diff --git a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
--- a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
+++ b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
@@ -572,10 +572,10 @@
     llvm::cl::init(fastVersion));
 
 static llvm::cl::opt<bool>
-    disableMlirComplex("disable-mlir-complex",
-                       llvm::cl::desc("Use libm instead of the MLIR complex "
-                                      "dialect to lower complex operations"),
-                       llvm::cl::init(false));
+    forceMlirComplex("force-mlir-complex",
+                     llvm::cl::desc("Force using MLIR complex operations "
+                                    "instead of libm complex operations"),
+                     llvm::cl::init(false));
 
 mlir::Value genLibCall(fir::FirOpBuilder &builder, mlir::Location loc,
                        llvm::StringRef libFuncName,
@@ -734,12 +734,19 @@
                              mlir::FunctionType mathLibFuncType,
                              llvm::ArrayRef<mlir::Value> args) {
   mlir::Value result;
-  bool hasApproxFunc = mlir::arith::bitEnumContainsAny(
+  bool canUseApprox = mlir::arith::bitEnumContainsAny(
       builder.getFastMathFlags(), mlir::arith::FastMathFlags::afn);
-  if ((disableMlirComplex || !hasApproxFunc) && !mathLibFuncName.empty()) {
-    result = genLibCall(builder, loc, mathLibFuncName, mathLibFuncType, args);
-    LLVM_DEBUG(result.dump(); llvm::dbgs() << "\n");
-    return result;
+
+  // If we have libm functions, we can attempt to generate the more precise
+  // version of the complex math operation.
+  if (!mathLibFuncName.empty()) {
+    // If we enabled MLIR complex or can use approximate operations, we should
+    // NOT use libm.
+    if (!forceMlirComplex && !canUseApprox) {
+      result = genLibCall(builder, loc, mathLibFuncName, mathLibFuncType, args);
+      LLVM_DEBUG(result.dump(); llvm::dbgs() << "\n");
+      return result;
+    }
   }
 
   LLVM_DEBUG(llvm::dbgs() << "Generating '" << mathLibFuncName
diff --git a/flang/test/Lower/Intrinsics/abs.f90 b/flang/test/Lower/Intrinsics/abs.f90
--- a/flang/test/Lower/Intrinsics/abs.f90
+++ b/flang/test/Lower/Intrinsics/abs.f90
@@ -1,9 +1,9 @@
 ! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: bbc --disable-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: bbc --force-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 ! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -emit-fir -mllvm --force-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 ! RUN: %flang_fc1 -fapprox-func -emit-fir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 
 ! Test abs intrinsic for various types (int, float, complex)
diff --git a/flang/test/Lower/Intrinsics/exp.f90 b/flang/test/Lower/Intrinsics/exp.f90
--- a/flang/test/Lower/Intrinsics/exp.f90
+++ b/flang/test/Lower/Intrinsics/exp.f90
@@ -1,10 +1,10 @@
 ! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: bbc -emit-fir --disable-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: bbc -emit-fir --force-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-MLIR"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-APPROX"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --force-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-MLIR"
 
 ! CHECK-LABEL: exp_testr
 ! CHECK-SAME: (%[[AREF:.*]]: !fir.ref<f32> {{.*}}, %[[BREF:.*]]: !fir.ref<f32> {{.*}})
@@ -56,8 +56,9 @@
 ! CHECK: %[[RESULT64_OUTLINE:.*]] = math.exp %[[ARG64_OUTLINE]] fastmath<contract> : f64
 ! CHECK: return %[[RESULT64_OUTLINE]] : f64
 
-! CMPLX-FAST-LABEL: private @fir.exp.contract_afn.z4.z4
+! CMPLX-APPROX-LABEL: private @fir.exp.contract_afn.z4.z4
 ! CMPLX-PRECISE-LABEL: private @fir.exp.contract.z4.z4
+! CMPLX-MLIR-LABEL: private @fir.exp.contract.z4.z4
 ! CMPLX-SAME: (%[[ARG32_OUTLINE:.*]]: !fir.complex<4>) -> !fir.complex<4>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG32_OUTLINE]] : (!fir.complex<4>) -> complex<f32>
 ! CMPLX-FAST: %[[E:.*]] = complex.exp %[[C]] : complex<f32>
@@ -65,8 +66,9 @@
 ! CMPLX-PRECISE: %[[RESULT32_OUTLINE:.*]] = fir.call @cexpf(%[[ARG32_OUTLINE]]) fastmath<contract> : (!fir.complex<4>) -> !fir.complex<4>
 ! CMPLX: return %[[RESULT32_OUTLINE]] : !fir.complex<4>
 
-! CMPLX-FAST-LABEL: private @fir.exp.contract_afn.z8.z8
+! CMPLX-APPROX-LABEL: private @fir.exp.contract_afn.z8.z8
 ! CMPLX-PRECISE-LABEL: private @fir.exp.contract.z8.z8
+! CMPLX-MLIR-LABEL: private @fir.exp.contract.z8.z8
 ! CMPLX-SAME: (%[[ARG64_OUTLINE:.*]]: !fir.complex<8>) -> !fir.complex<8>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG64_OUTLINE]] : (!fir.complex<8>) -> complex<f64>
 ! CMPLX-FAST: %[[E:.*]] = complex.exp %[[C]] : complex<f64>
diff --git a/flang/test/Lower/Intrinsics/log.f90 b/flang/test/Lower/Intrinsics/log.f90
--- a/flang/test/Lower/Intrinsics/log.f90
+++ b/flang/test/Lower/Intrinsics/log.f90
@@ -1,10 +1,10 @@
 ! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: bbc -emit-fir --disable-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: bbc -emit-fir --force-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-MLIR"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
+! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --force-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-MLIR"
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST,CMPLX-APPROX"
 
 ! CHECK-LABEL: log_testr
 ! CHECK-SAME: (%[[AREF:.*]]: !fir.ref<f32> {{.*}}, %[[BREF:.*]]: !fir.ref<f32> {{.*}})
@@ -76,8 +76,9 @@
 ! CHECK: %[[RESULT64_OUTLINE:.*]] = math.log %[[ARG64_OUTLINE]] fastmath<contract> : f64
 ! CHECK: return %[[RESULT64_OUTLINE]] : f64
 
-! CMPLX-FAST-LABEL: private @fir.log.contract_afn.z4.z4
+! CMPLX-APPROX-LABEL: private @fir.log.contract_afn.z4.z4
 ! CMPLX-PRECISE-LABEL: private @fir.log.contract.z4.z4
+! CMPLX-MLIR-LABEL: private @fir.log.contract.z4.z4
 ! CMPLX-SAME: (%[[ARG32_OUTLINE:.*]]: !fir.complex<4>) -> !fir.complex<4>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG32_OUTLINE]] : (!fir.complex<4>) -> complex<f32>
 ! CMPLX-FAST: %[[E:.*]] = complex.log %[[C]] : complex<f32>
@@ -85,8 +86,9 @@
 ! CMPLX-PRECISE: %[[RESULT32_OUTLINE:.*]] = fir.call @clogf(%[[ARG32_OUTLINE]]) fastmath<contract> : (!fir.complex<4>) -> !fir.complex<4>
 ! CMPLX: return %[[RESULT32_OUTLINE]] : !fir.complex<4>
 
-! CMPLX-FAST-LABEL: private @fir.log.contract_afn.z8.z8
+! CMPLX-APPROX-LABEL: private @fir.log.contract_afn.z8.z8
 ! CMPLX-PRECISE-LABEL: private @fir.log.contract.z8.z8
+! CMPLX-MLIR-LABEL: private @fir.log.contract.z8.z8
 ! CMPLX-SAME: (%[[ARG64_OUTLINE:.*]]: !fir.complex<8>) -> !fir.complex<8>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG64_OUTLINE]] : (!fir.complex<8>) -> complex<f64>
 ! CMPLX-FAST: %[[E:.*]] = complex.log %[[C]] : complex<f64>
diff --git a/flang/test/Lower/power-operator.f90 b/flang/test/Lower/power-operator.f90
--- a/flang/test/Lower/power-operator.f90
+++ b/flang/test/Lower/power-operator.f90
@@ -1,10 +1,10 @@
 ! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,PRECISE"
 ! RUN: bbc --math-runtime=precise -emit-fir %s -o - | FileCheck %s --check-prefixes="PRECISE"
-! RUN: bbc --disable-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="PRECISE"
+! RUN: bbc --force-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="FAST"
 ! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,PRECISE"
 ! RUN: %flang_fc1 -fapprox-func -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="PRECISE"
+! RUN: %flang_fc1 -emit-fir -mllvm --force-mlir-complex %s -o - | FileCheck %s --check-prefixes="FAST"
 
 ! Test power operation lowering
 
diff --git a/flang/test/Lower/sqrt.f90 b/flang/test/Lower/sqrt.f90
--- a/flang/test/Lower/sqrt.f90
+++ b/flang/test/Lower/sqrt.f90
@@ -1,10 +1,10 @@
 ! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-PRECISE"
 ! RUN: bbc --math-runtime=precise -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
-! RUN: bbc --disable-mlir-complex -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
+! RUN: bbc --force-mlir-complex -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
+! RUN: %flang_fc1 -emit-fir -mllvm --force-mlir-complex -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-FAST"
 
 ! CHECK-LABEL: sqrt_testr
 subroutine sqrt_testr(a, b)