scaled_rounding.h

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/******************************************************************************
The MIT License(MIT)
 
Embedded Template Library.
https://github.com/ETLCPP/etl
https://www.etlcpp.com
 
Copyright(c) 2018 John Wellbelove
 
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#ifndef ETL_SCALED_ROUNDING_INCLUDED
#define ETL_SCALED_ROUNDING_INCLUDED
 
#include "platform.h"
#include "absolute.h"
#include "static_assert.h"
#include "type_traits.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;
  };
 
  //*****************************************************************************
  //*****************************************************************************
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_ceiling_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
 
    if (value >= 0)
    {
      return T((value + scale_t(Scaling - 1U)) / scale_t(Scaling));
    }
    else
    {
      return T(value / scale_t(Scaling));
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_ceiling_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return round_ceiling_unscaled<Scaling>(value) * scale_t(Scaling);
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_floor_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
    if (Scaling == 1)
    {
      return value;
    }
 
    if (value >= 0)
    {
      return T(value / scale_t(Scaling));
    }
    else
    {
      return T((value - scale_t(Scaling - 1)) / scale_t(Scaling));
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_floor_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_floor_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_up_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
    else
    {
      if (value >= 0)
      {
        return T((value + scale_t(Scaling / 2U)) / scale_t(Scaling));
      }
      else
      {
        return T((value - scale_t(Scaling / 2U)) / scale_t(Scaling));
      }
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_up_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_half_up_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_down_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
 
    if (value >= 0)
    {
      return T((value + scale_t((Scaling - 1) / 2U)) / scale_t(Scaling));
    }
    else
    {
      return T((value - scale_t((Scaling - 1) / 2U)) / scale_t(Scaling));
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_down_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_half_down_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_zero_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
    else
    {
      return T(value / scale_t(Scaling));
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_zero_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_zero_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_infinity_unscaled(T value) ETL_NOEXCEPT
  {
    if (value >= 0)
    {
      return etl::round_ceiling_unscaled<Scaling>(value);
    }
    else
    {
      return etl::round_floor_unscaled<Scaling>(value);
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_infinity_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_infinity_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_even_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
    else
    {
      // Half?
      if ((etl::absolute(value) % scale_t(Scaling)) == scale_t(Scaling / 2U))
      {
        // Odd?
        if (static_cast<unsigned int>(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));
      }
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_even_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_half_even_unscaled<Scaling>(value) * scale_t(Scaling));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_odd_unscaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    if (Scaling == 1)
    {
      return value;
    }
    else
    {
      // Half?
      if ((etl::absolute(value) % scale_t(Scaling)) == scale_t(Scaling / 2U))
      {
        // Odd?
        if (static_cast<unsigned int>(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));
      }
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <uint32_t Scaling, typename T>
  ETL_NODISCARD ETL_CONSTEXPR14 T round_half_odd_scaled(T value) ETL_NOEXCEPT
  {
    typedef typename scaled_rounding_t<T>::type scale_t;
 
    return T(round_half_odd_unscaled<Scaling>(value) * scale_t(Scaling));
  }
} // namespace etl
 
#endif