fixed.cordicDivide

CORDIC-based fixed-point divide

Syntax

y = fixed.cordicDivide(num,den,OutputType)

Description

y = fixed.cordicDivide(num,den,OutputType) divides num by den with the output data type specified by OutputType using a CORDIC-based algorithm.

Note

The embblk.divide.cordicDivide function also performs CORDIC-based fixed-point division and outputs a solution which is bit-exact with the Real Divide HDL Optimized and Complex Divide HDL Optimized blocks. The fixed.cordicDivide function uses larger data types than the embblk.Divide.cordicDivice function, which provides more accurate results but requires additional hardware resources and computation time.

Examples

Fixed-Point Divide Using CORDIC

num = fi(1);
den = fi(10);
OutputType = fi([],1,16,15);
y = fixed.cordicDivide(num,den,OutputType)

y = 
    0.1000

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

Input Arguments

num — Numerator

scalar | vector | matrix | multidimensional array

Numerator, specified as a real-valued scalar, vector, matrix, or multidimensional array.

• If num is a floating-point type, den must also be a floating-point type and OutputType must specify a floating-point data type.

• If num is a fixed-point type, den must also be a fixed-point type and OutputType must specify a fixed-point data type.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

den — Denominator

scalar | vector | matrix | multidimensional array

Numerator, specified as a real-valued scalar, vector, matrix, or multidimensional array.

• If num is a floating-point type, den must also be a floating-point type and OutputType must specify a floating-point data type.

• If num is a fixed-point type, den must also be a fixed-point type and OutputType must specify a fixed-point data type.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

OutputType — Data type of output

fi object | numerictype object | Simulink.NumericType object

Data type of the output, specified as a fi object, numerictype object, or Simulink.NumericType object.

• If num is a floating-point type, den must also be a floating-point type and OutputType must specify a floating-point data type.

• If num is a fixed-point type, den must also be a fixed-point type and OutputType must specify a fixed-point data type.

Example: fi([],1,16,15)

Example: numerictype(1,16,15)

Example: fixdt(1,16,15)

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, arcsine, arccosine, arctangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

The precision of the CORDIC algorithm is a function of the data type used and the maximum shift value or number of iterations of the CORDIC kernel. Using a data type with a larger word length and performing more iterations of the CORDIC algorithm can reduce the numeric error of the result. However, doing so also increases the latency of the computation and the utilizes more hardware resources. For more information, see How to Set CORDIC Input Word Length and Maximum Shift Value to Achieve Desired Precision.

Division by Zero Behavior

The behavior for fixed-point division by zero is summarized below.

• 0/0 = upper bound

• 1/0 = upper bound

• -1/0 = lower bound

For floating-point inputs, the fixed.cordicDivide function follows IEEE^® Standard 754.

References

[1] Volder, Jack E. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers EC-8, no. 3 (Sept. 1959): 330–334.

[2] Andraka, Ray. “A Survey of CORDIC Algorithm for FPGA Based Computers.” In Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays, 191–200. https://dl.acm.org/doi/10.1145/275107.275139.

[3] Walther, J.S. “A Unified Algorithm for Elementary Functions.” In Proceedings of the May 18-20, 1971 Spring Joint Computer Conference, 379–386. https://dl.acm.org/doi/10.1145/1478786.1478840.

[4] Schelin, Charles W. “Calculator Function Approximation.” The American Mathematical Monthly, no. 5 (May 1983): 317–325. https://doi.org/10.2307/2975781.

Extended Capabilities

C/C++ Code Generation

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

Slope-bias representation is not supported for fixed-point data types.

HDL Code Generation

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

The fixed.cordicDivide function also supports MATLAB^® to High-Level Synthesis (HLS) code generation.

Fixed-Point Conversion

Design and simulate fixed-point systems using Fixed-Point Designer™.

Slope-bias representation is not supported for fixed-point data types.

Version History

Introduced in R2020b

R2026a: Change in division by zero behavior

The division by zero behavior for the fixed.cordicDivide function has changed to be consistent with the fixed-point divide function, the Real Divide HDL Optimized block, and the Complex Divide HDL Optimized block.

This table summarizes the division by zero behavior for the fixed.cordicDivide function.

Previous Releases	R2026a
0/0 = 0 1/0 = upper bound -1/0 = lower bound	0/0 = upper bound 1/0 = upper bound -1/0 = lower bound