# More Low-level Optimizations (3)

### This test can be made a test against a value of zero if the inital value of
scaledFraction has 2*dx subtracted from it. Giving outside the loop:

OffsetScaledFraction = dx + 2*dy - 2*dx = 2*dy - dx,

### and the inner loop becomes

OffsetScaledFraction += 2*dy
if (OffsetScaledFraction >= 0) {
y = y +1; OffsetScaledFraction -= 2*dx;
}

### The net result is that we might as well double the values of dy and dx (this
can be accomplished with either an add or a shift).