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Since x > 0, the term $$(1 - 2 x_i) < 0$$, so dividing gets:



\begin{align} 2 \left [ (x_i^2 + y_i^2 - r^2) + (2 y_i + 1) \right ] + (1 - 2 x_i) & > 0 \\ 2 \left [ RE(x_i,y_i) + Y_\text{Change} \right ] + X_\text{Change} & > 0 \\ \end{align} $$

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 $2(RE+Y_\text{Change})+X_\text{Change} > 0$, then decrement the X value. If $2(RE+Y_\text{Change})+X_\text{Change} \le 0$, 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 $E$ as $3-2r$ which is the initial value of the formula at $(x_0,y_0)=(r,0)$, then as above if $E>0$ we update it as $$ (and decrement X), otherwise $$ thence increment Y as usual.