Binary angular measurement: Difference between revisions

Revision as of 07:08, 3 September 2022

Revision as of 02:31, 3 October 2022

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===Signed fraction of turn===

Alternatively, the same ''n'' bits can also be interpreted as a signed integer in the range {−2^''n''−1 .. 2^''n''−1-1} in the [[two's complement]] convention. They can also be interpretesinterpreted as a fraction of a full turn between −0.5 (inclusive) and +0.5 (exclusive) in signed fixed-point format, with the same scaling factor; or a fraction of half-turn between −1.0 (inclusive) and +1.0 (exclusive) with scaling factor 1/2^''n''−1.

Either way, these numbers can then be interpreted as angles between -180° (inclusive) and +180° (exclusive), with −0.25 meaning −90° and +0.25 meaning +90°. The result of adding or subtracting the numerical values will have the same sign as the result of adding or subtracting angles, once reduced to this range. This interpretation eliminates the need to reduce angles to the range [−π,+π] when computing [[trigonometric functions]].