What I proposed was 16-bit integer math, not 32 bit. I can't believe float math -- which requires an add-on library -- is faster than 16-bit integer math, which is done through native instructions.
This is general information, unrelated to your post. The AVR microcontrollers used with Arduino do not have native instructions for multiply and divide and rely on compiler generated code. There is no reason whatsoever to avoid integer math, but speed is not a reason to get overly creative towards avoiding floats.
DCContrarian:
Converting to radians does nothing to improve your precision. You start with degrees anyway and then multiply and divide which introduce additional rounding errors. It makes no difference that degrees are 3-digit decimal numbers and radians are 1-digit, the internal representation is base-2.
Yes it does. Trigonometry in C requires radians and so keeping the source and intermediate results in the same format avoids repeated conversions and loss of precision. More significant however is to calculate distance as an arc. This prevents loss of precision resulting from intermediate calculations with small values (angles) and large values (distances).
DCContrarian:
With a float, you've got 23 bits of precision. Is that enough?
Actually you have 24 bits (sign bit included) and yes this is enough.
DCContrarian:
As a float, you are representing a value with a 23-bit binary times a multiplier. Your precision is determined by the incremental change when the lowest order bit flips. It's the circumference of the earth divided by 2^23. That's about 15 feet. Regardless of what units you pick, that's the smallest increment that can be measured. Unless you are very careful rounding errors can creep in and make your precision significantly worse.
Correct that for 24 bits and you will be close.
DCContrarian:
What it really gets down to is precision vs accuracy. The string you get reports a measurement in minutes with five decimal places. This level of precision implies the measurement is accurate to 1/100,000 of a minute. A degree of minute is roughly 1.1 miles; 1/100,000 of a minute is about one half inch. By using integers you maintain that precision. I agree that this precision is greater than the accuracy of the GPS.
GPS accuracy is referenced to absolute position. When we navigate and do repeated calculations we can expect relative position reports much better than the general stated accuracy. We can not expect inch accuracy with float calculations, but this was not what was asked for.
DCContrarian:
Is float precision enough? You tell me. It's probably close to the accuracy of the measurement. I know if it was me I'd rather design in greater precision than lesser, and design to preserve the precision I was given rather than lessen it.
The problem with your proposal is that you will have to write your own functions for trigonometry and basic arithmetic to maintain precision.
I have written a marine autopilot based on an AVR microcontroller and so it’s a bit more than speculations on my part.