cos

Cosine of fi object

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Syntax

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 single

  • fi double

  • fi fixed-point with binary point scaling

  • fi 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)).

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

More About

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Cosine

The cosine of angle Θ is defined as

cos(θ)=eiθ+e−iθ2

Algorithms

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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, theta. The output, y, is always associated with the default fimath.

Extended Capabilities

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

See Also

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Topics

Introduced in R2012a

Fixed-Point Designer Documentation

Support