diff --git a/backends/cxxrtl/cxxrtl.h b/backends/cxxrtl/cxxrtl.h
index 30f4667c5..c988c9e80 100644
--- a/backends/cxxrtl/cxxrtl.h
+++ b/backends/cxxrtl/cxxrtl.h
@@ -829,6 +829,48 @@ constexpr T max(const T &a, const T &b) {
 
 // Logic operations
 template<size_t BitsY, size_t BitsA>
+value<BitsY> logic_not(const value<BitsA> &a) {
+	return value<BitsY> { a ? 0u : 1u };
+}
+
+template<size_t BitsY, size_t BitsA, size_t BitsB>
+value<BitsY> logic_and(const value<BitsA> &a, const value<BitsB> &b) {
+	return value<BitsY> { (bool(a) & bool(b)) ? 1u : 0u };
+}
+
+template<size_t BitsY, size_t BitsA, size_t BitsB>
+value<BitsY> logic_or(const value<BitsA> &a, const value<BitsB> &b) {
+	return value<BitsY> { (bool(a) | bool(b)) ? 1u : 0u };
+}
+
+// Reduction operations
+template<size_t BitsY, size_t BitsA>
+value<BitsY> reduce_and(const value<BitsA> &a) {
+	return value<BitsY> { a.bit_not().is_zero() ? 1u : 0u };
+}
+
+template<size_t BitsY, size_t BitsA>
+value<BitsY> reduce_or(const value<BitsA> &a) {
+	return value<BitsY> { a ? 1u : 0u };
+}
+
+template<size_t BitsY, size_t BitsA>
+value<BitsY> reduce_xor(const value<BitsA> &a) {
+	return value<BitsY> { (a.ctpop() % 2) ? 1u : 0u };
+}
+
+template<size_t BitsY, size_t BitsA>
+value<BitsY> reduce_xnor(const value<BitsA> &a) {
+	return value<BitsY> { (a.ctpop() % 2) ? 0u : 1u };
+}
+
+template<size_t BitsY, size_t BitsA>
+value<BitsY> reduce_bool(const value<BitsA> &a) {
+	return value<BitsY> { a ? 1u : 0u };
+}
+
+// Bitwise operations
+template<size_t BitsY, size_t BitsA>
 value<BitsY> not_u(const value<BitsA> &a) {
 	return a.template zcast<BitsY>().bit_not();
 }
@@ -838,66 +880,6 @@ value<BitsY> not_s(const value<BitsA> &a) {
 	return a.template scast<BitsY>().bit_not();
 }
 
-template<size_t BitsY, size_t BitsA>
-value<BitsY> logic_not_u(const value<BitsA> &a) {
-	return value<BitsY> { a ? 0u : 1u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> logic_not_s(const value<BitsA> &a) {
-	return value<BitsY> { a ? 0u : 1u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_and_u(const value<BitsA> &a) {
-	return value<BitsY> { a.bit_not().is_zero() ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_and_s(const value<BitsA> &a) {
-	return value<BitsY> { a.bit_not().is_zero() ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_or_u(const value<BitsA> &a) {
-	return value<BitsY> { a ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_or_s(const value<BitsA> &a) {
-	return value<BitsY> { a ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_xor_u(const value<BitsA> &a) {
-	return value<BitsY> { (a.ctpop() % 2) ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_xor_s(const value<BitsA> &a) {
-	return value<BitsY> { (a.ctpop() % 2) ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_xnor_u(const value<BitsA> &a) {
-	return value<BitsY> { (a.ctpop() % 2) ? 0u : 1u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_xnor_s(const value<BitsA> &a) {
-	return value<BitsY> { (a.ctpop() % 2) ? 0u : 1u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_bool_u(const value<BitsA> &a) {
-	return value<BitsY> { a ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA>
-value<BitsY> reduce_bool_s(const value<BitsA> &a) {
-	return value<BitsY> { a ? 1u : 0u };
-}
-
 template<size_t BitsY, size_t BitsA, size_t BitsB>
 value<BitsY> and_uu(const value<BitsA> &a, const value<BitsB> &b) {
 	return a.template zcast<BitsY>().bit_and(b.template zcast<BitsY>());
@@ -938,26 +920,6 @@ value<BitsY> xnor_ss(const value<BitsA> &a, const value<BitsB> &b) {
 	return a.template scast<BitsY>().bit_xor(b.template scast<BitsY>()).bit_not();
 }
 
-template<size_t BitsY, size_t BitsA, size_t BitsB>
-value<BitsY> logic_and_uu(const value<BitsA> &a, const value<BitsB> &b) {
-	return value<BitsY> { (bool(a) & bool(b)) ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA, size_t BitsB>
-value<BitsY> logic_and_ss(const value<BitsA> &a, const value<BitsB> &b) {
-	return value<BitsY> { (bool(a) & bool(b)) ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA, size_t BitsB>
-value<BitsY> logic_or_uu(const value<BitsA> &a, const value<BitsB> &b) {
-	return value<BitsY> { (bool(a) | bool(b)) ? 1u : 0u };
-}
-
-template<size_t BitsY, size_t BitsA, size_t BitsB>
-value<BitsY> logic_or_ss(const value<BitsA> &a, const value<BitsB> &b) {
-	return value<BitsY> { (bool(a) | bool(b)) ? 1u : 0u };
-}
-
 template<size_t BitsY, size_t BitsA, size_t BitsB>
 value<BitsY> shl_uu(const value<BitsA> &a, const value<BitsB> &b) {
 	return a.template zcast<BitsY>().template shl(b);
diff --git a/backends/cxxrtl/cxxrtl_backend.cc b/backends/cxxrtl/cxxrtl_backend.cc
index bf01b263a..2646f9371 100644
--- a/backends/cxxrtl/cxxrtl_backend.cc
+++ b/backends/cxxrtl/cxxrtl_backend.cc
@@ -192,6 +192,13 @@ bool is_binary_cell(RTLIL::IdString type)
 		ID($add), ID($sub), ID($mul), ID($div), ID($mod));
 }
 
+bool is_extending_cell(RTLIL::IdString type)
+{
+	return !type.in(
+		ID($logic_not), ID($logic_and), ID($logic_or),
+		ID($reduce_and), ID($reduce_or), ID($reduce_xor), ID($reduce_xnor), ID($reduce_bool));
+}
+
 bool is_elidable_cell(RTLIL::IdString type)
 {
 	return is_unary_cell(type) || is_binary_cell(type) || type.in(
@@ -907,17 +914,19 @@ struct CxxrtlWorker {
 	{
 		// Unary cells
 		if (is_unary_cell(cell->type)) {
-			f << cell->type.substr(1) << '_' <<
-			     (cell->getParam(ID::A_SIGNED).as_bool() ? 's' : 'u') <<
-			     "<" << cell->getParam(ID::Y_WIDTH).as_int() << ">(";
+			f << cell->type.substr(1);
+			if (is_extending_cell(cell->type))
+				f << '_' << (cell->getParam(ID::A_SIGNED).as_bool() ? 's' : 'u');
+			f << "<" << cell->getParam(ID::Y_WIDTH).as_int() << ">(";
 			dump_sigspec_rhs(cell->getPort(ID::A));
 			f << ")";
 		// Binary cells
 		} else if (is_binary_cell(cell->type)) {
-			f << cell->type.substr(1) << '_' <<
-			     (cell->getParam(ID::A_SIGNED).as_bool() ? 's' : 'u') <<
-			     (cell->getParam(ID::B_SIGNED).as_bool() ? 's' : 'u') <<
-			     "<" << cell->getParam(ID::Y_WIDTH).as_int() << ">(";
+			f << cell->type.substr(1);
+			if (is_extending_cell(cell->type))
+				f << '_' << (cell->getParam(ID::A_SIGNED).as_bool() ? 's' : 'u') <<
+				            (cell->getParam(ID::B_SIGNED).as_bool() ? 's' : 'u');
+			f << "<" << cell->getParam(ID::Y_WIDTH).as_int() << ">(";
 			dump_sigspec_rhs(cell->getPort(ID::A));
 			f << ", ";
 			dump_sigspec_rhs(cell->getPort(ID::B));