Code for "My computer can't add (part 1)"

main.py

if __name__ == '__main__':
    import timeit
 
    print 'Initialising high-accuracy decimal values...'
    array_max = Decimal('1e6')
    deci_two = Decimal(2)
    values_decimal = np.arange(-array_max/deci_two, array_max/deci_two + Decimal(1), Decimal(1)) / array_max
    values_decimal[0] -= Decimal('1e-4')
    values = np.float32(values_decimal)
    values_rev = np.random.permutation(values)
    true_answer = Decimal('-1e-4')
    print('\nTesting plain addition...')
    print('Expected answer: {:s}'.format(str(true_answer)))
 
    # Print some pretty headings for the results.
    print('\n{:30s}|{:15s}|{:15s}|{:15s}'.format('Test', 'Result', 'Abs. error', 'Time (s)'))

results.txt

Initialising high-accuracy decimal values...
 
Testing plain addition...
Expected answer: -0.0001
 
Test                |Result             |Abs. error         |Time (s)
Serial summation    |0.001457870007     |0.001557870000     |0.230740897506
Numpy Sum           |0.001457870007     |0.001557870000     |0.000810961717
Serial Kahan        |-0.000097185373    |0.000002814627     |0.687989271230

serial kahan sum.py

import numpy as np
def serial_kahan_sum(values):
    zero_value = np.zeros(1, values.dtype)[0]
    s = zero_value
    c = zero_value
    r x in values:
        s, c = SCS(s, x+c)
    return s, c

serial_sum.py

def serial_sum(values):
    s = np.zeros(1, values.dtype)[0]
    for x in values:
        s += x return s
    return s

singly compensated summation.py

def SCS(a, b):
    sum = a + b
    return sum, b - (sum - a)

test_code.py

runtime = min(timeit.Timer('result = serial_sum(values)', setup='from __main__ import *').repeat(repeat=10, number=2)) / 2
result = serial_sum(values)
check_error(true_answer, result, runtime, 'Serial summation');
 
runtime = min(timeit.Timer('result = values.sum()', setup='from __main__ import *').repeat(repeat=10, number=2)) / 2
result = values.sum()
check_error(true_answer, result, runtime, 'Numpy Sum')
 
runtime = min(timeit.Timer('result = serial_kahan_sum(values)', setup='from __main__ import *').repeat(repeat=10, number=2)) / 2
result = serial_kahan_sum(values)
check_error(true_answer, result[0], runtime, 'Serial Kahan')