356 lines
12 KiB
C
356 lines
12 KiB
C
|
///\file
|
||
|
|
|
||
|
|
/******************************************************************************
|
||
|
|
The MIT License(MIT)
|
||
|
|
|
||
|
|
Embedded Template Library.
|
||
|
|
https://github.com/ETLCPP/etl
|
||
|
|
https://www.etlcpp.com
|
||
|
|
|
||
|
|
Copyright(c) 2018 John Wellbelove
|
||
|
|
|
||
|
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||
|
|
of this software and associated documentation files(the "Software"), to deal
|
||
|
|
in the Software without restriction, including without limitation the rights
|
||
|
|
to use, copy, modify, merge, publish, distribute, sublicense, and / or sell
|
||
|
|
copies of the Software, and to permit persons to whom the Software is
|
||
|
|
furnished to do so, subject to the following conditions :
|
||
|
|
|
||
|
|
The above copyright notice and this permission notice shall be included in all
|
||
|
|
copies or substantial portions of the Software.
|
||
|
|
|
||
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||
|
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE
|
||
|
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||
|
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
||
|
|
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
|
||
|
|
SOFTWARE.
|
||
|
|
******************************************************************************/
|
||
|
|
|
||
|
|
#ifndef ETL_SCALED_ROUNDING_INCLUDED
|
||
|
|
#define ETL_SCALED_ROUNDING_INCLUDED
|
||
|
|
|
||
|
|
#include "static_assert.h"
|
||
|
|
#include "type_traits.h"
|
||
|
|
#include "absolute.h"
|
||
|
|
|
||
|
|
namespace etl
|
||
|
|
{
|
||
|
|
template <typename T>
|
||
|
|
struct scaled_rounding_t
|
||
|
|
{
|
||
|
|
typedef typename etl::conditional<etl::is_signed<T>::value, int32_t, uint32_t>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
//*****************************************************************************
|
||
|
|
/// A set of rounding algorithms for scaled integrals.
|
||
|
|
/// \tparam T The integral type.
|
||
|
|
/// \tparam SCALING The scaling factor.
|
||
|
|
///
|
||
|
|
/// \example For emulating fixed point of two decimal places we could use a
|
||
|
|
/// scaling factor of '100'. To round the result of scaled int calculations
|
||
|
|
/// using 'Banker's Rounding' we would define this.
|
||
|
|
/// \code
|
||
|
|
/// typedef etl::scaled_rounding<int, 100> Rounding;
|
||
|
|
/// int final_result = Rounding::round_half_even_unscaled(accumulated_result);
|
||
|
|
/// \endcode
|
||
|
|
/// \link http://www.clivemaxfield.com/diycalculator/sp-round.shtml
|
||
|
|
//*****************************************************************************
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to more positive integer.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_ceiling_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
if (value >= 0)
|
||
|
|
{
|
||
|
|
return T((value + scale_t(SCALING)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T(value / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to more positive integer.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_ceiling_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return round_ceiling_unscaled<SCALING>(value) * scale_t(SCALING);
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to more negative integer.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_floor_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
if (value >= 0)
|
||
|
|
{
|
||
|
|
return T(value / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T((value - scale_t(SCALING)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to more negative integer.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_floor_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_floor_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded up (to infinity).
|
||
|
|
/// Uses 'symmetric up' rounding.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_up_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
ETL_STATIC_ASSERT((((SCALING / 2U) * 2U) == SCALING), "Scaling must be divisible by 2");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
if (value >= 0)
|
||
|
|
{
|
||
|
|
return T((value + scale_t(SCALING / 2U)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T((value - scale_t(SCALING / 2U)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded up (to infinity).
|
||
|
|
/// Uses 'symmetric up' rounding.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_up_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_half_up_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded down (to zero).
|
||
|
|
/// Uses 'symmetric down' rounding.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_down_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
ETL_STATIC_ASSERT((((SCALING / 2U) * 2U) == SCALING), "Scaling must be divisible by 2");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
if (value >= 0)
|
||
|
|
{
|
||
|
|
return T((value + scale_t((SCALING / 2U) - 1U)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T((value - scale_t((SCALING / 2U) - 1U)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded down (to zero).
|
||
|
|
/// Uses 'symmetric down' rounding.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_down_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_half_down_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round toward zero.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_zero_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(value / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round toward zero.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_zero_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_zero_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round toward infinity.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_infinity_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
if (value >= 0)
|
||
|
|
{
|
||
|
|
return T((value + scale_t(SCALING)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T((value - scale_t(SCALING)) / scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round toward infinity.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_infinity_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_infinity_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded to even integral.
|
||
|
|
/// Also known as 'Banker's Rounding'.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_even_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
// Half?
|
||
|
|
if ((etl::absolute(value) % scale_t(SCALING)) == scale_t(SCALING / 2U))
|
||
|
|
{
|
||
|
|
// Odd?
|
||
|
|
if ((value / scale_t(SCALING)) & 1U)
|
||
|
|
{
|
||
|
|
return T(round_half_up_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T(round_half_down_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T(round_half_up_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded to even integral.
|
||
|
|
/// Also known as 'Banker's Rounding'.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_even_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_half_even_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded to odd integral.
|
||
|
|
/// Also known as 'Banker's Rounding'.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Unscaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_odd_unscaled(T value)
|
||
|
|
{
|
||
|
|
ETL_STATIC_ASSERT(etl::is_integral<T>::value, "Type must be an integral");
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
// Half?
|
||
|
|
if ((etl::absolute(value) % scale_t(SCALING)) == scale_t(SCALING / 2U))
|
||
|
|
{
|
||
|
|
// Odd?
|
||
|
|
if ((value / scale_t(SCALING)) & 1U)
|
||
|
|
{
|
||
|
|
return T(round_half_down_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T(round_half_up_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return T(round_half_up_unscaled<SCALING>(value));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//***************************************************************************
|
||
|
|
/// Round to nearest integer. 'Half' value is rounded to odd integral.
|
||
|
|
/// Also known as 'Banker's Rounding'.
|
||
|
|
/// \param value Scaled integral.
|
||
|
|
/// \return Scaled, rounded integral.
|
||
|
|
//***************************************************************************
|
||
|
|
template <uint32_t SCALING, typename T>
|
||
|
|
T round_half_odd_scaled(T value)
|
||
|
|
{
|
||
|
|
typedef typename scaled_rounding_t<T>::type scale_t;
|
||
|
|
|
||
|
|
return T(round_half_odd_unscaled<SCALING>(value) * scale_t(SCALING));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|