Other uses of this exact specification are given in Exactly Rounded Operations. I actually have tried to keep away from making statements about floating-level without also giving explanation why the statements are true, particularly because the justifications contain nothing more sophisticated than elementary calculus. Those explanations that are not central to the principle argument have been grouped into a section referred to as “The Details,” in order that they are often skipped if desired.
All caps indicate the computed value of a operate, as in LN(x) or SQRT(x). Lowercase features and conventional mathematical notation denote their exact values as in ln(x) and . The expression x2 – y2 is one other formulation that reveals catastrophic cancellation.
In the numerical example given above, the computed worth of is 2.35, compared with a real worth of two.34216 for a relative error of 0.7, which is much lower than 11. The major reason … Read More