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342 lines
5.0 KiB
Markdown
342 lines
5.0 KiB
Markdown
---
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title: "Scaled Rounding"
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---
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Rounding algorithms for scaled integral values.
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From `20.40.1` all scaling functions are `ETL_NODISCARD` and `ETL_CONSTEXPR14`.
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It is often advantageous to use scaled integral values rather than floating point for performance reasons.
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These functions will round the supplied values according to various popular rounding algorithms.
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See [http://www.clivemaxfield.com/diycalculator/sp-round.shtml](http://www.clivemaxfield.com/diycalculator/sp-round.shtml)
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The results may be scaled or unscaled.
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**Scaled**
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The result has the same scaling as the input value.
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**Unscaled**
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The result has the scaling factor removed from the input value. 'Unscaled' is a little faster than 'scaled'.
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Assume a scaling factor of `10` for all of the examples below (simulated one decimal place).
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i.e. `5.1` => `51`
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## Round 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 <size_t Scaling, typename T>
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T round_ceiling_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50 -5.4 => -5.0
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-55 => -50 -5.5 => -5.0
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-56 => -50 -5.6 => -5.0
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54 => 60 5.4 => 6.0
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55 => 60 5.5 => 6.0
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56 => 60 5.5 => 6.0
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_ceiling_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5 -5.4 => -5
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-55 => -5 -5.5 => -5
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-56 => -5 -5.6 => -5
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54 => 6 5.4 => 6
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55 => 6 5.5 => 6
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56 => 6 5.6 => 6
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```
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## Round 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 <size_t Scaling, typename T>
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T round_floor_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -60 -5.4 => -6.0
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-55 => -60 -5.5 => -6.0
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-56 => -60 -5.6 => -6.0
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54 => 50 5.4 => 5.0
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55 => 50 5.5 => 5.0
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56 => 50 5.6 => 5.0
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_floor_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -6 -5.4 => -6
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-55 => -6 -5.5 => -6
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-56 => -6 -5.6 => -6
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54 => 5 5.4 => 5
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55 => 5 5.5 => 5
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56 => 5 5.6 => 5
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```
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## 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 <size_t Scaling, typename T>
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T round_half_up_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50 -5.4 => -5.0
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-55 => -60 -5.5 => -5.0
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-56 => -60 -5.6 => -5.0
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54 => 50
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55 => 60
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56 => 60
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_half_up_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5
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-55 => -6
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-56 => -6
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54 => 5
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55 => 6
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56 => 6
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```
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## Round Half Down
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Values are rounded to the nearest integral value.
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'Half' values are rounded down (towards zero).
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```cpp
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template <size_t Scaling, typename T>
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T round_half_down_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50
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-55 => -50
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-56 => -60
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54 => 50
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55 => 50
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56 => 60
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_half_down_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5
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-55 => -5
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-56 => -6
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54 => 5
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55 => 5
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56 => 6
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```
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---
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## Round To Zero
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Values are rounded towards zero.
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```cpp
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template <size_t Scaling, typename T>
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T round_zero_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50
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-55 => -50
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-56 => -50
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54 => 50
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55 => 50
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56 => 50
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_zero_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5
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-55 => -5
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-56 => -5
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54 => 5
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55 => 5
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56 => 5
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```
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## Round To Infinity
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Values are rounded towards infinity.
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```cpp
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template <size_t Scaling, typename T>
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T round_infinity_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -60
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-55 => -60
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-56 => -60
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54 => 60
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55 => 60
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56 => 60
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_infinity_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -6
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-55 => -6
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-56 => -6
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54 => 6
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55 => 6
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56 => 6
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```
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## Round Half Even (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 <size_t Scaling, typename T>
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T round_half_even_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50
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-55 => -60
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-56 => -60
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-64 => -60
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-65 => -60
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-66 => -70
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54 => 50
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55 => 60
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56 => 60
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64 => 60
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65 => 60
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66 => 70
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_half_even_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5
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-55 => -6
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-56 => -6
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-64 => -6
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-65 => -6
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-66 => -7
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54 => 5
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55 => 6
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56 => 6
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64 => 6
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65 => 6
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66 => 7
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```
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---
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## 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 <size_t Scaling, typename T>
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T round_half_even_scaled(T value)
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```
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**Description** |
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```cpp
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-54 => -50
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-55 => -50
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-56 => -60
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-64 => -60
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-65 => -70
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-66 => -70
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54 => 50
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55 => 50
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56 => 60
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64 => 60
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65 => 70
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66 => 70
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```
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---
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```cpp
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template <size_t Scaling, typename T>
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T round_half_even_unscaled(T value)
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```
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**Description** |
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```cpp
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-54 => -5
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-55 => -5
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-56 => -6
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-64 => -6
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-65 => -7
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-66 => -7
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54 => 5
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55 => 5
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56 => 6
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64 => 6
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65 => 7
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66 => 7
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```
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