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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
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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.

// 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 +
// (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.

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