diff --git a/src/libexpr-tests/primops.cc b/src/libexpr-tests/primops.cc
index c3e50863d..7695a587a 100644
--- a/src/libexpr-tests/primops.cc
+++ b/src/libexpr-tests/primops.cc
@@ -56,11 +56,31 @@ namespace nix {
     TEST_F(PrimOpTest, ceil) {
         auto v = eval("builtins.ceil 1.9");
         ASSERT_THAT(v, IsIntEq(2));
+        auto intMin = eval("builtins.ceil (-4611686018427387904 - 4611686018427387904)");
+        ASSERT_THAT(intMin, IsIntEq(std::numeric_limits<NixInt::Inner>::min()));
+        ASSERT_THROW(eval("builtins.ceil 1.0e200"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil -1.0e200"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil (1.0e200 * 1.0e200)"), EvalError); // inf
+        ASSERT_THROW(eval("builtins.ceil (-1.0e200 * 1.0e200)"), EvalError); // -inf
+        ASSERT_THROW(eval("builtins.ceil (1.0e200 * 1.0e200 - 1.0e200 * 1.0e200)"), EvalError); // nan
+        // bugs in previous Nix versions
+        ASSERT_THROW(eval("builtins.ceil (4611686018427387904 + 4611686018427387903)"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil (-4611686018427387904 - 4611686018427387903)"), EvalError);
     }
 
     TEST_F(PrimOpTest, floor) {
         auto v = eval("builtins.floor 1.9");
         ASSERT_THAT(v, IsIntEq(1));
+        auto intMin = eval("builtins.ceil (-4611686018427387904 - 4611686018427387904)");
+        ASSERT_THAT(intMin, IsIntEq(std::numeric_limits<NixInt::Inner>::min()));
+        ASSERT_THROW(eval("builtins.ceil 1.0e200"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil -1.0e200"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil (1.0e200 * 1.0e200)"), EvalError); // inf
+        ASSERT_THROW(eval("builtins.ceil (-1.0e200 * 1.0e200)"), EvalError); // -inf
+        ASSERT_THROW(eval("builtins.ceil (1.0e200 * 1.0e200 - 1.0e200 * 1.0e200)"), EvalError); // nan
+        // bugs in previous Nix versions
+        ASSERT_THROW(eval("builtins.ceil (4611686018427387904 + 4611686018427387903)"), EvalError);
+        ASSERT_THROW(eval("builtins.ceil (-4611686018427387904 - 4611686018427387903)"), EvalError);
     }
 
     TEST_F(PrimOpTest, tryEvalFailure) {
diff --git a/src/libexpr/primops.cc b/src/libexpr/primops.cc
index 5e331f84d..5b24849d2 100644
--- a/src/libexpr/primops.cc
+++ b/src/libexpr/primops.cc
@@ -888,18 +888,40 @@ static void prim_ceil(EvalState & state, const PosIdx pos, Value * * args, Value
 {
     auto value = state.forceFloat(*args[0], args[0]->determinePos(pos),
             "while evaluating the first argument passed to builtins.ceil");
-    v.mkInt(ceil(value));
+    auto ceilValue = ceil(value);
+    bool isInt = args[0]->type() == nInt;
+    constexpr NixFloat int_min = std::numeric_limits<NixInt::Inner>::min(); // power of 2, so that no rounding occurs
+    if (ceilValue >= int_min && ceilValue < -int_min) {
+        v.mkInt(ceilValue);
+    } else if (isInt) {
+        // a NixInt, e.g. INT64_MAX, can be rounded to -int_min due to the cast to NixFloat
+        state.error<EvalError>("Due to a bug (see https://github.com/NixOS/nix/issues/12899) the NixInt argument %1% caused undefined behavior in previous Nix versions.\n\tFuture Nix versions might implement the correct behavior.", args[0]->integer().value).atPos(pos).debugThrow();
+    } else {
+        state.error<EvalError>("NixFloat argument %1% is not in the range of NixInt", args[0]->fpoint()).atPos(pos).debugThrow();
+    }
+    // `forceFloat` casts NixInt to NixFloat, but instead NixInt args shall be returned unmodified
+    if (isInt) {
+        auto arg = args[0]->integer();
+        auto res = v.integer();
+        if (arg != res) {
+            state.error<EvalError>("Due to a bug (see https://github.com/NixOS/nix/issues/12899) a loss of precision occured in previous Nix versions because the NixInt argument %1% was rounded to %2%.\n\tFuture Nix versions might implement the correct behavior.", arg, res).atPos(pos).debugThrow();
+        }
+    }
 }
 
 static RegisterPrimOp primop_ceil({
     .name = "__ceil",
-    .args = {"double"},
+    .args = {"number"},
     .doc = R"(
-        Converts an IEEE-754 double-precision floating-point number (*double*) to
-        the next higher integer.
+        Rounds and converts *number* to the next higher NixInt value if possible, i.e. `ceil *number* >= *number*` and
+        `ceil *number* - *number* < 1`.
 
-        If the datatype is neither an integer nor a "float", an evaluation error will be
-        thrown.
+        An evaluation error is thrown, if there exists no such NixInt value `ceil *number*`.
+        Due to bugs in previous Nix versions an evaluation error might be thrown, if the datatype of *number* is
+        a NixInt and if `*number* < -9007199254740992` or `*number* > 9007199254740992`.
+
+        If the datatype of *number* is neither a NixInt (signed 64-bit integer) nor a NixFloat
+        (IEEE-754 double-precision floating-point number), an evaluation error will be thrown.
     )",
     .fun = prim_ceil,
 });
@@ -907,18 +929,40 @@ static RegisterPrimOp primop_ceil({
 static void prim_floor(EvalState & state, const PosIdx pos, Value * * args, Value & v)
 {
     auto value = state.forceFloat(*args[0], args[0]->determinePos(pos), "while evaluating the first argument passed to builtins.floor");
-    v.mkInt(floor(value));
+    auto floorValue = floor(value);
+    bool isInt = args[0]->type() == nInt;
+    constexpr NixFloat int_min = std::numeric_limits<NixInt::Inner>::min(); // power of 2, so that no rounding occurs
+    if (floorValue >= int_min && floorValue < -int_min) {
+        v.mkInt(floorValue);
+    } else if (isInt) {
+        // a NixInt, e.g. INT64_MAX, can be rounded to -int_min due to the cast to NixFloat
+        state.error<EvalError>("Due to a bug (see https://github.com/NixOS/nix/issues/12899) the NixInt argument %1% caused undefined behavior in previous Nix versions.\n\tFuture Nix versions might implement the correct behavior.", args[0]->integer().value).atPos(pos).debugThrow();
+    } else {
+        state.error<EvalError>("NixFloat argument %1% is not in the range of NixInt", args[0]->fpoint()).atPos(pos).debugThrow();
+    }
+    // `forceFloat` casts NixInt to NixFloat, but instead NixInt args shall be returned unmodified
+    if (isInt) {
+        auto arg = args[0]->integer();
+        auto res = v.integer();
+        if (arg != res) {
+            state.error<EvalError>("Due to a bug (see https://github.com/NixOS/nix/issues/12899) a loss of precision occured in previous Nix versions because the NixInt argument %1% was rounded to %2%.\n\tFuture Nix versions might implement the correct behavior.", arg, res).atPos(pos).debugThrow();
+        }
+    }
 }
 
 static RegisterPrimOp primop_floor({
     .name = "__floor",
-    .args = {"double"},
+    .args = {"number"},
     .doc = R"(
-        Converts an IEEE-754 double-precision floating-point number (*double*) to
-        the next lower integer.
+        Rounds and converts *number* to the next lower NixInt value if possible, i.e. `floor *number* <= *number*` and
+        `*number* - floor *number* < 1`.
 
-        If the datatype is neither an integer nor a "float", an evaluation error will be
-        thrown.
+        An evaluation error is thrown, if there exists no such NixInt value `floor *number*`.
+        Due to bugs in previous Nix versions an evaluation error might be thrown, if the datatype of *number* is
+        a NixInt and if `*number* < -9007199254740992` or `*number* > 9007199254740992`.
+
+        If the datatype of *number* is neither a NixInt (signed 64-bit integer) nor a NixFloat
+        (IEEE-754 double-precision floating-point number), an evaluation error will be thrown.
     )",
     .fun = prim_floor,
 });