Of course, there is CORDIC for sin() and cos(), and one could also use precomputed lookup tables for single variable functions like exp() and log(). However, common bivariate functions as pow(a,b) and atan2(a,b) seems to be a little trickier to implement.
I'm considering a simple RISC-like microcontroller such as the AVR. It can perform fast adds and shitfs and loads but it has no built-in multiplier hardware.
I know it is not 8/16 bit but I would suggest to switch to Cortex M0 MCUs, they have built-in multiplier HW and some are even cheaper than 8&16 bit micros. If you work with Atmel ARM, Atmel Studio provides different features through the ASF (Atmel Software Framework). Hope this was useful somehow...
Mr. Senzio
Actually I'm looking for some bit manipulation hacks for implementing these kind of functions on very low-profile or older embedded systems.
I'm attaching a link for this comment that will show to you an example of what I was thinking of.
Best Regards.
https://graphics.stanford.edu/~seander/bithacks.html
Mr. Breuer
Surely, for atan2(a,b) it is pretty much a consequence of the atan(a/b) function with some special cases treatment. However I couldn't clearly understand your idea on the 2 parameter interpolation methodology ( "on 2 parameters as on 1, modulo the size of the lookup table..." ). Would it be possible for you to detail it further ?
Also, i've found a couple Numerical Recipes refences, including Jean-Michel Muller's "Elementary Functions: Algorithms and Implementation". However, as most polynomial interpolations schema rely on the usage of floating-point arithmetic, I'm mostly looking for fixed-point "multiplyless" techniques which could be applied to microcontrollers/microprocessors with only very elemental built-in hardware.
Best Regards
Dears
I guess "Hacker's Delight" would be a pretty good reference for some of these implementations.
Best Regards
http://www.amazon.com/Hackers-Delight-Edition-Henry-Warren/dp/0321842685
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