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209 lines
4.1 KiB
Markdown
209 lines
4.1 KiB
Markdown
---
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title: "Rounded integral division"
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---
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{{< callout type="info">}}
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Header: `rounded_integral_division.h`
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From: `20.9.0`
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{{< /callout >}}
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Rounded division algorithms for integral values.
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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.
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## divide_round_to_ceiling
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Values are rounded to the next more positive integral value.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_to_ceiling(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 2
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.150 / 100 == 2
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.149 / 100 == 2
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.51 / 100 == 1
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..50 / 100 == 1
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..49 / 100 == 1
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.-49 / 100 == 0
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.-50 / 100 == 0
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.-51 / 100 == 0
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-149 / 100 == -1
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-150 / 100 == -1
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-151 / 100 == -1
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```
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## divide_round_to_floor
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Values are rounded to the next more negative integral value.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_to_floor(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 1
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.150 / 100 == 1
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.149 / 100 == 1
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..51 / 100 == 0
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..50 / 100 == 0
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..49 / 100 == 0
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.-49 / 100 == -1
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.-50 / 100 == -1
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.-51 / 100 == -1
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-149 / 100 == -2
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-150 / 100 == -2
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-151 / 100 == -2
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```
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## divide_round_to_zero
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Values are rounded towards zero.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_to_zero(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 1
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.150 / 100 == 1
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.149 / 100 == 1
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..51 / 100 == 0
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..50 / 100 == 0
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..49 / 100 == 0
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.-49 / 100 == 0
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.-50 / 100 == 0
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.-51 / 100 == 0
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-149 / 100 == -1
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-150 / 100 == -1
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-151 / 100 == -1
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```
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## divide_round_to_infinity
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Values are rounded towards infinity.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_to_infinity(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 2
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.150 / 100 == 2
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.149 / 100 == 2
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..51 / 100 == 1
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..50 / 100 == 1
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..49 / 100 == 1
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.-49 / 100 == -1
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.-50 / 100 == -1
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.-51 / 100 == -1
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-149 / 100 == -2
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-150 / 100 == -2
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-151 / 100 == -2
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```
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## divide_round_half_up
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Values are rounded to the nearest integral value.
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'Half' values are rounded up (towards infinity).
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_half_up(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 3
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.150 / 100 == 3
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.149 / 100 == 1
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..51 / 100 == 1
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..50 / 100 == 1
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..49 / 100 == 0
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.-49 / 100 == 0
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.-50 / 100 == -1
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.-51 / 100 == -1
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-149 / 100 == -1
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-150 / 100 == -3
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-151 / 100 == -3
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```
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## divide_round_half_down
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Values are rounded to the nearest integral value.
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'Half' values are rounded up (towards zero)
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_half_down(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 3
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.150 / 100 == 2
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.149 / 100 == 1
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..51 / 100 == 1
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..50 / 100 == 0
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..49 / 100 == 0
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.-49 / 100 == 0
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.-50 / 100 == 0
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.-51 / 100 == -1
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-149 / 100 == -1
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-150 / 100 == -2
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-151 / 100 == -3
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```
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## divide_round_half_even
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(Banker's rounding)
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Values are rounded to the nearest integral value.
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'Half' values are rounded to the nearest even value.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 2
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.150 / 100 == 2
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.149 / 100 == 1
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..51 / 100 == 1
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..50 / 100 == 0
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..49 / 100 == 0
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.-49 / 100 == 0
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.-50 / 100 == 0
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.-51 / 100 == -1
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-149 / 100 == -1
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-150 / 100 == -2
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-151 / 100 == -2
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```
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## divide_round_half_odd
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Values are rounded to the nearest integral value.
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'Half' values are rounded to the nearest odd value.
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```cpp
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template <typename T1, typename T2>
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ETL_CONSTEXPR14
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etl::common_type_t<T1, T2>
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divide_round_half_even(T1 numerator, T2 denominator) ETL_NOEXCEPT
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```
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```cpp
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.151 / 100 == 2
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.150 / 100 == 1
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.149 / 100 == 1
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..51 / 100 == 1
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..50 / 100 == 1
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..49 / 100 == 0
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.-49 / 100 == 0
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.-50 / 100 == -1
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.-51 / 100 == -1
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-149 / 100 == -1
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-150 / 100 == -1
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-151 / 100 == -2
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```
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