ClickHouse/dbms/src/Functions/FunctionsRound.h

#pragma once

#include <Functions/FunctionsArithmetic.h>
#include <Functions/FunctionHelpers.h>
#include <IO/WriteHelpers.h>

#include <cmath>
#include <type_traits>
#include <array>
#include <ext/bit_cast.h>

#if __SSE4_1__
    #include <smmintrin.h>
#endif


namespace DB
{

namespace ErrorCodes
{
    extern const int NUMBER_OF_ARGUMENTS_DOESNT_MATCH;
}


/** Rounding Functions:
    * round(x, N) - rounding to nearest (N = 0 by default). Use banker's rounding for floating point numbers.
    * floor(x, N) is the largest number <= x (N = 0 by default).
    * ceil(x, N) is the smallest number >= x (N = 0 by default).
    * trunc(x, N) - is the largest by absolute value number that is not greater than x by absolute value (N = 0 by default).
    *
    * The value of the parameter N (scale):
    * - N > 0: round to the number with N decimal places after the decimal point
    * - N < 0: round to an integer with N zero characters
    * - N = 0: round to an integer
    *
    * Type of the result is the type of argument.
    * For integer arguments, when passing negative scale, overflow can occur.
    * In that case, the behavior is implementation specific.
    *
    * roundToExp2 - down to the nearest power of two (see below);
    *
    * Deprecated functions:
    * roundDuration - down to the nearest of: 0, 1, 10, 30, 60, 120, 180, 240, 300, 600, 1200, 1800, 3600, 7200, 18000, 36000;
    * roundAge - down to the nearest of: 0, 18, 25, 35, 45, 55.
    */

template <typename T>
inline typename std::enable_if<std::is_integral<T>::value && (sizeof(T) <= sizeof(UInt32)), T>::type
roundDownToPowerOfTwo(T x)
{
    return x <= 0 ? 0 : (T(1) << (31 - __builtin_clz(x)));
}

template <typename T>
inline typename std::enable_if<std::is_integral<T>::value && (sizeof(T) == sizeof(UInt64)), T>::type
roundDownToPowerOfTwo(T x)
{
    return x <= 0 ? 0 : (T(1) << (63 - __builtin_clzll(x)));
}

template <typename T>
inline typename std::enable_if<std::is_same<T, Float32>::value, T>::type
roundDownToPowerOfTwo(T x)
{
    return ext::bit_cast<T>(ext::bit_cast<UInt32>(x) & ~((1ULL << 23) - 1));
}

template <typename T>
inline typename std::enable_if<std::is_same<T, Float64>::value, T>::type
roundDownToPowerOfTwo(T x)
{
    return ext::bit_cast<T>(ext::bit_cast<UInt64>(x) & ~((1ULL << 52) - 1));
}

/** For integer data types:
  * - if number is greater than zero, round it down to nearest power of two (example: roundToExp2(100) = 64, roundToExp2(64) = 64);
  * - otherwise, return 0.
  *
  * For floating point data types: zero out mantissa, but leave exponent.
  * - if number is greater than zero, round it down to nearest power of two (example: roundToExp2(3) = 2);
  * - negative powers are also used (example: roundToExp2(0.7) = 0.5);
  * - if number is zero, return zero;
  * - if number is less than zero, the result is symmetrical: roundToExp2(x) = -roundToExp2(-x). (example: roundToExp2(-0.3) = -0.25);
  */

template <typename T>
struct RoundToExp2Impl
{
    using ResultType = T;

    static inline T apply(T x)
    {
        return roundDownToPowerOfTwo<T>(x);
    }
};


template <typename A>
struct RoundDurationImpl
{
    using ResultType = UInt16;

    static inline ResultType apply(A x)
    {
        return x < 1 ? 0
            : (x < 10 ? 1
            : (x < 30 ? 10
            : (x < 60 ? 30
            : (x < 120 ? 60
            : (x < 180 ? 120
            : (x < 240 ? 180
            : (x < 300 ? 240
            : (x < 600 ? 300
            : (x < 1200 ? 600
            : (x < 1800 ? 1200
            : (x < 3600 ? 1800
            : (x < 7200 ? 3600
            : (x < 18000 ? 7200
            : (x < 36000 ? 18000
            : 36000))))))))))))));
    }
};

template <typename A>
struct RoundAgeImpl
{
    using ResultType = UInt8;

    static inline ResultType apply(A x)
    {
        return x < 1 ? 0
            : (x < 18 ? 17
            : (x < 25 ? 18
            : (x < 35 ? 25
            : (x < 45 ? 35
            : (x < 55 ? 45
            : 55)))));
    }
};


/** This parameter controls the behavior of the rounding functions.
  */
enum class ScaleMode
{
    Positive,   // round to a number with N decimal places after the decimal point
    Negative,   // round to an integer with N zero characters
    Zero,       // round to an integer
};

enum class RoundingMode
{
#if __SSE4_1__
    Round   = _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC,
    Floor   = _MM_FROUND_TO_NEG_INF | _MM_FROUND_NO_EXC,
    Ceil    = _MM_FROUND_TO_POS_INF | _MM_FROUND_NO_EXC,
    Trunc   = _MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC,
#else
    Round   = 8,    /// Values are correspond to above just in case.
    Floor   = 9,
    Ceil    = 10,
    Trunc   = 11,
#endif
};


/** Rounding functions for integer values.
  */
template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
struct IntegerRoundingComputation
{
    static const size_t data_count = 1;

    static size_t prepare(size_t scale)
    {
        return scale;
    }

    static ALWAYS_INLINE T computeImpl(T x, T scale)
    {
        switch (rounding_mode)
        {
            case RoundingMode::Trunc:
            {
                return x / scale * scale;
            }
            case RoundingMode::Floor:
            {
                if (x < 0)
                    x -= scale - 1;
                return x / scale * scale;
            }
            case RoundingMode::Ceil:
            {
                if (x >= 0)
                    x += scale - 1;
                return x / scale * scale;
            }
            case RoundingMode::Round:
            {
                bool negative = x < 0;
                if (negative)
                    x = -x;
                x = (x + scale / 2) / scale * scale;
                if (negative)
                    x = -x;
                return x;
            }
        }
    }

    static ALWAYS_INLINE T compute(T x, T scale)
    {
        switch (scale_mode)
        {
            case ScaleMode::Zero:
                return x;
            case ScaleMode::Positive:
                return x;
            case ScaleMode::Negative:
                return computeImpl(x, scale);
        }
    }

    static ALWAYS_INLINE void compute(const T * __restrict in, size_t scale, T * __restrict out)
    {
        *out = compute(*in, scale);
    }

};


#if __SSE4_1__

template <typename T>
class BaseFloatRoundingComputation;

template <>
class BaseFloatRoundingComputation<Float32>
{
public:
    using ScalarType = Float32;
    using VectorType = __m128;
    static const size_t data_count = 4;

    static VectorType load(const ScalarType * in) { return _mm_loadu_ps(in); }
    static VectorType load1(const ScalarType in) { return _mm_load1_ps(&in); }
    static void store(ScalarType * out, VectorType val) { _mm_storeu_ps(out, val);}
    static VectorType multiply(VectorType val, VectorType scale) { return _mm_mul_ps(val, scale); }
    static VectorType divide(VectorType val, VectorType scale) { return _mm_div_ps(val, scale); }
    template <RoundingMode mode> static VectorType apply(VectorType val) { return _mm_round_ps(val, int(mode)); }

    static VectorType prepare(size_t scale)
    {
        return load1(scale);
    }
};

template <>
class BaseFloatRoundingComputation<Float64>
{
public:
    using ScalarType = Float64;
    using VectorType = __m128d;
    static const size_t data_count = 2;

    static VectorType load(const ScalarType * in) { return _mm_loadu_pd(in); }
    static VectorType load1(const ScalarType in) { return _mm_load1_pd(&in); }
    static void store(ScalarType * out, VectorType val) { _mm_storeu_pd(out, val);}
    static VectorType multiply(VectorType val, VectorType scale) { return _mm_mul_pd(val, scale); }
    static VectorType divide(VectorType val, VectorType scale) { return _mm_div_pd(val, scale); }
    template <RoundingMode mode> static VectorType apply(VectorType val) { return _mm_round_pd(val, int(mode)); }

    static VectorType prepare(size_t scale)
    {
        return load1(scale);
    }
};

#else

/// Implementation for ARM. Not vectorized.

inline float roundWithMode(float x, RoundingMode mode)
{
    switch (mode)
    {
        case RoundingMode::Round: return roundf(x);
        case RoundingMode::Floor: return floorf(x);
        case RoundingMode::Ceil: return ceilf(x);
        case RoundingMode::Trunc: return truncf(x);
    }
}

inline double roundWithMode(double x, RoundingMode mode)
{
    switch (mode)
    {
        case RoundingMode::Round: return round(x);
        case RoundingMode::Floor: return floor(x);
        case RoundingMode::Ceil: return ceil(x);
        case RoundingMode::Trunc: return trunc(x);
    }
}

template <typename T>
class BaseFloatRoundingComputation
{
public:
    using ScalarType = T;
    using VectorType = T;
    static const size_t data_count = 1;

    static VectorType load(const ScalarType * in) { return *in; }
    static VectorType load1(const ScalarType in) { return in; }
    static VectorType store(ScalarType * out, ScalarType val) { return *out = val;}
    static VectorType multiply(VectorType val, VectorType scale) { return val * scale; }
    static VectorType divide(VectorType val, VectorType scale) { return val / scale; }
    template <RoundingMode mode> static VectorType apply(VectorType val) { return roundWithMode(val, mode); }

    static VectorType prepare(size_t scale)
    {
        return load1(scale);
    }
};

#endif


/** Implementation of low-level round-off functions for floating-point values.
  */
template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
class FloatRoundingComputation : public BaseFloatRoundingComputation<T>
{
    using Base = BaseFloatRoundingComputation<T>;

public:
    static inline void compute(const T * __restrict in, const typename Base::VectorType & scale, T * __restrict out)
    {
        auto val = Base::load(in);

        if (scale_mode == ScaleMode::Positive)
            val = Base::multiply(val, scale);
        else if (scale_mode == ScaleMode::Negative)
            val = Base::divide(val, scale);

        val = Base::template apply<rounding_mode>(val);

        if (scale_mode == ScaleMode::Positive)
            val = Base::divide(val, scale);
        else if (scale_mode == ScaleMode::Negative)
            val = Base::multiply(val, scale);

        Base::store(out, val);
    }
};


/** Implementing high-level rounding functions.
  */
template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
struct FloatRoundingImpl
{
private:
    using Op = FloatRoundingComputation<T, rounding_mode, scale_mode>;
    using Data = std::array<T, Op::data_count>;

public:
    static NO_INLINE void apply(const PaddedPODArray<T> & in, size_t scale, typename ColumnVector<T>::Container_t & out)
    {
        auto mm_scale = Op::prepare(scale);

        const size_t data_count = std::tuple_size<Data>();

        const T* end_in = in.data() + in.size();
        const T* limit = in.data() + in.size() / data_count * data_count;

        const T* __restrict p_in = in.data();
        T* __restrict p_out = out.data();

        while (p_in < limit)
        {
            Op::compute(p_in, mm_scale, p_out);
            p_in += data_count;
            p_out += data_count;
        }

        if (p_in < end_in)
        {
            Data tmp_src{{}};
            Data tmp_dst;

            size_t tail_size_bytes = (end_in - p_in) * sizeof(*p_in);

            memcpy(&tmp_src, p_in, tail_size_bytes);
            Op::compute(reinterpret_cast<T *>(&tmp_src), mm_scale, reinterpret_cast<T *>(&tmp_dst));
            memcpy(p_out, &tmp_dst, tail_size_bytes);
        }
    }
};

template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
struct IntegerRoundingImpl
{
private:
    using Op = IntegerRoundingComputation<T, rounding_mode, scale_mode>;
    using Data = T;

public:
    template <size_t scale>
    static NO_INLINE void applyImpl(const PaddedPODArray<T> & in, typename ColumnVector<T>::Container_t & out)
    {
        const T* end_in = in.data() + in.size();

        const T* __restrict p_in = in.data();
        T* __restrict p_out = out.data();

        while (p_in < end_in)
        {
            Op::compute(p_in, scale, p_out);
            ++p_in;
            ++p_out;
        }
    }

    static NO_INLINE void apply(const PaddedPODArray<T> & in, size_t scale, typename ColumnVector<T>::Container_t & out)
    {
        /// Manual function cloning for compiler to generate integer division by constant.
        switch (scale)
        {
            case 1ULL: return applyImpl<1ULL>(in, out);
            case 10ULL: return applyImpl<10ULL>(in, out);
            case 100ULL: return applyImpl<100ULL>(in, out);
            case 1000ULL: return applyImpl<1000ULL>(in, out);
            case 10000ULL: return applyImpl<10000ULL>(in, out);
            case 100000ULL: return applyImpl<100000ULL>(in, out);
            case 1000000ULL: return applyImpl<1000000ULL>(in, out);
            case 10000000ULL: return applyImpl<10000000ULL>(in, out);
            case 100000000ULL: return applyImpl<100000000ULL>(in, out);
            case 1000000000ULL: return applyImpl<1000000000ULL>(in, out);
            case 10000000000ULL: return applyImpl<10000000000ULL>(in, out);
            case 100000000000ULL: return applyImpl<100000000000ULL>(in, out);
            case 1000000000000ULL: return applyImpl<1000000000000ULL>(in, out);
            case 10000000000000ULL: return applyImpl<10000000000000ULL>(in, out);
            case 100000000000000ULL: return applyImpl<100000000000000ULL>(in, out);
            case 1000000000000000ULL: return applyImpl<1000000000000000ULL>(in, out);
            case 10000000000000000ULL: return applyImpl<10000000000000000ULL>(in, out);
            case 100000000000000000ULL: return applyImpl<100000000000000000ULL>(in, out);
            case 1000000000000000000ULL: return applyImpl<1000000000000000000ULL>(in, out);
            case 10000000000000000000ULL: return applyImpl<10000000000000000000ULL>(in, out);
            default:
                throw Exception("Logical error: unexpected 'scale' parameter passed to function IntegerRoundingComputation::compute",
                    ErrorCodes::LOGICAL_ERROR);
        }
    }
};

template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode>
using FunctionRoundingImpl = typename std::conditional<std::is_floating_point<T>::value,
    FloatRoundingImpl<T, rounding_mode, scale_mode>,
    IntegerRoundingImpl<T, rounding_mode, scale_mode>>::type;


/** Select the appropriate processing algorithm depending on the scale.
  */
template <typename T, RoundingMode rounding_mode>
struct Dispatcher
{
    static void apply(Block & block, const ColumnVector<T> * col, const ColumnNumbers & arguments, size_t result)
    {
        size_t scale = 1;
        Int64 scale_arg = 0;

        if (arguments.size() == 2)
        {
            const IColumn & scale_column = *block.getByPosition(arguments[1]).column;
            if (!scale_column.isConst())
                throw Exception("Scale argument for rounding functions must be constant.", ErrorCodes::ILLEGAL_COLUMN);

            Field scale_field = static_cast<const ColumnConst &>(scale_column).getField();
            if (scale_field.getType() != Field::Types::UInt64
                && scale_field.getType() != Field::Types::Int64)
                throw Exception("Scale argument for rounding functions must have integer type.", ErrorCodes::ILLEGAL_COLUMN);

            scale_arg = scale_field.get<Int64>();
        }

        auto col_res = std::make_shared<ColumnVector<T>>();
        block.getByPosition(result).column = col_res;

        typename ColumnVector<T>::Container_t & vec_res = col_res->getData();
        vec_res.resize(col->getData().size());

        if (vec_res.empty())
            return;

        if (scale_arg == 0)
        {
            scale = 1;
            FunctionRoundingImpl<T, rounding_mode, ScaleMode::Zero>::apply(col->getData(), scale, vec_res);
        }
        else if (scale_arg > 0)
        {
            scale = pow(10, scale_arg);
            FunctionRoundingImpl<T, rounding_mode, ScaleMode::Positive>::apply(col->getData(), scale, vec_res);
        }
        else
        {
            scale = pow(10, -scale_arg);
            FunctionRoundingImpl<T, rounding_mode, ScaleMode::Negative>::apply(col->getData(), scale, vec_res);
        }
    }
};

/** A template for functions that round the value of an input parameter of type
  * (U)Int8/16/32/64 or Float32/64, and accept an additional optional
  * parameter (default is 0).
  */
template <typename Name, RoundingMode rounding_mode>
class FunctionRounding : public IFunction
{
public:
    static constexpr auto name = Name::name;
    static FunctionPtr create(const Context & context) { return std::make_shared<FunctionRounding>(); }

private:
    template <typename T>
    bool executeForType(Block & block, const ColumnNumbers & arguments, size_t result)
    {
        if (auto col = checkAndGetColumn<ColumnVector<T>>(block.getByPosition(arguments[0]).column.get()))
        {
            Dispatcher<T, rounding_mode>::apply(block, col, arguments, result);
            return true;
        }
        return false;
    }

public:
    String getName() const override
    {
        return name;
    }

    bool isVariadic() const override { return true; }
    size_t getNumberOfArguments() const override { return 0; }

    /// Get result types by argument types. If the function does not apply to these arguments, throw an exception.
    DataTypePtr getReturnTypeImpl(const DataTypes & arguments) const override
    {
        if ((arguments.size() < 1) || (arguments.size() > 2))
            throw Exception("Number of arguments for function " + getName() + " doesn't match: passed "
                + toString(arguments.size()) + ", should be 1 or 2.",
                ErrorCodes::NUMBER_OF_ARGUMENTS_DOESNT_MATCH);

        for (const auto & type : arguments)
            if (!type->behavesAsNumber())
                throw Exception("Illegal type " + arguments[0]->getName() + " of argument of function " + getName(),
                    ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);

        return arguments[0];
    }

    bool useDefaultImplementationForConstants() const override { return true; }
    ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1}; }

    void executeImpl(Block & block, const ColumnNumbers & arguments, size_t result) override
    {
        if (!(    executeForType<UInt8>(block, arguments, result)
            ||    executeForType<UInt16>(block, arguments, result)
            ||    executeForType<UInt32>(block, arguments, result)
            ||    executeForType<UInt64>(block, arguments, result)
            ||    executeForType<Int8>(block, arguments, result)
            ||    executeForType<Int16>(block, arguments, result)
            ||    executeForType<Int32>(block, arguments, result)
            ||    executeForType<Int64>(block, arguments, result)
            ||    executeForType<Float32>(block, arguments, result)
            ||    executeForType<Float64>(block, arguments, result)))
        {
            throw Exception("Illegal column " + block.getByPosition(arguments[0]).column->getName()
                    + " of argument of function " + getName(),
                    ErrorCodes::ILLEGAL_COLUMN);
        }
    }

    bool hasInformationAboutMonotonicity() const override
    {
        return true;
    }

    Monotonicity getMonotonicityForRange(const IDataType & type, const Field & left, const Field & right) const override
    {
        return { true, true, true };
    }
};


struct NameRoundToExp2 { static constexpr auto name = "roundToExp2"; };
struct NameRoundDuration { static constexpr auto name = "roundDuration"; };
struct NameRoundAge { static constexpr auto name = "roundAge"; };

struct NameRound { static constexpr auto name = "round"; };
struct NameCeil { static constexpr auto name = "ceil"; };
struct NameFloor { static constexpr auto name = "floor"; };
struct NameTrunc { static constexpr auto name = "trunc"; };

using FunctionRoundToExp2 = FunctionUnaryArithmetic<RoundToExp2Impl, NameRoundToExp2, false>;
using FunctionRoundDuration = FunctionUnaryArithmetic<RoundDurationImpl, NameRoundDuration, false>;
using FunctionRoundAge = FunctionUnaryArithmetic<RoundAgeImpl, NameRoundAge, false>;

using FunctionRound = FunctionRounding<NameRound, RoundingMode::Round>;
using FunctionFloor = FunctionRounding<NameFloor, RoundingMode::Floor>;
using FunctionCeil = FunctionRounding<NameCeil, RoundingMode::Ceil>;
using FunctionTrunc = FunctionRounding<NameTrunc, RoundingMode::Trunc>;


struct PositiveMonotonicity
{
    static bool has() { return true; }
    static IFunction::Monotonicity get(const Field & left, const Field & right)
    {
        return { true };
    }
};

template <> struct FunctionUnaryArithmeticMonotonicity<NameRoundToExp2> : PositiveMonotonicity {};
template <> struct FunctionUnaryArithmeticMonotonicity<NameRoundDuration> : PositiveMonotonicity {};
template <> struct FunctionUnaryArithmeticMonotonicity<NameRoundAge> : PositiveMonotonicity {};

}