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round(x) = x+ :
Round towards zero.
round(x) is either x; or x+ , whichever is between zero and x.
Round to nearest.
round(x) is either x; or x+ , whichever is nearer to x. In the case of a
tie, the one with its least signi cant bit equal to zero is chosen. If x is positive, then x; is between zero and x, so round down and round
towards zero have the same e ect. If x is negative, then x+ is between zero
and x, so it is round up and round towards zero which have the same effect. In either case, round towards zero simply requires truncating the binary
expansion, i.e. discarding bits.
The most useful rounding mode, and the one which is almost always used,
is round to nearest, since this produces the oating point number which is
closest to x. In the case of \toy" precision, with x = 1:7, it is clear that
round to nearest gives a rounded value of x equal to 1.75. When the word
\round" is used without any quali cation, it almost always means \round to
nearest". In the more familiar decimal context, if we \round" the number
= 3:14159 : : : to four decimal digits, we obtain the result 3...
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- Spring '09