How can I set floating point precision to avoid floating point arithmetic error in Python?

Question

I keep running into a floating point arithmetic error in Python that I can’t seem to figure out.

Problem: I need to create a weighting such that all weights sum to 1, not, for example: 0.99999999999999.

As an example, the following code:

values = numpy.array([9626.40000000034,      0. ,      0. ,      0. ,      0. ,      0. ,
            0. ,      0. ,  36907.300000000000054])
weights = values/values.sum()
weights.sum()

yields:

0.99999999999999989

Instead of 1. I have tried multiplying by 1000, converting to string (to cut off precision), and then converting back to float and dividing by 1000. It doesn’t work. I have also tried using Decimal.

from decimal import *
string_weight = []
float_weight = []
getcontext().prec = 3
for number in weights:
    string_weight.append(Decimal(str(number)))
for string in string_weight:
    float_weight.append(float(string))
fuel_weights = numpy.array(fuel_weights_float)
fuel_weights.sum()  

The answer is:

1.0009999999999999

That is not what I want. I just want a simple “1.0”.

A sys.version report gives:

3.6.8 |Anaconda, Inc.| (default, Dec 29 2018, 19:04:46) 
[GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]

I’m working on Mac OS X Catalina.

Answer 1

The solution to this binary arithmetic problem is to use Decimal and here is how to use it properly.

First, let me share a cleaner example of the problem.

import numpy
from decimal import *

# creating dummy values and weights
values = 1e-10 * numpy.ones(5)
weights = values/values.sum()
weights.sum()

yields:

0.9999999999999999

When I applied Decimal to problem-solve this error, I ran into a nuance that wasn’t intuitive to me: Passing the result of a division operation through Decimal doesn’t do anything to the binary error, i.e.:

getcontext().prec = 5
Decimal(values[0])

yields:

Decimal('1.0000000000000000364321973154977415791655470655996396089904010295867919921875E-10')

In order for Decimal to correct for the binary arithmetic error, Decimal has to be included in the division operation as follows.

getcontext().prec = 5
Decimal(1)/Decimal(7)

Yielding the same answer as described on the Python docs website:

Decimal('0.14286')

In my case, the correct application looks something like this.

weights_list = []
values = 1e-10 * numpy.ones(5)
sum_values = values.sum()
for value in values:
    getcontext().prec = 5
    weight = Decimal(value)/Decimal(sum_values)
    weights_list.append(weight)
weights = numpy.array(weights_list)    
weights.sum()

with the result is the correct mathematical answer as opposed to the binary arithmetic answer.

Decimal('1.0000')

which can be converted to a number using numpy.float().