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Since x > 0, the term  , so dividing gets:

 

Thus, the decision criterion changes from using floating-point operations to simple integer addition, subtraction, and bit shifting (for the multiply by 2 operations). If  , then decrement the X value. If  , then keep the same X value. Again, by reflecting these points in all the octants, a full circle results.

We may reduce computation by only calculating the delta between the values of this condition formula from its value at the previous step. We start by assigning   as   which is the initial value of the formula at  , then as above if   we update it as   (and decrement X), otherwise   thence increment Y as usual.

References

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