Float vs fix math

[Nominal Animal]

Note that \$0.67913\lvert x \rvert + 0.67913 \lvert y \rvert + 0.28130 \bigl \lvert \lvert x \rvert - \lvert y \rvert \bigr \rvert\$ is within 4% of \$\sqrt{x^2 + y^2}\$, so for 0 ≤ y ≤ x ≤ 255, (174*(x + y) + 72*(x - y) + 80) / 256 is within ±10 (4%) of sqrt(x^2 + y^2).  (27% of all possible cases are exact.)

For general 0 ≤ x ≤ 255, 0 ≤ y ≤ 255, you can use(87*(x + y) + 36*(max(x, y) - min(x, y)) + 40) / 128, using signed 16-bit or unsigned 15-bit integer operations.

[langwadt]

Note that \$0.67913\lvert x \rvert + 0.67913 \lvert y \rvert + 0.28130 \bigl \lvert \lvert x \rvert - \lvert y \rvert \bigr \rvert\$ is within 4% of \$\sqrt{x^2 + y^2}\$, so for 0 ≤ y ≤ x ≤ 255, (174*(x + y) + 72*(x - y) + 80) / 256 is within ±10 (4%) of sqrt(x^2 + y^2).  (27% of all possible cases are exact.)

For general 0 ≤ x ≤ 255, 0 ≤ y ≤ 255, you can use(87*(x + y) + 36*(max(x, y) - min(x, y)) + 40) / 128, using signed 16-bit or unsigned 15-bit integer operations.

there are variations, https://dspguru.com/dsp/tricks/magnitude-estimator/

[ledtester]

On the topic of Pythagorean approximations, here's another one ...



Here x is the larger of the two values.

From this video:

https://youtu.be/NWBEA2ECX-A