afrunding

Afrunding is the process of reducing a number to a value that is less than or equal to the original value according to a chosen precision. In mathematics and computer science, this is typically achieved by the floor operation, often written as floor(x), which returns the greatest integer not greater than x. When rounding to a fixed number of decimal places, afrunding is performed by computing floor(x * 10^d) / 10^d, where d is the number of decimals.

Afrunding is distinct from rounding to the nearest value or rounding up. For example, afrunding 3.7 to an integer yields 3, and afrunding 12.349 to two decimals yields 12.34. The same operation applied to negative numbers can produce results that may surprise those unfamiliar with the floor function: afrunding -1.2 to the integer gives -2.

In computing and software, afrunding is implemented by functions such as floor in many programming languages (for example, Math.floor in JavaScript, math.floor in Python) and by equivalent operators in databases and calculators. In accounting and finance, afrunding is sometimes used to simplify figures, or to conform to currency units with limited denominations, by dropping excess decimals or units.

Variants include truncation, which removes digits without adjusting the remaining value toward negative infinity, and banker's rounding, which rounds to the nearest even number. Users should be aware of the difference when processing negative values or when combining multiple rounded figures to avoid bias in totals.

See also: floor function, truncation, rounding (mathematics).