Answer from cs61c-ax (Amanda Alfonso 15906918) for Question 3 Many programmers wrote (0.5 - x) + 0.5 because they had to compensate for the lack of a guard digit. In other words, "in the old days" hardware lacked a guard bit (bits on right during intermediate calculations - if every intermediate result truncated to the exact number of digits, there would otherwise be no opportunity to round the final answer) in double precision.