unexpected return from falling factorial function #521
Description
When the second argument is negative infinity, ff returns a zero regardless of the first argument. When the second argument is a positive infinity, ff returns a NaN which seems more appropriate; I don't believe the falling factorial function is well-defined with infinite second arguments. The fp namespace appears to behave in a more expected manner, throwing an error.
>>> mp.ff(1, -inf)
mpf('0.0')
>>> fp.ff(1, -inf)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/local/lib/python3.6/dist-packages/mpmath/functions/factorials.py", line 77, in ff
return ctx.gammaprod([x1], [xn1])
File "/usr/local/lib/python3.6/dist-packages/mpmath/functions/factorials.py", line 36, in gammaprod
for x in regular_den: p /= ctx.gamma(x)
File "/usr/local/lib/python3.6/dist-packages/mpmath/math2.py", line 30, in f
return f_real(x)
File "/usr/local/lib/python3.6/dist-packages/mpmath/math2.py", line 199, in _gamma_real
_intx = int(x)
OverflowError: cannot convert float infinity to integer
>>> mp.ff(1, inf)
mpf('nan')
>>> fp.ff(1, inf)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/local/lib/python3.6/dist-packages/mpmath/functions/factorials.py", line 77, in ff
return ctx.gammaprod([x1], [xn1])
File "/usr/local/lib/python3.6/dist-packages/mpmath/functions/factorials.py", line 13, in gammaprod
for x in b: [regular_den, poles_den][ctx.isnpint(x)].append(x)
File "/usr/local/lib/python3.6/dist-packages/mpmath/ctx_fp.py", line 105, in isnpint
return x <= 0.0 and round(x) == x
OverflowError: cannot convert float infinity to integer