# nearest

Round toward nearest integer with ties rounding toward positive infinity

## Syntax

``y = nearest(a)``

## Description

example

````y = nearest(a)` rounds `fi` object `a` to the nearest integer or, in case of a tie, to the nearest integer in the direction of positive infinity, and returns the result in `fi` object `y`.```

## Examples

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The following example demonstrates how the `nearest` function affects the `numerictype` properties of a signed `fi` object with a word length of 8 and a fraction length of 3.

`a = fi(pi,1,8,3)`
```a = 3.1250 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 8 FractionLength: 3 ```
`y = nearest(a)`
```y = 3 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 0 ```

The following example demonstrates how the `nearest` function affects the `numerictype` properties of a signed `fi` object with a word length of 8 and a fraction length of 12.

`a = fi(0.025,1,8,12)`
```a = 0.0249 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 8 FractionLength: 12 ```
`y = nearest(a)`
```y = 0 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 2 FractionLength: 0 ```

The functions `convergent`, `nearest`, and `round` differ in the way they treat values whose least significant digit is 5.

• The `convergent` function rounds ties to the nearest even integer.

• The `nearest` function rounds ties to the nearest integer toward positive infinity.

• The `round` function rounds ties to the nearest integer with greater absolute value.

This example illustrates these differences for a given input, a.

```a = fi([-3.5:3.5]'); y = [a convergent(a) nearest(a) round(a)]```
```y = -3.5000 -4.0000 -3.0000 -4.0000 -2.5000 -2.0000 -2.0000 -3.0000 -1.5000 -2.0000 -1.0000 -2.0000 -0.5000 0 0 -1.0000 0.5000 0 1.0000 1.0000 1.5000 2.0000 2.0000 2.0000 2.5000 2.0000 3.0000 3.0000 3.5000 3.9999 3.9999 3.9999 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13 ```

## Input Arguments

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Input `fi` array, specified as scalar, vector, matrix, or multidimensional array.

For complex `fi` objects, the imaginary and real parts are rounded independently.

`nearest` does not support `fi` objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0.

Data Types: `fi`
Complex Number Support: Yes

## Algorithms

• `y` and `a` have the same `fimath` object and `DataType` property.

• When the `DataType` property of `a` is `single`, `double`, or `boolean`, the `numerictype` of `y` is the same as that of `a`.

• When the fraction length of `a` is zero or negative, `a` is already an integer, and the `numerictype` of `y` is the same as that of `a`.

• When the fraction length of `a` is positive, the fraction length of `y` is `0`, its sign is the same as that of `a`, and its word length is the difference between the word length and the fraction length of `a`, plus one bit. If `a` is signed, then the minimum word length of `y` is `2`. If `a` is unsigned, then the minimum word length of `y` is `1`.

## Version History

Introduced in R2008a