Add nside2order and rename uniq ID scheme functions

[cdeil]

This PR is an attempt to improve the uniq related functions:

• Rename encode_id to orderpix2uniq and add docstring
• Rename decode_id to uniq2orderpix and add docstring
• Remove type alias export type HealpixId = number
• Add nside2order, because sometimes people have nside and then they need this to these functions that take order as an option.

Overall the goal is to have clearer and more consistent function and variable names with the rest of the package. Looking at the old encode_id and decode_id, I didn't know what they were. Having a new type HealpixId that's just number and using is only here, but not in all the other places where ipix is used doesn't seem useful.

I wonder if the implementation of these methods can be improved. Is there a reason to keep the bitshifting and wile loop in uniq2orderpix for performance reasons? Or would calling math.log2 and maybe also Math.pow like in the Python implementation by @tboch in https://github.com/cds-astro/mocpy/blob/master/mocpy/utils.py#L4 be better? Another alternative could be to add an ilog2 that's implemented in a similar way as in Python here?

@tboch - Thoughts?

Does someone already have a good set of unit test cases that we should add?

[michitaro]

IE doesn't have Math.log2. If we make some polyfill for Math.log2, it would be some thing like this Math.log(x) / Math.LN2. In such case I'm not sure it will have enough precision. This is why I didn't use Math.log2.

Of course, after ensuring that Math.log(x) / Math.LN2 has enough precision for our cases, there is no reason not to use Math.log2.

[michitaro]

I updated the last comment. I submitted by mistake.

[cdeil]

For nside2order where we need ilog2 we could also use nside.toString(2).length? https://stackoverflow.com/questions/9939760/how-do-i-convert-an-integer-to-binary-in-javascript

The we avoid the call to Math.log2 and this PR can go in? (and possible further improvements to the uniq2orderpix implementation could come later if someone finds a good way to do it)

[michitaro]

The we avoid the call to Math.log2 and this PR can go in?

Yes!

In my environment, nside.toString(2).length is bit slower. I prefer loop & bit-shifting one https://jsfiddle.net/k6u9oxs5/10/

ilog2_1: 18ms
ilog2_2: 205ms
Math.log2: 24ms
ilog2_1: 27ms
ilog2_2: 170ms
Math.log2: 15ms

[cdeil]

I added ilog2 as you suggest in c0c9b36 .

[michitaro]

Thanks!