Double vs Integer

I have spent a few days to sort out the Inverse Kinematics formulas. My mathematics skills have been much better in the old days. As I am using an AVR ATmega2560 I did the implementation in fixed point integers. As everyone knows float calculations are much too slow.

It took me days to get atanacos and sqrt functions working. I need reasonable resolution (<1°) and reasonable sized lookup tables. But generally flash isn’t an issue, the ATmega2560 has 128 kByte of it.

For the automated testing, that I always implement, I did check my integer functions against their double precision counterparts. And as the AVR has timers, I also tracked the execution times. I was surprised.

min / avg / max
in [us]
min / avg / max
in [us]
sqrt24 / 38 / 5628 / 31 / 36
acos48 / 49 / 52128 / 160 / 176
atan140 / 152 / 160168 / 184 / 204
inverse kinematics544 / 559 / 580829 / 926 / 976

Ok, double is slower than 16 bit integer. But, the overall difference is only 70%, but accuracy is much higher. The inverse kinematics results calculated with integers differ by 5° maximum, the double results are better than 0.1°. Writing the fixed point functions took about 4 days, the double version 30 minutes. The planning of accuracy and operand length for fixed point integer is a pain.

What do I take from this:

  • Never optimize before I have the proof that I need to.
  • Double isn’t as bad as I thought. And much much easier to handle.
  • I’ll use double for the project. As I am planning to split the control to leg and body control to multiple processors, I should have enough resources to get a reasonable cycle time.
  • If not, I can optimize later.