diff --git a/src/core_test/CMakeLists.txt b/src/core_test/CMakeLists.txt
index e9f174e..581d8ff 100644
--- a/src/core_test/CMakeLists.txt
+++ b/src/core_test/CMakeLists.txt
@@ -19,6 +19,7 @@ set(KLSK_TEST_CASES_SRC
     cases/all_cases.cc
     cases/group_union.cc
     cases/group.cc
+    cases/helper/helper.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 84ddd00..f2b1fe6 100644
--- a/src/core_test/cases/group_union.cc
+++ b/src/core_test/cases/group_union.cc
@@ -17,44 +17,42 @@ using klotski::cases::GroupUnion;
 using klotski::cases::TYPE_ID_LIMIT;
 using klotski::cases::ALL_GROUP_NUM;
 
+#define EXPECT_IOTA(R)           \
+    EXPECT_FALSE(R.empty());     \
+    EXPECT_EQ(R.front(), 0);     \
+    EXPECT_SORTED_AND_UNIQUE(R); \
+    EXPECT_EQ(R.back(), R.size() - 1)
+
 TEST(GroupUnion, basic) {
 
-    // TODO: loop for all
-    EXPECT_TRUE(GroupUnion::create(0).has_value());
-    EXPECT_EQ(GroupUnion::create(0).value().unwrap(), 0);
     EXPECT_FALSE(GroupUnion::create(TYPE_ID_LIMIT).has_value());
 
-    EXPECT_EQ(GroupUnion::unsafe_create(0).unwrap(), 0);
-
-    for (uint32_t type_id = 0; type_id < TYPE_ID_LIMIT; ++type_id) {
-        auto group_union = GroupUnion::unsafe_create(type_id);
+    type_id_parallel([](uint32_t type_id) {
 
-        auto num = group_union.group_num();
+        EXPECT_TRUE(GroupUnion::create(type_id).has_value());
+        EXPECT_EQ(GroupUnion::create(type_id).value().unwrap(), type_id);
+        EXPECT_EQ(GroupUnion::unsafe_create(type_id).unwrap(), type_id);
 
+        auto group_union = GroupUnion::unsafe_create(type_id);
         auto groups = group_union.groups();
-        for (auto x : groups) {
-            EXPECT_EQ(x.type_id(), type_id);
-        }
-        // TODO: add EXPECT_IOTA(...)
-//        auto group_ids = groups | std::ranges::transform([](Group x) { return x.group_id(); });
-        std::vector<uint32_t> group_ids;
-        group_ids.reserve(groups.size());
-        for (auto x : groups) {
-            group_ids.emplace_back(x.group_id());
+        for (const auto group : groups) {
+            EXPECT_EQ(group.type_id(), type_id);
         }
-        EXPECT_SORTED_AND_UNIQUE(group_ids);
-        EXPECT_EQ(group_ids[0], 0);
-        EXPECT_EQ(group_ids[num - 1], num - 1);
-        EXPECT_EQ(group_ids.size(), num);
 
-        // TODO: test all
-        EXPECT_TRUE(group_union.group(0).has_value());
-        EXPECT_EQ(group_union.group(0).value().type_id(), type_id);
-        EXPECT_EQ(group_union.group(0).value().group_id(), 0);
+        auto group_ids = groups | std::views::transform([](Group g) {
+            return g.group_id();
+        }) | std::ranges::to<std::vector>();
+        EXPECT_IOTA(group_ids);
 
-        EXPECT_FALSE(group_union.group(num).has_value());
-    }
+        for (auto group_id : group_ids) {
+            EXPECT_TRUE(group_union.group(group_id).has_value());
+            EXPECT_EQ(group_union.group(group_id).value().type_id(), type_id);
+            EXPECT_EQ(group_union.group(group_id).value().group_id(), group_id);
+        }
+
+        EXPECT_FALSE(group_union.group(group_ids.size()).has_value());
 
+    });
 }
 
 TEST(GroupUnion, constant) {
@@ -63,68 +61,58 @@ TEST(GroupUnion, constant) {
 
     // TODO: verify from local builder
 
-    EXPECT_EQ(TYPE_ID_LIMIT, group_union_num());
+    // TODO: verify TYPE_ID_LIMIT / ALL_GROUP_NUM data
 
-}
+    // TODO: verify GROUP_UNION_SIZE (size) / GROUP_NUM (group_num) / MAX_GROUP_SIZE (max_group_size)
+    //       test from member function directly?
 
-TEST(GroupUnion, size) {
-    for (uint32_t type_id = 0; type_id < TYPE_ID_LIMIT; ++type_id) {
-        auto &kk = group_union_cases(type_id);
-        EXPECT_EQ(GroupUnion::unsafe_create(type_id).size(), kk.size());
-    }
-}
+    EXPECT_EQ(TYPE_ID_LIMIT, group_union_num());
 
-TEST(GroupUnion, group_num) {
-    for (uint32_t type_id = 0; type_id < TYPE_ID_LIMIT; ++type_id) {
-        EXPECT_EQ(GroupUnion::unsafe_create(type_id).group_num(), group_num(type_id));
-    }
 }
 
-TEST(GroupUnion, cases) {
-    for (uint32_t type_id = 0; type_id < klotski::cases::TYPE_ID_LIMIT; ++type_id) {
-        auto cases = group_union_cases(type_id);
-        EXPECT_EQ(cases, GroupUnion::unsafe_create(type_id).cases().codes());
-    }
-}
+TEST(GroupUnion, values) {
 
-// TODO: test max_group_size
+    type_id_parallel([](uint32_t type_id) {
 
-TEST(GroupUnion, max_group_size) {
-    for (uint32_t type_id = 0; type_id < klotski::cases::TYPE_ID_LIMIT; ++type_id) {
+        auto &kk = group_union_cases(type_id);
+        EXPECT_EQ(GroupUnion::unsafe_create(type_id).size(), kk.size());
+        EXPECT_EQ(GroupUnion::unsafe_create(type_id).group_num(), group_num(type_id));
 
         auto groups = GroupUnion::unsafe_create(type_id).groups();
 
-        auto sizes = groups | std::views::transform([](Group group) {
+        auto kk_view = groups | std::views::transform([](Group group) {
             return group.size();
-        }) | std::ranges::to<std::vector>();
+        });
 
-//        std::cout << std::format("{} -> {}\n", type_id, sizes);
+        auto max_it = *std::ranges::max_element(kk_view);
 
-        auto max_item = *std::max_element(sizes.begin(), sizes.end()); // TODO: using std::ranges
+        EXPECT_EQ(GroupUnion::unsafe_create(type_id).max_group_size(), max_it);
 
-        EXPECT_EQ(GroupUnion::unsafe_create(type_id).max_group_size(), max_item);
+    });
 
-    }
 }
 
-TEST(GroupUnion, type_id) {
+TEST(GroupUnion, cases) {
+    type_id_parallel([](uint32_t type_id) {
+        auto cases = group_union_cases(type_id);
+        EXPECT_EQ(cases, GroupUnion::unsafe_create(type_id).cases().codes());
+    });
+}
 
+TEST(GroupUnion, type_id) {
     ShortCode::speed_up(true);
 
+    // TODO: using `common_code_parallel`
     for (uint64_t head = 0; head < 16; ++head) {
         for (const auto range : AllCases::instance().fetch()[head]) {
-
             auto common_code = CommonCode::unsafe_create(head << 32 | range);
             auto short_code = common_code.to_short_code();
             auto raw_code = common_code.to_raw_code();
 
             auto expect = to_type_id(cal_block_num(range));
-
-            EXPECT_EQ(GroupUnion::from_common_code(common_code).unwrap(), expect);
-            EXPECT_EQ(GroupUnion::from_short_code(short_code).unwrap(), expect);
             EXPECT_EQ(GroupUnion::from_raw_code(raw_code).unwrap(), expect);
-
+            EXPECT_EQ(GroupUnion::from_short_code(short_code).unwrap(), expect);
+            EXPECT_EQ(GroupUnion::from_common_code(common_code).unwrap(), expect);
         }
     }
-
 }
diff --git a/src/core_test/cases/helper/cases.h b/src/core_test/cases/helper/cases.h
index 685873b..de76804 100644
--- a/src/core_test/cases/helper/cases.h
+++ b/src/core_test/cases/helper/cases.h
@@ -116,3 +116,5 @@ const std::vector<CommonCode>& group_union_cases(uint32_t type_id);
 const std::vector<CommonCode>& group_cases(uint32_t type_id, uint32_t group_id);
 
 // ----------------------------------------------------------------------------------------- //
+
+void type_id_parallel(std::function<void(uint32_t type_id)> &&func);
diff --git a/src/core_test/cases/helper/helper.cc b/src/core_test/cases/helper/helper.cc
new file mode 100644
index 0000000..313b770
--- /dev/null
+++ b/src/core_test/cases/helper/helper.cc
@@ -0,0 +1,22 @@
+#include <gtest/gtest.h>
+
+#include "cases.h"
+
+using klotski::cases::TYPE_ID_LIMIT;
+
+void type_id_parallel(std::function<void(uint32_t type_id)> &&func) {
+
+    BS::thread_pool pool;
+
+    // TODO: using `detach_sequence`
+    for (uint32_t type_id = 0; type_id < TYPE_ID_LIMIT; ++type_id) {
+
+        pool.detach_task([type_id, func = std::move(func)]() {
+            func(type_id);
+        });
+
+    }
+
+    pool.wait();
+
+}