(magic_enum::enum_name(x), buf); }
 

src/IO/readFloatText.cpp

@@ -47,26 +47,35 @@ void assertNaN(ReadBuffer & buf)
 }
 
 
+template void readFloatTextPrecise<BFloat16>(BFloat16 &, ReadBuffer &);
 template void readFloatTextPrecise<Float32>(Float32 &, ReadBuffer &);
 template void readFloatTextPrecise<Float64>(Float64 &, ReadBuffer &);
+template bool tryReadFloatTextPrecise<BFloat16>(BFloat16 &, ReadBuffer &);
 template bool tryReadFloatTextPrecise<Float32>(Float32 &, ReadBuffer &);
 template bool tryReadFloatTextPrecise<Float64>(Float64 &, ReadBuffer &);
 
+template void readFloatTextFast<BFloat16>(BFloat16 &, ReadBuffer &);
 template void readFloatTextFast<Float32>(Float32 &, ReadBuffer &);
 template void readFloatTextFast<Float64>(Float64 &, ReadBuffer &);
+template bool tryReadFloatTextFast<BFloat16>(BFloat16 &, ReadBuffer &);
 template bool tryReadFloatTextFast<Float32>(Float32 &, ReadBuffer &);
 template bool tryReadFloatTextFast<Float64>(Float64 &, ReadBuffer &);
 
+template void readFloatTextSimple<BFloat16>(BFloat16 &, ReadBuffer &);
 template void readFloatTextSimple<Float32>(Float32 &, ReadBuffer &);
 template void readFloatTextSimple<Float64>(Float64 &, ReadBuffer &);
+template bool tryReadFloatTextSimple<BFloat16>(BFloat16 &, ReadBuffer &);
 template bool tryReadFloatTextSimple<Float32>(Float32 &, ReadBuffer &);
 template bool tryReadFloatTextSimple<Float64>(Float64 &, ReadBuffer &);
 
+template void readFloatText<BFloat16>(BFloat16 &, ReadBuffer &);
 template void readFloatText<Float32>(Float32 &, ReadBuffer &);
 template void readFloatText<Float64>(Float64 &, ReadBuffer &);
+template bool tryReadFloatText<BFloat16>(BFloat16 &, ReadBuffer &);
 template bool tryReadFloatText<Float32>(Float32 &, ReadBuffer &);
 template bool tryReadFloatText<Float64>(Float64 &, ReadBuffer &);
 
+template bool tryReadFloatTextNoExponent<BFloat16>(BFloat16 &, ReadBuffer &);
 template bool tryReadFloatTextNoExponent<Float32>(Float32 &, ReadBuffer &);
 template bool tryReadFloatTextNoExponent<Float64>(Float64 &, ReadBuffer &);
 

src/IO/readFloatText.h

@@ -222,7 +222,6 @@ ReturnType readFloatTextPreciseImpl(T & x, ReadBuffer & buf)
             break;
         }
 
-
         char tmp_buf[MAX_LENGTH];
         int num_copied_chars = 0;
 
@@ -597,22 +596,85 @@ ReturnType readFloatTextSimpleImpl(T & x, ReadBuffer & buf)
     return ReturnType(true);
 }
 
-template <typename T> void readFloatTextPrecise(T & x, ReadBuffer & in) { readFloatTextPreciseImpl<T, void>(x, in); }
-template <typename T> bool tryReadFloatTextPrecise(T & x, ReadBuffer & in) { return readFloatTextPreciseImpl<T, bool>(x, in); }
+template <typename T> void readFloatTextPrecise(T & x, ReadBuffer & in)
+{
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        readFloatTextPreciseImpl<Float32, void>(tmp, in);
+        x = BFloat16(tmp);
+    }
+    else
+        readFloatTextPreciseImpl<T, void>(x, in);
+}
+
+template <typename T> bool tryReadFloatTextPrecise(T & x, ReadBuffer & in)
+{
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextPreciseImpl<Float32, bool>(tmp, in);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+    }
+    else
+        return readFloatTextPreciseImpl<T, bool>(x, in);
+}
 
 template <typename T> void readFloatTextFast(T & x, ReadBuffer & in)
 {
     bool has_fractional;
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        readFloatTextFastImpl<Float32, void>(tmp, in, has_fractional);
+        x = BFloat16(tmp);
+    }
+    else
         readFloatTextFastImpl<T, void>(x, in, has_fractional);
 }
+
 template <typename T> bool tryReadFloatTextFast(T & x, ReadBuffer & in)
 {
     bool has_fractional;
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextFastImpl<Float32, bool>(tmp, in, has_fractional);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+    }
+    else
         return readFloatTextFastImpl<T, bool>(x, in, has_fractional);
 }
 
-template <typename T> void readFloatTextSimple(T & x, ReadBuffer & in) { readFloatTextSimpleImpl<T, void>(x, in); }
-template <typename T> bool tryReadFloatTextSimple(T & x, ReadBuffer & in) { return readFloatTextSimpleImpl<T, bool>(x, in); }
+template <typename T> void readFloatTextSimple(T & x, ReadBuffer & in)
+{
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        readFloatTextSimpleImpl<Float32, void>(tmp, in);
+        x = BFloat16(tmp);
+    }
+    else
+        readFloatTextSimpleImpl<T, void>(x, in);
+}
+
+template <typename T> bool tryReadFloatTextSimple(T & x, ReadBuffer & in)
+{
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextSimpleImpl<Float32, bool>(tmp, in);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+    }
+    else
+        return readFloatTextSimpleImpl<T, bool>(x, in);
+}
 
 
 /// Implementation that is selected as default.
@@ -624,6 +686,16 @@ template <typename T> bool tryReadFloatText(T & x, ReadBuffer & in) { return try
 template <typename T> bool tryReadFloatTextNoExponent(T & x, ReadBuffer & in)
 {
     bool has_fractional;
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextFastImpl<Float32, bool, false>(tmp, in, has_fractional);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+
+    }
+    else
         return readFloatTextFastImpl<T, bool, false>(x, in, has_fractional);
 }
 
@@ -631,10 +703,29 @@ template <typename T> bool tryReadFloatTextNoExponent(T & x, ReadBuffer & in)
 /// Used for input_format_try_infer_integers
 template <typename T> bool tryReadFloatTextExt(T & x, ReadBuffer & in, bool & has_fractional)
 {
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextFastImpl<Float32, bool>(tmp, in, has_fractional);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+    }
+    else
         return readFloatTextFastImpl<T, bool>(x, in, has_fractional);
 }
+
 template <typename T> bool tryReadFloatTextExtNoExponent(T & x, ReadBuffer & in, bool & has_fractional)
 {
+    if constexpr (std::is_same_v<T, BFloat16>)
+    {
+        Float32 tmp;
+        bool res = readFloatTextFastImpl<Float32, bool, false>(tmp, in, has_fractional);
+        if (res)
+            x = BFloat16(tmp);
+        return res;
+    }
+    else
         return readFloatTextFastImpl<T, bool, false>(x, in, has_fractional);
 }