Is "Taylor series" still used for calculating various maths functions?

[FlyingDutch]

Hello,

I would like to ask if Taylor's theorem (and Taylor's series) is still practical used in calculating various mathematical functions (for example: exponential functions, logarithmic function etc,) I am asking in context of using this method in programable logic devices (FPGAs). If not, why not - what are weaknesses, and what methods are use insted it?

Thanks in advance and Regards

 

[danadakk]

CORDIC is used, some processors have engine inside them -

CORDIC - Wikipedia

en.wikipedia.org

CORDIC - Wikipedia

en.wikipedia.org

Regards, Dana.,

 

[dick_freebird]

The only place I ever learned or used Taylor
series was in undergrad courses. And not
many of those. Like, one?

I would think that any decent compiler
would have a math package, and for hand
cacls, a calculator or Excel suffices for any
day-to-day figuring a circuit designer might
require.

But, hey, it's a chapter to pad a syllabus with
that a professor can reuse forever.

 

[FlyingDutch]

CORDIC is used, some processors have engine inside them -

CORDIC - Wikipedia

en.wikipedia.org

CORDIC - Wikipedia

en.wikipedia.org

Regards, Dana.,

Hello,

I know CORDIC and used it once in FPGA project.

Best Regards

--- Updated Jul 10, 2021 ---

The only place I ever learned or used Taylor
series was in undergrad courses. And not
many of those. Like, one?

I would think that any decent compiler
would have a math package, and for hand
cacls, a calculator or Excel suffices for any
day-to-day figuring a circuit designer might
require.

But, hey, it's a chapter to pad a syllabus with
that a professor can reuse forever.

Hello,

but what is reason this method is not used in FPGA - is it to slow convergent? Yes I know that for every compiler is math package but using it entails using CPU.

Best Regards

 

[wwfeldman]

from

https://www.jatit.org/volumes/Vol95No9/13Vol95No9.pdf

"The trigonometric sine/cosine angles can
be computed using Taylor series method which
involves division and multiplication operations
that requires many iterations and much hardware
.So, the CORDIC has come up with the beauty
that it is much efficient than any other
methodologies [3-4].The actual paper and the
proposed paper differs in the implementation as
it eliminates the sine block in the initial stages,
that doesn’t have any impact on the further
stages because the sine for the small angles is
almost zero [5-6]."

in short, CORDIC is used because it works better in a digital environment
and does not require a multiplier

@dick_freebird:
having taught math, physics and electrical engineering,
NOBODY pads the syllabus

 

[std_match]

The advantage with a series expansion (Taylor and others) is that it can be used to approximate any function that can be derivated.

The big problem with the Taylor series expansion is the error distribution. The expansion is made around a specific input value, and the Taylor series error increases as the input value deviates from that value.

Because of this, the coefficients are often created by a Chebyshev series expansion instead, or are tweaked by the iterative Remez exchange algorithm to distribute the error evenly for a fixed number of coefficients.
(the Chebyshev series expansion is close, but needs an infinite number of terms/coefficients to have the best possible error distribution).

Unfortunately, Taylor series are just about the worst choice possible for implem... | Hacker News

news.ycombinator.com

Remez algorithm - Wikipedia

en.wikipedia.org

 

[std_match]

Chebyshev Approximation and How It Can Help You Save Money, Win Friends, and Influence People - Jason Sachs

Well... maybe that's a stretch. I don't think I can recommend anything to help you win friends. Not my forte. But I am going to try to convince you why you should know about Chebyshev...

www.embeddedrelated.com

 

[kcmurphy88]

I use CORDICs all the time. Good, fast, easy to implement using nothing but adder/subtractors. You can do several stages per clock with modern FPGAs. There are pipelined forms and recursive ones. Good for FFTs.

Depending on the form you choose, it can be used for vector rotation, vector magnitude and trig. It reduces the problem to a binary tree. The only multiply you might need is at the end, as there is a CORDIC factor of about 1.6 gain on the answer.

No one should use a Taylor series in hardware.

Clearest description I've found is at https://dspguru.com/dsp/faqs/cordic/