What algorithms do FPUs use to compute transcendental functions?

StackOverflow https://stackoverflow.com/questions/13877303

Question

What methods would a modern FPU use to compute transcendental functions?

For example, Intel CPUs provide instructions such as FSIN, FCOS, FYL2X, etc. I am curious as to what algorithms would be used to actually implement these in hardware.

My naïve guess would be Taylor series perhaps combined with some lookup tables, but that's nothing more than a wild guess. Please enlighten me.

P.S. This question is more general than just Intel hardware.

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Solution

One place to start could be "New Algorithms for Improved Transcendental Functions on IA-64" by Shane Story and Ping Tak Peter Tang, both from Intel. It probably doesn't have as many details as you might like, but it includes several references.

Update 08/13/2014

The original link is broken. IEEE's public abstract/citation page can be found here:

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=762822&tag=1

OTHER TIPS

In hardware (as well as software where hardware multiply instruction is not available) it is usually implemented in CORDIC since this requires only addition, subtraction, bit shift and table lookup

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