You know how a 64-bit 0.3 shows up as 0.3 instead of its actual value, 0.299999999999999988897769753748434595763683319091796875?

It's a similar story here. numpy.finfo(numpy.float16).max is a float16, and those have very little precision. The exact mathematical value of the float16 is 65504, but a float16 doesn't have 5 decimal digits of precision, and by default, NumPy doesn't want to show you false precision.

It prints 65500.0, because '65500.0' is the shortest decimal representation (in terms of significant digits) such that converting the string back to float16 reproduces the original number.

Quoting from a numpy discussion list:

That information is available via numpy.finfo() and numpy.iinfo():

In [12]: finfo('d').max
Out[12]: 1.7976931348623157e+308

In [13]: iinfo('i').max
Out[13]: 2147483647

In [14]: iinfo('uint8').max
Out[14]: 255

Link here.

>>> import sys
>>> sys.float_info
sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308,
 min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15,
 mant_dig=53, epsilon=2.2204460492503131e-16, radix=2, rounds=1)

The smallest is sys.float_info.min (2.2250738585072014e-308) and the biggest is sys.float_info.max (1.7976931348623157e+308). See documentation for other properties.

sys.float_info.min is the normalized min. You can usually get the denormalized min as sys.float_info.min * sys.float_info.epsilon. Note that such numbers are represented with a loss of precision. As expected, the denormalized min is less than the normalized min.

min_value = np.iinfo(im.dtype).min
max_value = np.iinfo(im.dtype).max

docs:

• np.iinfo (machine limits for integer types)
• np.finfo (machine limits for floating point types)