How to Calculate Epsilon

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Machine epsilon provides information about the computations that computers can make.

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.

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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

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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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