Accuracy of Python Floating Point Numbers

Floating point numbers are represented by binary (base 2) fractions in computer hardware. On most computing machines, floats are approximated using a binary fraction with the numerator using the first 53 bits starting with the most significant bit and with the denominator as a power of two.

In this python program, we are going to test the accuracy of the Python floating point numbers, by testing to see if 1 + delta = 1 for different values of delta.

Python Source Code: Floating Point Accuracy

delta = 1
while delta > 1e-20:
    if 1 + delta == 1:
        print('1 +', delta, "  = 1")
        flag = delta/0.1
        break
    else:
        print('1 +', delta, "  != 1")

    delta=delta*0.1
    
print("\n\nAccuracy of Python floating point number is: ", flag)

Output

1 + 1   != 1
1 + 0.1   != 1
1 + 0.010000000000000002   != 1
1 + 0.0010000000000000002   != 1
1 + 0.00010000000000000003   != 1
1 + 1.0000000000000004e-05   != 1
1 + 1.0000000000000004e-06   != 1
1 + 1.0000000000000005e-07   != 1
1 + 1.0000000000000005e-08   != 1
1 + 1.0000000000000005e-09   != 1
1 + 1.0000000000000006e-10   != 1
1 + 1.0000000000000006e-11   != 1
1 + 1.0000000000000006e-12   != 1
1 + 1.0000000000000007e-13   != 1
1 + 1.0000000000000008e-14   != 1
1 + 1.0000000000000009e-15   != 1
1 + 1.000000000000001e-16   = 1


Accuracy of Python floating point number is:  1.0000000000000009e-15

From the above output, we can conclude that Python represents floating point numbers with precision of up to 15 significant digits.