diff --git a/Makefile b/Makefile
index 8f3e473ea..8a72e3c70 100644
--- a/Makefile
+++ b/Makefile
@@ -888,6 +888,7 @@ endif
 	+cd tests/verilog && bash run-test.sh
 	+cd tests/xprop && bash run-test.sh $(SEEDOPT)
 	+cd tests/fmt && bash run-test.sh
+	+cd tests/cxxrtl && bash run-test.sh
 	@echo ""
 	@echo "  Passed \"make test\"."
 	@echo ""
diff --git a/backends/cxxrtl/runtime/cxxrtl/cxxrtl.h b/backends/cxxrtl/runtime/cxxrtl/cxxrtl.h
index 2d5451287..d861b7e07 100644
--- a/backends/cxxrtl/runtime/cxxrtl/cxxrtl.h
+++ b/backends/cxxrtl/runtime/cxxrtl/cxxrtl.h
@@ -419,6 +419,7 @@ struct value : public expr_base<value<Bits>> {
 			carry = (shift_bits == 0) ? 0
 				: data[n] >> (chunk::bits - shift_bits);
 		}
+		result.data[result.chunks - 1] &= result.msb_mask;
 		return result;
 	}
 
@@ -429,12 +430,12 @@ struct value : public expr_base<value<Bits>> {
 		// Detect shifts definitely large than Bits early.
 		for (size_t n = 1; n < amount.chunks; n++)
 			if (amount.data[n] != 0)
-				return {};
+				return (Signed && is_neg()) ? value<Bits>().bit_not() : value<Bits>();
 		// Past this point we can use the least significant chunk as the shift size.
 		size_t shift_chunks = amount.data[0] / chunk::bits;
 		size_t shift_bits   = amount.data[0] % chunk::bits;
 		if (shift_chunks >= chunks)
-			return {};
+			return (Signed && is_neg()) ? value<Bits>().bit_not() : value<Bits>();
 		value<Bits> result;
 		chunk::type carry = 0;
 		for (size_t n = 0; n < chunks - shift_chunks; n++) {
@@ -443,12 +444,13 @@ struct value : public expr_base<value<Bits>> {
 				: data[chunks - 1 - n] << (chunk::bits - shift_bits);
 		}
 		if (Signed && is_neg()) {
-			size_t top_chunk_idx  = (Bits - shift_bits) / chunk::bits;
-			size_t top_chunk_bits = (Bits - shift_bits) % chunk::bits;
+			size_t top_chunk_idx  = amount.data[0] > Bits ? 0 : (Bits - amount.data[0]) / chunk::bits;
+			size_t top_chunk_bits = amount.data[0] > Bits ? 0 : (Bits - amount.data[0]) % chunk::bits;
 			for (size_t n = top_chunk_idx + 1; n < chunks; n++)
 				result.data[n] = chunk::mask;
-			if (shift_bits != 0)
+			if (amount.data[0] != 0)
 				result.data[top_chunk_idx] |= chunk::mask << top_chunk_bits;
+			result.data[result.chunks - 1] &= result.msb_mask;
 		}
 		return result;
 	}
@@ -509,7 +511,8 @@ struct value : public expr_base<value<Bits>> {
 		for (size_t n = 0; n < chunks; n++) {
 			chunk::type x = data[chunks - 1 - n];
 			// First add to `count` as if the chunk is zero
-			count += (n == 0 ? Bits % chunk::bits : chunk::bits);
+			constexpr size_t msb_chunk_bits = Bits % chunk::bits != 0 ? Bits % chunk::bits : chunk::bits;
+			count += (n == 0 ? msb_chunk_bits : chunk::bits);
 			// If the chunk isn't zero, correct the `count` value and return
 			if (x != 0) {
 				for (; x != 0; count--)
diff --git a/tests/cxxrtl/.gitignore b/tests/cxxrtl/.gitignore
new file mode 100644
index 000000000..91caee986
--- /dev/null
+++ b/tests/cxxrtl/.gitignore
@@ -0,0 +1 @@
+cxxrtl-test-*
diff --git a/tests/cxxrtl/run-test.sh b/tests/cxxrtl/run-test.sh
new file mode 100755
index 000000000..89de71c6b
--- /dev/null
+++ b/tests/cxxrtl/run-test.sh
@@ -0,0 +1,13 @@
+#!/bin/bash
+
+set -ex
+
+run_subtest () {
+    local subtest=$1; shift
+
+    ${CC:-gcc} -std=c++11 -O2 -o cxxrtl-test-${subtest} -I../../backends/cxxrtl/runtime test_${subtest}.cc -lstdc++
+    ./cxxrtl-test-${subtest}
+}
+
+run_subtest value
+run_subtest value_fuzz
diff --git a/tests/cxxrtl/test_value.cc b/tests/cxxrtl/test_value.cc
new file mode 100644
index 000000000..4d68372bb
--- /dev/null
+++ b/tests/cxxrtl/test_value.cc
@@ -0,0 +1,45 @@
+#include <cassert>
+#include <cstdint>
+
+#include "cxxrtl/cxxrtl.h"
+
+int main()
+{
+    {
+        // shl exceeding Bits should be masked
+        cxxrtl::value<6> a(1u);
+        cxxrtl::value<6> b(8u);
+        cxxrtl::value<6> c = a.shl(b);
+        assert(c.get<uint64_t>() == 0);
+    }
+
+    {
+        // sshr of unreasonably large size should sign extend correctly
+        cxxrtl::value<64> a(0u, 0x80000000u);
+        cxxrtl::value<64> b(0u, 1u);
+        cxxrtl::value<64> c = a.sshr(b);
+        assert(c.get<uint64_t>() == 0xffffffffffffffffu);
+    }
+
+    {
+        // sshr of exteeding Bits should sign extend correctly
+        cxxrtl::value<8> a(0x80u);
+        cxxrtl::value<8> b(10u);
+        cxxrtl::value<8> c = a.sshr(b);
+        assert(c.get<uint64_t>() == 0xffu);
+    }
+
+    {
+        // Sign extension should occur correctly
+        cxxrtl::value<64> a(0x23456789u, 0x8abcdef1u);
+        cxxrtl::value<8> b(32u);
+        cxxrtl::value<64> c = a.sshr(b);
+        assert(c.get<uint64_t>() == 0xffffffff8abcdef1u);
+    }
+
+    {
+        // ctlz should work with Bits that are a multiple of chunk size
+        cxxrtl::value<32> a(0x00040000u);
+        assert(a.ctlz() == 13);
+    }
+}
diff --git a/tests/cxxrtl/test_value_fuzz.cc b/tests/cxxrtl/test_value_fuzz.cc
new file mode 100644
index 000000000..4428e9f6e
--- /dev/null
+++ b/tests/cxxrtl/test_value_fuzz.cc
@@ -0,0 +1,251 @@
+#include <cstddef>
+#include <cstdint>
+#include <cstdio>
+#include <exception>
+#include <limits>
+#include <random>
+#include <type_traits>
+
+#include "cxxrtl/cxxrtl.h"
+
+template<typename T>
+T rand_int(T min = std::numeric_limits<T>::min(), T max = std::numeric_limits<T>::max())
+{
+	static_assert(std::is_integral<T>::value, "T must be an integral type.");
+	static_assert(!std::is_same<T, signed char>::value && !std::is_same<T, unsigned char>::value,
+			  "Using char with uniform_int_distribution is undefined behavior.");
+
+	static std::mt19937 generator = [] {
+		std::random_device rd;
+		std::mt19937 mt{rd()};
+		return mt;
+	}();
+
+	std::uniform_int_distribution<T> dist(min, max);
+	return dist(generator);
+}
+
+struct BinaryOperationBase
+{
+	void tweak_input(uint64_t &a, uint64_t &b) {}
+};
+
+template<size_t Bits, typename Operation>
+void test_binary_operation_for_bitsize(Operation &op)
+{
+	constexpr int iteration_count = 10000000;
+
+	constexpr uint64_t mask = std::numeric_limits<uint64_t>::max() >> (64 - Bits);
+
+	using chunk_type = typename cxxrtl::value<Bits>::chunk::type;
+	constexpr size_t chunk_bits = cxxrtl::value<Bits>::chunk::bits;
+
+	for (int iteration = 0; iteration < iteration_count; iteration++) {
+		uint64_t ia = rand_int<uint64_t>() >> (64 - Bits);
+		uint64_t ib = rand_int<uint64_t>() >> (64 - Bits);
+		op.tweak_input(ia, ib);
+
+		cxxrtl::value<Bits> va, vb;
+		for (size_t i = 0; i * chunk_bits < Bits; i++) {
+			va.data[i] = (chunk_type)(ia >> (i * chunk_bits));
+			vb.data[i] = (chunk_type)(ib >> (i * chunk_bits));
+		}
+
+		uint64_t iresult = op.reference_impl(Bits, ia, ib) & mask;
+		cxxrtl::value<Bits> vresult = op.template testing_impl<Bits>(va, vb);
+
+		for (size_t i = 0; i * chunk_bits < Bits; i++) {
+			if ((chunk_type)(iresult >> (i * chunk_bits)) != vresult.data[i]) {
+				std::printf("Test failure:\n");
+				std::printf("Bits:    %i\n", Bits);
+				std::printf("a:       %016lx\n", ia);
+				std::printf("b:       %016lx\n", ib);
+				std::printf("iresult: %016lx\n", iresult);
+				std::printf("vresult: %016lx\n", vresult.template get<uint64_t>());
+
+				std::terminate();
+			}
+		}
+	}
+	std::printf("Test passed @ Bits = %i.\n", Bits);
+}
+
+template<typename Operation>
+void test_binary_operation(Operation &op)
+{
+	// Test at a variety of bitwidths
+	test_binary_operation_for_bitsize<8>(op);
+	test_binary_operation_for_bitsize<32>(op);
+	test_binary_operation_for_bitsize<42>(op);
+	test_binary_operation_for_bitsize<63>(op);
+	test_binary_operation_for_bitsize<64>(op);
+}
+
+template<typename Operation>
+struct UnaryOperationWrapper : BinaryOperationBase 
+{
+	Operation &op;
+
+	UnaryOperationWrapper(Operation &op) : op(op) {}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		return op.reference_impl(bits, a);
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return op.template testing_impl<Bits>(a);
+	}
+};
+
+template<typename Operation>
+void test_unary_operation(Operation &op)
+{
+	UnaryOperationWrapper<Operation> wrapped(op);
+	test_binary_operation(wrapped);
+}
+
+struct ShlTest : BinaryOperationBase 
+{
+	ShlTest()
+	{
+		std::printf("Randomized tests for value::shl:\n");
+		test_binary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		return b >= 64 ? 0 : a << b;
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return a.shl(b);
+	}
+
+	void tweak_input(uint64_t &, uint64_t &b)
+	{
+		b &= 0x7f;
+	}
+} shl;
+
+struct ShrTest : BinaryOperationBase 
+{
+	ShrTest()
+	{
+		std::printf("Randomized tests for value::shr:\n");
+		test_binary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		return b >= 64 ? 0 : a >> b;
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return a.shr(b);
+	}
+
+	void tweak_input(uint64_t &, uint64_t &b)
+	{
+		b &= 0x7f;
+	}
+} shr;
+
+struct SshrTest : BinaryOperationBase 
+{
+	SshrTest()
+	{
+		std::printf("Randomized tests for value::sshr:\n");
+		test_binary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		int64_t sa = (int64_t)(a << (64 - bits));
+		return sa >> (b >= bits ? 63 : (b + 64 - bits));
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return a.sshr(b);
+	}
+
+	void tweak_input(uint64_t &, uint64_t &b)
+	{
+		b &= 0x7f;
+	}
+} sshr;
+
+struct AddTest : BinaryOperationBase 
+{
+	AddTest()
+	{
+		std::printf("Randomized tests for value::add:\n");
+		test_binary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		return a + b;
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return a.add(b);
+	}
+} add;
+
+struct SubTest : BinaryOperationBase 
+{
+	SubTest()
+	{
+		std::printf("Randomized tests for value::sub:\n");
+		test_binary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a, uint64_t b)
+	{
+		return a - b;
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a, cxxrtl::value<Bits> b)
+	{
+		return a.sub(b);
+	}
+} sub;
+
+struct CtlzTest
+{
+	CtlzTest()
+	{
+		std::printf("Randomized tests for value::ctlz:\n");
+		test_unary_operation(*this);
+	}
+
+	uint64_t reference_impl(size_t bits, uint64_t a)
+	{
+		if (a == 0)
+			return bits;
+		return __builtin_clzl(a) - (64 - bits);
+	}
+
+	template<size_t Bits>
+	cxxrtl::value<Bits> testing_impl(cxxrtl::value<Bits> a)
+	{
+		size_t result = a.ctlz();
+		return cxxrtl::value<Bits>((cxxrtl::chunk_t)result);
+	}
+} ctlz;
+
+int main()
+{
+}