Go: proposal: spec: multidimensional slices

[dadkins]

As per Rob and Andrew's request:
https://groups.google.com/forum/#!topic/golang-nuts/Q7lwBDPmQh4

[kisielk]

Comment 1:

Some more discussion on gonum-dev:
https://groups.google.com/d/topic/gonum-dev/WnptzWjqhmk/discussion

[gopherbot]

Comment 2 by [email protected]:

There's been some discussion about this.  Main points so far:
1. The general goal is to make it easy to do Matlab/Octave like work in Go.  Most
   engineering math today is prototyped in one of those languages, then translated
   to something faster for production use.   
2. It should be possible to easily convert standard libraries from "Numerical Methods" 
   (the book series, "Numerical Methods in Fortran, ... in C, in C++ etc.") to Go.
   That would get Go a needed set of standard numerical libraries.  And it should
   be reasonably easy to translate Matlab code to Go code. 
3. It's helpful to have only one standard way to represent matrices.  Otherwise,
   you get math libraries where a matrix coming out of one library won't go into
   another.  (This is one of Matlab's selling points.)
4. Performance is a major issue.  These constructs should go fast, approaching
   or exceeding C/FORTRAN performance.  
Language issues:
1. In general, multidimensional array/slice access syntax would look like "arr[i,j]".
2. Multidimensional slices would be supported, derived from multidimensional arrays.
3. While there is interest in generics and overloading, that's probably too radical.
   However, extending "+", "-", and "*" to vectors and matrices might be reasonable.
   Many machines have hardware that can speed up such operations (MMX, etc.) so
   that's something a compiler can do that a library alone cannot.
4. There's interest in "reshaping", where a subarray or sub-slice is derived from
   an array.  This can easily get overcomplicated (it did in FORTRAN 77) and needs
   to be carefully designed.  Further discussion and use cases are needed for this.
The machine learning community within Google might be consulted on what they want in
this area.  The machine learning theorists write in Matlab, and then someone has to
make that work in production code. 
It would be helpful to get agreement on needed functionality before putting too much
effort into syntax, so there are few specific syntax suggestions here yet.

[adg]

Comment 3:

Thanks for filing the issue.

_Labels changed: added feature, languagechange, removed priority-triage._

_Status changed to Thinking._

[dadkins]

Comment 5:

My desires are modest. I'd like to be able to write something like
// LUPDecompose performs an in-place LU factorization of a square
// matrix A. It returns a permutation vector P, such that PA = LU.
// On completion, A[i][j] = L[i][j] if i > j, U[i][j] if i <= j.
func LUPDecompose(A [][]float64) (P []float64, err error)
When writing this kind of code in C, I used to define a macro
#define A_(i,j) (A[(i)*rowsep + (j)])
That is precisely the kind of thing I wish the compiler would do for me.

[gopherbot]

Comment 6 by gexarcha1:

This document contains a collection of different proposals described in different levels
of detail:
https://docs.google.com/document/d/1gejfouITT25k29eHYTgdvi4cCLVt5dhYiJVvF46gp78/edit
It also contains links to any proposal or information relevant to the topic that we
found interesting. Feel free to edit the Document to clarify any questions relevant to
implementation.
I think most of the people in need of multi dimensional arrays in Go are not used to
writing proposals for programming language changes. If you have any input that would
make the process less awkward it would be highly appreciated.

[gopherbot]

Comment 7 by [email protected]:

There's been considerable discussion of this subject on "comp.lang.go.general".
Areas of agreement:
   There seems to be a consensus that multidimensional arrays and slices in Go would be useful for numerical work.
   The array element access syntax generally proposed is 
       arr[n,m]     // 2D
       arr[n,m,o]   // 3D
etc.  Existing arrays of arrays would be retained in Go. Arrays of arrays can be
"ragged",
(rows of different length) but multidimensional arrays are always of uniform length in
each dimension, allowing FORTRAN-type optimizations. 
   Both fixed-size multidimensional array types defined at compile time and arrays sized
at run time have use cases.  The former are widely used for graphics, and the latter are
widely used for general numerical work.  It should be possible to pass both as parameters
to functions, although not necessarily the same functions.
Areas of disagreement:
   There's much disagreement over what facilities for reslicing and reshaping should
be provided. 
   The minimum capability discussed is the ability to pass an entire array or 
multidimensional slice object to a function.  Creating a slice which refers
to a portion of an array, though, is controversial. Syntactically, this refers
to expressions of the form
         arr[a0:a1, b0:b1]
The problem is that values of b0 and b1 which are smaller than the array bounds
result in the need to represent a kind of sparse array, where the memory
distance between adjacent elements is not the same as the size of an element.
This complicates the internal representation of slices; even the lowest dimension
must have a "stride" value.  There's a performance penalty for this feature when it
not being used.  But it is convenient to have.  
   The other big issue is the ability to "grow" multidimensional slices. 
Should "append" be allowed for multidimensional arrays, and if so, how
general should it be?  Is growth allowed in all dimensions?  It's a useful
capability but complicates the implementation considerably. 
   Those are the two biggest issues being discussed.
   Lesser issues include whether operators "+", "-", and "*" should be provided
as built-in operations for multidimensional arrays and slices.  Providing them
permits easy transliteration for math libraries in other languages (C++, Matlab
especially).  But they're not essential; NumPy uses "A.dot(B)" for matrix multiply.
There are a lot of cases to handle for "*" - vector*scalar, vector*matrix, 
matrix*matrix...  "+" and "-" are somewhat simpler.
   That's roughly where the discussions are.  Once the slice and growth issues are
decided, the rest should fall into place.

[adg]

Comment 8:

The discussion referred to by nagle@ is on golang-nuts ("comp.lang.go.general" is just a
name made up by gmane.org):
https://groups.google.com/forum/#!topic/golang-nuts/Q7lwBDPmQh4

[gopherbot]

Comment 9 by norman.yarvin:

My proposal, at
https://docs.google.com/document/d/1xHyOK3hSxwMtyMH-pbXSXxo7Td9A_Teoj6cbr9ECeLM/edit?pli=1#
has now reached a reasonably mature state.  I'd appreciate if people had a look at it. 
It's a rather long proposal, but that's because this is not a small addition to the
language and I've tried to be thorough.  The proposal is purely about the basics of
multidimensional slices; math operations on whole slices are not part of it.  (It does
not preclude later adding them, but does not set up a situation where they'd be
necessary, either.)
As regards comments that people have made so far on the document, please keep in mind
that most of them were made against earlier versions, in which some things were not
explained as well.  Thus if any appear to be foolish that should not be held against the
commenter, or at least not too much.  (Though some comments have been marked as
resolved, I haven't marked them that way just because I disagree and have improved my
explanation, as that seems too dictatorial; I figure people can retire their own
comments if their objections have truly been addressed.)
As a personal comment, it is rather rare to have an opportunity to add a major feature
to a language so cleanly.  Usually one either has to break compatibility or introduce
some serious ugliness or severe compromise.  But here it's almost like Go was designed
for this feature to just be plugged in and almost seamlessly fill a gap in its
capabilities.  Or so I believe; go ahead, hammer on the proposal and prove me wrong.

[gopherbot]

Comment 10 by A.Vansteenkiste:

In my opinion, instead of changing the language, it might be useful if the standard
library simply provided a standard matrix format. That should guide the creation of
idiomatic, compatible matrix libraries. Cfr. database/sql, which guided the creation of
excellent database drivers.
The image package already provides nice guidance on how to handle 2D matrices. It uses
contiguous underlying storage which is needed when passing to external libraries. I
modelled a matrix (storage) package after image, this is how it looks like:
http://godoc.org/github.com/barnex/mat. However, many people wrote such kind of packages
with slightly different, incompatible, conventions. Hence it might be nice to have on a
standard convention in the standard library, once and for all.

[rsc]

Comment 11:

_Labels changed: added go1.3maybe._

[rsc]

Comment 12:

_Labels changed: removed feature._

[rsc]

Comment 13:

_Labels changed: added release-none, removed go1.3maybe._

[rsc]

Comment 14:

_Labels changed: added repo-main._

[btracey]

Comment 15:

About a month ago, I put together a proposal for this. Putting this comment as a
reference.
Here is a reduced proposal for multi-dimensional arrays
https://docs.google.com/document/d/1eHm7KqfKP9_s4vR1zToxq-FBazdUQ9ZYi-YhcEtdfR0/edit
Golang-nuts discussion thread
https://groups.google.com/forum/#!searchin/golang-nuts/tables$20in$20go/golang-nuts/osTLUEmB5Gk/3-f9_UKfE9MJ
In the thread, Dan Kortschak proposed a nice syntax for range which could be an addition
to the proposal (https://groups.google.com/d/msg/golang-nuts/osTLUEmB5Gk)/-A15bJpuTzsJ

[MichaelTJones]

Comment 16:

Related discussion in my go-nuts post:
https://groups.google.com/forum/#!topic/golang-nuts/ScFRRxqHTkY

[btracey]

Comment 17:

My proposal has been updated and now includes a proposal for range syntax.

[adg]

@nigeltao's response to the proposal: https://groups.google.com/d/msg/golang-dev/T2oH4MK5kj8/Kwpe8NfD45IJ

We appreciate the amount of work and care that went into this
proposal, but we're sorry that it's not likely to be adopted, at least
for Go 1.

The problem isn't with the proposal itself. The reason is that the
language is stable: the bar for new language features is high, and is
only getting higher. The "Changes to the language" sections of
http://golang.org/doc/go1.1, http://golang.org/doc/go1.2 and
http://golang.org/doc/go1.3 are getting smaller, not bigger. The
changes that did happen were also minor compared to introducing
tables, which touch make, literals, indexing, slices, len/cap, copy,
range, reflect and the type system in general.

We don't doubt that adding tables to the language has benefits. Any
reasonable language feature has benefits, and the gonum-dev mailing
list's existence clearly shows that it would make some people very
happy. Yet even if tables were part of the language, it's hard to see
any packages in the standard library, or even in the
code.google.com/p/go.foo sub-repositories, that would use them. There
is a chicken-and-egg factor here, but it's still not encouraging for
tables.

The only candidate seems to be the image-related packages, but even
then, we can't change, for instance, the image.RGBA type in the Go 1.x
time frame, and even for a hypothetical Go 2.0, it's not clear that
changing the design of the image package is a win. One of the
motivations for the current design is that, when decoding from or
encoding to formats like GIF or PNG, it's useful to linearize the
rectangle of pixels as a []byte, as spoken by general-purpose
compressors like LZW and ZLIB. Another deliberate design decision,
based on Plan 9 GUI experience, was that the top-left of an image
isn't necessarily at (0, 0).

In any case, debating the proposal's benefits is secondary. To repeat
the main point, we value API and language stability very highly. Yes,
the proposal is backwards-compatible, but it's a feature request, not
a bug fix, and we err on the side of making no changes.

As an alternative, one could define a computational language a la
halide-lang, and write a program that worked with "go generate". This
program would parse the specialized code and generate Go 1.x code
(which possibly uses package unsafe for pointer arithmetic), or
generate C code, or generate 6a-compatible assembly code, or generate
GPU-specific code. Of course, this still requires finding someone to
do the work, but that person or group of people don't have to be
familiar with the runtime and compilers, blocked on Go's release
cycles, or bound by the Go 1 compatibility promise.

[btracey]

Design document uploaded https://go-review.googlesource.com/16801

[ianlancetaylor]

A somewhat different suggestion at #13253.

[rsc]

For formatting: https://golang.org/design/6282-table-data.

[btracey]

Thanks Russ

[btracey]

The proposal was modified to allow tables of any dimension. Everything extended naturally, except make now accepts [N]int for consistency with len and cap.

[sbinet]

perhaps it should also mention https://github.com/golang/proposal/blob/master/design/12416-cgo-pointers.md ?
(especially for the part where we talk about compatibility/interoperability with C libraries)

[btracey]

Do you have something specific in mind? Part of the design of that proposal was to make cgo safer while expressly permitting our current use case. Assuming we can somehow deconstruct the table (which may need a stride built-in, I'm not sure), we should be able to call c just like now as far as I understand.

[sbinet]

Yes, of course.
I was merely pointing out that it would perhaps be beneficial for this section (reflect)

as there exists a large body of C libraries written for numerical work, with lots of time
spent in getting the codes to run efficiently. Being able to call these codes directly is 
a huge benefit for doing numerical work in Go (for example, the gonum and biogo
matrix libraries have options for calling a third party BLAS libraries for tuned matrix
math implementations)

to mention the new cgo-rules, even just to clearly show this proposal is aware of them.

[btracey]

Could the title of this be changed to "multidimensional slices"? The language already has multidimensional arrays

[ianlancetaylor]

@btracey Done.

[adg]

@griesemer @rsc @ianlancetaylor and others: this proposal was prepared a long time ago, but it is yet to be seriously addressed (apart from @ianlancetaylor's counterproposal) .

We need to make an explicit decision as to whether this proposal will be seriously considered for Go 1.

[gopherbot]

CL https://golang.org/cl/24271 mentions this issue.

[griesemer]

I believe this is a pretty important topic and good support here might allow Go to break into new application domains. The proposal is well written and pretty well thought out. I'll write some more feedback tomorrow.

[griesemer]

An initial design doc has been committed, with some additional feedback in the respective code review: https://github.com/golang/proposal/blob/master/design/6282-table-data.md . Work in progress.

[kokes]

Excellent, this is very nice. I have just one question.

I see the number of dimensions is set in make(), but then can be changed using reshape. But the way dimensions are passed, in an array, precludes any _runtime_ decisions about the number of dimensions, is that right?

Say I have a 16-element matrix in 4x4 and at runtime I'd like to reshape it into 28 or 22*4, depending on some other inputs. Since the reshaping dimension description is an array, not a slice, I cannot readily do that.

I presume this is due to the fact that the number of dimensions needs to be known at compile time to provide access index checks (just checking the number of dimensions would need to be shifted from compile time to runtime) and other checks and optimisations, I just wanted to know if I inferred it correctly.

Thank you!

[btracey]

I don't fully understand the question, but in this proposal every slice has a fixed dimension size. One cannot write a type of ,* that is an unknown dimensional slice.

You are correct that you cannot reshape a [4][4]T into a [,]T or [,,]T of arbitrary size. You can, however, reshape a [16]T into those sizes.

A [4][4]T could be reshaped just fine, but

var a [16][16]T
b := a[:4, :4]

could not be correctly reshaped. I don't see how to simply distinguish between those two cases.

[gopherbot]

CL https://golang.org/cl/25180 mentions this issue.

[griesemer]

@kokes You are correct. The number of dimensions is always a compile-time constant since it is given by the multi-dim. slice type, and that type is fixed (cannot change during runtime).

[griesemer]

Regarding the status of this proposal: I have just reviewed the latest version of the design doc and provided some more feedback. As far as I can tell, and ignoring details of the design doc wording and some syntax specifics (which just need to be decided), the proposal seems fairly clean, consistent, and implementable.

The proposal is also backward compatible with Go as it is now - that is, the generalization of slices into multi-dimensional slices could be done w/o affecting existing Go code.

However, this backward-compatibility also comes at a high price: It makes it impossible for an n-dimensional slice to be (sub-)sliced in arbitrary dimensions. Indexing must always be done from left-to-right (outer- to innermost dimension) so that a 1-dimensional slice gracefully degrades into an existing Go slice. The problem is that existing slices don't store an explicit 'stride' as it is always 1. For instance, given a 2-dim. matrix, I can "slice" a row vector, but I cannot "slice" a column vector (since the stride of that column would not be 1 in general).

Without paying a runtime cost, I don't see how backward-compatibility can be retained without the above-mentioned restriction.

I think this is the crucial question here: Is this restriction too restrictive?

[btracey]

I just pushed up a new version a new version of the proposal to the review. It contains a detailed description on why _I_ think the restriction is not too restrictive. I encourage others to comment.

[attaboonie]

Is it possible to get the "best of both worlds" where the slice (in reflect etc) always theoretically has a stride, but for the standard 1 dimension case this extra word of memory footprint is eliminated via a compiler optimisation?

[attaboonie]

At risk of appearing even more foolish ...
As length and capacity are currently both ints in the API, yet in practice can only be positive, there are in effect two spare bits available in the current slice header if these were needed to indicate multiple variants.

[griesemer]

@attaboonie Yes, something like this would be possible but it would require an additional runtime check for for regular slices, since those now might have a stride that is not 1 (I am hinting at that "runtime cost" in my comment above).

Maybe there's some clever ways to work around this to make it almost zero-cost in the common case (e.g. by storing a negative length and checking when the bounds-check triggers, or something along those lines), but it's going to be very tricky.

[dr2chase]

Supposing we start with the stride-1 restriction to see if it bites, and also do some experiments to see if it can be relaxed w/o harming performance? There are some SSA-ish optimizations that might help if we got around to implementing them (and if we have multidimensional strides, we'll be motivated to implement them for all the other dimensions that can have non-unit stride).

[yiyus]

First, I would like to thank Brendan Tracey and the gonum guys for their work in this proposal, and also the Go team for considering taking steps towards making Go more suitable for scientific computing. I know language changes at this stage are a very big deal.

However, I do not think this is the best approach. In my opinion, not allowing 1D strided slices from the beginning would be a huge mistake. It would be difficult to explain such a limitation to someone coming from Python, Fortran or Matlab, for example. I think the consistency you lose when you treat rows and columns differently is much bigger than the one you get from normal slices being a particular case of tables.

The proposal argues that having strided slices and normal slices would be harmful to the language, but I do not agree with this claim. It is not clear at all that it would lead to duplication of code for strided and non-strided slices, specially when other scientific languages only support strided slices without this being a problem. I think the choice for one or another would be obvious: a strided slice for anything that can be considered a vector (ie. for anything that could be eventually passed to a foreign Fortran function), and a non-strided slice for everything else (everywhere they are being used now). I imagine the conversion from a non-strided to a strided slice would be a very cheap operation, so you would only write numeric functions that take strided slices arguments (even non-strided slices could be accepted where a strided slice is required, eventually). Additionally, 1D strided slices would simplify the proposal, removing some special cases, in particular in range.

It also needs to be taken into account that not having a strided slice may lead to the abuse of [,]T types for vectors. This may be considered bad practice, but I can imagine myself doing it when porting something from other language where strided slices are supported. Then we would lose type safety, and we would still have all the problems attributed to strided slices (you will need to chose between using a []T, a [,]T with len[0] equal to 1, or both).

IIUC, @dr2chase suggests to start with the limitation and leave open the option to implement strides later, but I think that, then, a considerable amount of scientific code expecting a normal slice (or a [,]T "column table") would be written, and introducing a new type at a later stage would be problematic.

As an additional comment, I do not think it is necessary to modify make or implement literals, at least in a first step. I would be happy enough with reshape (maybe taking a variadic argument) and some help from gofmt.

[griesemer]

@yiyus Thanks for your comments. I have spoken with several people at Google about this proposal, some of which work on machine-learning, and they expressed similar concerns. Personally, I also think that the 1d stride-1 restriction is too limiting.

The example I've brought up repeatedly (in the design doc) is that it makes perfect sense to want to extract a row and column vector from a matrix, and that both these vectors should be 1d vectors so that they can be supplied to a dot-product function that takes two 1d vectors.

(At some point in the future one might want to supply more fancy "slicing" mechanisms, for instance one might want to select the diagonal of a matrix. If multi-dimensional slices/tables have strides in all directions, any such "linear" sub-section of a table can be represented w/o having to change the internal representation.)

I think the good news is that the proposal clarified these two implementations aspects (generalized slices that degrade into regular Go slices but have a restriction, and a more general multi-dimensional data structure "table" as this was the original name).

I'm going to review the latest draft update for the current version in the next few days and at that point it might be good to determine the next steps forward; e.g., should one explore an unrestricted proposal in detail.

[sbinet]

@griesemer: I suppose people having dealt with the sawzall -> lingo migration would also have some insights into data science use cases. (I suppose you may have facilities to tap into their brains :P)

before Go, I was into C++ and (C)python. There, numpy is king and builds on top of the "buffer protocol" to provide data interop' (between C-land and CPython, but also between various CPython extension modules, _e.g._ a SQL module and numpy, numpy and PIL/pillow (python image libraries)) and cheap slice'n'dice operations.

having a ndim-slice like the buffer protocol (so, with strides), without any allocation possible (so w/o cap) but with reshape would fit the bill in image processing, ML, high energy physics and, probably, all science-y data crunching applications.

having said that, between having this proposal implemented and the current status quo, I would go with this proposal (even if to somehow repeat the mistakes of the std::valarray<T> from C++).

[btracey]

Thanks for the comments @yiyus . It's a good conversation to have.

It would be difficult to explain such a limitation to someone coming from Python, Fortran or Matlab, for example.

In Matlab, such slicing creates a copy, so the behavior in Go is going to be surprising no matter what.

Could you give some examples in Fortran? I've only worked in old Fortran codebases. In BLAS and LAPACK, for instance, data arrays are contiguous, as in this proposal. Many of the operations do work on column vectors, of course, but that is implemented by explicitly passing the stride and doing the strided indexing manually. See the implementation of Dasum https://github.com/gonum/blas/blob/master/native/level1double.go#L91 or http://www.netlib.org/lapack/explore-html/de/d05/dasum_8f_source.html

Python does have the behavior you propose. Do you know how they deal with it? I suspect that they have to make a copy of the array before passing it to Lapack. I tried to read the source, but I when I got to the call for _makearray, I get lost in the c code for the array function and in wrap = getattr(a, "__array_prepare__", new.__array_wrap__)

I ask because the goals of Go are different than those of python/matlab/julia. Go will never have the syntactic flexibility of these languages. The benefit of Go is having a consistent language across users, and having a language that is possible to implement efficiently. In Matlab, the tradeoff is to allow really easy access to columns, even if that means a silent copy. In python, it's likely okay to sacrifice performance opportunities for syntactic ease -- python is not a fast language in general. Just because it's the right choice for those languages doesn't mean it's the right choice for Go -- the definition of "not a problem" is different.

---

I agree that we want to be able to perform operations on the data in columns, and I also agree that in some cases we want to do that copy-free. There is a problem with my proposal at the moment, one cannot extract a single column of a table. A few of us offline have been discussing this. The solution is to also add an unshape function that can take a table, and return the linear data.

func unshape([,*]T) ([]T, [N-1]int)

where [,*]T is shorthand for a table of dimension N, and the returned values are the underlying linear data of the table, and the strides in the dimension. With this function, one can extract a specific column of data, copy-free. Updating gonum/matrix, for instance, we would have

type Dense [,]float64

type Vector struct {
    data []float64
    stride int
}

func (d Dense) ColView(i int) Vector{
      data, stride := unshape(d)
      return Vector {
           data: data[i:],
           stride: stride,
     }  
}

The returned vector is a copy-free view on the column.

Personally, I think this meaningfully meets your desirata. You can use a Vector anywhere you "need something that is a vector", and you can use a []T anywhere else.

---

There are two costs to strided slices. The first is having two types that are basically the same thing. The second is the lost of optimization opportunities. It seems possible to me that strided slices are much harder to optimize than contiguous ones, especially in the area of SIMD. If SIMD optimizations are too difficult to implement, then Go is never going to be competitive with C and Fortran. It seems like there could still be this tension with where to use strided slices and contiguous slices.

I guess I'm playing the role of champion against strided slices. In that role, what I want to see is:

1) An argument for why the Vector type is insufficient, making strided slices necessary. Such an argument should keep in mind
a) Assuming inlining, accessing through a Vector is just as expensive as accessing a strided slice
b) As far as I understand, the storage costs for a strided slice are identical to the storage costs of a Vector

2) An explanation why a future Go compiler will still be able to implement SIMD operations, even understanding the goals of Go for fast compile times and small binaries

3) Rules of thumb on when to use a strided slice and when to use a contiguous one. Should the entirety of gonum change? Thus, anytime I would have had a []float64, I should instead have a [']float64 (or whatever the syntax is)? If not... clearly it should be type Vector [']float64. Should gonum/floats use [']float64 or []float64? Should there also be a duplicate "stridedfloats" package? What about the weights of a categorical random variable (https://github.com/gonum/stat/blob/master/distuv/categorical.go#L15)?

---

@griesemer Your post came in the middle of me writing mine. Should I update the proposal to add unshape operation? I think it's necessary for the proposal to be useful.

[sbinet]

@btracey no, numpy.array has all the informations to pass to lapack to hand it a pointer to C-array of floats with strides, row/col-major and rank informations. that's the buffer protocol I was talking about.
(it also has knobs for r/w access and ref-counting but that's only relevant to the CPython implementation)

see: https://docs.python.org/3/c-api/buffer.html
(the numpy.array was the champion for this protocol (during the python2 era) that it, of course, also implements in python3)

_wrt_ SIMD, even with the current proposal we might have some issues with alignment (especially when you sub-slice an n-dim slice (strided or not)).
SIMD has support for scatter/gather operations anyways. They are of course less efficient than in the case of completely adjacent data, but for the alignment issues evocated above, I'd say you would want to copy your data anyways to be sure to use the SIMD instructions. (in effect, that's what you would do to tap into GPUs and their remote device memory)

[yiyus]

@btracey Answering your question, since Fortran 90 it is possible to take rows from a matrix with a similar syntax as the one used by Python, as for example in: row = matrix(1,:). Fortran uses column major ordering, so col = matrix(:,1) would just be a sub-array of stride 1 (every array has a stride in Fortran).

Also, I do not think that supporting strided slices would suppose a problem for optimization, on the contrary. If they are not supported, some workaround will be needed to extract columns from a matrix, but this will disallow applying optimizations with SIMD instructions that support strided loads.

[btracey]

@sbinet it has the information to pass to Lapack, but I'm pretty sure it has to copy the data before passing to Lapack if the inner stride is not 1.
From http://docs.scipy.org/doc/numpy/user/c-info.how-to-extend.html
"Most third-party libraries expect contiguous arrays. But, often it is not difficult to support general-purpose striding. I encourage you to use the striding information in your own code whenever possible, and reserve single-segment requirements for wrapping third-party code. Using the striding information provided with the ndarray rather than requiring a contiguous striding reduces copying that otherwise must be made."

[yiyus]

To add to the discussion, I have cleaned up a bit my old proposal for "shaped slices":
https://docs.google.com/document/d/1IvvkX60AMObA11CB6Gcc3xxG14VayGqBOjfpwg3qIRY/edit?usp=sharing

It is not really a counter proposal (it is far less mature than the table proposal, and the syntax chosen or other details may not be the best options, or even possible). I just want to show how I think that everything essential to implement multidimensional slices in what I consider a useful form is a new type, a reshape operation and multi-dimensional slicing/indexing.

Please, if you have any specific comment, add them directly in the document, to avoid hijacking this issue.

[btracey]

I updated my proposal with the unpack built-in described above, and added some code examples of operations that are very similar to strided slices. I reworded the criticism of strided-slice based proposals.

Current PR still at https://go-review.googlesource.com/#/c/25180/

[sbinet]

with the new unshape builtin, I must say it's starting to become a bit crowded.

I am tempted to bring back my original suggestion (somewhere on gonum-dev):

slice := make([*]int, 2, 3, 4)      // a 2x3x4 n-dim slice
sub1 := slice[:,1,:]                // a 2x4 n-dim slice
sub2 := reshape(slice, 6, 4)[:2,:3] // a 2x3 n-dim slice

for i, v := range slice {
    for j, u := range v {
        for k := range w {
            fmt.Printf("slice[%d,%d,%d] = %v\n", slice[i,j,k])
        }
    }
}

• [*]T is a strided-ndim slice whose elements have type T.
• len(slice) returns a slice of length equal to the number of dimensions of the ndim-slice (ie: []int{2,3,4} for the above slice ndim-slice)
• a ndim-slice can not be appended to, and has a fixed capacity, equal to its length

at the reflect level, an ndim-slice could be represented like:

type NdSliceHeader struct {
    Data   unsafe.Pointer
    Len    []int
    Stride []int
}

nd-slice literals

v := [*]int{1,2,3,4} // a 1x4 nd-slice
u := reshape([*]int{1,2,3,4}, 2, 2) // a 2x2 nd-slice
w := reshape([*]int{1,2,3,4}, 2, 1, 2} // a 2x1x2 nd-slice

// reshaping a slice is also allowed and creates an nd-slice
v := reshape([]int{1,2,3,4}, 2, 2) // a 2x2 nd-slice
// perhaps also this conversion could be allowed, like string/[]byte:
v := [*]int([]int{1,2,3,4}) // a 1x4 nd-slice

copy

src := make([*]int, 2, 3)
dst := make([*]int, 4, 3)
// copy returns the number of elements copied in each dimension
n := copy(dst[:2,:], src[:1,1:]) // n == []int{1, 2}

---

_wrt_ to the non-strided proposal, you get the ability to slice in all dimensions.
you loose the compile-time check of rank (ie number of dimensions) of an ndim-slice, so you could imagine a situation where you'd pass a 2d ndim-slice to a functions expecting a 3d one.
and you probably loose a bit in random-access to elements because you need to multiply by the stride in each dimension (and fetch those strides).

[btracey]

This is similar in spirit to @yiyus proposal. I don't think it actually gets you around unshape though, unless you want to forbid people from ever getting the underlying slice without using unsafe. One important usage is passing data to C, I.e. Lapack and other programs. Also note that with strided slices one needs to allocate and make a copy before lapqck (and others) since they require contiguous data.

[sbinet]

_wrt_ using unsafe: that's already the case for a slice and its array. you can't go back at the underlying array of a slice.
I see "my" nd-slice and its non-reshaped slice as the same pair than a slice and its underlying array.

if/when a mechanism is devised to get (safely) the underlying array from a slice, I _suppose_ it could be transposed to the nd-slice/slice pair.
but, to pass data to C, you need to use unsafe in some way, so...

[sbinet]

ah! one thing I forgot to mention in my nd-slice post: slicing a nd-slice, modifying its stride.
as a nd-slice's capacity can't be modified, we can use the 3-index slice as a way to specify the stride when extracting a sub-nd-slice:

v := reshape([*]int{1,2,3,4,5,6}, 2, 3) // a 2x3 nd-slice
// 1 2 3
// 4 5 6
u := v[:, 0:3:2] // a 2x2 nd-slice, taking one column every two
// 1 3
// 4 6
w := v[::, ::2] // == u

[sbinet]

looking at how tensorflow wraps around its C api is interesting and a valuable data point, /me thinks:
https://github.com/tensorflow/tensorflow/blob/0e5d49d362a5ef72179e385d1f71ec29ab0392f6/tensorflow/go/tensor.go

[griesemer]

To make progress with this proposal with the goal to come to a decision eventually, here's an abbreviated summary of the discussion so far.

Primary goals

First of all, there are some overarching goals that this proposals attempts to achieve. To name a few (borrowing from https://github.com/golang/go/issues/6282#issuecomment-66084786, and https://github.com/golang/go/issues/6282#issuecomment-66084788):

• It should be straight-forward to write typical numerical algorithms in Go in a natural way.
• There should be a “standard” mechanism to represent multi-dimensional slices/matrices in Go (one standard way to represent matrices, for instance).
• Such algorithms should be implementable in a reasonably efficient manner, with a performance coming close to a typical C implementation.

Virtually everybody also seems to be in agreement with respect to indexing notation and memory layout:

• Slice/vector/matrix elements should be accessed via the familiar indexing notation, suitably extended to multiple dimensions: v[i], m[i, j], t[i, j, k], etc.

• A multi-dimensional slice or matrix must be laid out contiguously in memory, without pointers to sub-slices. Successive slice elements may not be adjacent in memory if they have a "stride" that is > 1 (where 1 is the size of a slice element).

Proposed design

@btracey, with input from the gonum team, has spent considerable effort coming up with a concrete design for multi-dimensional slices with the intent to address the goals of this proposal: https://github.com/golang/proposal/blob/master/design/6282-table-data.md .
Thank you @btracey , and the gonum team for your significant effort!

The above design addresses many of the desired goals of this proposal and, as a significant plus, the proposed multi-dimensional slices are in many ways a natural extension of the one-dim. slices we already have in Go.

Problem areas

The single-biggest issue with the proposal is that one-dim. slices don’t have a stride exactly because multi-dim. slices gracefully degrade into Go’s existing slices. This problem has been pointed out as early as https://github.com/golang/go/issues/6282#issuecomment-66084790, before a concrete design document was posted. The design document addresses this issue with various work-arounds.

As a concrete example, given a two-dim. slice m representing a matrix [,]float64, with the proposed design it is easy and efficient (no copy of matrix elements involved) to select a matrix row i as a sub-slice m[i, :] but it is impossible to select a matrix column j that way (m[:, j] is invalid). In other words, indexing is asymmetric, and the asymmetry will lead to special treatment in algorithms (columns must be explicitly copied element-wise).

To support various "reshaping" operations for multi-dim. slices, the design proposes operations such as reshape, and unshape. @sbinet points out that the design doc has become a bit crowded in terms of additional predeclared functions ( https://github.com/golang/go/issues/6282#issuecomment-242921725 ).

Alternatives

Several alternative proposals have been floated as well:

• https://github.com/golang/go/issues/6282#issuecomment-66084793 proposes that the std library simply define a standard Matrix format (and perhaps Vectors, etc.).

• https://github.com/golang/go/issues/6282#issuecomment-242226027 proposes a “shaped slice” type for Go which is similar to multi-dimensional slices but supports strides in each dimension, and consequently doesn’t gracefully degrade into a regular (unstrided) slice in the one-dim. case.

• https://talks.golang.org/2016/prototype-your-design.pdf discusses as an example for that talk the implementation of a rewriter that can automatically rewrite indexing expressions of the form a[i, j, k] and a[i, j, k] = x into method calls a.At(i, j, k), and a.Set(i, j, k, x) respectively. While this approach does not extend the language per se, it permits writing numerical algorithm using "nice" notation which is then automatically translated into regular Go. It also has the advantage of providing full control over the underlying implementation of multi-dim. slices. A complete prototype implementation can be found in https://github.com/griesemer/dotGo2016).

Summary

The proposed design of multi-dim. slices is a natural extension of Go's existing one-dim. slices. From a language point of view, the design appears backward-compatible with Go 1; and it does address many goals of the proposal. That said, the asymmetry of indexing operations requires non-obvious work-arounds when implementing numerical algorithms which runs counter one of the primary goals ( https://github.com/golang/go/issues/6282#issuecomment-66084786 ) of this proposal.

[btracey]

I agree with the summary above. Two quick comments (especially for those thinking of making a new proposal)

• I think any proposal that seeks to extend Go slices will have the same downsides as my proposal. The asymmetry is fundamental, but also I think it is difficult to reduce the scope of the changes without harming the benefits brought by the change. As a simple example, removing unshape and reshape makes it harder to interface multi-dim slices with data streams and C code
• Another alternative suggestion is to modify Go to allow index operator methods. This would be similar to the talk by @griesemer, except an actual change to the Go spec, and not just a rewriter program.

Thanks to @griesemer for the significant effort invested in this issue.

[j6k4m8]

Thank you @griesemer — a really good summary of the challenges and benefits.

To elaborate on my 👍 to @btracey's comment above, I especially want to get behind index-operator methods: I suspect that moving index-operator syntax from rewriter-land to native Go would buy considerable power, and would allow libraries to handle more of the heavy-lifting when our implementation preferences diverge (e.g. axis-reordering operations can exist in a library, and needn't exist in native implementation).

[griesemer]

This proposal addresses a large portion of the originally stated goal: better Go support for numerical applications. However, as also has become quite clear, it falls short in others (asymmetry of proposed solution, potential proliferation of builtins). Judging from the feedback received on this issue, there is no clear consensus that the shortcomings can be safely ignored.

Adding multi-dim. slices to the existing Go language would be a significant engineering effort. It seems unwise to make this effort with full knowledge of the proposal's inherent problems. Furthermore, exactly because the proposed solution ties so closely into the existing language, it would be nearly impossible to change or adjust the design down the road.

Thus, after repeated and careful consideration, we are going to decline this proposal.

That said, the discussions so far have been extremely helpful in delineating the problem domain, identifying key issues, and for identifying possible alternative approaches.

We suggest that this discussion continue with the intent to come up with a new and improved design (possibly along the lines of one of the alternatives above) with the intent of having a blueprint for consideration for Go 2.

Again, thanks to everybody, and particularly @btracey, for your contributions and time spent on this proposal.

-gri, for @golang/proposal-review

[dm319]

Time to revive this discussion? As a go and R fan, how does fortran approach the problems seen here?

[btracey]

This issue is closed (and the proposal declined) for good reason. If you're looking for similar functionality, please see the gonum packages (gonum.org)

[dm319]

We suggest that this discussion continue with the intent to come up with a new and improved design (possibly along the lines of one of the alternatives above) with the intent of having a blueprint for consideration for Go 2.

-gri

Maybe I should have mentioned that my comment was prompted by the recent announcement about working towards Go 2 (https://blog.golang.org/toward-go2).

[SamWhited]

Maybe I should have mentioned that my comment was prompted by the recent announcement about working towards Go 2

Consider filing an Experience Report with any specific issues you've run into with real code. We can't talk about proposals and solutions until we know what the actual underlying problems are.

[shelby3]

@griesemer wrote:

[…] but it is impossible to select a matrix column j that way (m[:, j] is invalid). In other words, indexing is asymmetric […]

I only had 5 minutes to learn about this issue by perusing this thread, thus my very rushed thought is that perhaps the problem can be _in theory_ solved with typeclasses.

Essentially the _3. Struct type_ is the most correct solution to the issue presuming monomorphisation (inlining) and a smart enough optimizing compiler¹. And btw, it’s the first solution that came to mind within 1 minute before I saw it proposed, so why did it take 4 years? So if we have typeclasses and operator overloading then the SetAt noise is replaced with the [] as we desire. Also the slice of a column as a matrix becomes another kind of struct which has a different typeclass implementation. Tada!

Afaics, with typeclasses the entire thing can be handled with libraries. And so we stop burdening the native with what can be in a library. ~Actually Go’s interfaces as is may be sufficient to implement the column slice as a specialized struct?~[Edit: on further thought no Go’s interfaces lack the concept of an associated type in order for instances of the typeclass to recursively declare the special struct needed to take slice on a column of a matrix.]

Remember that typeclass bounds at the call site select the correct interface automatically based on the input data type. Go’s interfaces sort of do that also, but there’s some differences and limitations.

Apologies if in my haste I missed some points that cause my post to be noise. Please courteously correct me if so.

^{P.S. Is this implicating that Go has been without subslicing matrix capability for 5 years because of a lack of sufficient higher-level abstractions support in the language? Yet, I presume combining higher-level abstractions and maintaining low-level control performance is a difficult design challenge and maybe even insurmountable in general.}

¹ _{One of the reasons along with higher-level abstractions perhaps OCaml is favored by hedgefunds?}

[Jonconradt]

It appears that this was not submitted as an Experience Report. I am wondering why not?

[sbinet]

Probably because this happened before that procedure.