Rounded integral division

Maths

Header: rounded_integral_division.h
From: 20.9.0

Rounded division algorithms for integral values.

These algorithms perform integer division while rounding the result as though the fractional part were actually present. They do not check for a denominator of zero.

divide_round_to_ceiling

Values are rounded to the next more positive integral value.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_to_ceiling(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  2
.150 / 100 ==  2
.149 / 100 ==  2
.51 / 100 ==  1
..50 / 100 ==  1
..49 / 100 ==  1
.-49 / 100 ==  0
.-50 / 100 ==  0
.-51 / 100 ==  0
-149 / 100 == -1
-150 / 100 == -1
-151 / 100 == -1

divide_round_to_floor

Values are rounded to the next more negative integral value.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_to_floor(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  1
.150 / 100 ==  1
.149 / 100 ==  1
..51 / 100 ==  0
..50 / 100 ==  0
..49 / 100 ==  0
.-49 / 100 == -1
.-50 / 100 == -1
.-51 / 100 == -1
-149 / 100 == -2
-150 / 100 == -2
-151 / 100 == -2

divide_round_to_zero

Values are rounded towards zero.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_to_zero(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  1
.150 / 100 ==  1
.149 / 100 ==  1
..51 / 100 ==  0
..50 / 100 ==  0
..49 / 100 ==  0
.-49 / 100 ==  0
.-50 / 100 ==  0
.-51 / 100 ==  0
-149 / 100 == -1
-150 / 100 == -1
-151 / 100 == -1

divide_round_to_infinity

Values are rounded towards infinity.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_to_infinity(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  2
.150 / 100 ==  2
.149 / 100 ==  2
..51 / 100 ==  1
..50 / 100 ==  1
..49 / 100 ==  1
.-49 / 100 == -1
.-50 / 100 == -1
.-51 / 100 == -1
-149 / 100 == -2
-150 / 100 == -2
-151 / 100 == -2

divide_round_half_up

Values are rounded to the nearest integral value.
‘Half’ values are rounded up (towards infinity).

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_half_up(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  3
.150 / 100 ==  3
.149 / 100 ==  1
..51 / 100 ==  1
..50 / 100 ==  1
..49 / 100 ==  0
.-49 / 100 ==  0
.-50 / 100 == -1
.-51 / 100 == -1
-149 / 100 == -1
-150 / 100 == -3
-151 / 100 == -3

divide_round_half_down

Values are rounded to the nearest integral value.
‘Half’ values are rounded up (towards zero)

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_half_down(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  3
.150 / 100 ==  2
.149 / 100 ==  1
..51 / 100 ==  1
..50 / 100 ==  0
..49 / 100 ==  0
.-49 / 100 ==  0
.-50 / 100 ==  0
.-51 / 100 == -1
-149 / 100 == -1
-150 / 100 == -2
-151 / 100 == -3

divide_round_half_even

(Banker’s rounding)
Values are rounded to the nearest integral value.
‘Half’ values are rounded to the nearest even value.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  2
.150 / 100 ==  2
.149 / 100 ==  1
..51 / 100 ==  1
..50 / 100 ==  0
..49 / 100 ==  0
.-49 / 100 ==  0
.-50 / 100 ==  0
.-51 / 100 == -1
-149 / 100 == -1
-150 / 100 == -2
-151 / 100 == -2

divide_round_half_odd

Values are rounded to the nearest integral value.
‘Half’ values are rounded to the nearest odd value.

template <typename T1, typename T2>
ETL_CONSTEXPR14
etl::common_type_t<T1, T2>
divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT

.151 / 100 ==  2
.150 / 100 ==  1
.149 / 100 ==  1
..51 / 100 ==  1
..50 / 100 ==  1
..49 / 100 ==  0
.-49 / 100 ==  0
.-50 / 100 == -1
.-51 / 100 == -1
-149 / 100 == -1
-150 / 100 == -1
-151 / 100 == -2

RMS (Root Mean Square)Scaled Rounding