I propose that we add three singletons to the float implementation:

PyFloat_NaN
PyFloat_Inf
PyFloat_NegInf

The singletons are returned from PyFloat_FromString() for "nan", "inf"
and "-inf". The other PyFloat_ method must return the singletons, too.
It's easy to check the signum, special and nan/inf status of an IEEE
double with a struct.

I've already started to work on a way to create nan, inf and -inf cross
platform conform. Right now float("nan"), float("inf") and float("-inf")
works on Linux but doesn't work on Windows. We could also add four
methods to math:

signum(float) -> 1/-1, finity(float) -> bool, infinite(float), nan(float)

Here is my work in progress:
#define Py_IEEE_DBL *(double*)&(ieee_double)
#if defined(LITTLE_ENDIAN_IEEE_DOUBLE) && !defined(BIG_ENDIAN_IEEE_DOUBLE)
typedef struct {
        unsigned int    m4 : 16;
        unsigned int    m3 : 16;
        unsigned int    m2 : 16;
        unsigned int    m1 :  4;
        unsigned int   exp : 11;
        unsigned int  sign :  1;
} ieee_double;
#define Py_IEEE_NAN Py_IEEE_DBL{0xffff, 0xffff, 0xffff, 0xf, 0x7ff, 0}
#define Py_IEEE_INF Py_IEEE_DBL{0, 0, 0, 0, 0x7ff, 0}
#define Py_IEEE_NEGINF Py_IEEE_DBL{0, 0, 0, 0, 0x7ff, 1}
#elif !defined(LITTLE_ENDIAN_IEEE_DOUBLE) && defined(BIG_ENDIAN_IEEE_DOUBLE)
typedef struct {
        unsigned int  sign :  1;
        unsigned int   exp : 11;
        unsigned int    m1 :  4;
        unsigned int    m2 : 16;
        unsigned int    m3 : 16;
        unsigned int    m4 : 16;
} ieee_double;
#define Py_IEEE_NAN Py_IEEE_DBL{0, 0x7ff, 0xf, 0xffff, 0xffff, 0xffff}
#define Py_IEEE_INF Py_IEEE_DBL{0, 0x7ff, 0, 0, 0, 0}
#define Py_IEEE_NEGINF Py_IEEE_DBL{1, 0x7ff, 0, 0, 0, 0}
#else
#error Unknown or no IEEE double implementation
#endif