normalizedReciprocal

Compute normalized reciprocal

Syntax

[y,e] = normalizedReciprocal(u)

Description

[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 = 1 – 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

Compute Normalized Reciprocal of a Fixed-Point Vector

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 = 1×3 int32 row vector

   -1    7   -1

Input Arguments

u — Input to take normalized reciprocal of

scalar | vector | matrix | N-dimensional array

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

y — Normalized reciprocal

scalar | vector | matrix | N-dimensional array

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.

e — Exponent

scalar | vector | matrix | N-dimensional array

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.

Tips

• The behavior of the Normalized Reciprocal HDL Optimized block is equivalent to the normalizedReciprocal function. When the data type of the input is fixed point with binary-point scaling, the function and block provide bit-exact results.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Fixed-Point Conversion

Design and simulate fixed-point systems using Fixed-Point Designer™.

Slope-bias representation is not supported for fixed-point data types.

Version History

Introduced in R2020a

R2025a: Bit-exact result with Simulink block

The output of the normalizedReciprocal function has changed to be bit-exact with the output of the Normalized Reciprocal HDL Optimized block when the input data type is fixed point with binary-point scaling. Small numerical differences may exist compared to previous releases.