Python: pow(x, y, z) less efficient than x**y % z

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The Python documentation on pow() states that pow(x,y,z) is computed more efficiently than pow(x,y) % z, but our tests don’t show that to be the case. In fact, we found x**y % z to be the most efficient way to complete the operation. Note that this is academic as all the methods we tested for raising one number to the power of another and then doing a modulus operation are lightning fast. You should use whichever method suits your coding style the most, but for those who are curious, here’s how we tested it:

import time
import math
x = 4
y = 2
z = 3
repeat = 1000000
results = {}
start_time = time.time()
i = 0
while i < repeat:
    result = x**y % z
results['x**y % z'] = time.time()-start_time
#pow() Function
start_time = time.time()
i = 0
while i < repeat:
    result = pow(x,y,z)
results['pow(x,y,z)'] = time.time()-start_time
#pow() with % operator Function
start_time = time.time()
i = 0
while i < repeat:
    result = pow(x,y) % z
results['pow(x,y) % z'] = time.time()-start_time
#math.pow() Function
start_time = time.time()
i = 0
while i < repeat:
    result = math.pow(x,y) % z
results['math.pow(x,y) % z'] = time.time()-start_time
#output results
results_list = sorted(results.items(), key = lambda t:t[1])
for i in range(0,len(results_list)):

And here are the results:

x**y % z : 0.5734121799468994
math.pow(x,y) % z : 0.6415011882781982
pow(x,y) % z : 0.6755549907684326
pow(x,y,z) : 1.101822853088379

Written by Nat Dunn.

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