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If it were not for the 0.5 fractional parts, the round-off errors introduced by the round to nearest method would be symmetric: for every fraction that gets rounded down (such as 0.268), there is a complementary fraction (namely, 0.732) that gets rounded up by the same amount.
This rounding rule is more accurate but more computationally expensive. Rounding so that the last stored digit is even when there is a tie ensures that it is not rounded up or down systematically. This is to try to avoid the possibility of an unwanted slow drift in long calculations due simply to a biased rounding.
Numbers with a magnitude strictly larger than k are rounded to the corresponding infinity. [18] "Round to nearest, ties to even" is the default for binary floating point and the recommended default for decimal. "Round to nearest, ties to away" is only required for decimal implementations. [19]
For example, to round 1.25 to 2 significant figures: Round half away from zero rounds up to 1.3. This is the default rounding method implied in many disciplines [citation needed] if the required rounding method is not specified. Round half to even, which rounds to the nearest even number. With this method, 1.25 is rounded down to 1.2.
An IEEE 754 compliant system allows programmers to round to the nearest floating-point number; alternatives are rounding towards 0 (truncating), rounding toward positive infinity (i.e., up), or rounding towards negative infinity (i.e., down). The required external rounding for interval arithmetic can thus be achieved by changing the rounding ...
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The sport believed it needed year-round racing. Santa Anita increased its signature meet to about six months, not including its fall meeting. Del Mar added a monthlong fall meeting to its summer meet.