July 2002
Intermediate to advanced
320 pages
8h 15m
English
Content preview from Hacker's Delight
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4-3. Propagating Bounds through Logical Operations
As in the preceding section, suppose we have bounds on two variables x and y as follows, where all quantities are unsigned:
Equation 9
Then what are some reasonably tight bounds on x | y, x & y, x ⊕ y, and ¬x?
Combining inequalities (9) with some inequalities from Section 2-3 on page 16, and noting that ¬x = 232 − 1 − x, yields
where it is assumed that the addition b + d does not overflow. These are easy to compute and might be good enough for the compiler application mentioned in the preceding ...
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