diff --git a/clang/include/clang/Driver/Options.td b/clang/include/clang/Driver/Options.td
index 096df56d0f183..2ef609831637e 100644
--- a/clang/include/clang/Driver/Options.td
+++ b/clang/include/clang/Driver/Options.td
@@ -2750,6 +2750,9 @@ def fno_unsafe_math_optimizations : Flag<["-"], "fno-unsafe-math-optimizations">
   Group<f_Group>;
 def fassociative_math : Flag<["-"], "fassociative-math">, Visibility<[ClangOption, FlangOption]>, Group<f_Group>;
 def fno_associative_math : Flag<["-"], "fno-associative-math">, Visibility<[ClangOption, FlangOption]>, Group<f_Group>;
+def fno_fast_real_mod : Flag<["-"], "fno-fast-real-mod">,
+  Group<f_Group>, Visibility<[FlangOption, FC1Option]>,
+  HelpText<"Disable optimization of MOD for REAL types in presence of -ffast-math">;
 defm reciprocal_math : BoolFOption<"reciprocal-math",
   LangOpts<"AllowRecip">, DefaultFalse,
   PosFlag<SetTrue, [], [ClangOption, CC1Option, FC1Option, FlangOption],
diff --git a/clang/lib/Driver/ToolChains/Flang.cpp b/clang/lib/Driver/ToolChains/Flang.cpp
index 426bc52f34859..a56fa41c49d34 100644
--- a/clang/lib/Driver/ToolChains/Flang.cpp
+++ b/clang/lib/Driver/ToolChains/Flang.cpp
@@ -822,6 +822,9 @@ static void addFloatingPointOptions(const Driver &D, const ArgList &Args,
                                          complexRangeKindToStr(Range)));
   }
 
+  if (Args.hasArg(options::OPT_fno_fast_real_mod))
+    CmdArgs.push_back("-fno-fast-real-mod");
+
   if (!HonorINFs && !HonorNaNs && AssociativeMath && ReciprocalMath &&
       ApproxFunc && !SignedZeros &&
       (FPContract == "fast" || FPContract.empty())) {
diff --git a/flang/include/flang/Support/LangOptions.def b/flang/include/flang/Support/LangOptions.def
index ba72d7b4b7212..e7185c836f45b 100644
--- a/flang/include/flang/Support/LangOptions.def
+++ b/flang/include/flang/Support/LangOptions.def
@@ -60,7 +60,8 @@ LANGOPT(OpenMPNoThreadState, 1, 0)
 LANGOPT(OpenMPNoNestedParallelism, 1, 0)
 /// Use SIMD only OpenMP support.
 LANGOPT(OpenMPSimd, 1, false)
-
+/// Enable fast MOD operations for REAL
+LANGOPT(NoFastRealMod, 1, false)
 LANGOPT(VScaleMin, 32, 0)  ///< Minimum vscale range value
 LANGOPT(VScaleMax, 32, 0)  ///< Maximum vscale range value
 
diff --git a/flang/lib/Frontend/CompilerInvocation.cpp b/flang/lib/Frontend/CompilerInvocation.cpp
index 81610edee36fb..548ca675db5ea 100644
--- a/flang/lib/Frontend/CompilerInvocation.cpp
+++ b/flang/lib/Frontend/CompilerInvocation.cpp
@@ -1425,6 +1425,9 @@ static bool parseFloatingPointArgs(CompilerInvocation &invoc,
     opts.setFPContractMode(Fortran::common::LangOptions::FPM_Fast);
   }
 
+  if (args.hasArg(clang::driver::options::OPT_fno_fast_real_mod))
+    opts.NoFastRealMod = true;
+
   return true;
 }
 
diff --git a/flang/lib/Frontend/FrontendActions.cpp b/flang/lib/Frontend/FrontendActions.cpp
index d5e0325911adf..0c630d2ba876d 100644
--- a/flang/lib/Frontend/FrontendActions.cpp
+++ b/flang/lib/Frontend/FrontendActions.cpp
@@ -277,6 +277,14 @@ bool CodeGenAction::beginSourceFileAction() {
                               ci.getInvocation().getLangOpts().OpenMPVersion);
   }
 
+  if (ci.getInvocation().getLangOpts().NoFastRealMod) {
+    mlir::ModuleOp mod = lb.getModule();
+    mod.getOperation()->setAttr(
+        mlir::StringAttr::get(mod.getContext(),
+                              llvm::Twine{"fir.no_fast_real_mod"}),
+        mlir::BoolAttr::get(mod.getContext(), true));
+  }
+
   // Create a parse tree and lower it to FIR
   parseAndLowerTree(ci, lb);
 
diff --git a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
index 71d35e37bbe94..de7694ffd468c 100644
--- a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
+++ b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
@@ -6989,8 +6989,33 @@ mlir::Value IntrinsicLibrary::genMergeBits(mlir::Type resultType,
 }
 
 // MOD
+static mlir::Value genFastMod(fir::FirOpBuilder &builder, mlir::Location loc,
+                              mlir::Value a, mlir::Value p) {
+  auto fastmathFlags = mlir::arith::FastMathFlags::contract;
+  auto fastmathAttr =
+      mlir::arith::FastMathFlagsAttr::get(builder.getContext(), fastmathFlags);
+  mlir::Value divResult =
+      mlir::arith::DivFOp::create(builder, loc, a, p, fastmathAttr);
+  mlir::Type intType = builder.getIntegerType(
+      a.getType().getIntOrFloatBitWidth(), /*signed=*/true);
+  mlir::Value intResult = builder.createConvert(loc, intType, divResult);
+  mlir::Value cnvResult = builder.createConvert(loc, a.getType(), intResult);
+  mlir::Value mulResult =
+      mlir::arith::MulFOp::create(builder, loc, cnvResult, p, fastmathAttr);
+  mlir::Value subResult =
+      mlir::arith::SubFOp::create(builder, loc, a, mulResult, fastmathAttr);
+  return subResult;
+}
+
 mlir::Value IntrinsicLibrary::genMod(mlir::Type resultType,
                                      llvm::ArrayRef<mlir::Value> args) {
+  auto mod = builder.getModule();
+  bool dontUseFastRealMod = false;
+  bool canUseApprox = mlir::arith::bitEnumContainsAny(
+      builder.getFastMathFlags(), mlir::arith::FastMathFlags::afn);
+  if (auto attr = mod->getAttrOfType<mlir::BoolAttr>("fir.no_fast_real_mod"))
+    dontUseFastRealMod = attr.getValue();
+
   assert(args.size() == 2);
   if (resultType.isUnsignedInteger()) {
     mlir::Type signlessType = mlir::IntegerType::get(
@@ -7002,9 +7027,16 @@ mlir::Value IntrinsicLibrary::genMod(mlir::Type resultType,
   if (mlir::isa<mlir::IntegerType>(resultType))
     return mlir::arith::RemSIOp::create(builder, loc, args[0], args[1]);
 
-  // Use runtime.
-  return builder.createConvert(
-      loc, resultType, fir::runtime::genMod(builder, loc, args[0], args[1]));
+  if (resultType.isFloat() && canUseApprox && !dontUseFastRealMod) {
+    // Treat MOD as an approximate function and code-gen inline code
+    // instead of calling into the Fortran runtime library.
+    return builder.createConvert(loc, resultType,
+                                 genFastMod(builder, loc, args[0], args[1]));
+  } else {
+    // Use runtime.
+    return builder.createConvert(
+        loc, resultType, fir::runtime::genMod(builder, loc, args[0], args[1]));
+  }
 }
 
 // MODULO
diff --git a/flang/test/Driver/fast-real-mod.f90 b/flang/test/Driver/fast-real-mod.f90
new file mode 100644
index 0000000000000..4ea9b26e64753
--- /dev/null
+++ b/flang/test/Driver/fast-real-mod.f90
@@ -0,0 +1,7 @@
+! RUN: %flang -fno-fast-real-mod -### -c %s 2>&1 | FileCheck %s -check-prefix CHECK-NO-FAST-REAL-MOD
+
+! CHECK-NO-FAST-REAL-MOD: "-fno-fast-real-mod"
+
+program test
+    ! nothing to be done in here
+end program test
diff --git a/flang/test/Lower/Intrinsics/fast-real-mod.f90 b/flang/test/Lower/Intrinsics/fast-real-mod.f90
new file mode 100644
index 0000000000000..f80f7203ad1a2
--- /dev/null
+++ b/flang/test/Lower/Intrinsics/fast-real-mod.f90
@@ -0,0 +1,83 @@
+! RUN: %flang_fc1 -ffast-math -emit-mlir -o - %s | FileCheck %s --check-prefixes=CHECK%if target=x86_64{{.*}} %{,CHECK-KIND10%}%if flang-supports-f128-math %{,CHECK-KIND16%}
+! RUN: %flang_fc1 -ffast-math -fno-fast-real-mod -emit-mlir -o - %s | FileCheck %s --check-prefixes=CHECK-NFRM%if target=x86_64{{.*}} %{,CHECK-NFRM-KIND10%}%if flang-supports-f128-math %{,CHECK-NFRM-KIND16%}
+
+! TODO: check line that fir.fast_real_mod is not there
+! CHECK-NFRM: module attributes {{{.*}}fir.no_fast_real_mod = true{{.*}}}
+
+! CHECK-LABEL: @_QPmod_real4
+subroutine mod_real4(r, a, p)
+    implicit none
+    real(kind=4) :: r, a, p
+! CHECK: %[[A:.*]] = fir.declare{{.*}}a"
+! CHECK: %[[P:.*]] = fir.declare{{.*}}p"
+! CHECK: %[[R:.*]] = fir.declare{{.*}}r"
+! CHECK: %[[A_LOAD:.*]] = fir.load %[[A]]
+! CHECK: %[[P_LOAD:.*]] = fir.load %[[P]]
+! CHECK: %[[DIV:.*]] = arith.divf %[[A_LOAD]], %[[P_LOAD]] fastmath<fast> : f32
+! CHECK: %[[CV1:.*]] = fir.convert %[[DIV]] : (f32) -> si32
+! CHECK: %[[CV2:.*]] = fir.convert %[[CV1]] : (si32) -> f32
+! CHECK: %[[MUL:.*]] = arith.mulf %[[CV2]], %[[P_LOAD]] fastmath<fast> : f32
+! CHECK: %[[SUB:.*]] = arith.subf %[[A_LOAD]], %[[MUL]] fastmath<fast> : f32
+! CHECK: fir.store %[[SUB]] to %[[R]] : !fir.ref<f32>
+! CHECK-NFRM: fir.call @_FortranAModReal4(%{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}) {{.*}}: (f32, f32, !fir.ref<i8>, i32) -> f32
+    r = mod(a, p)
+end subroutine mod_real4
+
+! CHECK-LABEL: @_QPmod_real8
+subroutine mod_real8(r, a, p)
+    implicit none
+    real(kind=8) :: r, a, p
+! CHECK: %[[A:.*]] = fir.declare{{.*}}a"
+! CHECK: %[[P:.*]] = fir.declare{{.*}}p"
+! CHECK: %[[R:.*]] = fir.declare{{.*}}r"
+! CHECK: %[[A_LOAD:.*]] = fir.load %[[A]]
+! CHECK: %[[P_LOAD:.*]] = fir.load %[[P]]
+! CHECK: %[[DIV:.*]] = arith.divf %[[A_LOAD]], %[[P_LOAD]] fastmath<fast> : f64
+! CHECK: %[[CV1:.*]] = fir.convert %[[DIV]] : (f64) -> si64
+! CHECK: %[[CV2:.*]] = fir.convert %[[CV1]] : (si64) -> f64
+! CHECK: %[[MUL:.*]] = arith.mulf %[[CV2]], %[[P_LOAD]] fastmath<fast> : f64
+! CHECK: %[[SUB:.*]] = arith.subf %[[A_LOAD]], %[[MUL]] fastmath<fast> : f64
+! CHECK: fir.store %[[SUB]] to %[[R]] : !fir.ref<f64>
+! CHECK-NFRM: fir.call @_FortranAModReal8(%{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}) {{.*}}: (f64, f64, !fir.ref<i8>, i32) -> f64
+    r = mod(a, p)
+end subroutine mod_real8
+
+! CHECK-LABEL: @_QPmod_real10
+subroutine mod_real10(r, a, p)
+    implicit none
+    integer, parameter :: kind10 = merge(10, 4, selected_real_kind(p=18).eq.10)
+    real(kind=kind10) :: r, a, p
+! CHECK-KIND10: %[[A:.*]] = fir.declare{{.*}}a"
+! CHECK-KIND10: %[[P:.*]] = fir.declare{{.*}}p"
+! CHECK-KIND10: %[[R:.*]] = fir.declare{{.*}}r"
+! CHECK-KIND10: %[[A_LOAD:.*]] = fir.load %[[A]]
+! CHECK-KIND10: %[[P_LOAD:.*]] = fir.load %[[P]]
+! CHECK-KIND10: %[[DIV:.*]] = arith.divf %[[A_LOAD]], %[[P_LOAD]] fastmath<fast> : f80
+! CHECK-KIND10: %[[CV1:.*]] = fir.convert %[[DIV]] : (f80) -> si80
+! CHECK-KIND10: %[[CV2:.*]] = fir.convert %[[CV1]] : (si80) -> f80
+! CHECK-KIND10: %[[MUL:.*]] = arith.mulf %[[CV2]], %[[P_LOAD]] fastmath<fast> : f80
+! CHECK-KIND10: %[[SUB:.*]] = arith.subf %[[A_LOAD]], %[[MUL]] fastmath<fast> : f80
+! CHECK-KIND10: fir.store %[[SUB]] to %[[R]] : !fir.ref<f80>
+! CHECK-NFRM-KIND10: fir.call @_FortranAModReal10(%{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}) {{.*}}: (f80, f80, !fir.ref<i8>, i32) -> f80
+    r = mod(a, p)
+end subroutine mod_real10
+
+! CHECK-LABEL: @_QPmod_real16
+subroutine mod_real16(r, a, p)
+    implicit none
+    integer, parameter :: kind16 = merge(16, 4, selected_real_kind(p=33).eq.16)
+    real(kind=kind16) :: r, a, p
+! CHECK-KIND16: %[[A:.*]] = fir.declare{{.*}}a"
+! CHECK-KIND16: %[[P:.*]] = fir.declare{{.*}}p"
+! CHECK-KIND16: %[[R:.*]] = fir.declare{{.*}}r"
+! CHECK-KIND16: %[[A_LOAD:.*]] = fir.load %[[A]]
+! CHECK-KIND16: %[[P_LOAD:.*]] = fir.load %[[P]]
+! CHECK-KIND16: %[[DIV:.*]] = arith.divf %[[A_LOAD]], %[[P_LOAD]] fastmath<fast> : f128
+! CHECK-KIND16: %[[CV1:.*]] = fir.convert %[[DIV]] : (f128) -> si128
+! CHECK-KIND16: %[[CV2:.*]] = fir.convert %[[CV1]] : (si128) -> f128
+! CHECK-KIND16: %[[MUL:.*]] = arith.mulf %[[CV2]], %[[P_LOAD]] fastmath<fast> : f128
+! CHECK-KIND16: %[[SUB:.*]] = arith.subf %[[A_LOAD]], %[[MUL]] fastmath<fast> : f128
+! CHECK-KIND16: fir.store %[[SUB]] to %[[R]] : !fir.ref<f128>
+! CHECK-NFRM-KIND16: fir.call @_FortranAModReal16(%{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}) {{.*}}: (f128, f128, !fir.ref<i8>, i32) -> f128
+    r = mod(a, p)
+end subroutine mod_real16