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# cos

Cosine of fi object

y = cos(theta)

## Description

y = cos(theta) returns the cosine of fi input theta using a table-lookup algorithm.

## Input Arguments

 theta theta can be a real-valued, signed or unsigned scalar, vector, matrix, or N-dimensional array containing the fixed-point angle values in radians. Valid data types of theta are:fi singlefi doublefi fixed-point with binary point scalingfi scaled double with binary point scaling

## Output Arguments

 y y is the cosine of theta. y is a signed, fixed-point number in the range [-1,1]. It has a 16-bit word length and 15-bit fraction length (numerictype(1,16,15)). This cosine calculation is accurate only to within the top 16 most-significant bits of the input.

## Examples

Calculate the cosine of fixed-point input values.

```theta = fi([0,pi/4,pi/3,pi/2,(2*pi)/3,(3*pi)/4,pi])

theta =

0  0.7854  1.0472  1.5708  2.0944  2.3562  3.1416

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13

y = cos(theta)

y =

1.0000  0.7072  0.4999  0.0001 -0.4999  -0.7070  -1.0000

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15```

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### Cosine

The cosine of angle Θ is defined as

$\mathrm{cos}\left(\theta \right)=\frac{{e}^{i\theta }+{e}^{-i\theta }}{2}$

### Algorithms

The cos function computes the cosine of fixed-point input using an 8-bit lookup table as follows:

1. Cast the input to a 16-bit stored integer value, using the 16 most-significant bits.

2. Perform a modulo 2π, so the input is in the range [0,2π) radians.

3. Compute the table index, based on the 16-bit stored integer value, normalized to the full uint16 range.

4. Use the 8 most-significant bits to obtain the first value from the table.

5. Use the next-greater table value as the second value.

6. Use the 8 least-significant bits to interpolate between the first and second values, using nearest-neighbor linear interpolation.

### fimath Propagation Rules

The cos function ignores and discards any fimath attached to the input, theta. The output, y, is always associated with the default fimath.