sin

Sine of fixed-point values

Syntax

y = sin(theta)

Description

y = sin(theta) returns the sine of fi input theta using a lookup table algorithm.

Examples

Calculate the Sine of Fixed-Point Input Values

theta = fi([-pi/2,-pi/3,-pi/4,0,pi/4,pi/3,pi/2]);
y = sin(theta)

y = 
   -1.0000   -0.8661   -0.7072         0    0.7070    0.8659    0.9999

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

Input Arguments

theta — Input angle in radians

real-valued fi object

Input angle in radians, specified as a real-valued fi object. theta can be a signed or unsigned scalar, vector, matrix, or multidimensional 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

Data Types: fi

Output Arguments

y — Sine of input angle

scalar | vector | matrix | multidimensional array

Sine of input angle, returned as a scalar, vector, matrix, or multidimensional array. y is a signed, fixed-point number in the range [-1,1].

If the DataTypeMode property of theta is Fixed-point: binary point scaling, then y is returned as a signed fixed-point data type with binary point scaling, a 16-bit word length, and a 15-bit fraction length (numerictype(1,16,15)). If theta is a fi single, fi double, or fi scaled double with binary point scaling, then y is returned with the same data type as theta.

More About

Sine

The sine of angle Θ is defined as

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

Algorithms

The sin function computes the sine 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 sin 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™.

Version History

Introduced in R2012a