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And you can specify the rounding you desire: ROUND_CEILING, ROUND_DOWN, ROUND_FLOOR, ROUND_HALF_DOWN, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_UP, and ROUND_05UP are all options.
We can decide to round towards even (or odd) numbers, or we can just choose randomly. Round to Even (Banker's Rounding) We round 0.5 to the nearest even digit
Round half to even: Rounding half to even can be used as a tie-breaking rule since it does not have any biases based on positive or negative numbers or rounding towards or away from zero, as some of the other rounding methods do. For this method, half values are rounded to the nearest even integer. For example:
With round half to even, a non-infinite number would round to infinity, and a small denormal value would round to a normal non-zero value. Effectively, this mode prefers preserving the existing scale of tie numbers, avoiding out-of-range results when possible for numeral systems of even radix (such as binary and decimal).
27 sie 2024 · In particular, for a number that's exactly midway between its two nearest integers, this algorithm rounds it to the nearest even integer. Applying rounding half to even: $$3.5\approx4\\\boldsymbol{2.59\approx3}\\2.5\approx2\\-2.5\approx-2\\-3.5\approx-4\\x\in(2.5,3.5)\implies x\approx3\\x\in[1.5,2.5]\implies x\approx2\\x\in(0.5,1.5)\implies x ...
25 sty 2015 · HALF_EVEN and HALF_ODD attempts to correct for this by choosing whether to rounding 0.5 up or down based on whether it is more likely to go to an even or odd number. This is statistically fairer, provided you have a 50/50 split of even and odd numbers, however harder for a human to understand.
11 paź 2023 · Rounding half to even is used as a tie-breaking rule as it has no biases towards a positive or a negative number or even towards or away from zero. Here, the half values are rounded to the nearest even integer.
