cos

Cosine of fi object in radians

Syntax

Y = cos(X)

Description

Y = cos(X) returns the cosine for each element of fi input X using an 8-bit lookup table algorithm.

Examples

Cosine of Fixed-Point Angles

Calculate the cosine of fixed-point input values.

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

X = 
         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(X)

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

Input Arguments

X — Input angle in radians

scalar | vector | matrix | multidimensional array

Input angle in radians, specified as a scalar, vector, matrix, or multidimensional array.

X can be a real-valued, signed or unsigned:

• fi single

• fi double

• fi fixed-point with binary-point scaling

• fi scaled double with binary-point scaling

Example: X = fi([pi pi/6],1,8);

Data Types: fi

Output Arguments

Y — Cosine of input angle

scalar | vector | matrix | multidimensional array

Cosine of input angle, returned as a real-valued fi scalar, vector, matrix, or multidimensional array.

More About

Cosine

The cosine of angle Θ is defined as

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

Algorithms

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

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

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

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, X. The output, Y, is always associated with the default fimath.

Extended Capabilities

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

Version History

Introduced in R2012a