CORDIC is pretty obsolete, AFAIK. Its advantage is that its hardware requirements are absolutely tiny: two (?) accumulator registers, and hardware adders and shift-ers—I think that's all. No multiplication needed, in particular. Very convenient if you're building things from discrete transistors, like the some of those earlier scientific calculators!
(Also has a nice property, apparently, that CORDIC-like routines exist for a bunch of special functions and they're very similar to each other. Does anyone have a good resource for learning the details of those algorithms? They sound elegant).
CORDIC still is used in tiny microcontrollers (smaller than Cortex-M0) and in FPGAs when you are very resource-constrained. Restricting the domain and using Chebyshev/Remez is the way to go pretty much everywhere.
I just recently came across CORDIC in a fun read I just finished, 'Empire of the Sum', by Keith Houston. It's a history of calculators, and there's a chapter on the HP-35 which used CORDIC. The author goes into some details how it was used by that constrained device.
There are a lot of references given in the book including more details on CORDIC.
CORDIC doesn't make sense if multiplies have a similar cost to adds. If you have cheap multiplications then a successive approximation is faster. If multiplications are expensive relative to adds then CORDIC can still generally win. Basically this is only the case nowadays if you are doing ASICs or FPGAs.
I have used CORDIC to compute fixed-point log/exp with 64 bits of precision, mostly because I wanted to avoid having to implement (portable) 64x64->128 bit integer multiplication in C. It is probably still slower than doing that, but the code was really simple, and very accurate.
Multiplication is pretty much needed in cordic! And is far from obsolete! It works perfectly fine, and dont have any of the problems said in the article.
CORDIC doesn't use multipliers. That's the whole appeal for low performance hardware since it's all shifts and adds. It can still be useful on more capable platforms when you want sin and cos in one operation since there is no extra cost.
Actually pretty much everyone implements double precision sin/cos using the same (IIRC) pair of 6th order polynomials. The same SunPro code exists unchnaged in essentially every C library everywehre. It's just a fitted curve, no fancy series definition beyond what appears in the output coefficients. One for the "mostly linear" segment where the line crosses the origin and another for the "mostly parabolic" peak of the curve.
yeah, but 52 adds can be a lot cheaper than a few multiplies, if you're making them out of shift registers and logic gates (or LUT). in a CPU or GPU, who cares, moving around the data is 100x more expensive than the ALU operation.
> in a CPU or GPU, who cares, moving around the data is 100x more expensive than the ALU operation
Moving data is indeed expensive, but there’s another reason to not care. Modern CPUs take same time to add or multiply floats.
For example, the computer I’m using, with AMD Zen3 CPU cores, takes 3 cycles to add or multiply numbers, which applies to both 32- and 64-bit flavors of floats. See addps, mulps, addpd, mulpd SSE instructions in that table: https://www.uops.info/table.html
It's great for hardware implementations, because it's simple and you get good/excellent accuracy. I wouldn't be surprised if that's still how modern x86-64 CPUs compute sin, cos, etc.
That said, last time I had to do that in software, I used Taylor series. Might not have been an optimal solution.
> EDIT: That's a paper for a software library, not the CPU's internal implementation.
Unless you're seeing something I'm not, it's talking about x87, which hasn't been anything other than 'internal' since they stopped selling the 80486sx.
(Also has a nice property, apparently, that CORDIC-like routines exist for a bunch of special functions and they're very similar to each other. Does anyone have a good resource for learning the details of those algorithms? They sound elegant).