Demonstrate Binary Floating Point Behavior with Decimal Fractions

floating_point_issue.py

# Note that standard binary computing floating point numbers cannot exactly represent simple decimal floating point numbers.
# This is the expected behavior for IEEE-754 compliant binary floating point processors
# https://en.wikipedia.org/wiki/IEEE_floating_point
# Case in point, 0.1 (1/10 = 10^-1) is between 1/8=2^-3 and 1/16=2^-4
# Since binary fraction cannot exacly store 1/10, accuracy of associated arithmetic is adversely impacted
# https://docs.python.org/3.5/tutorial/floatingpoint.html 
# See the following example using Python 3.x

def test_binary_fraction():
	mySum = 0
	for i in range(10):
		mySum += .1
	print("0.1 Added Ten Times = {}, (expected 1.0)".format(mySum))
	print("Subtract result from 1.0 = {}, (expected 0.0)".format(1.0-mySum))

test_binary_fraction()

# Sample Output ...
# 0.1 Added Ten Times = 0.9999999999999999, (expected 1.0)
# Subtract result from 1.0 = 1.1102230246251565e-16, (expected 0.0)

# For many applications, the default approximation in binary will be acceptable.

# To more precisely handle Decimal floating point numbers, we can use alternate
# arithmetic and math capabilities such as the Python "decimal" module
# https://docs.python.org/3.5/library/decimal.html