Truncation

For other uses, see Truncation (disambiguation).

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

Truncation and floor function

Main article: Floor and ceiling functions

Truncation of positive real numbers can be done using the floor function. Given a number $x\in {ℝ}_{+}$ to be truncated and $n\in {\mathbb{N}}_0$, the number of elements to be kept behind the decimal point, the truncated value of x is

$\mathrm{trunc}(x,n)=\frac{\lfloor 10^n\cdot x\rfloor }{10^n}.$

However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the $\mathrm{floor}$ function rounds towards negative infinity. For a given number $x\in {ℝ}_{-}$, the function $\mathrm{ceil}$ is used instead

$\mathrm{trunc}(x,n)=\frac{\lceil 10^n\cdot x\rceil }{10^n}$.

Causes of truncation

With computers, truncation can occur when a decimal number is typecast as an integer; it is truncated to zero decimal digits because integers cannot store non-integer real numbers.

In algebra

An analogue of truncation can be applied to polynomials. In this case, the truncation of a polynomial P to degree n can be defined as the sum of all terms of P of degree n or less. Polynomial truncations arise in the study of Taylor polynomials, for example.

See also

• Arithmetic precision
• Quantization (signal processing)
• Precision (computer science)
• Truncation (statistics)

External links

• Wall paper applet that visualizes errors due to finite precision