numpy.dot() result different with classic computation for large-size arrays

[geekgeek]

Basically I am testing the 1st sample code in URL https://www.geeksforgeeks.org/vectorization-in-python/

When I run the code as it is it is (array size is 100000), the result looks good - same as the output in the webpage.

But when I increase the array size to be 100000000 (100millions), I noticed the classic computation and numpy.dot result is different.

My environment:
OS: MacOS 11.6.2
Python: 3.8.9

The code:

# Dot product
import time
import numpy
import array

# 8 bytes size int
a = array.array('q')
N=100000000
for i in range(N):
        a.append(i);

b = array.array('q')
for i in range(N, 2*N):
        b.append(i)

# classic dot product of vectors implementation
tic = time.process_time()
dot = 0.0;

for i in range(len(a)):
        dot += a[i] * b[i]

toc = time.process_time()

print("dot_product = "+ str(dot));
print("Classic Computation time = " + str(1000*(toc - tic )) + "ms")

n_tic = time.process_time()
n_dot_product = numpy.dot(a, b)
n_toc = time.process_time()

print("\nn_dot_product = "+str(n_dot_product))
print("Vec Computation time = "+str(1000*(n_toc - n_tic ))+"ms")

The result is:

dot_product = 8.33333323333355e+23
Classic Computation time = 22549.694999999996ms

n_dot_product = 1659803504355747200
Vec Computation time = 131.33700000000204ms


I don't know why dot_product and n_dot_product are different. When I tried the code with N=100000, the dot_product and n_dot_product are same.
Thanks in advance.