Stratix® 10 Variable Precision DSP Blocks User Guide

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ID 683832
Date 7/08/2024
Public
Document Table of Contents
Document Table of Contents x
1. Stratix® 10 Variable Precision DSP Blocks Overview 2. Block Architecture Overview 3. Operational Mode Descriptions 4. Design Considerations 5. Stratix® 10 Variable Precision DSP Blocks Implementation Guide 6. Native Fixed Point DSP Stratix® 10 FPGA IP Core References 7. Multiply Adder IP Core References 8. ALTMULT_COMPLEX Intel® FPGA IP Core References 9. LPM_MULT Intel® FPGA IP Core References 10. Native Floating Point DSP Stratix® 10 FPGA IP References 11. LPM_DIVIDE (Divider) Intel FPGA IP Core 12. Stratix® 10 Variable Precision DSP Blocks User Guide Document Archives 13. Document Revision History for the Stratix® 10 Variable Precision DSP Blocks User Guide
1. Stratix® 10 Variable Precision DSP Blocks Overview x
1.1. Features 1.2. Supported Operational Modes in Stratix® 10 Devices 1.3. Resources
2. Block Architecture Overview x
2.1. Input Register Bank for Fixed-Point and Floating-Point Arithmetic 2.2. Pipeline Registers for Fixed-Point and Floating-Point Arithmetic 2.3. Pre-adder for Fixed-Point Arithmetic 2.4. Internal Coefficient for Fixed-Point Arithmetic 2.5. Multipliers for Fixed-Point and Floating-Point Arithmetic 2.6. Adder or Subtractor for Fixed-Point and Floating-Point Arithmetic 2.7. Accumulator, Chainout Adder, and Preload Constant for Fixed-Point Arithmetic 2.8. Systolic Register for Fixed-Point Arithmetic 2.9. Double Accumulation Register for Fixed-Point Arithmetic 2.10. Output Register Bank for Fixed-Point and Floating-Point Arithmetic 2.11. Exception Handling for Floating-Point Arithmetic
3. Operational Mode Descriptions x
3.1. Operational Modes for Fixed-Point Arithmetic 3.2. Operational Modes for Floating-Point Arithmetic
3.1. Operational Modes for Fixed-Point Arithmetic x
3.1.1. Independent Multiplier Mode 3.1.2. Multiplier Adder Sum Mode 3.1.3. Independent Complex Multiplier 3.1.4. 18 × 19 Multiplication Summed with 36-Bit Input Mode 3.1.5. Systolic FIR Mode
3.1.1. Independent Multiplier Mode x
3.1.1.1. 18 × 18 or 18 × 19 Independent Multiplier 3.1.1.2. 27 × 27 Independent Multiplier
3.1.5. Systolic FIR Mode x
3.1.5.1. Mapping Systolic Mode User View to Variable Precision Block Architecture View 3.1.5.2. 18-bit Systolic FIR Mode 3.1.5.3. 27-Bit Systolic FIR Mode
3.2. Operational Modes for Floating-Point Arithmetic x
3.2.1. Single Floating-Point Arithmetic Functions 3.2.2. Multiple Floating-Point Arithmetic Functions
3.2.1. Single Floating-Point Arithmetic Functions x
3.2.1.1. Multiplication Mode 3.2.1.2. Adder or Subtract Mode 3.2.1.3. Multiply Accumulate Mode
3.2.2. Multiple Floating-Point Arithmetic Functions x
3.2.2.1. Multiply-Add or Multiply-Subtract Mode 3.2.2.2. Vector One Mode 3.2.2.3. Vector Two Mode 3.2.2.4. Direct Vector Dot Product 3.2.2.5. Complex Multiplication
4. Design Considerations x
4.1. Internal Coefficient and Pre-Adder for Fixed-Point Arithmetic 4.2. Accumulator for Fixed-Point Arithmetic 4.3. Chainout Adder 4.4. Input Cascade for Fixed-Point Arithmetic 4.5. DSP Block Cascade Limit in Agilex™ 7 Devices
5. Stratix® 10 Variable Precision DSP Blocks Implementation Guide x
5.1. 'X' Propagation Support in Simulation
6. Native Fixed Point DSP Stratix® 10 FPGA IP Core References x
6.1. Native Fixed Point DSP Stratix® 10 FPGA IP Release Information 6.2. Supported Operational Modes 6.3. Maximum Input Data Width for Fixed-Point Arithmetic 6.4. Parameterizing Native Fixed Point DSP IP Core 6.5. Signals
6.3. Maximum Input Data Width for Fixed-Point Arithmetic x
6.3.1. Using Less Than 36-Bit Operand In 18 x 18 Plus 36 Mode Example
6.4. Parameterizing Native Fixed Point DSP IP Core x
6.4.1. Native Fixed Point DSP Stratix® 10 FPGA IP Parameters
7. Multiply Adder IP Core References x
7.1. Multiply Adder Intel FPGA IP Release Information 7.2. Features 7.3. Parameters 7.4. Signals
7.2. Features x
7.2.1. Pre-adder 7.2.2. Systolic Delay Register 7.2.3. Pre-load Constant 7.2.4. Double Accumulator
7.2.1. Pre-adder x
7.2.1.1. Pre-adder Simple Mode 7.2.1.2. Pre-adder Coefficient Mode 7.2.1.3. Pre-adder Input Mode 7.2.1.4. Pre-adder Square Mode 7.2.1.5. Pre-adder Constant Mode
7.3. Parameters x
7.3.1. General Tab 7.3.2. Extra Modes 7.3.3. Multipliers Tab 7.3.4. Preadder Tab 7.3.5. Accumulator Tab 7.3.6. Systolic/Chainout Tab 7.3.7. Pipelining Tab
8. ALTMULT_COMPLEX Intel® FPGA IP Core References x
8.1. ALTMULT_COMPLEX Intel FPGA IP Release Information 8.2. Features 8.3. Complex Multiplication 8.4. Parameters 8.5. Signals
9. LPM_MULT Intel® FPGA IP Core References x
9.1. LPM_MULT Intel FPGA IP Release Information 9.2. Features 9.3. Parameters 9.4. Signals
9.3. Parameters x
9.3.1. General Tab 9.3.2. General 2 Tab 9.3.3. Pipelining Tab
10. Native Floating Point DSP Stratix® 10 FPGA IP References x
10.1. Native Floating Point DSP Stratix® 10 FPGA IP Release Information 10.2. Native Floating Point DSP Stratix® 10 FPGA IP Core Supported Operational Modes 10.3. Parameterizing the Native Floating Point DSP Stratix® 10 FPGA IP 10.4. Native Floating Point DSP Stratix® 10 FPGA IP Core Signals
10.3. Parameterizing the Native Floating Point DSP Stratix® 10 FPGA IP x
10.3.1. Native Floating Point DSP Stratix® 10 FPGA IP Parameters
11. LPM_DIVIDE (Divider) Intel FPGA IP Core x
11.1. LPM_DIVIDE Intel® FPGA IP Release Information 11.2. Features 11.3. Verilog HDL Prototype 11.4. VHDL Component Declaration 11.5. VHDL LIBRARY_USE Declaration 11.6. Ports 11.7. Parameters
11.7. Parameters x
11.7.1. General Tab 11.7.2. General1 Tab
1. Stratix® 10 Variable Precision DSP Blocks Overview
2. Block Architecture Overview
3. Operational Mode Descriptions
4. Design Considerations
5. Stratix® 10 Variable Precision DSP Blocks Implementation Guide
6. Native Fixed Point DSP Stratix® 10 FPGA IP Core References
7. Multiply Adder IP Core References
8. ALTMULT_COMPLEX Intel® FPGA IP Core References
9. LPM_MULT Intel® FPGA IP Core References
10. Native Floating Point DSP Stratix® 10 FPGA IP References
11. LPM_DIVIDE (Divider) Intel FPGA IP Core
12. Stratix® 10 Variable Precision DSP Blocks User Guide Document Archives
13. Document Revision History for the Stratix® 10 Variable Precision DSP Blocks User Guide

8.3. Complex Multiplication

Complex numbers are numbers in the form of the following equation:

a + ib

Where:

  • a and b are real numbers
  • i is an imaginary unit that equals the square root of -1.
Two complex numbers, x = a + ib and y = c + id are multiplied, as shown in the following equations.
Figure 44. Equation for Two Complex Numbers Multiplication


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