[llvm-dev] [RFC] A new multidimensional array indexing intrinsic
Doerfert, Johannes via llvm-dev
llvm-dev at lists.llvm.org
Sat Aug 3 16:32:56 PDT 2019
Have you looked into this?
https://llvm.org/docs/LangRef.html#llvm-preserve-array-access-index-intrinsic
On 07/22, Siddharth Bhat via llvm-dev wrote:
> Hello,
>
> We would like to begin discussions around a new set of intrinsics, to
> better express
> multi-dimensional array indexing within LLVM. The motivations and a
> possible design
> are sketched out below.
>
> Rendered RFC link here
> <https://github.com/bollu/llvm-multidim-array-indexing-proposal/blob/master/RFC.md>
>
> Raw markdown:
>
> # Introducing a new multidimensional array indexing intrinsic
>
> ## The request for change: A new intrinsic, `llvm.multidim.array.index.*`.
>
> We propose the addition of a new family of intrinsics,
> `llvm.multidim.array.index.*`.
> This will allow us to represent array indexing into an array `A[d1][d2][..][dk]`
> as `llvm.multidim.array.index.k A d1, d2, d3, ... dk` instead of flattening
> the information into `gep A, d1 * n1 + d2 * n2 + ... + dk * nk`. The former
> unflattened representation is advantageous for analysis and
> optimisation. It also
> allows us to represent array indexing semantics of languages such as Fortran
> and Chapel, which differs from that of C based array indexing.
>
> ## Motivating the need for a multi-dimensional array indexing intrinsic
>
> There are primarily one of two views of array indexing involving
> multiple dimensions most languages take, which we discuss to motivate
> the need for a multi-dimensional array index. This consideration impacts
> the kinds of analysis we can perform on the program. In Polly, we care about
> dependence analysis, so the examples here will focus on that particular problem.
>
> Let us consider an array indexing operation of the form:
> ```cpp
> int ex1(int n, int m, B[n][m], int x1, int x2, int y1, int y2) {
> __builtin_assume(x1 != x2);
> __builtin_assume(y1 != y2);
> B[x1][y1] = 1;
> printf("%d", B[x2][y2]);
> exit(0);
> }
> ```
>
> One would like to infer that the array indices _interpreted as tuples_
> `(x1, y1)` and `(x2, y2)` do not have the same value, due to the
> guarding asserts
> that `x1 != x2` and `y1 != y2`. As a result, the write `B[x1][y1] = 1` can
> in no way interfere with the value of `B[x2][y2]`. Consquently,
> we can optimise the program into:
>
>
> ```cpp
> int ex1_opt(int n, int m, B[n][m], int x1, int x2, int y1, int y2) {
> // B[x1][y1] = 1 is omitted because the result
> // cannot be used:
> // It is not used in the print and then the program exits
> printf("%d", B[x2][y2]);
> exit(0);
> }
> ```
>
> However, alas, this is illegal, for the C language does not provide
> semantics that allow the final inference above. It is conceivable that
> `x1 != x2, y1 != y2`, but the indices do actually alias, since
> according to C semantics, the two indices alias if the _flattened
> representation of the indices alias_. Consider the parameter
> values:
>
> ```
> n = m = 3
> x1 = 1, y1 = 0; B[x1][y1] = nx1+y1 = 3*1+0=3
> x2 = 0, y2 = 3; B[x2][y2] = nx2+y2 = 3*0+3=3
> ```
>
> Hence, the array elements `B[x1][y1]` and `B[x2][y2]` _can alias_, and
> so the transformation proposed in `ex1_opt` is unsound in general.
>
>
> In contrast, many langagues other than C require that index
> expressions for multidimensional arrays have each component within the
> array dimension for that component. As a result, in the example above,
> the index pair `(0,3)` would be out-of-bounds. In languages with these
> semantics, one can infer that the indexing:
>
> `[x1][y1] != [x2][y2]` iff `x1 != x2 || y1 != y2`.
>
> While this particular example is not very interesting, it shows the
> spirit of the lack of expressiveness in LLVM we are trying to
> improve.
>
> Julia, Fortran, and Chapel are examples of such languages which target
> LLVM.
>
> Currently, the LLVM semantics of `getelementptr` talk purely of
> the C style flattened views of arrays. This inhibits the ability of
> the optimiser
> to understand the multidimensional examples as given above, and we
> are forced to make conservative assumptions, inhibiting optimisation.
> This information must ideally be expressible in LLVM, such that LLVM's
> optimisers and
> alias analysis can use this information to model multidimensional-array
> semantics.
>
> There is a more realistic (and involved) example in [Appendix A](#Appendix-A)
> in the same spirit as the above simple example, but one a compiler might
> realistically wish to perform.
>
> ## Evaluation of the impact of the intrinsic on accuracy of dependence analysis
>
> - This has been implemented in an exprimental branch of Polly, and was used
> on the COSMO climate weather model. This greatly helped increase the accuracy
> of Polly's analysis, since we eliminated the guessing game from the
> array analysis.
>
> - This has also been implemented as part of a GSoC effort to unify
> Chapel and Polly.
>
> - Molly, the distributed version of Polly written by Michael Kruse for his PhD
> also implemented a similar scheme. In his use-case, optimistic run-time checks
> with delinearization was not possible, so this kind of intrinsic was
> _necessary_
> for the application, not just _good to have_. More details are available
> in his PhD thesis: [Lattice QCD Optimization and Polytopic
> Representations of Distributed
> Memory](https://tel.archives-ouvertes.fr/tel-01078440).
> In particular, Chapter 9 contains a detailed discussion.
>
> # Representations
>
> ## Intrinsic
>
> ### Syntax
> ```
> <result> = llvm.multidim.array.index.* <ty> <ty>* <ptrval> {<stride>, <idx>}*
> ```
>
> ### Overview:
>
> The `llvm.multidim.array.index.*` intrinsic is used to get the address of
> an element from an array. It performs address calcuation only and
> does not access memory. It is similar to `getelementptr`. However, it imposes
> additional semantics which allows the optimiser to provide better optimisations
> than `getlementptr`.
>
>
>
> ### Arguments:
>
> The first argument is always a type used as the basis for the calculations. The
> second argument is always a pointer, and is the base address to start the
> calculation from. The remaining arguments are a list of pairs. Each pair
> contains a dimension stride, and an offset with respect to that stride.
>
>
> ### Semantics:
>
> `llvm.multidim.array.index.*` represents a multi-dimensional array
> index, In particular, this will
> mean that we will assume that all indices `<idx_i>` are non-negative.
>
> Additionally, we assume that, for each `<str_i>`, `<idx_i>` pair, that
> `0 <= idx_i < str_i`.
>
> Optimizations can assume that, given two llvm.multidim.array.index.*
> instructions with matching types:
>
> ```
> llvm.multidim.array.index.* <ty> <ty>* <ptrvalA> <strA_1>, <idxA_1>,
> ..., <strA_N>, <idxA_N>
> llvm.multidim.array.index.* <ty> <ty>* <ptrvalB> <strB_1>, <idxB_1>,
> ..., <strB_N>, <idxb_N>
> ```
>
> If `ptrvalA == ptrvalB` and the strides are equal `(strA_1 == strB_1
> && ... && strA_N == strB_N)` then:
>
> - If all the indices are equal (that is, `idxA_1 == idxB_1 && ... &&
> idxA_N == idxB_N`),
> then the resulting pointer values are equal.
>
> - If any index value is not equal (that is, there exists an `i` such
> that `idxA_i != idxB_i`),
> then the resulting pointer values are not equal.
>
>
> ##### Address computation:
> Consider an invocation of `llvm.multidim.array.index.*`:
>
> ```
> <result> = call @llvm.multidim.array.index.* <ty> <ty>* <ptrval>
> <str_0>, <idx_0>, <str_1> <idx_1>, ..., <str_n> <idx_n>
> ```
>
> If the pairs are denoted by `(str_i, idx_i)`, where `str_i` denotes the stride
> and `idx_i` denotes the index of the ith pair, then the final address (in bytes)
> is computed as:
>
> ```
> ptrval + len(ty) * [(str_0 * idx_0) + (str_1 * idx_1) + ... (str_n * idx_n)]
> ```
>
> ## Transitioning to `llvm.multidim.array.index.*`: Allow
> `multidim_array_index` to refer to a GEP instruction:
>
> This is a sketch of how we might gradually introduce the
> `llvm.multidim.array.index.*`
> intrinsic into LLVM without immediately losing the analyses
> that are performed on `getelememtptr` instructions. This section
> lists out some possible choices that we have, since the authors
> do not have a "best" solution.
>
> ##### Choice 1: Write a `llvm.multidim.array.index.*` to `GEP` pass,
> with the `GEP` annotated with metadata
>
> This pass will flatten all `llvm.multidim.array.index.*` expressions
> into a `GEP` annotated with metadata. This metadata will indicate that
> the index expression computed by the lowered GEP is guaranteed to be
> in a canonical form which allows the analysis
> to infer stride and index sizes.
>
> A multidim index of the form:
> ```
> %arrayidx = llvm.multidim.array.index.* i64 i64* %A, %str_1, %idx_1,
> %str_2, %idx_2
> ```
>
> is lowered to:
>
> ```
> %mul1 = mul nsw i64 %str_1, %idx_1
> %mul2 = mul1 nsw i64 %str_2, %idx_2
> %total = add nsw i64 %mul2, %mul1
> %arrayidx = getelementptr inbounds i64, i64* %A, i64 %total, !multidim !1
> ```
> with guarantees that the first term in each multiplication is the stride
> and the second term in each multiplication is the index. (What happens
> if intermediate transformation passes decide to change the order? This seems
> complicated).
>
> **TODO:** Lookup how to attach metadata such that the metadata can communicate
> which of the values are strides and which are indeces
>
>
>
> # Caveats
>
> Currently, we assume that the array shape is immutable. However, we
> will need to deal with
> being able to express `reshape` like primitives where the array shape
> can be mutated. However,
> this appears to make expressing this information quite difficult: We
> now need to attach the shape
> information to an array per "shape-live-range".
>
>
> ## Appendix-A
>
> ##### A realistic, more involved example of dependence analysis going wrong
>
> ```cpp
> // In an array A of size (n0 x n1),
> // fill a subarray of size (s0 x s1)
> // which starts at an offset (o0 x o1) in the larger array A
> void set_subarray(unsigned n0, unsigned n1,
> unsigned o0, unsigned o1,
> unsigned s0, unsigned s1,
> float A[n0][n1]) {
> for (unsigned i = 0; i < s0; i++)
> for (unsigned j = 0; j < s1; j++)
> S: A[i + o0][j + o1] = 1;
> }
> ```
> We first reduce this index expression to a sum of products:
>
> ```
> (i + o0) * n1 + (j + o1) = n1i + n1o0 + j + o1
> ix(i, j, n0, n1, o0, o1) = n1i + n1o0 + j + o1
> ```
>
> `ix` is the index expression which `LLVM` will see, since it is fully
> flattened, in comparison with the multi-dimensional index expression
> `index:[i + o0][j + o1] | sizes:[][n1]`.
>
> We will now show _why_ this multi-dimensional index is not always correct,
> and why guessing for one language will not work for another:
>
> Consider a call `set_subarray(n0=8, n1=9, o0=4, o1=6, s0=3, s1=6)`. At face
> value, this is incorrect if we view the array as 2D grid, since the size
> of the array is `(n0, n1) = (8, 9)`, but we are writing an array of size
> `(s0, s1) = (3, 6)` starting from `(o0, o1) = (4, 6)`. Clearly, we will
> exceed the width of the array, since `(s1 + o1 = 6 + 6 = 12) > (n1 = 9)`.
> However, now think of the array as a flattened 1D representation. In this
> case, the total size of the array is `n1xn2 = 8x9 = 72`, while the largest
> element we will access is at the largest value of `(i, j)`. That is,
> `i = s0 - 1 = 2`, and `j = s1 - 1 = 5`.
>
> The largest index will be `ix(i=2, j=5, n0=8, n1=9, o0=4, o1=6) =
> 8*2+8*4+5+6=59`.
> Since `59 < 72`, we are clearly at _legal_ array indices, by C semantics!
>
> The definition of the semantics of the language **changed the illegal
> multidimensional access** (which is illegal since it exceeds the `n1`
> dimension), into a **legal flattened 1D access** (which is legal since the
> flattened array indices are inbounds).
>
> LLVM has no way of expressing these two different semantics. Hence, we are
> forced to:
> 1. Consider flattened 1D accesses, which makes analysis of index expressions
> equivalent to analysis of polynomials over the integers, which is hard.
> 2. Guess multidimensional representations, and use them at the expense of
> soundness bugs as shown above.
> 3. Guess multidimensional representations, use them, and check their validity
> at runtime, causing a runtime performance hit. This implementation follows
> the description from the paper [Optimistic Delinearization of
> Parametrically Sized Arrays](optim-delin-parametrically-sized-arrays).
>
>
> Currently, Polly opts for option (3), which is to emit runtime checks. If
> the run-time checks fail, then Polly will not run its optimised code. Instead,
> It keeps a copy of the unoptimised code around, which is run in this case.
> Note that this effectively doubles the amount of performance-sensitive code
> which is finally emitted after running Polly.
>
> Ideally, we would like a mechanism to directly express the multidimensional
> semantics, which would eliminate this kind of guesswork from Polly/LLVM,
> which would both make code faster, and easier to analyze.
>
> ## References
> - [The chapel language
> specification](https://chapel-lang.org/docs/1.13/_downloads/chapelLanguageSpec.pdf)
> - [Fortran 2003
> standard](http://www.j3-fortran.org/doc/year/04/04-007.pdf}{Fortran
> 2003 standard)
> - [C++ subscripting](http://eel.is/c++draft/expr.sub)
> - [Michael Kruse's PhD thesis: Lattice QCD Optimization and Polytopic
> Representations of Distributed
> Memory](https://tel.archives-ouvertes.fr/tel-01078440).
> - [Molly source code link for the
> intrinsic](https://github.com/Meinersbur/llvm/blob/molly/include/llvm/IR/IntrinsicsMolly.td#L3)
> -[Optimistic Delinearization of Parametrically Sized
> Arrays](optim-delin-parametrically-sized-arrays)
>
> [optim-delin-parametrically-sized-arrays]:
> http://delivery.acm.org/10.1145/2760000/2751248/p351-grosser.pdf?ip=93.3.109.183&id=2751248&acc=CHORUS&key=4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E6D218144511F3437&__acm__=1557948443_2f56675c6d04796f27b84593535c9f70
> _______________________________________________
> LLVM Developers mailing list
> llvm-dev at lists.llvm.org
> https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev
--
Johannes Doerfert
Researcher
Argonne National Laboratory
Lemont, IL 60439, USA
jdoerfert at anl.gov
-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 228 bytes
Desc: not available
URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20190803/a916ac5e/attachment.sig>
More information about the llvm-dev
mailing list