Numba performance issue with np.nan and np.inf

Question

I am playing around with numba to accelerate my code. I notice that the performance varies significantly when using np.inf instead np.nan inside the function. Below I have attached three sample functions for illustration.

• function1 is not accelerated by numba .
• function2 and function3 are both accelerated by numba , but one uses np.nan while the other uses np.inf .

On my machine, the average runtime of the three functions are 0.032284s , 0.041548s and 0.019712s respectively. It appears that using np.nan is much slower than np.inf . Why does the performance vary significantly? Thanks in advance.

Edit : I am using Python 3.7.11 and Numba 0.55.Orc1 .

import numpy as np
import numba as nb

def function1(array1, array2):
    nr, nc = array1.shape
    output1 = np.empty((nr, nc), dtype='float')
    output2 = np.empty((nr, nc), dtype='float')
    output1[:] = np.nan
    output2[:] = np.nan

    for r in range(nr):
        row1 = array1[r]
        row2 = array2[r]
        diff = row1 - row2
        id_threshold =np.nonzero( (row1 - row2) > 8 )
        output1[r][id_threshold] = 1
        output2[r][id_threshold] = 0

    output1 = output1.flatten()
    output2 = output2.flatten()
    id_keep = np.nonzero(output1 != np.nan)
    output1 = output1[id_keep]
    output2 = output2[id_keep]
    output = np.vstack((output1, output2))
    return output

@nb.njit('float64[:,::1](float64[:,::1], float64[:,::1])', parallel=True)
def function2(array1, array2):
    nr, nc = array1.shape
    output1 = np.empty((nr,nc), dtype='float')
    output2 = np.empty((nr, nc), dtype='float')
    output1[:] = np.nan
    output2[:] = np.nan

    for r in nb.prange(nr):
        row1 = array1[r]
        row2 = array2[r]
        diff = row1 - row2
        id_threshold =np.nonzero( (row1 - row2) > 8 )
        output1[r][id_threshold] = 1
        output2[r][id_threshold] = 0

    output1 = output1.flatten()
    output2 = output2.flatten()
    id_keep = np.nonzero(output1 != np.nan)
    output1 = output1[id_keep]
    output2 = output2[id_keep]
    output = np.vstack((output1, output2))
    return output

@nb.njit('float64[:,::1](float64[:,::1], float64[:,::1])', parallel=True)
def function3(array1, array2):
    nr, nc = array1.shape
    output1 = np.empty((nr,nc), dtype='float')
    output2 = np.empty((nr, nc), dtype='float')
    output1[:] = np.inf
    output2[:] = np.inf

    for r in nb.prange(nr):
        row1 = array1[r]
        row2 = array2[r]
        diff = row1 - row2
        id_threshold =np.nonzero( (row1 - row2) > 8 )
        output1[r][id_threshold] = 1
        output2[r][id_threshold] = 0
    output1 = output1.flatten()
    output2 = output2.flatten()
    id_keep = np.nonzero(output1 != np.inf)
    output1 = output1[id_keep]
    output2 = output2[id_keep]
    output = np.vstack((output1, output2))
    return output


array1 = 10*np.random.random((1000,1000))
array2 = 10*np.random.random((1000,1000))

output1 = function1(array1, array2)
output2 = function2(array1, array2)
output3 = function3(array1, array2)

Answer 1

The second one is much slower because output1.= np.nan returns a copy output1 since np.nan.= np.nan is True (like any other value -- v.= np.nan is always true). Thus, the resulting array to compute are much bigger causing a slower execution.

The point is you must never compare a value to np.nan using comparison operators: use np.isnan(value) instead. In your case, you should use np.logical_not(np.isnan(output1)) .

The second implementation may be slightly slower due to the temporary array created by np.logical_not (I did not see any statistically significant difference on my machine between using NaN or Inf once the code has been corrected).