Allow @SVector comprehension to eval range with locals?

[dbeach24]

Because the @SVector macro does not evaluate the range using the local scope, I find myself transforming code like this:

function mytransform{N}(x::SVector{N})
    @SVector [x[i] * i for i=1:N]
end

into this:

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(ntuple(i -> x[i] * i, N) ...)
end

I'm not sure if the second form is as efficient, but in either case, the first version is far easier to read.

Is there any chance that @SVector comprehensions can be made to support local variables in the range? Or, is there some other way I should be writing this?

[c42f]

Normally @SVector unrolls the generator expression, but that's not possible in this case without extra compiler support since N isn't a literal known to the macro.

However, the second version can be written directly with a generator which isn't too bad:

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(x[i]*i for i=1:N)
end

From a quick look at code_native, it seems that a call is still being made so this probably won't be super fast. It may be possible to improve the codegen with an extra generated function, to unroll once N is known?

[andyferris]

@dbeach24 This is something I'd like to do but as @c42f mentions its a little difficult with current compiler support. I have an idea for one hack which would end up using a call and a loop yet AFAIK it still should be faster to write

function mytransform{N,T}(x::SVector{N,T})
    @inbounds return SVector{N,T}(x[i]*i for i=1:N)
end

as @c42f we need an @inbounds somewhere for the x[i] (otherwise I don't know why it would call, but if that doesn't work then I should investigate).

Another approach is to have a statically valued thing like SUnitRange{1, N}() <: StaticVector{Int} and call map on it. This will probably be implemented sometime soonish.

To my understanding, this one:

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(ntuple(i -> x[i] * i, N) ...)
end

should be performant up until N = 16 and slow afterwards, The compiler people are interested in making this fast for all N (a longer term goal, however).

[andyferris]

I've started to look at this in #30

[andyferris]

OK I've had a thought. First we implement function initialization for all StaticArrays such that

SVector{N}(f::Function)

populates SVector{N}((f(1), f(2), ..., f(N)) (and so-on for higher dimensional arrays). This would be useful in its own right.

Furthermore, transform this:

@SVector [f(i) for i = inds]

into this

N = size(inds) # can we check/enforce if this is statically determinable? E.g. size(typeof(inds)) is OK.
SVector{N}(j -> f(inds[i]))

We can assume the inds collection is an indexable collection, since it's useless (speed wise) if its size is unknown...

It would help syntactically if we made colon(a,b) into a @pure function, as well as size(::UnitRange).

[andyferris]

BTW @dbeach24 the ... in the below is unnecessary (in fact, a tuple is desirable) and you should use ntuple(f, Val{N}).

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(ntuple(i -> x[i] * i, N) ...)
end

So this is fast (up to N = 15 or so)

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(ntuple(i -> x[i] * i, Val{N}))
end

[ChristianKurz]

The construct in question

function mytransform{N}(x::SVector{N})
    @SVector [x[i] * i for i=1:N]
end

can be written without the macro like this:

function mytransform{N}(x::SVector{N})
    SVector([x[i] * i for i=1:N]...)
end

Though i feel like the SVector()-constructor should be able to handle arrays without the splatting.

[KristofferC]

That would allocate a temporary array as well as causing the output type to not be inferrable.

[garrison]

Slightly OT: In two comments above it is mentioned that the following workaround should work

function mytransform{N,T}(x::SVector{N,T})
    SVector{N,T}(x[i]*i for i=1:N)
end

however, when I call it as mytransform(@SVector [1,2,3]), I get ERROR: No precise constructor for SVector{3,Int64} found. Length of input was 1.

Did passing a generator to the SVector constructor in this way work in a previous version of StaticArrays? (Should this be considered a regression?)

[andyferris]

We've never robustly supported generators in the past. It's something I'd like to improve on, though. Hmm...

[c42f]

I think this issue is basically the same as #97

[kbarros]

Note that SVector{3}(f(x) for x in xs) works as of #792. See also: #97 (comment).