ClickHouse/src/Functions/FunctionsRound.h
2021-08-09 18:01:08 +03:00

816 lines
28 KiB
C++

#pragma once
#include <Functions/FunctionHelpers.h>
#include <IO/WriteHelpers.h>
#include <DataTypes/getLeastSupertype.h>
#include <DataTypes/DataTypeArray.h>
#include <DataTypes/DataTypesNumber.h>
#include <DataTypes/DataTypesDecimal.h>
#include <DataTypes/DataTypeDateTime64.h>
#include <Columns/ColumnVector.h>
#include <Interpreters/castColumn.h>
#include "IFunction.h"
#include <Common/intExp.h>
#include <Common/assert_cast.h>
#include <Core/Defines.h>
#include <cmath>
#include <type_traits>
#include <array>
#include <common/bit_cast.h>
#include <algorithm>
#ifdef __SSE4_1__
#include <smmintrin.h>
#else
#include <fenv.h>
#endif
namespace DB
{
namespace ErrorCodes
{
extern const int NUMBER_OF_ARGUMENTS_DOESNT_MATCH;
extern const int ILLEGAL_TYPE_OF_ARGUMENT;
extern const int ARGUMENT_OUT_OF_BOUND;
extern const int ILLEGAL_COLUMN;
extern const int BAD_ARGUMENTS;
extern const int CANNOT_SET_ROUNDING_MODE;
}
/** Rounding Functions:
* round(x, N) - rounding to nearest (N = 0 by default). Use banker's rounding for floating point numbers.
* roundBankers(x, N) - rounding to nearest (N = 0 by default). Use banker's rounding for all 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.
*/
/** 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
{
#ifdef __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
};
enum class TieBreakingMode
{
Auto, // use banker's rounding for floating point numbers, round up otherwise
Bankers, // use banker's rounding
};
/// For N, no more than the number of digits in the largest type.
using Scale = Int16;
/** Rounding functions for integer values.
*/
template <typename T, RoundingMode rounding_mode, ScaleMode scale_mode, TieBreakingMode tie_breaking_mode>
struct IntegerRoundingComputation
{
static const size_t data_count = 1;
static size_t prepare(size_t scale)
{
return scale;
}
/// Integer overflow is Ok.
static ALWAYS_INLINE_NO_SANITIZE_UNDEFINED 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:
{
if (x < 0)
x -= scale;
switch (tie_breaking_mode)
{
case TieBreakingMode::Auto:
x = (x + scale / 2) / scale * scale;
break;
case TieBreakingMode::Bankers:
{
T quotient = (x + scale / 2) / scale;
if (quotient * scale == x + scale / 2)
// round half to even
x = ((quotient + (x < 0)) & ~1) * scale;
else
// round the others as usual
x = quotient * scale;
break;
}
}
return x;
}
}
__builtin_unreachable();
}
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);
}
__builtin_unreachable();
}
static ALWAYS_INLINE void compute(const T * __restrict in, size_t scale, T * __restrict out)
{
if (sizeof(T) <= sizeof(scale) && scale > size_t(std::numeric_limits<T>::max()))
*out = 0;
else
*out = compute(*in, scale);
}
};
#ifdef __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 nearbyintf(x);
case RoundingMode::Floor: return floorf(x);
case RoundingMode::Ceil: return ceilf(x);
case RoundingMode::Trunc: return truncf(x);
}
__builtin_unreachable();
}
inline double roundWithMode(double x, RoundingMode mode)
{
switch (mode)
{
case RoundingMode::Round: return nearbyint(x);
case RoundingMode::Floor: return floor(x);
case RoundingMode::Ceil: return ceil(x);
case RoundingMode::Trunc: return trunc(x);
}
__builtin_unreachable();
}
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:
static_assert(!IsDecimalNumber<T>);
using Op = FloatRoundingComputation<T, rounding_mode, scale_mode>;
using Data = std::array<T, Op::data_count>;
using ColumnType = std::conditional_t<IsDecimalNumber<T>, ColumnDecimal<T>, ColumnVector<T>>;
using Container = typename ColumnType::Container;
public:
static NO_INLINE void apply(const Container & in, size_t scale, Container & 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, TieBreakingMode tie_breaking_mode>
struct IntegerRoundingImpl
{
private:
using Op = IntegerRoundingComputation<T, rounding_mode, scale_mode, tie_breaking_mode>;
using Container = typename ColumnVector<T>::Container;
public:
template <size_t scale>
static NO_INLINE void applyImpl(const Container & in, Container & 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 Container & in, size_t scale, Container & 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("Unexpected 'scale' parameter passed to function",
ErrorCodes::BAD_ARGUMENTS);
}
}
};
template <typename T, RoundingMode rounding_mode, TieBreakingMode tie_breaking_mode>
class DecimalRoundingImpl
{
private:
static_assert(IsDecimalNumber<T>);
using NativeType = typename T::NativeType;
using Op = IntegerRoundingComputation<NativeType, rounding_mode, ScaleMode::Negative, tie_breaking_mode>;
using Container = typename ColumnDecimal<T>::Container;
public:
static NO_INLINE void apply(const Container & in, Container & out, Scale scale_arg)
{
scale_arg = in.getScale() - scale_arg;
if (scale_arg > 0)
{
size_t scale = intExp10(scale_arg);
const NativeType * __restrict p_in = reinterpret_cast<const NativeType *>(in.data());
const NativeType * end_in = reinterpret_cast<const NativeType *>(in.data()) + in.size();
NativeType * __restrict p_out = reinterpret_cast<NativeType *>(out.data());
while (p_in < end_in)
{
Op::compute(p_in, scale, p_out);
++p_in;
++p_out;
}
}
else
{
memcpy(out.data(), in.data(), in.size() * sizeof(T));
}
}
};
/** Select the appropriate processing algorithm depending on the scale.
*/
template <typename T, RoundingMode rounding_mode, TieBreakingMode tie_breaking_mode>
class Dispatcher
{
template <ScaleMode scale_mode>
using FunctionRoundingImpl = std::conditional_t<std::is_floating_point_v<T>,
FloatRoundingImpl<T, rounding_mode, scale_mode>,
IntegerRoundingImpl<T, rounding_mode, scale_mode, tie_breaking_mode>>;
static ColumnPtr apply(const ColumnVector<T> * col, Scale scale_arg)
{
auto col_res = ColumnVector<T>::create();
typename ColumnVector<T>::Container & vec_res = col_res->getData();
vec_res.resize(col->getData().size());
if (!vec_res.empty())
{
if (scale_arg == 0)
{
size_t scale = 1;
FunctionRoundingImpl<ScaleMode::Zero>::apply(col->getData(), scale, vec_res);
}
else if (scale_arg > 0)
{
size_t scale = intExp10(scale_arg);
FunctionRoundingImpl<ScaleMode::Positive>::apply(col->getData(), scale, vec_res);
}
else
{
size_t scale = intExp10(-scale_arg);
FunctionRoundingImpl<ScaleMode::Negative>::apply(col->getData(), scale, vec_res);
}
}
return col_res;
}
static ColumnPtr apply(const ColumnDecimal<T> * col, Scale scale_arg)
{
const typename ColumnDecimal<T>::Container & vec_src = col->getData();
auto col_res = ColumnDecimal<T>::create(vec_src.size(), vec_src.getScale());
auto & vec_res = col_res->getData();
if (!vec_res.empty())
DecimalRoundingImpl<T, rounding_mode, tie_breaking_mode>::apply(col->getData(), vec_res, scale_arg);
return col_res;
}
public:
static ColumnPtr apply(const IColumn * column, Scale scale_arg)
{
if constexpr (is_arithmetic_v<T>)
return apply(checkAndGetColumn<ColumnVector<T>>(column), scale_arg);
else if constexpr (IsDecimalNumber<T>)
return apply(checkAndGetColumn<ColumnDecimal<T>>(column), scale_arg);
}
};
/** A template for functions that round the value of an input parameter of type
* (U)Int8/16/32/64, Float32/64 or Decimal32/64/128, and accept an additional optional parameter (default is 0).
*/
template <typename Name, RoundingMode rounding_mode, TieBreakingMode tie_breaking_mode>
class FunctionRounding : public IFunction
{
public:
static constexpr auto name = Name::name;
static FunctionPtr create(ContextPtr) { return std::make_shared<FunctionRounding>(); }
String getName() const override
{
return name;
}
bool isVariadic() const override { return true; }
size_t getNumberOfArguments() const override { return 0; }
bool isSuitableForShortCircuitArgumentsExecution(const DataTypesWithConstInfo & /*arguments*/) const override { return false; }
/// 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.empty()) || (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 (!isNumber(type))
throw Exception("Illegal type " + arguments[0]->getName() + " of argument of function " + getName(),
ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
return arguments[0];
}
static Scale getScaleArg(const ColumnsWithTypeAndName & arguments)
{
if (arguments.size() == 2)
{
const IColumn & scale_column = *arguments[1].column;
if (!isColumnConst(scale_column))
throw Exception("Scale argument for rounding functions must be constant", ErrorCodes::ILLEGAL_COLUMN);
Field scale_field = assert_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);
Int64 scale64 = scale_field.get<Int64>();
if (scale64 > std::numeric_limits<Scale>::max()
|| scale64 < std::numeric_limits<Scale>::min())
throw Exception("Scale argument for rounding function is too large", ErrorCodes::ARGUMENT_OUT_OF_BOUND);
return scale64;
}
return 0;
}
bool useDefaultImplementationForConstants() const override { return true; }
ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1}; }
ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t /*input_rows_count*/) const override
{
const ColumnWithTypeAndName & column = arguments[0];
Scale scale_arg = getScaleArg(arguments);
ColumnPtr res;
auto call = [&](const auto & types) -> bool
{
using Types = std::decay_t<decltype(types)>;
using DataType = typename Types::LeftType;
if constexpr (IsDataTypeNumber<DataType> || IsDataTypeDecimal<DataType>)
{
using FieldType = typename DataType::FieldType;
res = Dispatcher<FieldType, rounding_mode, tie_breaking_mode>::apply(column.column.get(), scale_arg);
return true;
}
return false;
};
#if !defined(__SSE4_1__)
/// In case of "nearbyint" function is used, we should ensure the expected rounding mode for the Banker's rounding.
/// Actually it is by default. But we will set it just in case.
if constexpr (rounding_mode == RoundingMode::Round)
if (0 != fesetround(FE_TONEAREST))
throw Exception("Cannot set floating point rounding mode", ErrorCodes::CANNOT_SET_ROUNDING_MODE);
#endif
if (!callOnIndexAndDataType<void>(column.type->getTypeId(), call))
{
throw Exception("Illegal column " + column.name + " of argument of function " + getName(),
ErrorCodes::ILLEGAL_COLUMN);
}
return res;
}
bool hasInformationAboutMonotonicity() const override
{
return true;
}
Monotonicity getMonotonicityForRange(const IDataType &, const Field &, const Field &) const override
{
return { true, true, true };
}
};
/** Rounds down to a number within explicitly specified array.
* If the value is less than the minimal bound - returns the minimal bound.
*/
class FunctionRoundDown : public IFunction
{
public:
static constexpr auto name = "roundDown";
static FunctionPtr create(ContextPtr) { return std::make_shared<FunctionRoundDown>(); }
String getName() const override { return name; }
bool isVariadic() const override { return false; }
size_t getNumberOfArguments() const override { return 2; }
bool useDefaultImplementationForConstants() const override { return true; }
ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1}; }
bool isSuitableForShortCircuitArgumentsExecution(const DataTypesWithConstInfo & /*arguments*/) const override { return false; }
DataTypePtr getReturnTypeImpl(const DataTypes & arguments) const override
{
const DataTypePtr & type_x = arguments[0];
if (!isNumber(type_x))
throw Exception{"Unsupported type " + type_x->getName()
+ " of first argument of function " + getName()
+ ", must be numeric type.", ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT};
const DataTypeArray * type_arr = checkAndGetDataType<DataTypeArray>(arguments[1].get());
if (!type_arr)
throw Exception{"Second argument of function " + getName()
+ ", must be array of boundaries to round to.", ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT};
const auto type_arr_nested = type_arr->getNestedType();
if (!isNumber(type_arr_nested))
{
throw Exception{"Elements of array of second argument of function " + getName()
+ " must be numeric type.", ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT};
}
return getLeastSupertype({type_x, type_arr_nested});
}
ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr & result_type, size_t) const override
{
auto in_column = arguments[0].column;
const auto & in_type = arguments[0].type;
auto array_column = arguments[1].column;
const auto & array_type = arguments[1].type;
const auto & return_type = result_type;
auto column_result = return_type->createColumn();
auto * out = column_result.get();
if (!in_type->equals(*return_type))
in_column = castColumn(arguments[0], return_type);
if (!array_type->equals(*return_type))
array_column = castColumn(arguments[1], std::make_shared<DataTypeArray>(return_type));
const auto * in = in_column.get();
auto boundaries = typeid_cast<const ColumnConst &>(*array_column).getValue<Array>();
size_t num_boundaries = boundaries.size();
if (!num_boundaries)
throw Exception("Empty array is illegal for boundaries in " + getName() + " function", ErrorCodes::BAD_ARGUMENTS);
if (!executeNum<UInt8>(in, out, boundaries)
&& !executeNum<UInt16>(in, out, boundaries)
&& !executeNum<UInt32>(in, out, boundaries)
&& !executeNum<UInt64>(in, out, boundaries)
&& !executeNum<Int8>(in, out, boundaries)
&& !executeNum<Int16>(in, out, boundaries)
&& !executeNum<Int32>(in, out, boundaries)
&& !executeNum<Int64>(in, out, boundaries)
&& !executeNum<Float32>(in, out, boundaries)
&& !executeNum<Float64>(in, out, boundaries)
&& !executeDecimal<Decimal32>(in, out, boundaries)
&& !executeDecimal<Decimal64>(in, out, boundaries)
&& !executeDecimal<Decimal128>(in, out, boundaries))
{
throw Exception{"Illegal column " + in->getName() + " of first argument of function " + getName(), ErrorCodes::ILLEGAL_COLUMN};
}
return column_result;
}
private:
template <typename T>
bool executeNum(const IColumn * in_untyped, IColumn * out_untyped, const Array & boundaries) const
{
const auto in = checkAndGetColumn<ColumnVector<T>>(in_untyped);
auto out = typeid_cast<ColumnVector<T> *>(out_untyped);
if (!in || !out)
return false;
executeImplNumToNum(in->getData(), out->getData(), boundaries);
return true;
}
template <typename T>
bool executeDecimal(const IColumn * in_untyped, IColumn * out_untyped, const Array & boundaries) const
{
const auto in = checkAndGetColumn<ColumnDecimal<T>>(in_untyped);
auto out = typeid_cast<ColumnDecimal<T> *>(out_untyped);
if (!in || !out)
return false;
executeImplNumToNum(in->getData(), out->getData(), boundaries);
return true;
}
template <typename Container>
void NO_INLINE executeImplNumToNum(const Container & src, Container & dst, const Array & boundaries) const
{
using ValueType = typename Container::value_type;
std::vector<ValueType> boundary_values(boundaries.size());
for (size_t i = 0; i < boundaries.size(); ++i)
boundary_values[i] = boundaries[i].get<ValueType>();
std::sort(boundary_values.begin(), boundary_values.end());
boundary_values.erase(std::unique(boundary_values.begin(), boundary_values.end()), boundary_values.end());
size_t size = src.size();
dst.resize(size);
if (boundary_values.size() < 32) /// Just a guess
{
/// Linear search with value on previous iteration as a hint.
/// Not optimal if the size of list is large and distribution of values is uniform random.
auto begin = boundary_values.begin();
auto end = boundary_values.end();
auto it = begin + (end - begin) / 2;
for (size_t i = 0; i < size; ++i)
{
auto value = src[i];
if (*it < value)
{
while (it != end && *it <= value)
++it;
if (it != begin)
--it;
}
else
{
while (*it > value && it != begin)
--it;
}
dst[i] = *it;
}
}
else
{
for (size_t i = 0; i < size; ++i)
{
auto it = std::upper_bound(boundary_values.begin(), boundary_values.end(), src[i]);
if (it == boundary_values.end())
{
dst[i] = boundary_values.back();
}
else if (it == boundary_values.begin())
{
dst[i] = boundary_values.front();
}
else
{
dst[i] = *(it - 1);
}
}
}
}
};
struct NameRound { static constexpr auto name = "round"; };
struct NameRoundBankers { static constexpr auto name = "roundBankers"; };
struct NameCeil { static constexpr auto name = "ceil"; };
struct NameFloor { static constexpr auto name = "floor"; };
struct NameTrunc { static constexpr auto name = "trunc"; };
using FunctionRound = FunctionRounding<NameRound, RoundingMode::Round, TieBreakingMode::Auto>;
using FunctionRoundBankers = FunctionRounding<NameRoundBankers, RoundingMode::Round, TieBreakingMode::Bankers>;
using FunctionFloor = FunctionRounding<NameFloor, RoundingMode::Floor, TieBreakingMode::Auto>;
using FunctionCeil = FunctionRounding<NameCeil, RoundingMode::Ceil, TieBreakingMode::Auto>;
using FunctionTrunc = FunctionRounding<NameTrunc, RoundingMode::Trunc, TieBreakingMode::Auto>;
}