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.

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

Examples

Compare Results of cordicsin and sin Functions

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

theta — Input angle in radians

scalar | vector | matrix | multidimensional array

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).

niters — Number of iterations

positive integer-valued scalar

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

y — CORDIC-based approximation of sine

scalar | vector | matrix | multidimensional array

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

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:

$$\begin{array}{l}{z}_0\text{ is initialized to the }\theta \text{ input argument value}\\ x_0\text{ is initialized to }\frac{1}{A_N}\\ y_0\text{ is initialized to }0\end{array}$$

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Variable-size signals are not supported.

• The number of iterations the CORDIC algorithm performs, niters, must be a constant.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

You can generate HDL code for cordicsin function.

Version History

Introduced in R2010a