It appears to me that either the documentation of np.finfo() is somewhat misleading or the functions returns a wrong result for the parameter tiny.

According to the doc of np.finfo() tiny is

the smallest positive usable number.

According to the script below that is not true.

I am not sure if this is really a bug. I suspect that tiny in np.finfo() actually refers to the smallest normalized floating-point number. However, the IEEE 754 standard also includes subnormal floating-point numbers. This is also implemented in np.float64. The smallest positive subnormal is 2**(-1022)*2**(-52). See Wiki.

It may make sense to distinguish between these two classes of floats since the latter does not have the full resolution of up to 16 decimals, but may have considerably less precision. However, from my point of view np.float64 supports subnormals and they are usable numbers. Hence either the documentation should be adapted or a further attribute may be added to np.finfo such as tiny_norm vs. tiny_subn.

Reproducing code example:

import numpy as np

print('Output of np.finfo(np.float64)')
print(np.finfo(np.float64))

# value for tiny equals
tiny = 2**(-1022)

# define some smaller number
x = np.zeros(3)
x[0] = 2**(-1023)
x[1] = 2**(-1074)
x[2] = 2**(-1075) # underflow occurs

print('Print decimal representations of tiny and some smaller floats:')
print('2**(-1022) = Tiny = ', tiny)
print('2**(-1023) =', x[0])
print('2**(-1074) =', x[1])
print('2**(-1075) =', x[2])

Output:

Output of np.finfo(np.float64)
Machine parameters for float64
---------------------------------------------------------------
precision =  15   resolution = 1.0000000000000001e-15
machep =    -52   eps =        2.2204460492503131e-16
negep =     -53   epsneg =     1.1102230246251565e-16
minexp =  -1022   tiny =       2.2250738585072014e-308
maxexp =   1024   max =        1.7976931348623157e+308
nexp =       11   min =        -max
---------------------------------------------------------------

Print decimal representations of tiny and some smaller floats:
2**(-1022) = Tiny =  2.2250738585072014e-308
2**(-1023) = 1.1125369292536007e-308
2**(-1074) = 5e-324
2**(-1075) = 0.0

Numpy/Python version information:

1.16.2 3.7.5 (default, Apr 19 2020, 20:18:17)
[GCC 9.2.1 20191008]