apacheGH-43536: [Python] Declare support for free-threading in Cython

This is done by passing an extra flag when building the Cython extension
modules. It is needed so that the GIL is not dynamically reenabled
when importing `pyarrow.lib`.

cpp/cmake_modules/UseCython.cmake

@@ -184,4 +184,24 @@ function(cython_add_module _name pyx_target_name generated_files)
   add_dependencies(${_name} ${pyx_target_name})
 endfunction()
 
+execute_process(COMMAND ${PYTHON_EXECUTABLE} -m cython --version
+                OUTPUT_VARIABLE CYTHON_version_output
+                ERROR_VARIABLE CYTHON_version_error
+                RESULT_VARIABLE CYTHON_version_result
+                OUTPUT_STRIP_TRAILING_WHITESPACE
+                ERROR_STRIP_TRAILING_WHITESPACE)
+if(NOT ${CYTHON_version_result} EQUAL 0)
+  set(_error_msg "Command \"${PYTHON_EXECUTABLE} -m cython --version\" failed with")
+  set(_error_msg "${_error_msg} output:\n${CYTHON_version_error}")
+  message(SEND_ERROR "${_error_msg}")
+else()
+  if("${CYTHON_version_output}" MATCHES "^[Cc]ython version ([^,]+)")
+    set(CYTHON_VERSION "${CMAKE_MATCH_1}")
+  else()
+    if("${CYTHON_version_error}" MATCHES "^[Cc]ython version ([^,]+)")
+      set(CYTHON_VERSION "${CMAKE_MATCH_1}")
+    endif()
+  endif()
+endif()
+
 include(CMakeParseArguments)

python/CMakeLists.txt

@@ -260,6 +260,7 @@ message(STATUS "Found NumPy version: ${Python3_NumPy_VERSION}")
 message(STATUS "NumPy include dir: ${NUMPY_INCLUDE_DIRS}")
 
 include(UseCython)
+message(STATUS "Found Cython version: ${CYTHON_VERSION}")
 
 # Arrow C++ and set default PyArrow build options
 include(GNUInstallDirs)
@@ -855,6 +856,10 @@ set(CYTHON_FLAGS "${CYTHON_FLAGS}" "--warning-errors")
 # undocumented Cython feature.
 set(CYTHON_FLAGS "${CYTHON_FLAGS}" "--no-c-in-traceback")
 
+if(CYTHON_VERSION VERSION_GREATER_EQUAL "3.1.0a0")
+  set(CYTHON_FLAGS "${CYTHON_FLAGS}" "-Xfreethreading_compatible=True")
+endif()
+
 foreach(module ${CYTHON_EXTENSIONS})
   string(REPLACE "." ";" directories ${module})
   list(GET directories -1 module_name)