Editing Rounding (section)

====Rounding half up====
One may '''round half up''' (or '''round half toward positive infinity'''), a tie-breaking rule that is widely used in many disciplines.{{citation needed|reason=This is surprising. A confusion with ''round half away from zero''?|date=June 2017}} That is, half-way values of {{mvar|x}} are always rounded up. If the fractional part of {{mvar|x}} is exactly 0.5, then {{math|1=''y'' = ''x'' + 0.5}}

: <math>y = \left\lfloor x + \tfrac12 \right\rfloor = -\left\lceil -x - \tfrac12 \right\rceil = \left\lceil \tfrac12 \lfloor 2x \rfloor \right\rceil</math>

For example, 23.5 gets rounded to 24, and −23.5 gets rounded to −23.

Some programming languages (such as Java and Python) use "half up" to refer to ''[[#Rounding half away from zero|round half away from zero]]'' rather than ''round half toward positive infinity''.<ref name="java">{{cite web |title=java.math.RoundingMode |url=https://docs.oracle.com/javase/8/docs/api/java/math/RoundingMode.html |publisher=Oracle}}</ref><ref name="python">{{cite web |title=decimal – Decimal fixed point and floating point arithmetic |url=https://docs.python.org/3/library/decimal.html#rounding-modes |publisher=Python Software Foundation}}</ref>

This method only requires checking one digit to determine rounding direction in [[two's complement]] and similar representations.