>  File ".../Lib/test/test_time.py", line 351, in test_mktime
>    self.assertEqual(time.mktime(tt), t)
> OverflowError: mktime argument out of range

I don't know which values are "out of range". But I guess that the test fails because of t=-1, which would mean that tm_wday field is not modified by mktime().

I don't know if mktime() does really not support t=-1, or if we should use another sentinel. The original patch to fix this issue (support t=-1, issue #1726687) used tm_wday=42 instead of tm_wday=-1:

+	/* invalid value that will not be changed if there is an error. */
+	buf.tm_wday = 42;
 	tt = mktime(&buf);
-	if (tt == (time_t)(-1)) {
+	if ((tt == (time_t)(-1)) && (buf.tm_wday == 42)) {
 		PyErr_SetString(PyExc_OverflowError,
 				"mktime argument out of range");
 		return NULL;

The current code uses:

    buf.tm_wday = -1;  /* sentinel; original value ignored */                   
    tt = mktime(&buf);                                                          
    /* Return value of -1 does not necessarily mean an error, but tm_wday       
     * cannot remain set to -1 if mktime succedded. */                          
    if (tt == (time_t)(-1) && buf.tm_wday == -1) {                              
        PyErr_SetString(PyExc_OverflowError,                                    
                        "mktime argument out of range");                        
        return NULL;                                                            
    }                 


>  File ".../Lib/test/test_time.py", line 337, in test_negative
>    self.assertIn(text, ('-1', '-001'))
> AssertionError: '000/' not found in ('-1', '-001')

AIX doesn't support negative tm_year value. It should be added to the timemodule blacklist (#ifdef):

#if defined(_MSC_VER) || defined(sun)
    if (buf.tm_year + 1900 < 1 || 9999 < buf.tm_year + 1900) {
        PyErr_Format(PyExc_ValueError,
                     "strftime() requires year in [1; 9999]",
                     buf.tm_year + 1900);
        return NULL;
    }
#endif

I don't know if there is a reliable C define to check if the current OS is AIX (something like #ifdef sun). Python configure script checks if "uname -s" output starts with "AIX". We should maybe add a Python define in pyconfig.h using the configure script.