[llvm-dev] [RFC] A new multidimensional array indexing intrinsic

Philip Reames via llvm-dev
2019-07-22T17:13:30Z

We could also simply extend the existing inrange mechanism to
non-constantexpr GEPs.  It would remove an inconsistency in the
semantics, be relatively straight forward, and solve the motivating
example.

(I didn't read the proposal in full, so there may be other examples it
doesn't solve.)

Philip

On 7/22/19 10:01 AM, Peter Collingbourne via llvm-dev
wrote:
> The restrictions of this new intrinsic seem very similar to those of
> the inrange attribute on GEPs. It seems that the main advantage of
> your proposal is that it would allow for non-constant strides (i.e.
> variable length arrays) in dimensions other than the first one. Do
> these appear frequently enough in the programs that you're interested
> in to be worth optimizing for?
>
> Peter
>
> On Sun, Jul 21, 2019 at 3:54 PM Siddharth Bhat via llvm-dev
> <llvm-dev at lists.llvm.org <mailto:llvm-dev at
lists.llvm.org>> 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
<http://www.j3-fortran.org/doc/year/04/04-007.pdf%7D%7BFortran>  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
>
>
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>
>
>
> --
> --
> Peter
>
> _______________________________________________
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