Catastrophic Cancellation

In [2]: 
import numpy as np

Let's make two numbers with very similar magnitude:

In [44]: 
x = 1.48234
y = 1.48235

Now let's compute their difference in double precision:

In [45]: 
x_dbl = np.float64(x)
y_dbl = np.float64(y)
diff_dbl = x_dbl-y_dbl

print(repr(diff_dbl))

-1.0000000000065512e-05
  • What would the correct result be?
  • What has happened here?

Can you predict what will happen in single precision?

In [46]: 
x_sng = np.float32(x)
y_sng = np.float32(y)
diff_sng = x_sng-y_sng

print(diff_sng)

-1.00136e-05