Missing method for ^

[laurentbartholdi]

I added the following to my code:

While I'm eagerly waiting for transcendental functions, it's a useful if dirty workaround for code that relies on powers. Perhaps you want to add it?

[dzhang314]

Hi @laurentbartholdi, thanks for your interest in MultiFloats.jl! I appreciate your suggestion, and I do agree that this is a nice quick-and-dirty fix if you need floating-point exponentiation in your program. However, I am deliberately not going to add support for the ^ operator in MultiFloats.jl until there is a highly-efficient pure MultiFloat implementation, as I do not want to give user the impression that this is a supported operation until I have put in the work to support it.

In general, many users have the misconception that floating-point exponentiation ^ is just another arithmetic operator, when in fact it is very expensive and requires evaluating transcendental functions. Therefore, I actually consider it a feature, not a bug, that a user has to write exp(y*log(x)) instead of x^y, making them consciously aware that exp and log are being called.

[dzhang314]

Adding a reference to issue #28, which I am designating as the tracking issue for a new, higher-performance implementation of exp and log.

[laurentbartholdi]

Great! While I respect fully your argument, I wish to point out that

• MultiFloats is soo good that I use it extensively, including when calling other packages
• Lots of packages require powers, even if in silly manners; for example, NonlinearSolve computes precisely once x^(4/5) to make an estimation on the required precision of something. I understand that the "correct" thing to do is to contact the author of NonlinearSolve and ask him/her to avoid the power operation since it's the only place the code uses other operations than +,-,*,/; but life is so short, and it would be so nice if MultiFloats worked out of the box.

[dzhang314]

Hey @laurentbartholdi, that's an excellent point -- compatibility with other packages, even ones that do silly things, is worth pursuing. I will prioritize implementation of exp and log for MultiFloats.jl and provide an implementation of ^ as soon as it is finished.