rounded_integral_division.h

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/******************************************************************************
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Embedded Template Library.
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Copyright(c) 2025 John Wellbelove
 
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#ifndef ETL_ROUNDED_INTEGRAL_DIVISION_INCLUDED
#define ETL_ROUNDED_INTEGRAL_DIVISION_INCLUDED
 
#include "platform.h"
#include "type_traits.h"
#include "absolute.h"
#include "utility.h"
 
namespace etl
{
  namespace private_rounded_integral_division
  {
    //*****************************************************************************
    // Checks if two values have the same sign.
    // For signed integral types.
    //*****************************************************************************
    template <typename T>
    ETL_CONSTEXPR
    typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, bool>::type
      are_same_sign(T a, T b) ETL_NOEXCEPT
    {
      return ((a ^ b) >= 0);
    }
 
    //*****************************************************************************
    // Checks if two values have the same sign.
    // For unsigned integral types.
    //*****************************************************************************
    template <typename T>
    ETL_CONSTEXPR
    typename etl::enable_if<etl::is_integral<T>::value && etl::is_unsigned<T>::value, bool>::type
      are_same_sign(T /*a*/, T /*b*/) ETL_NOEXCEPT
    {
      return true;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value && etl::is_signed<T>::value, T>::type
    divide_round_to_ceiling(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
 
    // If remainder is zero, already exact
    if (remainder == 0)
    {
      return quotient;
    }
 
    // If signs are the same, increment quotient
    return private_rounded_integral_division::are_same_sign(numerator, denominator) ? quotient + 1 : quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_ceiling(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_to_ceiling(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_unsigned<T>::value,
                          T>::type
    divide_round_to_ceiling(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
    
    // If remainder is zero, already exact, otherwise, increment quotient
    return remainder == 0U ? quotient : quotient + 1U;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_ceiling(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_to_ceiling(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value,
                          T>::type
    divide_round_to_floor(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
 
    // If remainder is zero, already exact
    if (remainder == 0)
    {
      return quotient;
    }
 
    // If signs are different, decrement quotient
    return private_rounded_integral_division::are_same_sign(numerator, denominator) ? quotient : quotient - 1;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
    typename etl::enable_if<etl::is_integral<T1>::value &&
                            etl::is_integral<T2>::value &&
                            etl::is_signed<T1>::value &&
                            etl::is_signed<T2>::value,
                            typename etl::common_type<T1, T2>::type>::type
    divide_round_to_floor(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_to_floor(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_unsigned<T>::value,
                          T>::type
    divide_round_to_floor(T numerator, T denominator) ETL_NOEXCEPT
  {
    return numerator / denominator;
  }
 
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_floor(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    const type common_numerator = numerator;
    const type common_denominator = denominator;
 
    return common_numerator / common_denominator;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value, 
                          T>::type
    divide_round_to_infinity(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
    
    if (private_rounded_integral_division::are_same_sign(numerator, denominator))
    {
      // Same sign, round towards +infinity
      return (remainder != 0) ? quotient + 1 : quotient;
    }
    else
    {
      // Different signs, round towards -infinity
      return (remainder != 0) ? quotient - 1 : quotient;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value && 
                          etl::is_integral<T2>::value && 
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value, 
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_infinity(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_to_infinity(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value && 
                          etl::is_unsigned<T>::value, 
                          T>::type
    divide_round_to_infinity(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
 
    return remainder ? quotient + 1U : quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value && 
                          etl::is_integral<T2>::value && 
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value, 
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_infinity(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_to_infinity(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value && 
                          etl::is_unsigned<T>::value, 
                          T>::type
    divide_round_to_zero(T numerator, T denominator) ETL_NOEXCEPT
  {
    return numerator / denominator;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value && 
                          etl::is_integral<T2>::value, 
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_to_zero(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    // Cast to common type to avoid overflow.
    const type common_numerator   = numerator;
    const type common_denominator = denominator;
 
    return common_numerator / common_denominator;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value,
                          T>::type
    divide_round_half_up(T numerator, T denominator) ETL_NOEXCEPT
  {
    // Normal division
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
 
    // Work with magnitudes in unsigned form (avoids abs() overflow)
    typedef typename std::make_unsigned<T>::type utype;
    utype abs_remainder   = remainder < 0 ? utype(0) - utype(remainder) : utype(remainder);
    utype abs_denominator = denominator < 0 ? utype(0) - utype(denominator)       : utype(denominator);
 
    // Threshold for rounding up (half the denominatorominator, rounded up)
    utype half_denominator = (abs_denominator + 1) / 2;
 
    if (abs_remainder >= half_denominator) 
    {
      // Round away from zero
      if (private_rounded_integral_division::are_same_sign(numerator, denominator)) 
      {
        return quotient + 1; // same sign ? increment
      }
      else 
      {
        return quotient - 1; // different sign ? decrement
      }
    }
 
    return quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_up(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_up(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value && 
                          etl::is_unsigned<T>::value, 
                          T>::type
    divide_round_half_up(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient = numerator / denominator;
 
    // If remainder is at least half the divisor, round up
    return (remainder >= (denominator / 2U) + (denominator % 2U)) ? quotient + 1U : quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value && 
                          etl::is_integral<T2>::value && 
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value, typename etl::common_type<T1, T2>::type>::type
    divide_round_half_up(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_up(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value,
                          T>::type
    divide_round_half_down(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T quotient            = numerator / denominator;
    const T remainder           = numerator % denominator;
    const T abs_denominator     = etl::absolute(denominator);
    const T abs_remainderainder = etl::absolute(remainder);
 
    // Direction: +1 if result should be more positive, -1 if more negative
    const T direction = ((numerator >= 0) == (denominator >= 0)) ? 1 : -1;
 
    // Only round away from zero if remainder is strictly greater than half the divisor
    return abs_remainderainder > (abs_denominator / 2) ? quotient + direction : quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_down(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_down(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_unsigned<T>::value, 
                          T>::type
    divide_round_half_down(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T remainder = numerator % denominator;
    const T quotient  = numerator / denominator;
 
    // If remainder is at least half the divisor, round down
    return (remainder > (denominator / 2U)) ? quotient + 1U : quotient;
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value && 
                          etl::is_integral<T2>::value && 
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value, typename etl::common_type<T1, T2>::type>::type
    divide_round_half_down(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_down(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value, 
                          T>::type
    divide_round_half_even(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T quotient            = numerator / denominator;
    const T remainder           = numerator % denominator;
    const T abs_denominator     = etl::absolute(denominator);
    const T abs_remainderainder = etl::absolute(remainder);
    const T direction           = ((numerator >= 0) == (denominator >= 0)) ? 1 : -1;
 
    if ((abs_remainderainder * 2) < abs_denominator)
    {
      return quotient;
    }
    else if ((abs_remainderainder * 2) > abs_denominator)
    {
      return quotient + direction;
    }
    else
    {
      // Exactly halfway, round to even
      return (quotient & 1) == 0 ? quotient : quotient + direction;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_even(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_unsigned<T>::value,
                          T>::type
    divide_round_half_even(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T quotient  = numerator / denominator;
    const T remainder = numerator % denominator;
 
    if ((remainder * 2U) < denominator)
    {
      // Less than halfway, round down
      return quotient;
    }
    else if ((remainder * 2U) > denominator)
    {
      // More than halfway, round up
      return quotient + 1U;
    }
    else
    {
      // Exactly halfway, round to even
      return (quotient & 1U) == 0U ? quotient : quotient + 1;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_even(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_signed<T>::value,
                          T>::type
    divide_round_half_odd(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T quotient            = numerator / denominator;
    const T remainder           = numerator % denominator;
    const T abs_denominator     = etl::absolute(denominator);
    const T abs_remainderainder = etl::absolute(remainder);
    const T direction           = ((numerator >= 0) == (denominator >= 0)) ? 1 : -1;
 
    if ((abs_remainderainder * 2) < abs_denominator)
    {
      return quotient;
    }
    else if ((abs_remainderainder * 2) > abs_denominator)
    {
      return quotient + direction;
    }
    else
    {
      // Exactly halfway, round to odd
      return (quotient & 1) != 0 ? quotient : quotient + direction;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_signed<T1>::value &&
                          etl::is_signed<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_odd(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_odd(static_cast<type>(numerator), static_cast<type>(denominator));
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T>::value &&
                          etl::is_unsigned<T>::value,
                          T>::type
    divide_round_half_odd(T numerator, T denominator) ETL_NOEXCEPT
  {
    const T quotient  = numerator / denominator;
    const T remainder = numerator % denominator;
    const T direction = ((numerator >= 0U) == (denominator >= 0U)) ? 1 : -1;
 
    if ((remainder * 2U) < denominator)
    {
      return quotient;
    }
    else if ((remainder * 2U) > denominator)
    {
      return quotient + direction;
    }
    else
    {
      // Exactly halfway, round to odd
      return (quotient & 1U) != 0U ? quotient : quotient + direction;
    }
  }
 
  //***************************************************************************
  //***************************************************************************
  template <typename T1, typename T2>
  ETL_CONSTEXPR14
  typename etl::enable_if<etl::is_integral<T1>::value &&
                          etl::is_integral<T2>::value &&
                          etl::is_unsigned<T1>::value &&
                          etl::is_unsigned<T2>::value,
                          typename etl::common_type<T1, T2>::type>::type
    divide_round_half_odd(T1 numerator, T2 denominator) ETL_NOEXCEPT
  {
    typedef typename etl::common_type<T1, T2>::type type;
 
    return divide_round_half_odd(static_cast<type>(numerator), static_cast<type>(denominator));
  }
}
 
#endif