diff --git a/mlir/include/mlir/Dialect/ArmSVE/ArmSVE.td b/mlir/include/mlir/Dialect/ArmSVE/ArmSVE.td
--- a/mlir/include/mlir/Dialect/ArmSVE/ArmSVE.td
+++ b/mlir/include/mlir/Dialect/ArmSVE/ArmSVE.td
@@ -65,6 +65,14 @@
     "Type":$elementType
   );
 
+  let builders = [
+    TypeBuilderWithInferredContext<(ins
+      "ArrayRef<int64_t>":$shape, "Type":$elementType
+    ), [{
+      return $_get(elementType.getContext(), shape, elementType);
+    }]>
+  ];
+
   let printer = [{
     $_printer << "vector<";
     for (int64_t dim : getShape())
@@ -76,7 +84,7 @@
     VectorType vector;
     if ($_parser.parseType(vector))
       return Type();
-    return get($_ctxt, vector.getShape(), vector.getElementType());
+    return get(vector.getShape(), vector.getElementType());
   }];
 
   let extraClassDeclaration = [{
@@ -93,6 +101,9 @@
       return num;
     }
   }];
+
+  let skipDefaultBuilders = 1;
+  let genVerifyDecl = 1;
 }
 
 //===----------------------------------------------------------------------===//
@@ -266,6 +277,222 @@
     "attr-dict `:` type($res)";
 }
 
+def ScalableAddIOp : ArmSVE_Op<"addi",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "addition for scalable vectors of integers";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.addi` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.addi` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src1,
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[I8, I16, I32, I64]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableAddFOp : ArmSVE_Op<"addf",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "addition for scalable vectors of floats";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.addf` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.addf` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[AnyFloat]>:$src1,
+          ScalableVectorOf<[AnyFloat]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[AnyFloat]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableSubIOp : ArmSVE_Op<"subi",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "subtraction for scalable vectors of integers";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.subi` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.subi` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src1,
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[I8, I16, I32, I64]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableSubFOp : ArmSVE_Op<"subf",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "subtraction for scalable vectors of floats";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.subf` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.subf` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[AnyFloat]>:$src1,
+          ScalableVectorOf<[AnyFloat]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[AnyFloat]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableMulIOp : ArmSVE_Op<"muli",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "multiplication for scalable vectors of integers";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.muli` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.muli` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src1,
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[I8, I16, I32, I64]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableMulFOp : ArmSVE_Op<"mulf",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "multiplication for scalable vectors of floats";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.mulf` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.mulf` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[AnyFloat]>:$src1,
+          ScalableVectorOf<[AnyFloat]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[AnyFloat]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableSDivIOp : ArmSVE_Op<"divi_signed",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "signed division for scalable vectors of integers";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.divi_signed` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.divi_signed` operations takes two scalable vectors and returns
+    one scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src1,
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[I8, I16, I32, I64]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableUDivIOp : ArmSVE_Op<"divi_unsigned",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "unsigned division for scalable vectors of integers";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.divi_unsigned` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.divi_unsigned` operations takes two scalable vectors and returns
+    one scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src1,
+          ScalableVectorOf<[I8, I16, I32, I64]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[I8, I16, I32, I64]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
+def ScalableDivFOp : ArmSVE_Op<"divf",
+                       [Commutative,
+                       AllTypesMatch<["src1", "src2", "dst"]>
+                     ]> {
+  let summary = "division for scalable vectors of floats";
+  let description = [{
+    Syntax:
+
+    ```
+    operation ::= ssa-id `=` `arm_sve.divf` ssa-use `,` ssa-use `:` !arm_sve.vector
+    ```
+
+    The `arm_sve.divf` operations takes two scalable vectors and returns one
+    scalable vector with the result of the operation.
+  }];
+  let arguments = (ins
+          ScalableVectorOf<[AnyFloat]>:$src1,
+          ScalableVectorOf<[AnyFloat]>:$src2
+  );
+  let results = (outs ScalableVectorOf<[AnyFloat]>:$dst);
+  let assemblyFormat =
+    "$src1 `,` $src2 attr-dict `:` type($src1)";
+}
+
 def UmmlaIntrOp :
   ArmSVE_IntrBinaryOverloadedOp<"ummla">,
   Arguments<(ins LLVM_AnyVector, LLVM_AnyVector, LLVM_AnyVector)>;
diff --git a/mlir/lib/Dialect/ArmSVE/IR/ArmSVEDialect.cpp b/mlir/lib/Dialect/ArmSVE/IR/ArmSVEDialect.cpp
--- a/mlir/lib/Dialect/ArmSVE/IR/ArmSVEDialect.cpp
+++ b/mlir/lib/Dialect/ArmSVE/IR/ArmSVEDialect.cpp
@@ -42,6 +42,20 @@
 // ScalableVectorType
 //===----------------------------------------------------------------------===//
 
+LogicalResult arm_sve::ScalableVectorType::verify(
+    function_ref<mlir::InFlightDiagnostic()> emitError, ArrayRef<int64_t> shape,
+    Type elementType) {
+  if (shape.empty() || shape.size() > 1)
+    return emitError()
+           << "scalable vector types must have exactly one dimension";
+
+  if (shape[0] <= 0)
+    return emitError()
+           << "scalable vector types must have a positive constant size";
+
+  return success();
+}
+
 Type arm_sve::ArmSVEDialect::parseType(DialectAsmParser &parser) const {
   llvm::SMLoc typeLoc = parser.getCurrentLocation();
   {
diff --git a/mlir/lib/Dialect/ArmSVE/Transforms/LegalizeForLLVMExport.cpp b/mlir/lib/Dialect/ArmSVE/Transforms/LegalizeForLLVMExport.cpp
--- a/mlir/lib/Dialect/ArmSVE/Transforms/LegalizeForLLVMExport.cpp
+++ b/mlir/lib/Dialect/ArmSVE/Transforms/LegalizeForLLVMExport.cpp
@@ -84,6 +84,38 @@
 using VectorScaleOpLowering =
     OneToOneConvertToLLVMPattern<VectorScaleOp, VectorScaleIntrOp>;
 
+static void
+populateBasicSVEArithmeticExportPatterns(LLVMTypeConverter &converter,
+                                         OwningRewritePatternList &patterns) {
+  // clang-format off
+  patterns.add<OneToOneConvertToLLVMPattern<ScalableAddIOp, LLVM::AddOp>,
+               OneToOneConvertToLLVMPattern<ScalableAddFOp, LLVM::FAddOp>,
+               OneToOneConvertToLLVMPattern<ScalableSubIOp, LLVM::SubOp>,
+               OneToOneConvertToLLVMPattern<ScalableSubFOp, LLVM::FSubOp>,
+               OneToOneConvertToLLVMPattern<ScalableMulIOp, LLVM::MulOp>,
+               OneToOneConvertToLLVMPattern<ScalableMulFOp, LLVM::FMulOp>,
+               OneToOneConvertToLLVMPattern<ScalableSDivIOp, LLVM::SDivOp>,
+               OneToOneConvertToLLVMPattern<ScalableUDivIOp, LLVM::UDivOp>,
+               OneToOneConvertToLLVMPattern<ScalableDivFOp, LLVM::FDivOp>
+              >(converter);
+  // clang-format on
+}
+
+static void
+configureBasicSVEArithmeticLegalizations(LLVMConversionTarget &target) {
+  // clang-format off
+  target.addIllegalOp<ScalableAddIOp,
+                      ScalableAddFOp,
+                      ScalableSubIOp,
+                      ScalableSubFOp,
+                      ScalableMulIOp,
+                      ScalableMulFOp,
+                      ScalableSDivIOp,
+                      ScalableUDivIOp,
+                      ScalableDivFOp>();
+  // clang-format on
+}
+
 /// Populate the given list with patterns that convert from ArmSVE to LLVM.
 void mlir::populateArmSVELegalizeForLLVMExportPatterns(
     LLVMTypeConverter &converter, OwningRewritePatternList &patterns) {
@@ -106,20 +138,14 @@
                UmmlaOpLowering,
                VectorScaleOpLowering>(converter);
   // clang-format on
+  populateBasicSVEArithmeticExportPatterns(converter, patterns);
 }
 
 void mlir::configureArmSVELegalizeForExportTarget(
     LLVMConversionTarget &target) {
-  target.addLegalOp<SdotIntrOp>();
-  target.addIllegalOp<SdotOp>();
-  target.addLegalOp<SmmlaIntrOp>();
-  target.addIllegalOp<SmmlaOp>();
-  target.addLegalOp<UdotIntrOp>();
-  target.addIllegalOp<UdotOp>();
-  target.addLegalOp<UmmlaIntrOp>();
-  target.addIllegalOp<UmmlaOp>();
-  target.addLegalOp<VectorScaleIntrOp>();
-  target.addIllegalOp<VectorScaleOp>();
+  target.addLegalOp<SdotIntrOp, SmmlaIntrOp, UdotIntrOp, UmmlaIntrOp,
+                    VectorScaleIntrOp>();
+  target.addIllegalOp<SdotOp, SmmlaOp, UdotOp, UmmlaOp, VectorScaleOp>();
   auto hasScalableVectorType = [](TypeRange types) {
     for (Type type : types)
       if (type.isa<arm_sve::ScalableVectorType>())
@@ -135,4 +161,5 @@
         return !hasScalableVectorType(op->getOperandTypes()) &&
                !hasScalableVectorType(op->getResultTypes());
       });
+  configureBasicSVEArithmeticLegalizations(target);
 }
diff --git a/mlir/test/Dialect/ArmSVE/legalize-for-llvm.mlir b/mlir/test/Dialect/ArmSVE/legalize-for-llvm.mlir
--- a/mlir/test/Dialect/ArmSVE/legalize-for-llvm.mlir
+++ b/mlir/test/Dialect/ArmSVE/legalize-for-llvm.mlir
@@ -40,6 +40,40 @@
   return %0 : !arm_sve.vector<4xi32>
 }
 
+func @arm_sve_arithi(%a: !arm_sve.vector<4xi32>,
+                     %b: !arm_sve.vector<4xi32>,
+                     %c: !arm_sve.vector<4xi32>,
+                     %d: !arm_sve.vector<4xi32>,
+                     %e: !arm_sve.vector<4xi32>) -> !arm_sve.vector<4xi32> {
+  // CHECK: llvm.mul
+  %0 = arm_sve.muli %a, %b : !arm_sve.vector<4xi32>
+  // CHECK: llvm.add
+  %1 = arm_sve.addi %0, %c : !arm_sve.vector<4xi32>
+  // CHECK: llvm.sub
+  %2 = arm_sve.subi %1, %d : !arm_sve.vector<4xi32>
+  // CHECK: llvm.sdiv
+  %3 = arm_sve.divi_signed %2, %e : !arm_sve.vector<4xi32>
+  // CHECK: llvm.udiv
+  %4 = arm_sve.divi_unsigned %2, %e : !arm_sve.vector<4xi32>
+  return %3 : !arm_sve.vector<4xi32>
+}
+
+func @arm_sve_arithf(%a: !arm_sve.vector<4xf32>,
+                     %b: !arm_sve.vector<4xf32>,
+                     %c: !arm_sve.vector<4xf32>,
+                     %d: !arm_sve.vector<4xf32>,
+                     %e: !arm_sve.vector<4xf32>) -> !arm_sve.vector<4xf32> {
+  // CHECK: llvm.fmul
+  %0 = arm_sve.mulf %a, %b : !arm_sve.vector<4xf32>
+  // CHECK: llvm.fadd
+  %1 = arm_sve.addf %0, %c : !arm_sve.vector<4xf32>
+  // CHECK: llvm.fsub
+  %2 = arm_sve.subf %1, %d : !arm_sve.vector<4xf32>
+  // CHECK: llvm.fdiv
+  %3 = arm_sve.divf %2, %e : !arm_sve.vector<4xf32>
+  return %3 : !arm_sve.vector<4xf32>
+}
+
 func @get_vector_scale() -> index {
   // CHECK: arm_sve.vscale
   %0 = arm_sve.vector_scale : index
diff --git a/mlir/test/Dialect/ArmSVE/roundtrip.mlir b/mlir/test/Dialect/ArmSVE/roundtrip.mlir
--- a/mlir/test/Dialect/ArmSVE/roundtrip.mlir
+++ b/mlir/test/Dialect/ArmSVE/roundtrip.mlir
@@ -36,6 +36,26 @@
   return %0 : !arm_sve.vector<4xi32>
 }
 
+func @arm_sve_arithi(%a: !arm_sve.vector<4xi32>,
+                     %b: !arm_sve.vector<4xi32>,
+                     %c: !arm_sve.vector<4xi32>) -> !arm_sve.vector<4xi32> {
+  // CHECK: arm_sve.muli {{.*}}: !arm_sve.vector<4xi32>
+  %0 = arm_sve.muli %a, %b : !arm_sve.vector<4xi32>
+  // CHECK: arm_sve.addi {{.*}}: !arm_sve.vector<4xi32>
+  %1 = arm_sve.addi %0, %c : !arm_sve.vector<4xi32>
+  return %1 : !arm_sve.vector<4xi32>
+}
+
+func @arm_sve_arithf(%a: !arm_sve.vector<4xf32>,
+                     %b: !arm_sve.vector<4xf32>,
+                     %c: !arm_sve.vector<4xf32>) -> !arm_sve.vector<4xf32> {
+  // CHECK: arm_sve.mulf {{.*}}: !arm_sve.vector<4xf32>
+  %0 = arm_sve.mulf %a, %b : !arm_sve.vector<4xf32>
+  // CHECK: arm_sve.addf {{.*}}: !arm_sve.vector<4xf32>
+  %1 = arm_sve.addf %0, %c : !arm_sve.vector<4xf32>
+  return %1 : !arm_sve.vector<4xf32>
+}
+
 func @get_vector_scale() -> index {
   // CHECK: arm_sve.vector_scale : index
   %0 = arm_sve.vector_scale : index
diff --git a/mlir/test/Target/LLVMIR/arm-sve.mlir b/mlir/test/Target/LLVMIR/arm-sve.mlir
--- a/mlir/test/Target/LLVMIR/arm-sve.mlir
+++ b/mlir/test/Target/LLVMIR/arm-sve.mlir
@@ -48,6 +48,30 @@
   llvm.return %0 : !llvm.vec<?x4 x i32>
 }
 
+// CHECK-LABEL: define <vscale x 4 x i32> @arm_sve_arithi
+llvm.func @arm_sve_arithi(%arg0: !llvm.vec<? x 4 x i32>,
+                          %arg1: !llvm.vec<? x 4 x i32>,
+                          %arg2: !llvm.vec<? x 4 x i32>)
+                          -> !llvm.vec<? x 4 x i32> {
+  // CHECK: mul <vscale x 4 x i32>
+  %0 = llvm.mul %arg0, %arg1 : !llvm.vec<? x 4 x i32>
+  // CHECK: add <vscale x 4 x i32>
+  %1 = llvm.add %0, %arg2 : !llvm.vec<? x 4 x i32>
+  llvm.return %1 : !llvm.vec<? x 4 x i32>
+}
+
+// CHECK-LABEL: define <vscale x 4 x float> @arm_sve_arithf
+llvm.func @arm_sve_arithf(%arg0: !llvm.vec<? x 4 x f32>,
+                          %arg1: !llvm.vec<? x 4 x f32>,
+                          %arg2: !llvm.vec<? x 4 x f32>)
+                          -> !llvm.vec<? x 4 x f32> {
+  // CHECK: fmul <vscale x 4 x float>
+  %0 = llvm.fmul %arg0, %arg1 : !llvm.vec<? x 4 x f32>
+  // CHECK: fadd <vscale x 4 x float>
+  %1 = llvm.fadd %0, %arg2 : !llvm.vec<? x 4 x f32>
+  llvm.return %1 : !llvm.vec<? x 4 x f32>
+}
+
 // CHECK-LABEL: define i64 @get_vector_scale()
 llvm.func @get_vector_scale() -> i64 {
   // CHECK: call i64 @llvm.vscale.i64()