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