Epsilon, or machine epsilon, is an important number in computing. Machine epsilon gives the distance between 1 and the next largest floating point number on your computer. This is important to calculate, as the size of the floating point number may lead to round-off errors for certain calculations. Calculating machine epsilon can be done a number of ways, and many programming languages have built-in functions that can determine this value. However, it also can be determined algorithmically with a fairly simple routine.
Step 1
Choose a programming language to program the algorithm in. Make sure you understand the language's syntax well enough to make a simple program within the language.
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Step 2
Initialize a variable to be equal to 1. In pseudocode, this will look like
x -> 1.
Step 3
Divide the initialized value by 2, and add that to 1. In pseudocode, this looks like
y -> x/2 + 1.
Step 4
Add a conditional statement, such that if y is less than 2, set
x -> x/2,
and repeat the step
y -> x/2 + 1.
Once the condition that y is greater than 2 is met, the resulting number is machine epsilon.
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