roundhalftoeven

Round half to even is a method of rounding numeric values to the nearest representable value. When a number is exactly halfway between two candidates, it is rounded to the candidate whose least-significant rounded digit is even. For non-half cases, standard rounding to the nearest value applies, such that values with a fractional part greater than 0.5 round up and those less than 0.5 round down.

Examples illustrate the rule. 2.5 rounds to 2, and 3.5 rounds to 4. Rounding to one decimal place, 1.25 becomes 1.2, while 1.35 becomes 1.4. The essence is that halfway cases are split toward the even result, balancing rounding directions over many calculations.

This approach reduces systematic bias that can accumulate when rounding occurs repeatedly. It is used in floating-point arithmetic and is the round-to-nearest, ties-to-even rule specified in the IEEE 754 standard for floating-point computations. Because of its bias-reducing property, it is sometimes called banker's rounding.

Implementation and usage vary by language and framework. The half-to-even rule is commonly available under labels such as “round to even” or “banker’s rounding.” In many numerical libraries and in languages that comply with IEEE 754, it can be selected as the default rounding mode or used explicitly for rounding operations.

Cautions include the fact that binary floating-point representations can introduce small errors around halfway cases, so for exact decimal arithmetic it is often better to use decimal types or integer scaling. Rounding rules should be chosen with awareness of downstream effects on sums, statistics, and financial calculations.