Why is numpy array's .tolist() creating long doubles?

Question

I have some math operations that produce a numpy array of results with about 8 significant figures. When I use tolist() on my array y_axis, it creates what I assume are 32-bit numbers.

However, I wonder if this is just garbage. I assume it is garbage, but it seems intelligent enough to change the last number so that rounding makes sense.

print "y_axis:",y_axis
y_axis = y_axis.tolist()
print "y_axis:",y_axis

y_axis: [-0.99636686  0.08357361 -0.01638707]
y_axis: [-0.9963668578012771, 0.08357361233570479, -0.01638706796138937]

So my question is: if this is not garbage, does using tolist actually help in accuracy for my calculations, or is Python always using the entire number, but just not displaying it?

Answer 1

When you call print y_axis on a numpy array, you are getting a truncated version of the numbers that numpy is actually storing internally. The way in which it is truncated depends on how numpy's printing options are set.

>>> arr = np.array([22/7, 1/13])           # init array
>>> arr                                    # np.array default printing
array([ 3.14285714,  0.07692308])
>>> arr[0]                                 # int default printing
3.1428571428571428
>>> np.set_printoptions(precision=24)      # increase np.array print "precision"
>>> arr                                    # np.array high-"precision" print
array([ 3.142857142857142793701541,  0.076923076923076927347012])
>>> float.hex(arr[0])                      # actual underlying representation
'0x1.9249249249249p+1'

The reason it looks like you're "gaining accuracy" when you print out the .tolist()ed form of y_axis is that by default, more digits are printed when you call print on a list than when you call print on a numpy array.

In actuality, the numbers stored internally by either a list or a numpy array should be identical (and should correspond to the last line above, generated with float.hex(arr[0])), since numpy uses numpy.float64 by default, and python float objects are also 64 bits by default.

Answer 2

My understanding is that numpy is not showing you the full precision to make the matrices lay out consistently. The list shouldn't have any more precision than its numpy.array counterpart:

>>> v = -0.9963668578012771
>>> a = numpy.array([v])
>>> a
array([-0.99636686])
>>> a.tolist()
[-0.9963668578012771]
>>> a[0] == v
True
>>> a.tolist()[0] == v
True