Why is `np.sum(range(N))` very slow?

I saw a video about speed of loops in python, where it was explained that doing sum(range(N)) is much faster than manually looping through range and adding the variables together, since the former runs in C due to built-in functions being used, while in the latter the summation is done in (slow) python. I was curious what happens when adding numpy to the mix. As I expected np.sum(np.arange(N)) is the fastest, but sum(np.arange(N)) and np.sum(range(N)) are even slower than doing the naive for loop.

Why is this?

Here’s the script I used to test, some comments about the supposed cause of slowing done where I know (taken mostly from the video) and the results I got on my machine (python 3.10.0, numpy 1.21.2):

updated script:

import numpy as np
from timeit import timeit

N = 10_000_000
repetition = 10

def sum0(N = N):
    s = 0
    i = 0
    while i < N: # condition is checked in python
        s += i
        i += 1 # both additions are done in python
    return s

def sum1(N = N):
    s = 0
    for i in range(N): # increment in C
        s += i # addition in python
    return s

def sum2(N = N):
    return sum(range(N)) # everything in C

def sum3(N = N):
    return sum(list(range(N)))

def sum4(N = N):
    return np.sum(range(N)) # very slow np.array conversion

def sum5(N = N):
    # much faster np.array conversion
    return np.sum(np.fromiter(range(N),dtype = int))

def sum5v2_(N = N):
    # much faster np.array conversion
    return np.sum(np.fromiter(range(N),dtype = np.int_))

def sum6(N = N):
    # possibly slow conversion to Py_long from np.int
    return sum(np.arange(N))

def sum7(N = N):
    # list returns a list of np.int-s
    return sum(list(np.arange(N)))

def sum7v2(N = N):
    # tolist conversion to python int seems faster than the implicit conversion
    # in sum(list()) (tolist returns a list of python int-s)
    return sum(np.arange(N).tolist())

def sum8(N = N):
    return np.sum(np.arange(N)) # everything in numpy (fortran libblas?)

def sum9(N = N):
    return np.arange(N).sum() # remove dispatch overhead

def array_basic(N = N):
    return np.array(range(N))

def array_dtype(N = N):
    return np.array(range(N),dtype = np.int_)

def array_iter(N = N):
    # np.sum's source code mentions to use fromiter to convert from generators
    return np.fromiter(range(N),dtype = np.int_)

print(f"while loop:         {timeit(sum0, number = repetition)}")
print(f"for loop:           {timeit(sum1, number = repetition)}")
print(f"sum_range:          {timeit(sum2, number = repetition)}")
print(f"sum_rangelist:      {timeit(sum3, number = repetition)}")
print(f"npsum_range:        {timeit(sum4, number = repetition)}")
print(f"npsum_iterrange:    {timeit(sum5, number = repetition)}")
print(f"npsum_iterrangev2:  {timeit(sum5, number = repetition)}")
print(f"sum_arange:         {timeit(sum6, number = repetition)}")
print(f"sum_list_arange:    {timeit(sum7, number = repetition)}")
print(f"sum_arange_tolist:  {timeit(sum7v2, number = repetition)}")
print(f"npsum_arange:       {timeit(sum8, number = repetition)}")
print(f"nparangenpsum:      {timeit(sum9, number = repetition)}")
print(f"array_basic:        {timeit(array_basic, number = repetition)}")
print(f"array_dtype:        {timeit(array_dtype, number = repetition)}")
print(f"array_iter:         {timeit(array_iter,  number = repetition)}")

print(f"npsumarangeREP:     {timeit(lambda : sum8(N/1000), number = 100000*repetition)}")
print(f"npsumarangeREP:     {timeit(lambda : sum9(N/1000), number = 100000*repetition)}")

# Example output:
#
# while loop:         11.493371912998555
# for loop:           7.385945574002108
# sum_range:          2.4605720699983067
# sum_rangelist:      4.509678105998319
# npsum_range:        11.85120212900074
# npsum_iterrange:    4.464334709002287
# npsum_iterrangev2:  4.498494338993623
# sum_arange:         9.537815956995473
# sum_list_arange:    13.290120724996086
# sum_arange_tolist:  5.231948580003518
# npsum_arange:       0.241889145996538
# nparangenpsum:      0.21876695199898677
# array_basic:        11.736577274998126
# array_dtype:        8.71628468400013
# array_iter:         4.303306431000237
# npsumarangeREP:     21.240833958996518
# npsumarangeREP:     16.690092379001726