Here's the code:
def IsApproximatelyEqual(x, y, epsilon):
# Check absolute precision.
if -epsilon <= x - y <= epsilon:
return True
# Are x or y too close to zero?
if -epsilon <= x <= epsilon or -epsilon <= y <= epsilon:
return False
# Check relative precision.
return (-epsilon <= (x - y) / x <= epsilon
or -epsilon <= (x - y) / y <= epsilon)
As you can see, the "relative" part is basically abs(x-y)/max(x,y) <=
epsilon. The previous two clauses are for absolute differences and to make
sure we don't get huge numbers when we divide by x and y.
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