# normalizedReciprocal

Compute normalized reciprocal

Since R2020a

## Syntax

``[y,e] = normalizedReciprocal(u)``

## Description

example

````[y,e] = normalizedReciprocal(u)` returns `y` and `e` such that ```(2.^e).*y = 1./u``` and ```0.5 < abs(y) <= 1```. If `u = 0` and `u` is a fixed-point or scaled-double data type, then ```y = 2 – eps(y)``` and ```e = 2^(nextpow2(w)) – w + f```, where w is the word length of `u` and f is the fraction length of `u`.If `u = 0` and `u` is a floating-point data type, then `y = Inf` and `t = 1`. ```

## Examples

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This example shows how to compute the element-wise normalized reciprocal of a vector of fixed-point values.

`u = fi([-pi,0.01,pi])`
```u = -3.1416 0.0100 3.1416 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13 ```
`[y,e] = normalizedReciprocal(u)`
```y = -0.6367 0.7806 0.6367 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 14 ```
```e = 1x3 int32 row vector -1 7 -1 ```

## Input Arguments

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Input to take the normalized reciprocal of, specified as a real-valued scalar, vector, matrix, or N-dimensional array.

Data Types: `single` | `double` | `fi`

## Output Arguments

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Normalized reciprocal that satisfies ```0.5 < abs(y) <= 1``` and ```(2.^e).*y = 1./u```, returned as a scalar, vector, matrix, or N-dimensional array.

• If the input `u` is a signed fixed-point or scaled-double data type with word length w, then `y` is a signed fixed-point or scaled-double with word length w and fraction length `w – 2`.

• If the input `u` is an unsigned fixed-point or scaled-double data type with word length w, then `y` is an unsigned fixed-point or scaled-double with word length w and fraction length `w – 1`.

• If the input `u` is a double, then `y` is a double.

• If the input `u` is a single, the `y` is a single.

Exponent that satisfies ```0.5 < abs(y) <= 1``` and ```(2.^e).*y = 1./u```, returned as an integer scalar, vector, matrix, or N-dimensional array.

## Version History

Introduced in R2020a