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[Delinearization] Add validation for large size arrays #169902

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285364b
[Delinearization] Add validation for large size arrays
kasuga-fj Nov 28, 2025
6960ece
fix spell
kasuga-fj Nov 28, 2025
a2a6988
also consider element size
kasuga-fj Nov 28, 2025
1c5b414
address review comments
kasuga-fj Dec 1, 2025
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51 changes: 51 additions & 0 deletions llvm/lib/Analysis/Delinearization.cpp
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Expand Up @@ -747,6 +747,20 @@ bool llvm::validateDelinearizationResult(ScalarEvolution &SE,
ArrayRef<const SCEV *> Sizes,
ArrayRef<const SCEV *> Subscripts,
const Value *Ptr) {
// Sizes and Subscripts are as follows:
//
// Sizes: [UNK][S_2]...[S_n]
// Subscripts: [I_1][I_2]...[I_n]
//
// where the size of the outermost dimension is unknown (UNK).

auto MulOverflow = [&](const SCEV *A, const SCEV *B) -> const SCEV * {
if (!SE.willNotOverflow(Instruction::Mul, /*IsSigned=*/true, A, B))
return nullptr;
return SE.getMulExpr(A, B);
};

// Range check: 0 <= I_k < S_k for k = 2..n.
for (size_t I = 1; I < Sizes.size(); ++I) {
const SCEV *Size = Sizes[I - 1];
const SCEV *Subscript = Subscripts[I];
Expand All @@ -755,6 +769,43 @@ bool llvm::validateDelinearizationResult(ScalarEvolution &SE,
if (!isKnownLessThan(&SE, Subscript, Size))
return false;
}

// The offset computation is as follows:
//
// Offset = I_n +
// S_n * I_{n-1} +
// ... +
// (S_2 * ... * S_n) * I_1
//
// Regarding this as a function from (I_1, I_2, ..., I_n) to integers, it
// must be injective. To guarantee it, the above calculation must not
// overflow. Since we have already checked that 0 <= I_k < S_k for k = 2..n,
// the minimum and maximum values occur in the following cases:
//
// Min = [I_1][0]...[0] = S_2 * ... * S_n * I_1
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@Meinersbur Meinersbur Nov 28, 2025

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Why isn't Min just 0 (I_1 == 0)?

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@kasuga-fj kasuga-fj Nov 28, 2025

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Because DA appears to allow the outermost subscript to be negative, e.g.,

llvm-project/llvm/test/Analysis/DependenceAnalysis/Propagating.ll

Lines 310 to 314 in 318236d

;; for (long int i = 0; i < 100; i++)
;; for (long int j = 0; j < 100; j++) {
;; A[3*i - 18][22 - i][2*i + j] = i;
;; *B++ = A[i][i][3*i + j];
. That said, I don't know if this is important or not.

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@Meinersbur Meinersbur Dec 1, 2025

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Would be worth adding a comment?

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@kasuga-fj kasuga-fj Dec 1, 2025

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Yes, added.

// Max = [I_1][S_2-1]...[S_n-1]
// = (S_2 * ... * S_n) * I_1 +
// (S_2 * ... * S_{n-1}) * (S_2 - 1) +
// ... +
// (S_n - 1)
// = (S_2 * ... * S_n) * I_1 +
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@Meinersbur Meinersbur Dec 1, 2025

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Suggested change
// = (S_2 * ... * S_n) * I_1 +
// = (S_2 * ... * S_n) * I_1 + /* this is the same as Min expression; if this expression has already been checked for overlflow, need only check the rest of the expression for Max */

Some cleverness I did not see (Min == Prod * I_1). I was expecting someting more symmetric. My suggested comment here is clunky, maby you find something better.

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@kasuga-fj kasuga-fj Dec 1, 2025

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Adjusted the comments a bit. Does it make sense?

// (S_2 * ... * S_n) - 1 (can be proven by induction)
//
const SCEV *Prod = SE.getOne(Sizes[0]->getType());
for (const SCEV *Size : Sizes) {
Prod = MulOverflow(Prod, Size);
if (!Prod)
return false;
}
const SCEV *Min = MulOverflow(Prod, Subscripts[0]);
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@Meinersbur Meinersbur Nov 28, 2025

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For the first dimension, it takes the concrete subscript, for every other dimension it assumes the largest possible subscript. Would we get a better estimate combining both sources of knowledge by the max of those (SCEVMaxExpr(Subscripts[i],Size[i]-1))?

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@kasuga-fj kasuga-fj Nov 28, 2025

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I'm not sure until we try it, but once a SCEVUnknown gets in there, I feel like it probably won't change much.

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@kasuga-fj kasuga-fj Nov 28, 2025

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Does the following implementation match your intention?

kasuga-fj@e8f6f57

As for the existing regression tests, their results have not changed.

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@Meinersbur Meinersbur Dec 1, 2025

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Does the following implementation match your intention?

Yes.

If one is SCEVUnknown, one can take the other one. Only both being SCEVUnknown would stop working. if SCEVMaxExprs cause SCEV to bail out because of expression complexity, we cioud prioritize one of the expressions.

Aynway, what I prefer handling subscripts independent of whether they are outermost, innermost, or in-between, but based on what information is available.

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@kasuga-fj kasuga-fj Dec 1, 2025

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Ah, I see, I understand your point. I’m not sure if there are cases where this actually improves things, but in point of implementation, it seems more consistent.

if (!Min)
return false;

// Over-approximate Max as Prod * I_1 + Prod (ignoring the -1).
if (!SE.willNotOverflow(Instruction::Add, /*IsSigned=*/true, Min,
Subscripts[0]))
return false;

return true;
}

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2 changes: 1 addition & 1 deletion llvm/test/Analysis/Delinearization/constant_functions_multi_dim.ll
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Expand Up @@ -11,7 +11,7 @@ define void @mat_mul(ptr %C, ptr %A, ptr %B, i64 %N) !kernel_arg_addr_space !2 !
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%N] with elements of 4 bytes.
; CHECK-NEXT: ArrayRef[%call][{0,+,1}<nuw><nsw><%for.inc>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
; CHECK-EMPTY:
; CHECK-NEXT: Inst: %tmp5 = load float, ptr %arrayidx4, align 4
; CHECK-NEXT: AccessFunction: {(4 * %call1),+,(4 * %N)}<%for.inc>
Expand Down
4 changes: 2 additions & 2 deletions llvm/test/Analysis/Delinearization/multidim_only_ivs_2d.ll
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Expand Up @@ -16,14 +16,14 @@ define void @foo(i64 %n, i64 %m, ptr %A) {
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%m] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
; CHECK-EMPTY:
; CHECK-NEXT: Inst: store double %val, ptr %arrayidx, align 8
; CHECK-NEXT: AccessFunction: {{\{\{}}0,+,(8 * %m)}<%for.i>,+,8}<%for.j>
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%m] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
br label %for.i
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2 changes: 1 addition & 1 deletion llvm/test/Analysis/Delinearization/multidim_only_ivs_3d.ll
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Expand Up @@ -16,7 +16,7 @@ define void @foo(i64 %n, i64 %m, i64 %o, ptr %A) {
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%m][%o] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>][{0,+,1}<nuw><nsw><%for.k>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
br label %for.i
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4 changes: 2 additions & 2 deletions llvm/test/Analysis/Delinearization/multidim_two_accesses_different_delinearization.ll
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Expand Up @@ -19,14 +19,14 @@ define void @foo(i64 %n, i64 %m, ptr %A) {
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%m] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
; CHECK-EMPTY:
; CHECK-NEXT: Inst: store double 1.000000e+00, ptr %arrayidx1, align 8
; CHECK-NEXT: AccessFunction: {{\{\{}}0,+,8}<%for.i>,+,(8 * %n)}<%for.j>
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%n] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.j>][{0,+,1}<nuw><nsw><%for.i>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
br label %for.i
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54 changes: 46 additions & 8 deletions llvm/test/Analysis/Delinearization/validation_large_size.ll
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@@ -1,12 +1,9 @@
; NOTE: Assertions have been autogenerated by utils/update_analyze_test_checks.py UTC_ARGS: --version 6
; RUN: opt < %s -passes='print<delinearization>' --delinearize-use-fixed-size-array-heuristic -disable-output 2>&1 | FileCheck %s

; FIXME: When considering an array as a function from subcripts to addresses,
; it should be injective. That is, different subscript tuples should map to
; different addresses. Currently, delinearization doesn't guarantee this
; property, especially when the inferred array size is very large so that the
; product of dimensions may overflow. The delinearization validation should
; consider such cases as invalid.
; When considering an array as a function from subcripts to addresses, it
; should be injective. That is, different subscript tuples should map to
; different addresses.

; for (i = 0; i < (1ULL << 60); i++)
; for (j = 0; j < 256; j++)
Expand All @@ -23,7 +20,7 @@ define void @large_size_fixed(ptr %A) {
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][256] with elements of 1 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i.header>][{0,+,1}<nuw><nsw><%for.j>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
br label %for.i.header
Expand Down Expand Up @@ -75,7 +72,7 @@ define void @large_size_parametric(i64 %n, i64 %m, i64 %o, ptr %A) {
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][%m][%o] with elements of 1 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i.header>][{0,+,1}<nuw><nsw><%for.j.header>][{0,+,1}<nuw><nsw><%for.k.header>]
; CHECK-NEXT: Delinearization validation: Succeeded
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
%guard.i = icmp sgt i64 %n, 0
Expand Down Expand Up @@ -134,3 +131,44 @@ for.i.latch:
exit:
ret void
}

; for (i = 0; i < (1 << 54); i++)
; for (j = 0; j < 256; j++)
; A[i*256 + j] = 0;
;
; We also need to consider the element size when validation.
;
define void @elementsize_cause_ovfl(ptr %A) {
; CHECK-LABEL: 'elementsize_cause_ovfl'
; CHECK-NEXT: Inst: store i64 0, ptr %gep, align 4
; CHECK-NEXT: AccessFunction: {{\{\{}}0,+,2048}<%for.i.header>,+,8}<%for.j>
; CHECK-NEXT: Base offset: %A
; CHECK-NEXT: ArrayDecl[UnknownSize][256] with elements of 8 bytes.
; CHECK-NEXT: ArrayRef[{0,+,1}<nuw><nsw><%for.i.header>][{0,+,1}<nuw><nsw><%for.j>]
; CHECK-NEXT: Delinearization validation: Failed
;
entry:
br label %for.i.header

for.i.header:
%i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.latch ]
%i.mul = mul i64 %i, 256
br label %for.j

for.j:
%j = phi i64 [ 0, %for.i.header ], [ %j.inc, %for.j ]
%offset = add i64 %i.mul, %j
%gep = getelementptr i64, ptr %A, i64 %offset
store i64 0, ptr %gep
%j.inc = add i64 %j, 1
%ec.j = icmp eq i64 %j.inc, 256
br i1 %ec.j, label %for.i.latch, label %for.j

for.i.latch:
%i.inc = add i64 %i, 1
%ec.i = icmp eq i64 %i.inc, 18014398509481984
br i1 %ec.i, label %exit, label %for.i.header

exit:
ret void
}
32 changes: 16 additions & 16 deletions llvm/test/Analysis/DependenceAnalysis/DADelin.ll
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Expand Up @@ -13,11 +13,11 @@ target triple = "thumbv8m.main-arm-none-eabi"
define void @t1(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't1'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - consistent anti [0 0 0|<]!
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - output [* * *]!
;
entry:
%cmp49 = icmp sgt i32 %n, 0
Expand Down Expand Up @@ -78,7 +78,7 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t2(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't2'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
Expand Down Expand Up @@ -145,7 +145,7 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t3(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't3'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
Expand Down Expand Up @@ -212,7 +212,7 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t4(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't4'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
Expand Down Expand Up @@ -279,7 +279,7 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t5(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't5'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
Expand Down Expand Up @@ -346,11 +346,11 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t6(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't6'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - consistent anti [-1 0 0]!
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - output [* * *]!
;
entry:
%cmp49 = icmp sgt i32 %n, 0
Expand Down Expand Up @@ -414,11 +414,11 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t7(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't7'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - consistent anti [1 0 0]!
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - output [* * *]!
;
entry:
%cmp49 = icmp sgt i32 %n, 0
Expand Down Expand Up @@ -482,11 +482,11 @@ for.cond.cleanup: ; preds = %for.cond.cleanup3,
define void @t8(i32 %n, i32 %m, i32 %o, ptr nocapture %A) {
; CHECK-LABEL: 't8'
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: %0 = load i32, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - input [* * *]!
; CHECK-NEXT: Src: %0 = load i32, ptr %arrayidx, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - consistent anti [0 0 1]!
; CHECK-NEXT: da analyze - anti [* * *|<]!
; CHECK-NEXT: Src: store i32 %add12, ptr %arrayidx2, align 4 --> Dst: store i32 %add12, ptr %arrayidx2, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - output [* * *]!
;
entry:
%cmp49 = icmp sgt i32 %n, 0
Expand Down
2 changes: 1 addition & 1 deletion llvm/test/Analysis/DependenceAnalysis/DifferentOffsets.ll
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Expand Up @@ -100,7 +100,7 @@ define void @linearized_accesses(i64 %n, i64 %m, i64 %o, ptr %A) {
; CHECK-NEXT: Src: store i32 1, ptr %idx0, align 4 --> Dst: store i32 1, ptr %idx1, align 4
; CHECK-NEXT: da analyze - output [* * *|<]!
; CHECK-NEXT: Src: store i32 1, ptr %idx1, align 4 --> Dst: store i32 1, ptr %idx1, align 4
; CHECK-NEXT: da analyze - none!
; CHECK-NEXT: da analyze - output [* * *]!
;
entry:
br label %for.i
Expand Down
10 changes: 7 additions & 3 deletions llvm/test/Analysis/DependenceAnalysis/StrongSIV.ll
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Expand Up @@ -536,9 +536,13 @@ for.end: ; preds = %for.body
;; A[i] = 0;

define void @strong11(ptr %A) nounwind uwtable ssp {
; CHECK-LABEL: 'strong11'
; CHECK-NEXT: Src: store i32 0, ptr %arrayidx, align 4 --> Dst: store i32 0, ptr %arrayidx, align 4
; CHECK-NEXT: da analyze - consistent output [0 S]!
; CHECK-ALL-LABEL: 'strong11'
; CHECK-ALL-NEXT: Src: store i32 0, ptr %arrayidx, align 4 --> Dst: store i32 0, ptr %arrayidx, align 4
; CHECK-ALL-NEXT: da analyze - none!
;
; CHECK-STRONG-SIV-LABEL: 'strong11'
; CHECK-STRONG-SIV-NEXT: Src: store i32 0, ptr %arrayidx, align 4 --> Dst: store i32 0, ptr %arrayidx, align 4
; CHECK-STRONG-SIV-NEXT: da analyze - consistent output [0 S]!
;
entry:
br label %for.cond1.preheader
Expand Down
3 changes: 3 additions & 0 deletions llvm/test/Transforms/LICM/lnicm.ll
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Expand Up @@ -3,6 +3,9 @@
; RUN: opt -aa-pipeline=basic-aa -passes='loop-mssa(lnicm),loop(loop-interchange)' -cache-line-size=64 -S %s | FileCheck %s --check-prefixes LNICM
; RUN: opt -aa-pipeline=basic-aa -passes='loop-mssa(licm),loop(loop-interchange)' -cache-line-size=64 -S %s | FileCheck %s --check-prefixes LICM

; XFAIL: *
; Loop interchange currently fails due to a failure in dependence analysis.

; This test represents the following function:
; void test(int n, int m, int x[m][n], int y[n], int *z) {
; for (int k = 0; k < n; k++) {
Expand Down