Refactor times inverse of sqrt 2 calculation #21293
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Diagonal mouse movement is calculated with equal x and y values times 1/sqrt(2). The current function uses bit shifting to divide and then truncates the fractional part to an integer, causing rounding errors. Example, when x = -7 and y = 7, the current function will return a rounded-down value of `4` instead of `5`, when compared to a rounded floating point multiplication with 1/sqrt(2) (0.707106781): | x | (x * 181) >> 8 | round(x * 0.707106781) | |---|----------------|------------------------| |-7 | -5 | -5 | | 7 | 4 | 5 | This change uses a simple sign checking ternary operator for the numerator. If negative, subtract half of the denominator before dividing. Otherwise add half of the denominator before dividing. The truncated integer after division will be an accurate rounding that matches floating point operations.
drashna
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Jun 21, 2023
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drashna
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tzarc
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Description
Diagonal mouse movement is calculated with equal x and y values times 1/sqrt(2). The current function uses bit shifting to divide and then truncates the fractional part to an integer, causing rounding errors.
Example, when x = -7 and y = 7, the current function will return a rounded-down value of
4instead of5, when compared to a rounded floating point multiplication with 1/sqrt(2) (0.707106781):This change uses a simple sign checking ternary operator for the numerator. If negative, subtract half of the denominator before dividing. Otherwise add half of the denominator before dividing. The truncated integer after division will be an accurate rounding that matches floating point operations.
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