diff --git a/CMakeLists.txt b/CMakeLists.txt
index 46123f56e..8e1b27826 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -473,7 +473,7 @@ install(
   LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
   )
 install(
-  DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}/include/ctranslate2"
+  DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}/include/"
   DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}
   FILES_MATCHING PATTERN "*.h*"
   )
diff --git a/include/ctranslate2/types.h b/include/ctranslate2/types.h
index 025e63dff..906b3b362 100644
--- a/include/ctranslate2/types.h
+++ b/include/ctranslate2/types.h
@@ -3,11 +3,14 @@
 #include <cstdint>
 #include <string>
 
+#include <half_float/half.hpp>
+
 #include "devices.h"
 
 namespace ctranslate2 {
 
   using dim_t = int64_t;  // This type should be signed.
+  using float16_t = half_float::half;
 
   enum class DataType {
     FLOAT,
diff --git a/third_party/half_float/half.hpp b/include/half_float/half.hpp
similarity index 100%
rename from third_party/half_float/half.hpp
rename to include/half_float/half.hpp
diff --git a/src/cuda/helpers.h b/src/cuda/helpers.h
index d980d80fa..581fa7ef9 100644
--- a/src/cuda/helpers.h
+++ b/src/cuda/helpers.h
@@ -7,7 +7,6 @@
 #include "ctranslate2/types.h"
 
 #include "utils.h"
-#include "type_dispatch.h"
 
 #if !defined(__CUDACC__) || !defined(__CUDA_ARCH__) || __CUDA_ARCH__ >= 530
 #  define CUDA_CAN_USE_HALF 1
diff --git a/src/ops/multinomial_cpu.cc b/src/ops/multinomial_cpu.cc
index 4d0b35600..7f29c78b3 100644
--- a/src/ops/multinomial_cpu.cc
+++ b/src/ops/multinomial_cpu.cc
@@ -2,8 +2,6 @@
 
 #include "ctranslate2/random.h"
 
-#include "type_dispatch.h"
-
 namespace ctranslate2 {
   namespace ops {
 
diff --git a/src/ops/multinomial_gpu.cu b/src/ops/multinomial_gpu.cu
index 3de7618e7..e01f64f35 100644
--- a/src/ops/multinomial_gpu.cu
+++ b/src/ops/multinomial_gpu.cu
@@ -3,7 +3,6 @@
 #include <cub/block/block_reduce.cuh>
 #include <cub/block/block_scan.cuh>
 
-#include "type_dispatch.h"
 #include "cuda/helpers.h"
 #include "cuda/random.h"
 
diff --git a/src/type_dispatch.h b/src/type_dispatch.h
index 2f8d23eba..ffe1720fb 100644
--- a/src/type_dispatch.h
+++ b/src/type_dispatch.h
@@ -1,13 +1,9 @@
 #pragma once
 
-#include <half_float/half.hpp>
-
 #include "ctranslate2/types.h"
 
 namespace ctranslate2 {
 
-  using float16_t = half_float::half;
-
   // Inspired by
   // https://github.com/tensorflow/tensorflow/blob/master/tensorflow/core/framework/types.h
   // for matching enum values and C++ types.
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index eb4c02856..8633faf29 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -16,7 +16,6 @@ add_executable(ctranslate2_test
   test.cc)
 target_include_directories(ctranslate2_test PRIVATE
   ${CMAKE_CURRENT_SOURCE_DIR}/../src
-  ${CMAKE_CURRENT_SOURCE_DIR}/../third_party
   )
 target_link_libraries(ctranslate2_test
   ${PROJECT_NAME}