# cordicsin

CORDIC-based approximation of sine

## Syntax

``y = cordicsin(theta)``
``y = cordicsin(theta,niters)``

## Description

````y = cordicsin(theta)` computes the sine of `theta` using a CORDIC algorithm approximation.```

example

````y = cordicsin(theta,niters)` computes the sine of `theta` using a CORDIC algorithm approximation with specified number of iterations, `niters`.```

## Examples

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This example compares the results produced by the `cordicsin` algorithm to the results of the double-precision `sin` function.

Create 1024 points between `[0, 2*pi)`.

```stepSize = pi/512; thRadDbl = 0:stepSize:(2*pi - stepSize); thRadFxp = sfi(thRadDbl, 12); % signed, 12-bit fixed point sinThRef = sin(double(thRadFxp)); % reference results```

Set the number of iterations to 10.

```niters = 10; cdcSinTh = cordicsin(thRadFxp, niters); errCdcRef = sinThRef - double(cdcSinTh);```

Compare the fixed-point `cordicsin` function results to the results of the double-precision `sin` function.

```figure hold on axis([0 2*pi -1.25 1.25]) plot(thRadFxp, sinThRef, 'b'); plot(thRadFxp, cdcSinTh, 'g'); plot(thRadFxp, errCdcRef, 'r'); ylabel('sin(\Theta)'); gca.XTick = 0:pi/2:2*pi; gca.XTickLabel = {'0','pi/2','pi','3*pi/2','2*pi'}; gca.YTick = -1:0.5:1; gca.YTickLabel = {'-1.0','-0.5','0','0.5','1.0'}; ref_str = 'Reference: sin(double(\Theta))'; cdc_str = sprintf('12-bit CORDIC sine; N = %d', niters); err_str = sprintf('Error (max = %f)', max(abs(errCdcRef))); legend(ref_str, cdc_str, err_str);```

After 10 iterations, the CORDIC algorithm has approximated the sine of `theta` to within 0.005492 of the double-precision sine result.

## Input Arguments

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Input angle in radians, specified as a signed or unsigned scalar, vector, matrix, or multidimensional array. All values of `theta` must be real and in the range [–2π 2π).

Number of iterations the CORDIC algorithm performs, specified as a positive, integer-valued scalar.

If you do not specify `niters`, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of `theta`. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency.

## Output Arguments

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CORDIC-based approximation of sine of `theta`, returned as a scalar, vector, matrix, or multidimensional array.

When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the `WordLength``2`.

## Algorithms

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### CORDIC

CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see References). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

Increasing the number of CORDIC iterations can produce more accurate results, but doing so increases the expense of the computation and adds latency.

### Signal Flow Diagrams

CORDIC Rotation Kernel

X represents the sine, Y represents the cosine, and Z represents theta. The accuracy of the CORDIC rotation kernel depends on the choice of initial values for X, Y, and Z. This algorithm uses the following initial values:

### fimath Propagation Rules

CORDIC functions discard any local `fimath` attached to the input.

The CORDIC functions use their own internal `fimath` when performing calculations:

• `OverflowAction``Wrap`

• `RoundingMethod``Floor`

The output has no attached `fimath`.

## Version History

Introduced in R2010a