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Replace FP division with fixed-point shift in atan2 #110

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Replace FP division with fixed-point shift in atan2 #110

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3 changes: 2 additions & 1 deletion src/trig.c
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Original file line number Diff line number Diff line change
Expand Up @@ -148,7 +148,8 @@ static twin_angle_t twin_atan2_first_quadrant(twin_fixed_t y, twin_fixed_t x)
}
}

return (twin_angle_t) (double) angle / (32768.0) * TWIN_ANGLE_360;
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Does this commit also aim to fix the incorrect casting of the variable angle from twin_angle_t to double?

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Does this commit also aim to fix the incorrect casting of the variable angle from twin_angle_t to double?

Yes, intentionally.

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Then, why didn't you write this purpose on this commit log ?

/* Fixed-point conversion: angle * TWIN_ANGLE_360 / 32768 */
return (twin_angle_t) ((angle * TWIN_ANGLE_360) >> 15);
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Since TWIN_ANGLE_360=4096 = 2^12by simple simplification, the original expression can be represented as

$$\frac{\text{angle} * 4096}{32768} = \text{angle} * 2^{12} *2^{-15} = \text{angle} * 2^{-3}$$

which is equivalent to

+/* Fixed-point conversion: angle * TWIN_ANGLE_360 / 32768 */
+    return (twin_angle_t) (angle >> 3);

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When the value range of angle is $[-9092,9092]$, using the original expression:

(angle * TWIN_ANGLE_360) >> 15

with TWIN_ANGLE_360 = 4096 can cause overflow. The maximum possible result of the multiplication is:

$$9092 * 4096 = 37,249,024$$

This value exceeds the limits of 16-bit, it may result in integer overflow and unpredictable behavior.

To avoid this issue, the multiplication and division can be replaced with a simple bit shift:

angle >> 3

}

twin_angle_t twin_atan2(twin_fixed_t y, twin_fixed_t x)
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