[mlir][complex] Prevent underflow in complex.abs #76316

Lewuathe · 2023-12-24T05:44:47Z

complex.abs op may causes the underflow issue with the large input. We can prevent the problem by using the algorithm listed in "ALGORITHM 312 ABSOLUTE VALUE AND SQUARE ROOT OF A COMPLEX NUMBER" as well as the complex.sqrt.

See: #62011

llvmbot · 2023-12-24T05:45:13Z

@llvm/pr-subscribers-mlir-complex

Author: Kai Sasaki (Lewuathe)

Changes

complex.abs op may causes the underflow issue with the large input. We can prevent the problem by using the algorithm listed in "ALGORITHM 312 ABSOLUTE VALUE AND SQUARE ROOT OF A COMPLEX NUMBER" as well as the complex.sqrt.

See: #62011

Full diff: https://github.com/llvm/llvm-project/pull/76316.diff

4 Files Affected:

(modified) mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp (+42-14)
(modified) mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir (+93-22)
(modified) mlir/test/Conversion/ComplexToStandard/full-conversion.mlir (+21-4)
(modified) mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir (+38)

diff --git a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
index bf753c7062f366..7c1db57b55f996 100644
--- a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
+++ b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
@@ -26,29 +26,57 @@ namespace mlir {
 using namespace mlir;
 
 namespace {
+// The algorithm is listed in https://dl.acm.org/doi/pdf/10.1145/363717.363780.
 struct AbsOpConversion : public OpConversionPattern<complex::AbsOp> {
   using OpConversionPattern<complex::AbsOp>::OpConversionPattern;
 
   LogicalResult
   matchAndRewrite(complex::AbsOp op, OpAdaptor adaptor,
                   ConversionPatternRewriter &rewriter) const override {
-    auto loc = op.getLoc();
-    auto type = op.getType();
+    mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
 
     arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
 
-    Value real =
-        rewriter.create<complex::ReOp>(loc, type, adaptor.getComplex());
-    Value imag =
-        rewriter.create<complex::ImOp>(loc, type, adaptor.getComplex());
-    Value realSqr =
-        rewriter.create<arith::MulFOp>(loc, real, real, fmf.getValue());
-    Value imagSqr =
-        rewriter.create<arith::MulFOp>(loc, imag, imag, fmf.getValue());
-    Value sqNorm =
-        rewriter.create<arith::AddFOp>(loc, realSqr, imagSqr, fmf.getValue());
-
-    rewriter.replaceOpWithNewOp<math::SqrtOp>(op, sqNorm);
+    Type elementType = op.getType();
+    Value arg = adaptor.getComplex();
+
+    Value zero =
+        b.create<arith::ConstantOp>(elementType, b.getZeroAttr(elementType));
+    Value one = b.create<arith::ConstantOp>(elementType,
+                                            b.getFloatAttr(elementType, 1.0));
+
+    Value real = b.create<complex::ReOp>(elementType, arg);
+    Value imag = b.create<complex::ImOp>(elementType, arg);
+
+    Value realIsZero =
+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, zero);
+    Value imagIsZero =
+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero);
+
+    // Real > Imag
+    Value imagDivReal = b.create<arith::DivFOp>(imag, real, fmf.getValue());
+    Value imagSq =
+        b.create<arith::MulFOp>(imagDivReal, imagDivReal, fmf.getValue());
+    Value imagSqPlusOne = b.create<arith::AddFOp>(imagSq, one, fmf.getValue());
+    Value imagSqrt = b.create<math::SqrtOp>(imagSqPlusOne, fmf.getValue());
+    Value absImag = b.create<arith::MulFOp>(imagSqrt, real, fmf.getValue());
+
+    // Real <= Imag
+    Value realDivImag = b.create<arith::DivFOp>(real, imag, fmf.getValue());
+    Value realSq =
+        b.create<arith::MulFOp>(realDivImag, realDivImag, fmf.getValue());
+    Value realSqPlusOne = b.create<arith::AddFOp>(realSq, one, fmf.getValue());
+    Value realSqrt = b.create<math::SqrtOp>(realSqPlusOne, fmf.getValue());
+    Value absReal = b.create<arith::MulFOp>(realSqrt, imag, fmf.getValue());
+
+    rewriter.replaceOpWithNewOp<arith::SelectOp>(
+        op, realIsZero, imag,
+        b.create<arith::SelectOp>(
+            imagIsZero, real,
+            b.create<arith::SelectOp>(
+                b.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, real, imag),
+                absImag, absReal)));
+
     return success();
   }
 };
diff --git a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
index 3af28150fd5c3f..1028c9aae92c05 100644
--- a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
@@ -7,13 +7,28 @@ func.func @complex_abs(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg: complex<f32>
   return %abs : f32
 }
+
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK-DAG: %[[REAL_SQ:.*]] = arith.mulf %[[REAL]], %[[REAL]] : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[REAL_SQ]], %[[IMAG_SQ]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
-// CHECK: return %[[NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
+// CHECK: return %[[ABS3]] : f32
 
 // -----
 
@@ -241,12 +256,26 @@ func.func @complex_log(%arg: complex<f32>) -> complex<f32> {
   %log = complex.log %arg: complex<f32>
   return %log : complex<f32>
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL]], %[[REAL]] : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
 // CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
@@ -469,12 +498,26 @@ func.func @complex_sign(%arg: complex<f32>) -> complex<f32> {
 // CHECK: %[[REAL_IS_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
 // CHECK: %[[IMAG_IS_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
 // CHECK: %[[IS_ZERO:.*]] = arith.andi %[[REAL_IS_ZERO]], %[[IMAG_IS_ZERO]] : i1
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL2]], %[[REAL2]] : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG2]], %[[IMAG2]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL2]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG2]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG2]], %[[REAL2]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL2]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL2]], %[[IMAG2]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG2]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL2]], %[[IMAG2]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL2]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG2]], %[[ABS2]] : f32
 // CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[NORM]] : f32
 // CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[NORM]] : f32
 // CHECK: %[[SIGN:.*]] = complex.create %[[REAL_SIGN]], %[[IMAG_SIGN]] : complex<f32>
@@ -716,13 +759,27 @@ func.func @complex_abs_with_fmf(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg fastmath<nnan,contract> : complex<f32>
   return %abs : f32
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK-DAG: %[[REAL_SQ:.*]] = arith.mulf %[[REAL]], %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[REAL_SQ]], %[[IMAG_SQ]] fastmath<nnan,contract> : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
-// CHECK: return %[[NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
+// CHECK: return %[[ABS3]] : f32
 
 // -----
 
@@ -807,12 +864,26 @@ func.func @complex_log_with_fmf(%arg: complex<f32>) -> complex<f32> {
   %log = complex.log %arg fastmath<nnan,contract> : complex<f32>
   return %log : complex<f32>
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL]], %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
 // CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] fastmath<nnan,contract> : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
diff --git a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
index 9983dd46f09433..d710dc8e1adeb7 100644
--- a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
@@ -6,12 +6,29 @@ func.func @complex_abs(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg: complex<f32>
   return %abs : f32
 }
+// CHECK: %[[ZERO:.*]] = llvm.mlir.constant(0.000000e+00 : f32) : f32
+// CHECK: %[[ONE:.*]] = llvm.mlir.constant(1.000000e+00 : f32) : f32
 // CHECK: %[[REAL:.*]] = llvm.extractvalue %[[ARG]][0] : ![[C_TY]]
 // CHECK: %[[IMAG:.*]] = llvm.extractvalue %[[ARG]][1] : ![[C_TY]]
-// CHECK-DAG: %[[REAL_SQ:.*]] = llvm.fmul %[[REAL]], %[[REAL]]  : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = llvm.fmul %[[IMAG]], %[[IMAG]]  : f32
-// CHECK: %[[SQ_NORM:.*]] = llvm.fadd %[[REAL_SQ]], %[[IMAG_SQ]]  : f32
-// CHECK: %[[NORM:.*]] = llvm.intr.sqrt(%[[SQ_NORM]]) : (f32) -> f32
+// CHECK: %[[REAL_IS_ZERO:.*]] = llvm.fcmp "oeq" %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_IS_ZERO:.*]] = llvm.fcmp "oeq" %[[IMAG]], %[[ZERO]] : f32
+
+// CHECK: %[[IMAG_DIV_REAL:.*]] = llvm.fdiv %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = llvm.fmul %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]]  : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = llvm.fadd %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = llvm.intr.sqrt(%[[IMAG_SQ_PLUS_ONE]]) : (f32) -> f32
+// CHECK: %[[ABS_IMAG:.*]] = llvm.fmul %[[IMAG_SQRT]], %[[REAL]] : f32
+
+// CHECK: %[[REAL_DIV_IMAG:.*]] = llvm.fdiv %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = llvm.fmul %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = llvm.fadd %[[REAL_SQ]], %[[ONE]]  : f32
+// CHECK: %[[REAL_SQRT:.*]] = llvm.intr.sqrt(%[[REAL_SQ_PLUS_ONE]])  : (f32) -> f32
+// CHECK: %[[ABS_REAL:.*]] = llvm.fmul %[[REAL_SQRT]], %[[IMAG]]  : f32
+
+// CHECK: %[[REAL_GT_IMAG:.*]] = llvm.fcmp "ogt" %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = llvm.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : i1, f32
+// CHECK: %[[ABS2:.*]] = llvm.select %[[IMAG_IS_ZERO]], %[[REAL]], %[[ABS1]] : i1, f32
+// CHECK: %[[NORM:.*]] = llvm.select %[[REAL_IS_ZERO]], %[[IMAG]], %[[ABS2]] : i1, f32
 // CHECK: llvm.return %[[NORM]] : f32
 
 // CHECK-LABEL: llvm.func @complex_eq
diff --git a/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir b/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
index 349b92a7aefa2e..b7849945b3cf49 100644
--- a/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
+++ b/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
@@ -106,6 +106,27 @@ func.func @angle(%arg: complex<f32>) -> f32 {
   func.return %angle : f32
 }
 
+func.func @test_element_f64(%input: tensor<?xcomplex<f64>>,
+                      %func: (complex<f64>) -> f64) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %size = tensor.dim %input, %c0: tensor<?xcomplex<f64>>
+
+  scf.for %i = %c0 to %size step %c1 {
+    %elem = tensor.extract %input[%i]: tensor<?xcomplex<f64>>
+
+    %val = func.call_indirect %func(%elem) : (complex<f64>) -> f64
+    vector.print %val : f64
+    scf.yield
+  }
+  func.return
+}
+
+func.func @abs(%arg: complex<f64>) -> f64 {
+  %abs = complex.abs %arg : complex<f64>
+  func.return %abs : f64
+}
+
 func.func @entry() {
   // complex.sqrt test
   %sqrt_test = arith.constant dense<[
@@ -300,5 +321,22 @@ func.func @entry() {
   call @test_element(%angle_test_cast, %angle_func)
     : (tensor<?xcomplex<f32>>, (complex<f32>) -> f32) -> ()
 
+  // complex.abs test
+  %abs_test = arith.constant dense<[
+    (1.0, 1.0),
+    // CHECK:  1.414
+    (1.0e300, 1.0e300),
+    // CHECK-NEXT:  1.41421e+300
+    (1.0e-300, 1.0e-300)
+    // CHECK-NEXT:  1.41421e-300
+  ]> : tensor<3xcomplex<f64>>
+  %abs_test_cast = tensor.cast %abs_test
+    :  tensor<3xcomplex<f64>> to tensor<?xcomplex<f64>>
+
+  %abs_func = func.constant @abs : (complex<f64>) -> f64
+
+  call @test_element_f64(%abs_test_cast, %abs_func)
+    : (tensor<?xcomplex<f64>>, (complex<f64>) -> f64) -> ()
+
   func.return
 }

llvmbot · 2023-12-24T05:45:14Z

@llvm/pr-subscribers-mlir

Author: Kai Sasaki (Lewuathe)

Changes

complex.abs op may causes the underflow issue with the large input. We can prevent the problem by using the algorithm listed in "ALGORITHM 312 ABSOLUTE VALUE AND SQUARE ROOT OF A COMPLEX NUMBER" as well as the complex.sqrt.

See: #62011

Full diff: https://github.com/llvm/llvm-project/pull/76316.diff

4 Files Affected:

(modified) mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp (+42-14)
(modified) mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir (+93-22)
(modified) mlir/test/Conversion/ComplexToStandard/full-conversion.mlir (+21-4)
(modified) mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir (+38)

diff --git a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
index bf753c7062f366..7c1db57b55f996 100644
--- a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
+++ b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
@@ -26,29 +26,57 @@ namespace mlir {
 using namespace mlir;
 
 namespace {
+// The algorithm is listed in https://dl.acm.org/doi/pdf/10.1145/363717.363780.
 struct AbsOpConversion : public OpConversionPattern<complex::AbsOp> {
   using OpConversionPattern<complex::AbsOp>::OpConversionPattern;
 
   LogicalResult
   matchAndRewrite(complex::AbsOp op, OpAdaptor adaptor,
                   ConversionPatternRewriter &rewriter) const override {
-    auto loc = op.getLoc();
-    auto type = op.getType();
+    mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
 
     arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
 
-    Value real =
-        rewriter.create<complex::ReOp>(loc, type, adaptor.getComplex());
-    Value imag =
-        rewriter.create<complex::ImOp>(loc, type, adaptor.getComplex());
-    Value realSqr =
-        rewriter.create<arith::MulFOp>(loc, real, real, fmf.getValue());
-    Value imagSqr =
-        rewriter.create<arith::MulFOp>(loc, imag, imag, fmf.getValue());
-    Value sqNorm =
-        rewriter.create<arith::AddFOp>(loc, realSqr, imagSqr, fmf.getValue());
-
-    rewriter.replaceOpWithNewOp<math::SqrtOp>(op, sqNorm);
+    Type elementType = op.getType();
+    Value arg = adaptor.getComplex();
+
+    Value zero =
+        b.create<arith::ConstantOp>(elementType, b.getZeroAttr(elementType));
+    Value one = b.create<arith::ConstantOp>(elementType,
+                                            b.getFloatAttr(elementType, 1.0));
+
+    Value real = b.create<complex::ReOp>(elementType, arg);
+    Value imag = b.create<complex::ImOp>(elementType, arg);
+
+    Value realIsZero =
+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, real, zero);
+    Value imagIsZero =
+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero);
+
+    // Real > Imag
+    Value imagDivReal = b.create<arith::DivFOp>(imag, real, fmf.getValue());
+    Value imagSq =
+        b.create<arith::MulFOp>(imagDivReal, imagDivReal, fmf.getValue());
+    Value imagSqPlusOne = b.create<arith::AddFOp>(imagSq, one, fmf.getValue());
+    Value imagSqrt = b.create<math::SqrtOp>(imagSqPlusOne, fmf.getValue());
+    Value absImag = b.create<arith::MulFOp>(imagSqrt, real, fmf.getValue());
+
+    // Real <= Imag
+    Value realDivImag = b.create<arith::DivFOp>(real, imag, fmf.getValue());
+    Value realSq =
+        b.create<arith::MulFOp>(realDivImag, realDivImag, fmf.getValue());
+    Value realSqPlusOne = b.create<arith::AddFOp>(realSq, one, fmf.getValue());
+    Value realSqrt = b.create<math::SqrtOp>(realSqPlusOne, fmf.getValue());
+    Value absReal = b.create<arith::MulFOp>(realSqrt, imag, fmf.getValue());
+
+    rewriter.replaceOpWithNewOp<arith::SelectOp>(
+        op, realIsZero, imag,
+        b.create<arith::SelectOp>(
+            imagIsZero, real,
+            b.create<arith::SelectOp>(
+                b.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, real, imag),
+                absImag, absReal)));
+
     return success();
   }
 };
diff --git a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
index 3af28150fd5c3f..1028c9aae92c05 100644
--- a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
@@ -7,13 +7,28 @@ func.func @complex_abs(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg: complex<f32>
   return %abs : f32
 }
+
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK-DAG: %[[REAL_SQ:.*]] = arith.mulf %[[REAL]], %[[REAL]] : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[REAL_SQ]], %[[IMAG_SQ]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
-// CHECK: return %[[NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
+// CHECK: return %[[ABS3]] : f32
 
 // -----
 
@@ -241,12 +256,26 @@ func.func @complex_log(%arg: complex<f32>) -> complex<f32> {
   %log = complex.log %arg: complex<f32>
   return %log : complex<f32>
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL]], %[[REAL]] : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
 // CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
@@ -469,12 +498,26 @@ func.func @complex_sign(%arg: complex<f32>) -> complex<f32> {
 // CHECK: %[[REAL_IS_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
 // CHECK: %[[IMAG_IS_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
 // CHECK: %[[IS_ZERO:.*]] = arith.andi %[[REAL_IS_ZERO]], %[[IMAG_IS_ZERO]] : i1
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL2]], %[[REAL2]] : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG2]], %[[IMAG2]] : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL2]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG2]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG2]], %[[REAL2]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL2]] : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL2]], %[[IMAG2]] : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG2]] : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL2]], %[[IMAG2]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL2]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG2]], %[[ABS2]] : f32
 // CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[NORM]] : f32
 // CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[NORM]] : f32
 // CHECK: %[[SIGN:.*]] = complex.create %[[REAL_SIGN]], %[[IMAG_SIGN]] : complex<f32>
@@ -716,13 +759,27 @@ func.func @complex_abs_with_fmf(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg fastmath<nnan,contract> : complex<f32>
   return %abs : f32
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK-DAG: %[[REAL_SQ:.*]] = arith.mulf %[[REAL]], %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[REAL_SQ]], %[[IMAG_SQ]] fastmath<nnan,contract> : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
-// CHECK: return %[[NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
+// CHECK: return %[[ABS3]] : f32
 
 // -----
 
@@ -807,12 +864,26 @@ func.func @complex_log_with_fmf(%arg: complex<f32>) -> complex<f32> {
   %log = complex.log %arg fastmath<nnan,contract> : complex<f32>
   return %log : complex<f32>
 }
+// CHECK: %[[ZERO:.*]] = arith.constant 0.000000e+00 : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
 // CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[SQR_REAL:.*]] = arith.mulf %[[REAL]], %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQR_IMAG:.*]] = arith.mulf %[[IMAG]], %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[SQ_NORM:.*]] = arith.addf %[[SQR_REAL]], %[[SQR_IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[NORM:.*]] = math.sqrt %[[SQ_NORM]] : f32
+// CHECK: %[[IS_REAL_ZERO:.*]] = arith.cmpf oeq, %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IS_IMAG_ZERO:.*]] = arith.cmpf oeq, %[[IMAG]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_DIV_REAL:.*]] = arith.divf %[[IMAG]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ:.*]] = arith.mulf %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = arith.addf %[[IMAG_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SQRT:.*]] = math.sqrt %[[IMAG_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ:.*]] = arith.mulf %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = arith.addf %[[REAL_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_SQRT:.*]] = math.sqrt %[[REAL_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[REAL_GT_IMAG:.*]] = arith.cmpf ogt, %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = arith.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : f32
+// CHECK: %[[ABS2:.*]] = arith.select %[[IS_IMAG_ZERO]], %[[REAL]], %[[ABS1]] : f32
+// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG]], %[[ABS2]] : f32
 // CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] fastmath<nnan,contract> : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
diff --git a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
index 9983dd46f09433..d710dc8e1adeb7 100644
--- a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
@@ -6,12 +6,29 @@ func.func @complex_abs(%arg: complex<f32>) -> f32 {
   %abs = complex.abs %arg: complex<f32>
   return %abs : f32
 }
+// CHECK: %[[ZERO:.*]] = llvm.mlir.constant(0.000000e+00 : f32) : f32
+// CHECK: %[[ONE:.*]] = llvm.mlir.constant(1.000000e+00 : f32) : f32
 // CHECK: %[[REAL:.*]] = llvm.extractvalue %[[ARG]][0] : ![[C_TY]]
 // CHECK: %[[IMAG:.*]] = llvm.extractvalue %[[ARG]][1] : ![[C_TY]]
-// CHECK-DAG: %[[REAL_SQ:.*]] = llvm.fmul %[[REAL]], %[[REAL]]  : f32
-// CHECK-DAG: %[[IMAG_SQ:.*]] = llvm.fmul %[[IMAG]], %[[IMAG]]  : f32
-// CHECK: %[[SQ_NORM:.*]] = llvm.fadd %[[REAL_SQ]], %[[IMAG_SQ]]  : f32
-// CHECK: %[[NORM:.*]] = llvm.intr.sqrt(%[[SQ_NORM]]) : (f32) -> f32
+// CHECK: %[[REAL_IS_ZERO:.*]] = llvm.fcmp "oeq" %[[REAL]], %[[ZERO]] : f32
+// CHECK: %[[IMAG_IS_ZERO:.*]] = llvm.fcmp "oeq" %[[IMAG]], %[[ZERO]] : f32
+
+// CHECK: %[[IMAG_DIV_REAL:.*]] = llvm.fdiv %[[IMAG]], %[[REAL]] : f32
+// CHECK: %[[IMAG_SQ:.*]] = llvm.fmul %[[IMAG_DIV_REAL]], %[[IMAG_DIV_REAL]]  : f32
+// CHECK: %[[IMAG_SQ_PLUS_ONE:.*]] = llvm.fadd %[[IMAG_SQ]], %[[ONE]] : f32
+// CHECK: %[[IMAG_SQRT:.*]] = llvm.intr.sqrt(%[[IMAG_SQ_PLUS_ONE]]) : (f32) -> f32
+// CHECK: %[[ABS_IMAG:.*]] = llvm.fmul %[[IMAG_SQRT]], %[[REAL]] : f32
+
+// CHECK: %[[REAL_DIV_IMAG:.*]] = llvm.fdiv %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[REAL_SQ:.*]] = llvm.fmul %[[REAL_DIV_IMAG]], %[[REAL_DIV_IMAG]] : f32
+// CHECK: %[[REAL_SQ_PLUS_ONE:.*]] = llvm.fadd %[[REAL_SQ]], %[[ONE]]  : f32
+// CHECK: %[[REAL_SQRT:.*]] = llvm.intr.sqrt(%[[REAL_SQ_PLUS_ONE]])  : (f32) -> f32
+// CHECK: %[[ABS_REAL:.*]] = llvm.fmul %[[REAL_SQRT]], %[[IMAG]]  : f32
+
+// CHECK: %[[REAL_GT_IMAG:.*]] = llvm.fcmp "ogt" %[[REAL]], %[[IMAG]] : f32
+// CHECK: %[[ABS1:.*]] = llvm.select %[[REAL_GT_IMAG]], %[[ABS_IMAG]], %[[ABS_REAL]] : i1, f32
+// CHECK: %[[ABS2:.*]] = llvm.select %[[IMAG_IS_ZERO]], %[[REAL]], %[[ABS1]] : i1, f32
+// CHECK: %[[NORM:.*]] = llvm.select %[[REAL_IS_ZERO]], %[[IMAG]], %[[ABS2]] : i1, f32
 // CHECK: llvm.return %[[NORM]] : f32
 
 // CHECK-LABEL: llvm.func @complex_eq
diff --git a/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir b/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
index 349b92a7aefa2e..b7849945b3cf49 100644
--- a/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
+++ b/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
@@ -106,6 +106,27 @@ func.func @angle(%arg: complex<f32>) -> f32 {
   func.return %angle : f32
 }
 
+func.func @test_element_f64(%input: tensor<?xcomplex<f64>>,
+                      %func: (complex<f64>) -> f64) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %size = tensor.dim %input, %c0: tensor<?xcomplex<f64>>
+
+  scf.for %i = %c0 to %size step %c1 {
+    %elem = tensor.extract %input[%i]: tensor<?xcomplex<f64>>
+
+    %val = func.call_indirect %func(%elem) : (complex<f64>) -> f64
+    vector.print %val : f64
+    scf.yield
+  }
+  func.return
+}
+
+func.func @abs(%arg: complex<f64>) -> f64 {
+  %abs = complex.abs %arg : complex<f64>
+  func.return %abs : f64
+}
+
 func.func @entry() {
   // complex.sqrt test
   %sqrt_test = arith.constant dense<[
@@ -300,5 +321,22 @@ func.func @entry() {
   call @test_element(%angle_test_cast, %angle_func)
     : (tensor<?xcomplex<f32>>, (complex<f32>) -> f32) -> ()
 
+  // complex.abs test
+  %abs_test = arith.constant dense<[
+    (1.0, 1.0),
+    // CHECK:  1.414
+    (1.0e300, 1.0e300),
+    // CHECK-NEXT:  1.41421e+300
+    (1.0e-300, 1.0e-300)
+    // CHECK-NEXT:  1.41421e-300
+  ]> : tensor<3xcomplex<f64>>
+  %abs_test_cast = tensor.cast %abs_test
+    :  tensor<3xcomplex<f64>> to tensor<?xcomplex<f64>>
+
+  %abs_func = func.constant @abs : (complex<f64>) -> f64
+
+  call @test_element_f64(%abs_test_cast, %abs_func)
+    : (tensor<?xcomplex<f64>>, (complex<f64>) -> f64) -> ()
+
   func.return
 }

Lewuathe · 2023-12-24T05:46:46Z

mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir

+    (1.0e300, 1.0e300),
+    // CHECK-NEXT:  1.41421e+300
+    (1.0e-300, 1.0e-300)
+    // CHECK-NEXT:  1.41421e-300


The returned values are inf and 0 without this change.

rikhuijzer · 2023-12-27T10:33:58Z

I looked into the flang overflow issue too a while back and opened a topic about it: https://discourse.llvm.org/t/overflows-during-folding-of-basic-arith-ops/73952.

So as far as I understand, the fix would be for Flang to generate code which does not overflow. MLIR does not promise to handle it.

Lewuathe

@rikhuijzer Thanks for giving me the pointer to the past discussion. The discussion originated from the issue in flang but the problem this is trying to solve could be more general.

complex.abs cannot treat the full range of f64 due to overflow. The conversion to standard should be responsible for.
complex dialect can be regarded as the user of lower level dialect. We can let it control how the lower level ops are used.
complex.sqrt is already taking care of this case. Treating the f64 precision similarly in a dialect is consistent.
the double in C++ seems to treat the 1.414+300e value properly in the original issue. This may be also expected to complex dialect.

rikhuijzer · 2023-12-28T06:53:36Z

Sorry I don't know enough about this to be able to review. I hope someone else can pick this up.

Lewuathe · 2024-01-11T00:35:18Z

@kiranchandramohan @Leporacanthicus @joker-eph Sorry for taking your time but can I ask you guys to review this change when you get a chance? I requested a review to the people listed in the original issue so please correct me if I am wrong.

Lewuathe · 2024-01-23T00:14:41Z

Could someone take a look at this change? I think complex.sqrt uses the similar algorithm to prevent the rounding error. We should avoid the rounding error for the big complex number by the complex.abs too.

mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir

matthias-springer · 2024-01-23T08:19:41Z

mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp

+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero);
+
+    // Real > Imag
+    Value imagDivReal = b.create<arith::DivFOp>(imag, real, fmf.getValue());


I'm wondering what's going to happen here if real is zero. Should the computation be wrapped in scf.if instead of using an arith.select below?

I think it should be no problem as long as the realIsZero is being true. The decision operator does not seem to be evaluated. The case with real is zero is returning expected value.

https://github.com/llvm/llvm-project/pull/76316/files#diff-01fda3fd3b20157ca6cbd39d5c8203a33814516e46c22a544d65dddb3008644aR333

Yes, the value is not used afterwards but I'm wondering if executing a division by zero could cause a crash (maybe only on some platforms). Maybe ask on Discourse before merging. If you don't get an answer, I'd say just merge as is and if it causes issues in the future it will be a simple fix (wrapping the computation in scf.if instead of using arith.select).

Thanks. That makes sense. I posted the question here.

https://discourse.llvm.org/t/devision-by-zero-semantics-in-arith-divf/76514

Lewuathe

@matthias-springer Thank you for reviewing! I added some test cases accordingly.

matthias-springer · 2024-01-24T11:07:54Z

mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp

+        b.create<arith::CmpFOp>(arith::CmpFPredicate::OEQ, imag, zero);
+
+    // Real > Imag
+    Value imagDivReal = b.create<arith::DivFOp>(imag, real, fmf.getValue());


Yes, the value is not used afterwards but I'm wondering if executing a division by zero could cause a crash (maybe only on some platforms). Maybe ask on Discourse before merging. If you don't get an answer, I'd say just merge as is and if it causes issues in the future it will be a simple fix (wrapping the computation in scf.if instead of using arith.select).

Lewuathe

From the MLIR viewpoint, it can be treated as undefined as it is. The language frontend or the hardware seem to be responsible how the division-by-zero case is treated.
https://discourse.llvm.org/t/devision-by-zero-semantics-in-arith-divf/76514/3

Therefore, I think we can merge this as it is for now. Thanks for reviewing this change anyway!

Reverts #76316 Buildbot test is broken.

joker-eph · 2024-01-28T03:26:22Z

I had to revert because this broke a bot: https://lab.llvm.org/buildbot/#/builders/264/builds/6131

# RUN: at line 1
/vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/mlir-opt /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir    -func-bufferize -tensor-bufferize -arith-bufferize --canonicalize    -convert-scf-to-cf --convert-complex-to-standard    -finalize-memref-to-llvm -convert-math-to-llvm -convert-math-to-libm    -convert-vector-to-llvm -convert-complex-to-llvm    -convert-func-to-llvm -reconcile-unrealized-casts | /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/mlir-cpu-runner   -e entry -entry-point-result=void    -shared-libs=/vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/lib/libmlir_c_runner_utils.so | /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/FileCheck /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
# executed command: /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/mlir-opt /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir -func-bufferize -tensor-bufferize -arith-bufferize --canonicalize -convert-scf-to-cf --convert-complex-to-standard -finalize-memref-to-llvm -convert-math-to-llvm -convert-math-to-libm -convert-vector-to-llvm -convert-complex-to-llvm -convert-func-to-llvm -reconcile-unrealized-casts
# executed command: /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/mlir-cpu-runner -e entry -entry-point-result=void -shared-libs=/vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/lib/libmlir_c_runner_utils.so
# executed command: /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.obj/bin/FileCheck /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
# .---command stderr------------
# | /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir:135:17: error: CHECK-NEXT: expected string not found in input
# |  // CHECK-NEXT: -1.098
# |                 ^
# | <stdin>:3:6: note: scanning from here
# | 0.45509
# |      ^
# | <stdin>:4:1: note: possible intended match here
# | 1.09868
# | ^
# | 
# | Input file: <stdin>
# | Check file: /vol/worker/mlir-nvidia/mlir-nvidia-gcc7/llvm.src/mlir/test/Integration/Dialect/Complex/CPU/correctness.mlir
# | 
# | -dump-input=help explains the following input dump.
# | 
# | Input was:
# | <<<<<<
# |             1: nan 
# |             2: nan 
# |             3: 0.45509 
# | next:135'0          X~~ error: no match found
# |             4: 1.09868 
# | next:135'0     ~~~~~~~~
# | next:135'1     ?        possible intended match
# |             5: 0 
# | next:135'0     ~~
# |             6: 0 
# | next:135'0     ~~
# |             7: 0.707107 
# | next:135'0     ~~~~~~~~~
# |             8: 0.707107 
# | next:135'0     ~~~~~~~~~
# |             9: 1.09868 
# | next:135'0     ~~~~~~~~
# |             .
# |             .
# |             .
# | >>>>>>
# `-----------------------------
# error: command failed with exit status: 1

Lewuathe · 2024-01-29T01:03:14Z

@joker-eph Oh, sorry for bothering you. I'll check what's going on.

But I have a question about reproducing the problem in the topic branch. I think it was not running in the PR request. Is there any way to check the test passes before merging into the main branch?

The previous PR was not correct on the way to handle the negative value. It is necessary to take the absolute value of the given real (or imaginary) part to be multiplied with the sqrt part. See: #76316

The previous PR was not enough about the way to handle the negative value. It is necessary to take the absolute value of the given real (or imaginary) part to be multiplied with the sqrt part in the case of either is zero. See: llvm#76316

[mlir][complex] Prevent underflow in complex.abs

a581036

llvmbot added mlir mlir:complex MLIR complex dialect labels Dec 24, 2023

Lewuathe commented Dec 24, 2023

View reviewed changes

Lewuathe requested review from joker-eph and Leporacanthicus December 25, 2023 03:46

Lewuathe commented Dec 27, 2023

View reviewed changes

Lewuathe requested a review from kiranchandramohan January 9, 2024 00:37

Lewuathe requested review from okkwon, matthias-springer and rsuderman January 16, 2024 04:37

matthias-springer reviewed Jan 23, 2024

View reviewed changes

[mlir][complex] Add test case to check zero element handling

c4e8c8b

Lewuathe commented Jan 24, 2024

View reviewed changes

Lewuathe requested a review from matthias-springer January 24, 2024 00:29

matthias-springer approved these changes Jan 24, 2024

View reviewed changes

Lewuathe commented Jan 26, 2024

View reviewed changes

Lewuathe added 4 commits January 26, 2024 09:14

Merge branch 'main' into llvmgh-62011

f865a29

Merge branch 'main' into llvmgh-62011

3e838e1

Merge branch 'main' into llvmgh-62011

d3e818d

Merge branch 'main' into llvmgh-62011

e5a2f57

Lewuathe merged commit 69f99cd into llvm:main Jan 27, 2024

k-arrows mentioned this pull request Jan 27, 2024

[flang][mlir] complex arithmetic dialect conversion for absolute value is incorrect in face of underflow #62011

Closed

joker-eph mentioned this pull request Jan 28, 2024

Revert "[mlir][complex] Prevent underflow in complex.abs" #79722

Merged

joker-eph added a commit that referenced this pull request Jan 28, 2024

Revert "[mlir][complex] Prevent underflow in complex.abs" (#79722)

c41bb11

Reverts #76316 Buildbot test is broken.

Lewuathe mentioned this pull request Jan 29, 2024

[mlir][complex] Prevent underflow in complex.abs #79786

Merged

[mlir][complex] Prevent underflow in complex.abs #76316

[mlir][complex] Prevent underflow in complex.abs #76316

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