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Embedded Template Library
Maths
Scaled Rounding

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
Rounded integral divisionstandard_deviation