diff --git a/flang/lib/Evaluate/host.cpp b/flang/lib/Evaluate/host.cpp
--- a/flang/lib/Evaluate/host.cpp
+++ b/flang/lib/Evaluate/host.cpp
@@ -141,7 +141,7 @@
   }
 
   if (!flags_.empty()) {
-    RealFlagWarnings(context, flags_, "intrinsic function");
+    RealFlagWarnings(context, flags_, "intrinsic function call");
   }
   errno = 0;
   if (fesetenv(&originalFenv_) != 0) {
diff --git a/flang/lib/Evaluate/intrinsics-library.cpp b/flang/lib/Evaluate/intrinsics-library.cpp
--- a/flang/lib/Evaluate/intrinsics-library.cpp
+++ b/flang/lib/Evaluate/intrinsics-library.cpp
@@ -477,10 +477,243 @@
   return type;
 }
 
+/// Structure to register intrinsic argument checks that must be performed.
+using ArgumentVerifierFunc = bool (*)(
+    const std::vector<Expr<SomeType>> &, FoldingContext &);
+struct ArgumentVerifier {
+  using Key = std::string_view;
+  // Needed for implicit compare with keys.
+  constexpr operator Key() const { return key; }
+  Key key; // intrinsic name
+  ArgumentVerifierFunc verifier;
+};
+
+static constexpr int lastArg{-1};
+static constexpr int firstArg{0};
+
+static const Expr<SomeType> &getArg(
+    int position, const std::vector<Expr<SomeType>> &args) {
+  if (position == lastArg) {
+    CHECK(!args.empty());
+    return args.back();
+  }
+  CHECK(position >= 0 && static_cast<std::size_t>(position) < args.size());
+  return args[position];
+}
+
+template <typename T>
+static bool IsInRange(const Expr<T> &expr, int lb, int ub) {
+  if (auto scalar{GetScalarConstantValue<T>(expr)}) {
+    auto lbValue{Scalar<T>::FromInteger(value::Integer<8>{lb}).value};
+    auto ubValue{Scalar<T>::FromInteger(value::Integer<8>{ub}).value};
+    return Satisfies(RelationalOperator::LE, lbValue.Compare(*scalar)) &&
+        Satisfies(RelationalOperator::LE, scalar->Compare(ubValue));
+  }
+  return true;
+}
+
+/// Verify that the argument in an intrinsic call belongs to [lb, ub] if is
+/// real.
+template <int lb, int ub>
+static bool VerifyInRangeIfReal(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someReal =
+          std::get_if<Expr<SomeReal>>(&getArg(firstArg, args).u)) {
+    const bool isInRange{
+        std::visit([&](const auto &x) -> bool { return IsInRange(x, lb, ub); },
+            someReal->u)};
+    if (!isInRange) {
+      context.messages().Say(
+          "argument is out of range [%d., %d.]"_en_US, lb, ub);
+    }
+    return isInRange;
+  }
+  return true;
+}
+
+template <int argPosition, const char *argName>
+static bool VerifyStrictlyPositiveIfReal(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someReal =
+          std::get_if<Expr<SomeReal>>(&getArg(argPosition, args).u)) {
+    const bool isStrictlyPositive{std::visit(
+        [&](const auto &x) -> bool {
+          using T = typename std::decay_t<decltype(x)>::Result;
+          auto scalar{GetScalarConstantValue<T>(x)};
+          return Satisfies(
+              RelationalOperator::LT, Scalar<T>{}.Compare(*scalar));
+        },
+        someReal->u)};
+    if (!isStrictlyPositive) {
+      context.messages().Say(
+          "argument '%s' must be strictly positive"_en_US, argName);
+    }
+    return isStrictlyPositive;
+  }
+  return true;
+}
+
+/// Verify that an intrinsic call argument is not zero if it is real.
+template <int argPosition, const char *argName>
+static bool VerifyNotZeroIfReal(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someReal =
+          std::get_if<Expr<SomeReal>>(&getArg(argPosition, args).u)) {
+    const bool isNotZero{std::visit(
+        [&](const auto &x) -> bool {
+          using T = typename std::decay_t<decltype(x)>::Result;
+          auto scalar{GetScalarConstantValue<T>(x)};
+          return !scalar || !scalar->IsZero();
+        },
+        someReal->u)};
+    if (!isNotZero) {
+      context.messages().Say(
+          "argument '%s' must be different from zero"_en_US, argName);
+    }
+    return isNotZero;
+  }
+  return true;
+}
+
+/// Verify that the argument in an intrinsic call is not zero if is complex.
+static bool VerifyNotZeroIfComplex(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someComplex =
+          std::get_if<Expr<SomeComplex>>(&getArg(firstArg, args).u)) {
+    const bool isNotZero{std::visit(
+        [&](const auto &z) -> bool {
+          using T = typename std::decay_t<decltype(z)>::Result;
+          auto scalar{GetScalarConstantValue<T>(z)};
+          return !scalar || !scalar->IsZero();
+        },
+        someComplex->u)};
+    if (!isNotZero) {
+      context.messages().Say(
+          "complex argument must be different from zero"_en_US);
+    }
+    return isNotZero;
+  }
+  return true;
+}
+
+// Verify that the argument in an intrinsic call is not zero and not a negative
+// integer.
+static bool VerifyGammaLikeArgument(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someReal =
+          std::get_if<Expr<SomeReal>>(&getArg(firstArg, args).u)) {
+    const bool isValid{std::visit(
+        [&](const auto &x) -> bool {
+          using T = typename std::decay_t<decltype(x)>::Result;
+          auto scalar{GetScalarConstantValue<T>(x)};
+          if (scalar) {
+            return !scalar->IsZero() &&
+                !(scalar->IsNegative() &&
+                    scalar->ToWholeNumber().value == scalar);
+          }
+          return true;
+        },
+        someReal->u)};
+    if (!isValid) {
+      context.messages().Say(
+          "argument must not be a negative integer or zero"_en_US);
+    }
+    return isValid;
+  }
+  return true;
+}
+
+// Verify that two real arguments are not both zero.
+static bool VerifyAtan2LikeArguments(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  if (const auto *someReal =
+          std::get_if<Expr<SomeReal>>(&getArg(firstArg, args).u)) {
+    const bool isValid{std::visit(
+        [&](const auto &typedExpr) -> bool {
+          using T = typename std::decay_t<decltype(typedExpr)>::Result;
+          auto x{GetScalarConstantValue<T>(typedExpr)};
+          auto y{GetScalarConstantValue<T>(getArg(lastArg, args))};
+          if (x && y) {
+            return !(x->IsZero() && y->IsZero());
+          }
+          return true;
+        },
+        someReal->u)};
+    if (!isValid) {
+      context.messages().Say(
+          "'x' and 'y' arguments must not be both zero"_en_US);
+    }
+    return isValid;
+  }
+  return true;
+}
+
+template <ArgumentVerifierFunc... F>
+static bool CombineVerifiers(
+    const std::vector<Expr<SomeType>> &args, FoldingContext &context) {
+  return (... & F(args, context));
+}
+
+/// Define argument names to be used error messages when the intrinsic have
+/// several arguments.
+static constexpr char xName[]{"x"};
+static constexpr char pName[]{"p"};
+
+/// Register argument verifiers for all intrinsics folded with runtime.
+static constexpr ArgumentVerifier intrinsicArgumentVerifiers[]{
+    {"acos", VerifyInRangeIfReal<-1, 1>},
+    {"asin", VerifyInRangeIfReal<-1, 1>},
+    {"atan2", VerifyAtan2LikeArguments},
+    {"bessel_y0", VerifyStrictlyPositiveIfReal<firstArg, xName>},
+    {"bessel_y1", VerifyStrictlyPositiveIfReal<firstArg, xName>},
+    {"bessel_yn", VerifyStrictlyPositiveIfReal<lastArg, xName>},
+    {"gamma", VerifyGammaLikeArgument},
+    {"log",
+        CombineVerifiers<VerifyStrictlyPositiveIfReal<firstArg, xName>,
+            VerifyNotZeroIfComplex>},
+    {"log10", VerifyStrictlyPositiveIfReal<firstArg, xName>},
+    {"log_gamma", VerifyGammaLikeArgument},
+    {"mod", VerifyNotZeroIfReal<lastArg, pName>},
+};
+
+const ArgumentVerifierFunc *findVerifier(const std::string &intrinsicName) {
+  static constexpr Fortran::common::StaticMultimapView<ArgumentVerifier>
+      verifiers(intrinsicArgumentVerifiers);
+  static_assert(verifiers.Verify(), "map must be sorted");
+  auto range{verifiers.equal_range(intrinsicName)};
+  if (range.first != range.second) {
+    return &range.first->verifier;
+  }
+  return nullptr;
+}
+
+/// Ensure argument verifiers, if any, are run before calling the runtime
+/// wrapper to fold an intrinsic.
+static HostRuntimeWrapper AddArgumentVerifierIfAny(
+    const std::string &intrinsicName, const HostRuntimeFunction &hostFunction) {
+  if (const auto *verifier{findVerifier(intrinsicName)}) {
+    const HostRuntimeFunction *hostFunctionPtr = &hostFunction;
+    return [hostFunctionPtr, verifier](
+               FoldingContext &context, std::vector<Expr<SomeType>> &&args) {
+      const bool validArguments{(*verifier)(args, context)};
+      if (!validArguments) {
+        // Silence fp signal warnings since a more detailed warning about
+        // invalid arguments was already emitted.
+        parser::Messages localBuffer;
+        parser::ContextualMessages localMessages{&localBuffer};
+        FoldingContext localContext{context, localMessages};
+        return hostFunctionPtr->folder(localContext, std::move(args));
+      }
+      return hostFunctionPtr->folder(context, std::move(args));
+    };
+  }
+  return hostFunction.folder;
+}
+
 std::optional<HostRuntimeWrapper> GetHostRuntimeWrapper(const std::string &name,
     DynamicType resultType, const std::vector<DynamicType> &argTypes) {
   if (const auto *hostFunction{SearchHostRuntime(name, resultType, argTypes)}) {
-    return hostFunction->folder;
+    return AddArgumentVerifierIfAny(name, *hostFunction);
   }
   // If no exact match, search with "bigger" types and insert type
   // conversions around the folder.
@@ -491,7 +724,8 @@
   }
   if (const auto *hostFunction{
           SearchHostRuntime(name, biggerResultType, biggerArgTypes)}) {
-    return [hostFunction, resultType](
+    auto hostFolderWithChecks{AddArgumentVerifierIfAny(name, *hostFunction)};
+    return [hostFunction, resultType, hostFolderWithChecks](
                FoldingContext &context, std::vector<Expr<SomeType>> &&args) {
       auto nArgs{args.size()};
       for (size_t i{0}; i < nArgs; ++i) {
@@ -501,7 +735,7 @@
       }
       return Fold(context,
           ConvertToType(
-              resultType, hostFunction->folder(context, std::move(args)))
+              resultType, hostFolderWithChecks(context, std::move(args)))
               .value());
     };
   }
diff --git a/flang/test/Evaluate/folding04.f90 b/flang/test/Evaluate/folding04.f90
--- a/flang/test/Evaluate/folding04.f90
+++ b/flang/test/Evaluate/folding04.f90
@@ -17,23 +17,46 @@
   !WARN: division by zero
   real(4), parameter :: r4_ninf = -1._4/0._4
 
-  !WARN: invalid argument on intrinsic function
+  !WARN: argument is out of range [-1., 1.]
   real(4), parameter :: nan_r4_acos1 = acos(1.1)
   TEST_ISNAN(nan_r4_acos1)
-  !WARN: invalid argument on intrinsic function
+  !WARN: argument is out of range [-1., 1.]
   real(4), parameter :: nan_r4_acos2 = acos(r4_pmax)
   TEST_ISNAN(nan_r4_acos2)
-  !WARN: invalid argument on intrinsic function
+  !WARN: argument is out of range [-1., 1.]
   real(4), parameter :: nan_r4_acos3 = acos(r4_nmax)
   TEST_ISNAN(nan_r4_acos3)
-  !WARN: invalid argument on intrinsic function
+  !WARN: argument is out of range [-1., 1.]
   real(4), parameter :: nan_r4_acos4 = acos(r4_ninf)
   TEST_ISNAN(nan_r4_acos4)
-  !WARN: invalid argument on intrinsic function
+  !WARN: argument is out of range [-1., 1.]
   real(4), parameter :: nan_r4_acos5 = acos(r4_pinf)
   TEST_ISNAN(nan_r4_acos5)
+  !WARN: argument is out of range [-1., 1.]
+  real(8), parameter :: nan_r8_dasin1 = dasin(-1.1_8)
+  TEST_ISNAN(nan_r8_dasin1)
+  !WARN: argument 'x' must be strictly positive
+  real(8), parameter :: nan_r8_dlog1 = dlog(-0.1_8)
+  TEST_ISNAN(nan_r8_dlog1)
+  !WARN: complex argument must be different from zero
+  complex(4), parameter :: c4_clog1 = clog((0., 0.))
+  !WARN: argument 'p' must be different from zero
+  real(4), parameter :: nan_r4_mod = mod(3.5, 0.)
+  TEST_ISNAN(nan_r4_mod)
+  real(4), parameter :: ok_r4_gamma = gamma(-1.1)
+  !WARN: argument must not be a negative integer or zero
+  real(4), parameter :: r4_gamma1 = gamma(0.)
+  !WARN: argument must not be a negative integer or zero
+  real(4), parameter :: r4_gamma2 = gamma(-1.)
+  real(4), parameter :: ok_r4_log_gamma = log_gamma(-2.001)
+  !WARN: argument must not be a negative integer or zero
+  real(4), parameter :: r4_log_gamma1 = log_gamma(0.)
+  !WARN: argument must not be a negative integer or zero
+  real(4), parameter :: r4_log_gamma2 = log_gamma(-100001.)
+  !WARN: 'x' and 'y' arguments must not be both zero
+  real(4), parameter :: r4_atan2 = atan2(0., 0.)
 
-  !WARN: overflow on intrinsic function
+  !WARN: overflow on intrinsic function call
   logical, parameter :: test_exp_overflow = exp(256._4).EQ.r4_pinf
 end module