cordicatan2
CORDIC-based four quadrant inverse tangent
Description
Examples
Compute CORDIC Arctangent
Define floating-point Cartesian coordinates.
y = 0.5; x = -0.5;
Use cordicatan2
to compute floating-point CORDIC arctangent. Compare the result to the arctangent computed using atan2
.
theta_cdat2_float = cordicatan2(y,x)
theta_cdat2_float = 2.3562
theta_atan2_float = atan2(y,x)
theta_atan2_float = 2.3562
Define fixed-point Cartesian coordinates.
y = fi(0.5,1,16,15); x = fi(-0.5,1,16,15);
Use cordicatan2
to compute fixed-point CORDIC arctangent. Compare the result to the arctangent computed using atan2
.
theta_cdat2_fixpt = cordicatan2(y,x)
theta_cdat2_fixpt = 2.3562 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13
theta_atan2_fixpt = atan2(y,x)
theta_atan2_fixpt = 2.3562 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13
Input Arguments
y
— Cartesian y-coordinate
scalar | vector | matrix | multidimensional array
Cartesian y-coordinate, specified as a scalar, vector, matrix, or multidimensional array.
y
and x
must be the same size. If they are
not the same size, at least one value must be a scalar value. y
and
x
must have the same data type.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| fi
Complex Number Support: Yes
x
— Cartesian x-coordinate
scalar | vector | matrix | multidimensional array
Cartesian x-coordinate, specified as a scalar, vector, matrix, or multidimensional array.
y
and x
must be the same size. If they are
not the same size, at least one value must be a scalar value. y
and
x
must have the same data type.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| fi
Complex Number Support: Yes
niters
— Number of iterations of CORDIC algorithm
positive integer-valued scalar
Number of iterations of CORDIC algorithm, specified as a positive, integer-valued scalar.
Increasing the number of iterations can produce more accurate results, but also increases the expense of the computation and adds latency.
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 y
or
x
. For floating-point operation, the maximum value is 52 for
double or 23 for single.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| fi
Output Arguments
theta
— Arctangent value
scalar | vector | matrix | multidimensional array
Arctangent value in the range [-pi, pi] radians, returned as a scalar, vector, matrix, or multidimensional array.
If y
and x
are floating-point numbers,
then theta
has the same data type as y
and
x
. Otherwise, theta
is a fixed-point data
type with the same word length as y
and x
and
with a best-precision fraction length for the [-pi, pi] range.
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 Diagram
CORDIC Vectoring Kernel
The accuracy of the CORDIC kernel depends on the choice of initial values for X, Y, and Z. This algorithm uses the following initial values:
X0 is initialized to the X input value
Y0 is initialized to the Y input value
Z0 is initialized
0
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™.
The cordicatan2
function also supports MATLAB® to High-Level Synthesis (HLS) code generation.
Version History
Introduced in R2011b
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