diff --git a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
index a6fcf6a758c07..462036e51a1f1 100644
--- a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
+++ b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
@@ -26,7 +26,7 @@ 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;
 
@@ -35,49 +35,27 @@ struct AbsOpConversion : public OpConversionPattern<complex::AbsOp> {
                   ConversionPatternRewriter &rewriter) const override {
     mlir::ImplicitLocOpBuilder b(op.getLoc(), rewriter);
 
-    arith::FastMathFlagsAttr fmf = op.getFastMathFlagsAttr();
+    arith::FastMathFlags fmf = op.getFastMathFlagsAttr().getValue();
 
     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);
+    Value real = b.create<complex::ReOp>(adaptor.getComplex());
+    Value imag = b.create<complex::ImOp>(adaptor.getComplex());
+    Value absReal = b.create<math::AbsFOp>(real, fmf);
+    Value absImag = b.create<math::AbsFOp>(imag, fmf);
 
-    // 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 realAbs = b.create<math::AbsFOp>(real, fmf.getValue());
-    Value absImag = b.create<arith::MulFOp>(imagSqrt, realAbs, 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 imagAbs = b.create<math::AbsFOp>(imag, fmf.getValue());
-    Value absReal = b.create<arith::MulFOp>(realSqrt, imagAbs, fmf.getValue());
-
-    rewriter.replaceOpWithNewOp<arith::SelectOp>(
-        op, realIsZero, imagAbs,
-        b.create<arith::SelectOp>(
-            imagIsZero, realAbs,
-            b.create<arith::SelectOp>(
-                b.create<arith::CmpFOp>(arith::CmpFPredicate::OGT, real, imag),
-                absImag, absReal)));
+    Value max = b.create<arith::MaximumFOp>(absReal, absImag, fmf);
+    Value min = b.create<arith::MinimumFOp>(absReal, absImag, fmf);
+    Value ratio = b.create<arith::DivFOp>(min, max, fmf);
+    Value ratioSq = b.create<arith::MulFOp>(ratio, ratio, fmf);
+    Value ratioSqPlusOne = b.create<arith::AddFOp>(ratioSq, one, fmf);
+    Value sqrt = b.create<math::SqrtOp>(ratioSqPlusOne, fmf);
+    Value result = b.create<arith::MulFOp>(max, sqrt, fmf);
+    Value isNaN =
+        b.create<arith::CmpFOp>(arith::CmpFPredicate::UNO, result, result, fmf);
+    rewriter.replaceOpWithNewOp<arith::SelectOp>(op, isNaN, min, result);
 
     return success();
   }
diff --git a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
index 46dba04a88aa0..a1de61d10bb22 100644
--- a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
@@ -8,29 +8,21 @@ func.func @complex_abs(%arg: complex<f32>) -> 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: %[[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: %[[REAL_ABS:.*]] = math.absf %[[REAL]] : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] : 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG]] : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] : 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_ABS]], %[[ABS1]] : f32
-// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: return %[[ABS3]] : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: return %[[ABS]] : f32
 
 // -----
 
@@ -258,29 +250,21 @@ 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: %[[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: %[[REAL_ABS:.*]] = math.absf %[[REAL]] : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] : 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG]] : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] : 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_ABS]], %[[ABS1]] : f32
-// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] : f32
+// CHECK: %[[RESULT:.*]] = arith.mulf %[[MAX]], %[[SQRT]] : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[RESULT]], %[[RESULT]] : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[RESULT]] : f32
+// CHECK: %[[RESULT_REAL:.*]] = math.log %[[ABS]] : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
 // CHECK: %[[RESULT_IMAG:.*]] = math.atan2 %[[IMAG2]], %[[REAL2]] : f32
@@ -509,30 +493,22 @@ 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: %[[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: %[[REAL_ABS:.*]] = math.absf %[[REAL2]] : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] : 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG2]] : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] : 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]], %[[REAL_ABS]], %[[ABS1]] : f32
-// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[NORM]] : f32
-// CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[NORM]] : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL2]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG2]] : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[ABS]] : f32
+// CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[ABS]] : f32
 // CHECK: %[[SIGN:.*]] = complex.create %[[REAL_SIGN]], %[[IMAG_SIGN]] : complex<f32>
 // CHECK: %[[RESULT:.*]] = arith.select %[[IS_ZERO]], %[[ARG]], %[[SIGN]] : complex<f32>
 // CHECK: return %[[RESULT]] : complex<f32>
@@ -725,29 +701,21 @@ func.func @complex_sqrt(%arg: complex<f32>) -> complex<f32> {
 // CHECK: %[[VAR0:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[VAR1:.*]] = complex.im %[[ARG]] : complex<f32>
 // CHECK: %[[VAR2:.*]] = math.absf %[[VAR0]] : f32
-// CHECK: %[[CST0:.*]] = arith.constant 0.000000e+00 : f32
-// CHECK: %[[CST1:.*]] = arith.constant 1.000000e+00 : f32
-// CHECK: %[[VAR3:.*]] = complex.re %[[ARG]] : complex<f32>
-// CHECK: %[[VAR4:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[VAR5:.*]] = arith.cmpf oeq, %[[VAR3]], %[[CST0]] : f32
-// CHECK: %[[VAR6:.*]] = arith.cmpf oeq, %[[VAR4]], %[[CST0]] : f32
-// CHECK: %[[VAR7:.*]] = arith.divf %[[VAR4]], %[[VAR3]] : f32
-// CHECK: %[[VAR8:.*]] = arith.mulf %[[VAR7]], %[[VAR7]] : f32
-// CHECK: %[[VAR9:.*]] = arith.addf %[[VAR8]], %[[CST1]] : f32
-// CHECK: %[[VAR10:.*]] = math.sqrt %[[VAR9]] : f32
-// CHECK: %[[VAR11:.*]] = math.absf %[[VAR3]] : f32
-// CHECK: %[[VAR12:.*]] = arith.mulf %[[VAR10]], %[[VAR11]] : f32
-// CHECK: %[[VAR13:.*]] = arith.divf %[[VAR3]], %[[VAR4]] : f32
-// CHECK: %[[VAR14:.*]] = arith.mulf %[[VAR13]], %[[VAR13]] : f32
-// CHECK: %[[VAR15:.*]] = arith.addf %[[VAR14]], %[[CST1]] : f32
-// CHECK: %[[VAR16:.*]] = math.sqrt %[[VAR15]] : f32
-// CHECK: %[[VAR17:.*]] = math.absf %[[VAR4]] : f32
-// CHECK: %[[VAR18:.*]] = arith.mulf %[[VAR16]], %[[VAR17]] : f32
-// CHECK: %[[VAR19:.*]] = arith.cmpf ogt, %[[VAR3]], %[[VAR4]] : f32
-// CHECK: %[[VAR20:.*]] = arith.select %[[VAR19]], %[[VAR12]], %[[VAR18]] : f32
-// CHECK: %[[VAR21:.*]] = arith.select %[[VAR6]], %[[VAR11]], %[[VAR20]] : f32
-// CHECK: %[[VAR22:.*]] = arith.select %[[VAR5]], %[[VAR17]], %[[VAR21]] : f32
-// CHECK: %[[VAR23:.*]] = arith.addf %[[VAR2]], %[[VAR22]] : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
+// CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[VAR23:.*]] = arith.addf %[[VAR2]], %[[ABS]] : f32
 // CHECK: %[[CST2:.*]]  = arith.constant 5.000000e-01 : f32
 // CHECK: %[[VAR24:.*]] = arith.mulf %[[VAR23]], %[[CST2]] : f32
 // CHECK: %[[VAR25:.*]] = math.sqrt %[[VAR24]] : f32
@@ -821,29 +789,21 @@ 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: %[[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: %[[REAL_ABS:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] 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_ABS]], %[[ABS1]] : f32
-// CHECK: %[[ABS3:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: return %[[ABS3]] : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract> : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: return %[[ABS]] : f32
 
 // -----
 
@@ -928,29 +888,21 @@ 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: %[[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: %[[REAL_ABS:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] 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_ABS]], %[[ABS1]] : f32
-// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: %[[RESULT_REAL:.*]] = math.log %[[NORM]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract> : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[RESULT_REAL:.*]] = math.log %[[ABS]] fastmath<nnan,contract> : f32
 // CHECK: %[[REAL2:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[IMAG2:.*]] = complex.im %[[ARG]] : complex<f32>
 // CHECK: %[[RESULT_IMAG:.*]] = math.atan2 %[[IMAG2]], %[[REAL2]] fastmath<nnan,contract> : f32
@@ -1318,29 +1270,21 @@ func.func @complex_atan2_with_fmf(%lhs: complex<f32>,
 // CHECK: %[[VAR187:.*]] = complex.re %[[VAR186]] : complex<f32>
 // CHECK: %[[VAR188:.*]] = complex.im %[[VAR186]] : complex<f32>
 // CHECK: %[[VAR189:.*]] = math.absf %[[VAR187]] fastmath<nnan,contract> : f32
-// CHECK: %[[CST_7:.*]] = arith.constant 0.000000e+00 : f32
-// CHECK: %[[CST_8:.*]] = arith.constant 1.000000e+00 : f32
-// CHECK: %[[VAR190:.*]] = complex.re %[[VAR186]] : complex<f32>
-// CHECK: %[[VAR191:.*]] = complex.im %[[VAR186]] : complex<f32>
-// CHECK: %[[VAR192:.*]] = arith.cmpf oeq, %[[VAR190]], %[[CST_7]] : f32
-// CHECK: %[[VAR193:.*]] = arith.cmpf oeq, %[[VAR191]], %[[CST_7]] : f32
-// CHECK: %[[VAR194:.*]] = arith.divf %[[VAR191]], %[[VAR190]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR195:.*]] = arith.mulf %[[VAR194]], %[[VAR194]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR196:.*]] = arith.addf %[[VAR195]], %[[CST_8]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR197:.*]] = math.sqrt %[[VAR196]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR198:.*]] = math.absf %[[VAR190]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR199:.*]] = arith.mulf %[[VAR197]], %[[VAR198]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR200:.*]] = arith.divf %[[VAR190]], %[[VAR191]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR201:.*]] = arith.mulf %[[VAR200]], %[[VAR200]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR202:.*]] = arith.addf %[[VAR201]], %[[CST_8]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR203:.*]] = math.sqrt %[[VAR202]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR204:.*]] = math.absf %[[VAR191]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR205:.*]] = arith.mulf %[[VAR203]], %[[VAR204]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR206:.*]] = arith.cmpf ogt, %[[VAR190]], %[[VAR191]] : f32
-// CHECK: %[[VAR207:.*]] = arith.select %[[VAR206]], %[[VAR199]], %[[VAR205]] : f32
-// CHECK: %[[VAR208:.*]] = arith.select %[[VAR193]], %[[VAR198]], %[[VAR207]] : f32
-// CHECK: %[[VAR209:.*]] = arith.select %[[VAR192]], %[[VAR204]], %[[VAR208]] : f32
-// CHECK: %[[VAR210:.*]] = arith.addf %[[VAR189]], %[[VAR209]] fastmath<nnan,contract> : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
+// CHECK: %[[REAL:.*]] = complex.re %[[VAR186]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[VAR186]] : complex<f32>
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] fastmath<nnan,contract>  : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract>  : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract>  : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract>  : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract>  : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract>  : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract>  : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract>  : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract>  : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract>  : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[VAR210:.*]] = arith.addf %[[VAR189]], %[[ABS]] fastmath<nnan,contract> : f32
 // CHECK: %[[CST_9:.*]] = arith.constant 5.000000e-01 : f32
 // CHECK: %[[VAR211:.*]] = arith.mulf %[[VAR210]], %[[CST_9]] fastmath<nnan,contract> : f32
 // CHECK: %[[VAR212:.*]] = math.sqrt %[[VAR211]] fastmath<nnan,contract> : f32
@@ -1556,29 +1500,21 @@ func.func @complex_atan2_with_fmf(%lhs: complex<f32>,
 // CHECK: %[[VAR413:.*]] = arith.select %[[VAR412]], %[[VAR408]], %[[VAR402]] : f32
 // CHECK: %[[VAR414:.*]] = arith.select %[[VAR412]], %[[VAR409]], %[[VAR403]] : f32
 // CHECK: %[[VAR415:.*]] = complex.create %[[VAR413]], %[[VAR414]] : complex<f32>
-// CHECK: %[[CST_19:.*]] = arith.constant 0.000000e+00 : f32
-// CHECK: %[[CST_20:.*]] = arith.constant 1.000000e+00 : f32
-// CHECK: %[[VAR416:.*]] = complex.re %[[VAR415]] : complex<f32>
-// CHECK: %[[VAR417:.*]] = complex.im %[[VAR415]] : complex<f32>
-// CHECK: %[[VAR418:.*]] = arith.cmpf oeq, %[[VAR416]], %[[CST_19]] : f32
-// CHECK: %[[VAR419:.*]] = arith.cmpf oeq, %[[VAR417]], %[[CST_19]] : f32
-// CHECK: %[[VAR420:.*]] = arith.divf %[[VAR417]], %[[VAR416]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR421:.*]] = arith.mulf %[[VAR420]], %[[VAR420]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR422:.*]] = arith.addf %[[VAR421]], %[[CST_20]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR423:.*]] = math.sqrt %[[VAR422]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR424:.*]] = math.absf %[[VAR416]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR425:.*]] = arith.mulf %[[VAR423]], %[[VAR424]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR426:.*]] = arith.divf %[[VAR416]], %[[VAR417]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR427:.*]] = arith.mulf %[[VAR426]], %[[VAR426]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR428:.*]] = arith.addf %[[VAR427]], %[[CST_20]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR429:.*]] = math.sqrt %[[VAR428]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR430:.*]] = math.absf %[[VAR417]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR431:.*]] = arith.mulf %[[VAR429]], %[[VAR430]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR432:.*]] = arith.cmpf ogt, %[[VAR416]], %[[VAR417]] : f32
-// CHECK: %[[VAR433:.*]] = arith.select %[[VAR432]], %[[VAR425]], %[[VAR431]] : f32
-// CHECK: %[[VAR434:.*]] = arith.select %[[VAR419]], %[[VAR424]], %[[VAR433]] : f32
-// CHECK: %[[VAR435:.*]] = arith.select %[[VAR418]], %[[VAR430]], %[[VAR434]] : f32
-// CHECK: %[[VAR436:.*]] = math.log %[[VAR435]] fastmath<nnan,contract> : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
+// CHECK: %[[REAL:.*]] = complex.re %[[VAR415]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[VAR415]] : complex<f32>
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract> : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[VAR436:.*]] = math.log %[[ABS]] fastmath<nnan,contract> : f32
 // CHECK: %[[VAR437:.*]] = complex.re %[[VAR415]] : complex<f32>
 // CHECK: %[[VAR438:.*]] = complex.im %[[VAR415]] : complex<f32>
 // CHECK: %[[VAR439:.*]] = math.atan2 %[[VAR438]], %[[VAR437]] fastmath<nnan,contract> : f32
@@ -1805,29 +1741,21 @@ func.func @complex_sqrt_with_fmf(%arg: complex<f32>) -> complex<f32> {
 // CHECK: %[[VAR0:.*]] = complex.re %[[ARG]] : complex<f32>
 // CHECK: %[[VAR1:.*]] = complex.im %[[ARG]] : complex<f32>
 // CHECK: %[[VAR2:.*]] = math.absf %[[VAR0]] fastmath<nnan,contract> : f32
-// CHECK: %[[CST0:.*]] = arith.constant 0.000000e+00 : f32
-// CHECK: %[[CST1:.*]] = arith.constant 1.000000e+00 : f32
-// CHECK: %[[VAR3:.*]] = complex.re %[[ARG]] : complex<f32>
-// CHECK: %[[VAR4:.*]] = complex.im %[[ARG]] : complex<f32>
-// CHECK: %[[VAR5:.*]] = arith.cmpf oeq, %[[VAR3]], %[[CST0]] : f32
-// CHECK: %[[VAR6:.*]] = arith.cmpf oeq, %[[VAR4]], %[[CST0]] : f32
-// CHECK: %[[VAR7:.*]] = arith.divf %[[VAR4]], %[[VAR3]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR8:.*]] = arith.mulf %[[VAR7]], %[[VAR7]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR9:.*]] = arith.addf %[[VAR8]], %[[CST1]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR10:.*]] = math.sqrt %[[VAR9]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR11:.*]] = math.absf %[[VAR3]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR12:.*]] = arith.mulf %[[VAR10]], %[[VAR11]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR13:.*]] = arith.divf %[[VAR3]], %[[VAR4]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR14:.*]] = arith.mulf %[[VAR13]], %[[VAR13]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR15:.*]] = arith.addf %[[VAR14]], %[[CST1]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR16:.*]] = math.sqrt %[[VAR15]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR17:.*]] = math.absf %[[VAR4]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR18:.*]] = arith.mulf %[[VAR16]], %[[VAR17]] fastmath<nnan,contract> : f32
-// CHECK: %[[VAR19:.*]] = arith.cmpf ogt, %[[VAR3]], %[[VAR4]] : f32
-// CHECK: %[[VAR20:.*]] = arith.select %[[VAR19]], %[[VAR12]], %[[VAR18]] : f32
-// CHECK: %[[VAR21:.*]] = arith.select %[[VAR6]], %[[VAR11]], %[[VAR20]] : f32
-// CHECK: %[[VAR22:.*]] = arith.select %[[VAR5]], %[[VAR17]], %[[VAR21]] : f32
-// CHECK: %[[VAR23:.*]] = arith.addf %[[VAR2]], %[[VAR22]] fastmath<nnan,contract> : f32
+// CHECK: %[[ONE:.*]] = arith.constant 1.000000e+00 : f32
+// CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract> : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[VAR23:.*]] = arith.addf %[[VAR2]], %[[ABS]] fastmath<nnan,contract> : f32
 // CHECK: %[[CST2:.*]]  = arith.constant 5.000000e-01 : f32
 // CHECK: %[[VAR24:.*]] = arith.mulf %[[VAR23]], %[[CST2]] fastmath<nnan,contract> : f32
 // CHECK: %[[VAR25:.*]] = math.sqrt %[[VAR24]] fastmath<nnan,contract> : f32
@@ -1910,30 +1838,22 @@ func.func @complex_sign_with_fmf(%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: %[[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]] 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: %[[REAL_ABS:.*]] = math.absf %[[REAL2]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_IMAG:.*]] = arith.mulf %[[IMAG_SQRT]], %[[REAL_ABS]] fastmath<nnan,contract> : f32
-// CHECK: %[[REAL_DIV_IMAG:.*]] = arith.divf %[[REAL2]], %[[IMAG2]] 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: %[[IMAG_ABS:.*]] = math.absf %[[IMAG2]] fastmath<nnan,contract> : f32
-// CHECK: %[[ABS_REAL:.*]] = arith.mulf %[[REAL_SQRT]], %[[IMAG_ABS]] fastmath<nnan,contract> : 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]], %[[REAL_ABS]], %[[ABS1]] : f32
-// CHECK: %[[NORM:.*]] = arith.select %[[IS_REAL_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : f32
-// CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[NORM]] fastmath<nnan,contract> : f32
-// CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[NORM]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_REAL:.*]] = math.absf %[[REAL2]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_IMAG:.*]] = math.absf %[[IMAG2]] fastmath<nnan,contract> : f32
+// CHECK: %[[MAX:.*]] = arith.maximumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[MIN:.*]] = arith.minimumf %[[ABS_REAL]], %[[ABS_IMAG]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO:.*]] = arith.divf %[[MIN]], %[[MAX]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ:.*]] = arith.mulf %[[RATIO]], %[[RATIO]] fastmath<nnan,contract> : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = arith.addf %[[RATIO_SQ]], %[[ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[SQRT:.*]] = math.sqrt %[[RATIO_SQ_PLUS_ONE]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS_OR_NAN:.*]] = arith.mulf %[[MAX]], %[[SQRT]] fastmath<nnan,contract> : f32
+// CHECK: %[[IS_NAN:.*]] = arith.cmpf uno, %[[ABS_OR_NAN]], %[[ABS_OR_NAN]] fastmath<nnan,contract> : f32
+// CHECK: %[[ABS:.*]] = arith.select %[[IS_NAN]], %[[MIN]], %[[ABS_OR_NAN]] : f32
+// CHECK: %[[REAL_SIGN:.*]] = arith.divf %[[REAL]], %[[ABS]] fastmath<nnan,contract> : f32
+// CHECK: %[[IMAG_SIGN:.*]] = arith.divf %[[IMAG]], %[[ABS]] fastmath<nnan,contract> : f32
 // CHECK: %[[SIGN:.*]] = complex.create %[[REAL_SIGN]], %[[IMAG_SIGN]] : complex<f32>
 // CHECK: %[[RESULT:.*]] = arith.select %[[IS_ZERO]], %[[ARG]], %[[SIGN]] : complex<f32>
 // CHECK: return %[[RESULT]] : complex<f32>
diff --git a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
index 0f23e20167f49..2649d004a76ac 100644
--- a/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/full-conversion.mlir
@@ -6,32 +6,22 @@ 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: %[[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: %[[REAL_ABS:.*]] = llvm.intr.fabs(%[[REAL]]) : (f32) -> f32
-// CHECK: %[[ABS_IMAG:.*]] = llvm.fmul %[[IMAG_SQRT]], %[[REAL_ABS]] : 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: %[[IMAG_ABS:.*]] = llvm.intr.fabs(%[[IMAG]]) : (f32) -> f32
-// CHECK: %[[ABS_REAL:.*]] = llvm.fmul %[[REAL_SQRT]], %[[IMAG_ABS]]  : 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_ABS]], %[[ABS1]] : i1, f32
-// CHECK: %[[NORM:.*]] = llvm.select %[[REAL_IS_ZERO]], %[[IMAG_ABS]], %[[ABS2]] : i1, f32
-// CHECK: llvm.return %[[NORM]] : f32
+// CHECK: %[[ABS_REAL:.*]] = llvm.intr.fabs(%[[REAL]]) : (f32) -> f32
+// CHECK: %[[ABS_IMAG:.*]] = llvm.intr.fabs(%[[IMAG]]) : (f32) -> f32
+// CHECK: %[[MAX:.*]] = llvm.intr.maximum(%[[ABS_REAL]], %[[ABS_IMAG]]) : (f32, f32) -> f32
+// CHECK: %[[MIN:.*]] = llvm.intr.minimum(%[[ABS_REAL]], %[[ABS_IMAG]]) : (f32, f32) -> f32
+// CHECK: %[[RATIO:.*]] = llvm.fdiv %[[MIN]], %[[MAX]] : f32
+// CHECK: %[[RATIO_SQ:.*]] = llvm.fmul %[[RATIO]], %[[RATIO]] : f32
+// CHECK: %[[RATIO_SQ_PLUS_ONE:.*]] = llvm.fadd %[[RATIO_SQ]], %[[ONE]] : f32
+// CHECK: %[[SQRT:.*]] = llvm.intr.sqrt(%[[RATIO_SQ_PLUS_ONE]]) : (f32) -> f32
+// CHECK: %[[RESULT:.*]] = llvm.fmul %[[MAX]], %[[SQRT]] : f32
+// CHECK: %[[IS_NAN:.*]] = llvm.fcmp "uno" %[[RESULT]], %11 : f32
+// CHECK: %[[RET:.*]] = llvm.select %[[IS_NAN]], %[[MIN]], %[[RESULT]] : i1, f32
+// CHECK: llvm.return %[[RET]] : f32
 
 // CHECK-LABEL: llvm.func @complex_eq
 // CHECK-SAME: %[[LHS:.*]]: ![[C_TY:.*]], %[[RHS:.*]]: ![[C_TY:.*]])