Fixed-Point Math Operations in MATLAB and Simulink
R2026bThe Fixed-Point Designer™ library of blocks provide hardware-efficient implementations of common math and matrix operations using algorithms such as CORDIC. Generate HDL code for designs that incorporate these blocks using HDL Coder™. The Fixed-Point Designer library of functions include CORDIC-based and other hardware-efficient implementations of math operations such as division, exponential operations, and trigonometric functions. Use coder to generate C/C++ code for designs that incorporate these functions.
CORDIC (COordinate Rotation DIgital Computer) based algorithms are some of the most hardware efficient algorithms because they require only iterative shift-add operations. The CORDIC algorithm eliminates the need for explicit multipliers, and is suitable for calculating a variety of functions.
For CORDIC-based implementations of matrix operations, including linear system solvers and matrix decompositions in MATLAB® and Simulink®, see Fixed-Point Matrix Operations in MATLAB and Fixed-Point Matrix Operations in Simulink.
Functions
Blocks
 | CORDIC Sigmoid HDL Optimized | Compute CORDIC-based sigmoid activation and generate optimized HDL code (Since R2024a) |
 | Complex Divide HDL Optimized | Divide one input by another using CORDIC algorithm and generate optimized HDL code |
 | Real Divide HDL Optimized | Divide one real input by another using CORDIC algorithm and generate optimized HDL code |
 | Divide by Constant HDL Optimized | Divide input by a constant and round to integer and generate optimized HDL code |
 | Divide by Constant and Round | Divide input by a constant and round to integer |
 | Modulo by Constant HDL Optimized | Perform mod operation with a constant denominator and generate optimized HDL code |
 | Modulo by Constant | Perform modulo operation with a constant denominator |
 | Normalized Reciprocal HDL Optimized | Computes normalized reciprocal using CORDIC algorithm and generates optimized HDL code |
 | Real Reciprocal HDL Optimized | Compute reciprocal and generate optimized HDL code |
 | Real Reciprocal Square Root HDL Optimized | Compute reciprocal of square root of real input and generate optimized HDL code (Since R2026b) |
 | CORDIC Square Root HDL Optimized | CORDIC-based approximation of square root (Since R2024a) |
 | Complex to Magnitude-Angle | Compute magnitude and phase angle of complex signal using CORDIC algorithm |
 | Magnitude-Angle to Complex | Convert magnitude and/or a phase angle signal to complex signal |
 | Exp HDL Optimized | Compute base-e exponential of input (Since R2026b) |
 | Log10 HDL Optimized | Compute base-10 logarithm of input (Since R2026b) |
 | Log2 HDL Optimized | Compute base-2 logarithm of input (Since R2026b) |
 | Logarithm HDL Optimized | Compute arbitrary-base logarithm of input (Since R2026b) |
 | Natural Logarithm HDL Optimized | Compute natural (base-e) logarithm of input (Since R2026b) |
 | Pow10 HDL Optimized | Compute base-10 exponential of input (Since R2026b) |
 | Pow2 HDL Optimized | Compute base-2 exponential of input (Since R2026b) |
 | Power HDL Optimized | Compute arbitrary-base exponential of input (Since R2026b) |
 | Hyperbolic Tangent HDL Optimized | Computes CORDIC-based hyperbolic tangent and generates optimized HDL code |
 | Trigonometric Function | Specified trigonometric function on input |
 | Euler to NED Transformation HDL Optimized | Computes Euler to North-East-Down transformation using pipelined or burst architecture and generates optimized HDL code (Since R2022b) |
 | Extract MSB | Extract most significant bit (MSB) of input (Since R2026b) |
Topics
- How to Set CORDIC Input Word Length and Maximum Shift Value to Achieve Desired Precision
This example provides a starting point for the input data type and number of iterations or maximum shift value required for the CORDIC algorithm to achieve a desired accuracy.
- Implement Hardware-Efficient Complex Divide HDL Optimized
How to use the Complex Divide HDL Optimized block.
- Implement Hardware-Efficient Real Divide HDL Optimized
How to use the Real Divide HDL Optimized block.
- Customize Output Value of Real Divide HDL Optimized Block When Denominator Is Zero
Use the divideByZero port to customize the value of the block output when division by zero occurs. (Since R2024b)
- Implement HDL Optimized Modulo by Constant
How to use the Modulo by Constant HDL Optimized block.
- How to Use HDL Optimized Normalized Reciprocal
This example shows how and when to use the
normalizedReciprocalfunction and the Normalized Reciprocal HDL Optimized block to compute the normalized reciprocal of an input. - Data Type Agent for Reciprocal HDL Optimized Blocks
Use the Data Type Agent to explore tradeoffs of algorithm, datatype, and latency for Reciprocal HDL Optimized blocks. (Since R2026b)
- Implement Hardware-Efficient Hyperbolic Tangent
Implement a hardware-efficient hyperbolic tangent.
- Hardware-Efficient Rotation About Arbitrary Axis Using CORDIC
This example shows how to implement rotation about an arbitrary axis using the CORDIC algorithm in Simulink®.
- Hardware-Efficient Euler Rotations Using CORDIC
This example shows how to implement Euler rotations using a CORDIC kernel.
- Hardware-Efficient Rotation About Arbitrary Axis Using CORDIC
This example shows how to implement rotation about an arbitrary axis using the CORDIC algorithm in Simulink®.
Featured Examples
Compute Square Root Using CORDIC
Compute square root using a CORDIC kernel algorithm in MATLAB.
Digital Waveform Generation: Approximate a Sine Wave
Design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.
Implement HDL-Optimized CORDIC-Based Square Root for Positive Real Numbers
Implement HDL-optimized CORDIC-based square root for positive real numbers.
