When I use the following configuration (in order to build a 32-bit Python a 64-bit OS):
  ./configure --with-computed-gotos CFLAGS=-m32 LDFLAGS=-m32

I then get two failures in test_distutils:

test_build_ext (distutils.tests.test_build_ext.BuildExtTestCase) ... /tmp/tmpssz80G/tmp/tmpssz80G/xxmodule.o: could not read symbols: File in wrong format
collect2: ld a retourné 1 code d'état d'exécution
ERROR
[...]
test_get_outputs (distutils.tests.test_build_ext.BuildExtTestCase) ... /tmp/tmphxwa1S/tempt/tmp/tmpuD17us/foo.o: could not read symbols: File in wrong format
collect2: ld a retourné 1 code d'état d'exécution
ERROR
[...]

======================================================================
ERROR: test_build_ext (distutils.tests.test_build_ext.BuildExtTestCase)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/antoine/py3k/m32/Lib/distutils/unixccompiler.py", line 254, in link
    self.spawn(linker + ld_args)
  File "/home/antoine/py3k/m32/Lib/distutils/ccompiler.py", line 909, in spawn
    spawn(cmd, dry_run=self.dry_run)
  File "/home/antoine/py3k/m32/Lib/distutils/spawn.py", line 34, in spawn
    _spawn_posix(cmd, search_path, dry_run=dry_run)
  File "/home/antoine/py3k/m32/Lib/distutils/spawn.py", line 138, in _spawn_posix
    % (cmd[0], exit_status))
distutils.errors.DistutilsExecError: command 'gcc' failed with exit status 1

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/home/antoine/py3k/m32/Lib/distutils/tests/test_build_ext.py", line 65, in test_build_ext
    cmd.run()
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 347, in run
    self.build_extensions()
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 456, in build_extensions
    self.build_extension(ext)
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 543, in build_extension
    target_lang=language)
  File "/home/antoine/py3k/m32/Lib/distutils/ccompiler.py", line 719, in link_shared_object
    extra_preargs, extra_postargs, build_temp, target_lang)
  File "/home/antoine/py3k/m32/Lib/distutils/unixccompiler.py", line 256, in link
    raise LinkError(msg)
distutils.errors.LinkError: command 'gcc' failed with exit status 1

======================================================================
ERROR: test_get_outputs (distutils.tests.test_build_ext.BuildExtTestCase)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/antoine/py3k/m32/Lib/distutils/unixccompiler.py", line 254, in link
    self.spawn(linker + ld_args)
  File "/home/antoine/py3k/m32/Lib/distutils/ccompiler.py", line 909, in spawn
    spawn(cmd, dry_run=self.dry_run)
  File "/home/antoine/py3k/m32/Lib/distutils/spawn.py", line 34, in spawn
    _spawn_posix(cmd, search_path, dry_run=dry_run)
  File "/home/antoine/py3k/m32/Lib/distutils/spawn.py", line 138, in _spawn_posix
    % (cmd[0], exit_status))
distutils.errors.DistutilsExecError: command 'gcc' failed with exit status 1

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/home/antoine/py3k/m32/Lib/distutils/tests/test_build_ext.py", line 321, in test_get_outputs
    cmd.run()
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 347, in run
    self.build_extensions()
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 456, in build_extensions
    self.build_extension(ext)
  File "/home/antoine/py3k/m32/Lib/distutils/command/build_ext.py", line 543, in build_extension
    target_lang=language)
  File "/home/antoine/py3k/m32/Lib/distutils/ccompiler.py", line 719, in link_shared_object
    extra_preargs, extra_postargs, build_temp, target_lang)
  File "/home/antoine/py3k/m32/Lib/distutils/unixccompiler.py", line 256, in link
    raise LinkError(msg)
distutils.errors.LinkError: command 'gcc' failed with exit status 1