diff --git a/src/core_test/CMakeLists.txt b/src/core_test/CMakeLists.txt
index ee1eac8..4a7c11f 100644
--- a/src/core_test/CMakeLists.txt
+++ b/src/core_test/CMakeLists.txt
@@ -13,6 +13,7 @@ include_directories(${CMAKE_CURRENT_SOURCE_DIR})
 # ------------------------------------------------------------------------------------ #
 
 add_library(test_helper
+    helper/internal/block_num.cc
     helper/internal/concurrent.cc
     helper/internal/parallel.cc
     helper/internal/hash.cc
@@ -28,7 +29,6 @@ set(KLSK_TEST_CASES_SRC
     cases/all_cases.cc
     cases/group_union.cc
     cases/group.cc
-    cases/helper/block_num.cc
     cases/helper/group_impl.cc
 )
 
diff --git a/src/core_test/cases/group_union.cc b/src/core_test/cases/group_union.cc
index 1f7038b..77d6d87 100644
--- a/src/core_test/cases/group_union.cc
+++ b/src/core_test/cases/group_union.cc
@@ -1,16 +1,16 @@
 #include <gtest/gtest.h>
 
+#include <ranges>
 #include <cstdint>
 #include <algorithm>
 
-#include <ranges>
+#include "helper/cases.h"
+#include "helper/parallel.h"
+#include "helper/block_num.h"
 
 #include "group/group.h"
-#include "helper/cases.h"
 #include "common_code/common_code.h"
 
-#include "helper/parallel.h"
-
 using klotski::codec::ShortCode;
 
 using klotski::cases::Group;
@@ -93,7 +93,7 @@ TEST(GroupUnion, values) {
 TEST(GroupUnion, type_id) {
     ShortCode::speed_up(true);
     COMMON_CODE_PARALLEL({
-         auto type_id = to_type_id(cal_block_num(code.unwrap()));
+         auto type_id = to_type_id(helper::cal_block_num(code.unwrap()));
          EXPECT_EQ(GroupUnion::from_common_code(code).unwrap(), type_id);
          EXPECT_EQ(GroupUnion::from_raw_code(code.to_raw_code()).unwrap(), type_id);
          EXPECT_EQ(GroupUnion::from_short_code(code.to_short_code()).unwrap(), type_id);
diff --git a/src/core_test/cases/helper/cases.h b/src/core_test/cases/helper/cases.h
index ca3ab9e..f60d530 100644
--- a/src/core_test/cases/helper/cases.h
+++ b/src/core_test/cases/helper/cases.h
@@ -69,40 +69,6 @@ protected:
 
 // ----------------------------------------------------------------------------------------- //
 
-/// The number of blocks in one klotski layout.
-struct block_num_t {
-    int n_1x1; // 4-bit
-    int n_1x2; // 3-bit
-    int n_2x1; // 3-bit
-};
-
-template <>
-struct std::hash<block_num_t> {
-    size_t operator()(const block_num_t val) const noexcept {
-        return (val.n_1x1 << 6) ^ (val.n_1x2 << 3) ^ val.n_2x1;
-    }
-};
-
-constexpr bool operator==(const block_num_t &lhs, const block_num_t &rhs) {
-    return lhs.n_1x1 == rhs.n_1x1 && lhs.n_1x2 == rhs.n_1x2 && lhs.n_2x1 == rhs.n_2x1;
-}
-
-// ----------------------------------------------------------------------------------------- //
-
-/// Calculate the block number from Range.
-block_num_t cal_block_num(uint32_t range);
-
-/// Calculate type id value from the block number.
-uint32_t to_type_id(block_num_t block_num);
-
-/// Calculate the block number value from type id.
-block_num_t to_block_num(uint32_t type_id);
-
-/// Get all block number combinations without dependencies.
-const std::vector<block_num_t>& block_nums();
-
-// ----------------------------------------------------------------------------------------- //
-
 /// Get the type_id upper limit.
 uint32_t group_union_num();
 
diff --git a/src/core_test/cases/helper/group_impl.cc b/src/core_test/cases/helper/group_impl.cc
index ef08fb0..325557c 100644
--- a/src/core_test/cases/helper/group_impl.cc
+++ b/src/core_test/cases/helper/group_impl.cc
@@ -1,5 +1,7 @@
 #include "cases.h"
 
+#include "helper/block_num.h"
+
 // TODO: multi-threads builder
 
 /// Extend ordered Group from the specified CommonCode seed.
@@ -33,9 +35,9 @@ static std::vector<std::vector<CommonCode>> split_groups(std::vector<CommonCode>
 static const std::vector<std::vector<CommonCode>>& group_union_data() {
     static auto data = [] {
         std::vector<std::vector<CommonCode>> codes;
-        codes.resize(block_nums().size());
+        codes.resize(helper::block_nums().size());
         for (auto code: AllCases::instance().fetch().codes()) {
-            codes[to_type_id(cal_block_num(code.unwrap()))].emplace_back(code);
+            codes[to_type_id(helper::cal_block_num(code.unwrap()))].emplace_back(code);
         }
         return codes;
     }();
diff --git a/src/core_test/cases/ranges.cc b/src/core_test/cases/ranges.cc
index 75cc82a..fb9ef13 100644
--- a/src/core_test/cases/ranges.cc
+++ b/src/core_test/cases/ranges.cc
@@ -1,7 +1,9 @@
 #include <gtest/gtest.h>
 
-#include "group/group.h"
 #include "helper/cases.h"
+#include "helper/block_num.h"
+
+#include "group/group.h"
 #include "ranges/ranges.h"
 
 using klotski::range_reverse;
@@ -26,7 +28,7 @@ TEST(Ranges, spawn) {
         ranges.spawn(n, n_2x1, n_1x1);
         EXPECT_SORTED_AND_UNIQUE(ranges); // sorted and unique
         for (const auto range : ranges) {
-            const auto [val_1x1, val_1x2, val_2x1] = cal_block_num(range);
+            const auto [val_1x1, val_1x2, val_2x1] = helper::cal_block_num(range);
             EXPECT_EQ(val_1x1, n_1x1);
             EXPECT_EQ(val_2x1, n_2x1);
             EXPECT_EQ(val_1x2 + val_2x1, n); // verify block nums
diff --git a/src/core_test/helper/block_num.h b/src/core_test/helper/block_num.h
new file mode 100644
index 0000000..e726229
--- /dev/null
+++ b/src/core_test/helper/block_num.h
@@ -0,0 +1,48 @@
+#pragma once
+
+#include <cstdint>
+
+// ----------------------------------------------------------------------------------------- //
+
+namespace helper {
+
+struct block_num_t {
+    int n_1x1; // 4-bit
+    int n_1x2; // 3-bit
+    int n_2x1; // 3-bit
+};
+
+constexpr bool operator==(const block_num_t &lhs, const block_num_t &rhs) {
+    return lhs.n_1x1 == rhs.n_1x1
+        && lhs.n_1x2 == rhs.n_1x2
+        && lhs.n_2x1 == rhs.n_2x1;
+}
+
+/// Calculate the block number from Range.
+block_num_t cal_block_num(uint32_t range);
+
+/// Calculate type id value from the block number.
+uint32_t to_type_id(block_num_t block_num);
+
+/// Calculate the block number value from type id.
+block_num_t to_block_num(uint32_t type_id);
+
+/// Get all block number combinations without dependencies.
+const std::vector<block_num_t>& block_nums();
+
+} // namespace helper
+
+// ----------------------------------------------------------------------------------------- //
+
+namespace std {
+
+template <>
+struct std::hash<helper::block_num_t> {
+    size_t operator()(const helper::block_num_t val) const noexcept {
+        return (val.n_1x1 << 6) ^ (val.n_1x2 << 3) ^ val.n_2x1;
+    }
+};
+
+} // namespace std
+
+// ----------------------------------------------------------------------------------------- //
diff --git a/src/core_test/cases/helper/block_num.cc b/src/core_test/helper/internal/block_num.cc
similarity index 76%
rename from src/core_test/cases/helper/block_num.cc
rename to src/core_test/helper/internal/block_num.cc
index d68d29d..fb38320 100644
--- a/src/core_test/cases/helper/block_num.cc
+++ b/src/core_test/helper/internal/block_num.cc
@@ -1,9 +1,12 @@
 #include <ranges>
 #include <vector>
+#include <algorithm>
 #include <unordered_map>
 
-#include "cases.h"
+#include "ranges/ranges.h"
+#include "helper/block_num.h"
 
+using helper::block_num_t;
 using klotski::range_reverse;
 
 /// Build the sequence list of all block numbers.
@@ -33,18 +36,18 @@ static std::vector<block_num_t> build_block_nums() {
 /// Build the mapping table from block_num to type_id.
 static std::unordered_map<block_num_t, uint32_t> build_type_id_map() {
     std::unordered_map<block_num_t, uint32_t> ids;
-    for (uint64_t i = 0; i < block_nums().size(); ++i) {
-        ids.emplace(block_nums()[i], i); // TODO: using `std::views::enumerate`
+    for (uint64_t i = 0; i < helper::block_nums().size(); ++i) {
+        ids.emplace(helper::block_nums()[i], i); // TODO: using `std::views::enumerate`
     }
     return ids;
 }
 
-const std::vector<block_num_t>& block_nums() {
+const std::vector<block_num_t>& helper::block_nums() {
     static auto data = build_block_nums();
     return data;
 }
 
-block_num_t cal_block_num(uint32_t range) {
+block_num_t helper::cal_block_num(uint32_t range) {
     block_num_t result {};
     for (range = range_reverse(range); range; range >>= 2) {
         switch (range & 0b11) {
@@ -63,14 +66,14 @@ block_num_t cal_block_num(uint32_t range) {
     return result;
 }
 
-block_num_t to_block_num(const uint32_t type_id) {
-    if (type_id < block_nums().size()) {
-        return block_nums()[type_id];
+block_num_t helper::to_block_num(const uint32_t type_id) {
+    if (type_id < helper::block_nums().size()) {
+        return helper::block_nums()[type_id];
     }
     std::abort();
 }
 
-uint32_t to_type_id(const block_num_t block_num) {
+uint32_t helper::to_type_id(const block_num_t block_num) {
     static auto data = build_type_id_map();
     if (const auto match = data.find(block_num); match != data.end()) {
         return match->second;