Integer Arithmetic Intel® FPGA IP Cores User Guide

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ID 683490
Date 7/30/2024
Public
Document Table of Contents
Document Table of Contents x
1. Integer Arithmetic Intel® FPGA IP Cores 2. LPM_COUNTER (Counter) IP Core 3. LPM_DIVIDE Intel® FPGA IP Core References 4. LPM_MULT (Multiplier) IP Core 5. LPM_ADD_SUB (Adder/Subtractor) 6. LPM_COMPARE (Comparator) 7. ALTECC (Error Correction Code: Encoder/Decoder) IP Core 8. Intel FPGA Multiply Adder IP Core 9. ALTMEMMULT (Memory-based Constant Coefficient Multiplier) IP Core 10. ALTMULT_ACCUM (Multiply-Accumulate) IP Core 11. ALTMULT_ADD (Multiply-Adder) IP Core 12. ALTMULT_COMPLEX (Complex Multiplier) IP Core 13. ALTSQRT (Integer Square Root) IP Core 14. PARALLEL_ADD (Parallel Adder) IP Core 15. Integer Arithmetic Intel® FPGA IP Cores User Guide Document Archives 16. Document Revision History for Integer Arithmetic Intel® FPGA IP Cores User Guide
2. LPM_COUNTER (Counter) IP Core x
2.1. Features 2.2. Verilog HDL Prototype 2.3. VHDL Component Declaration 2.4. VHDL LIBRARY_USE Declaration 2.5. Ports 2.6. Parameters
3. LPM_DIVIDE Intel® FPGA IP Core References x
3.1. Features 3.2. Verilog HDL Prototype 3.3. VHDL Component Declaration 3.4. VHDL LIBRARY_USE Declaration 3.5. Ports 3.6. Parameters
4. LPM_MULT (Multiplier) IP Core x
4.1. Features 4.2. Verilog HDL Prototype 4.3. VHDL Component Declaration 4.4. VHDL LIBRARY_USE Declaration 4.5. Signals 4.6. Parameters for Stratix V, Arria V, Cyclone V, and Cyclone® 10 LP Devices 4.7. Parameters for Stratix® 10, Arria® 10, and Cyclone® 10 GX Devices
4.6. Parameters for Stratix V, Arria V, Cyclone V, and Cyclone® 10 LP Devices x
4.6.1. General Tab 4.6.2. General 2 Tab 4.6.3. Pipelining Tab
4.7. Parameters for Stratix® 10, Arria® 10, and Cyclone® 10 GX Devices x
4.7.1. General Tab 4.7.2. General 2 Tab 4.7.3. Pipelining
5. LPM_ADD_SUB (Adder/Subtractor) x
5.1. Features 5.2. Verilog HDL Prototype 5.3. VHDL Component Declaration 5.4. VHDL LIBRARY_USE Declaration 5.5. Ports 5.6. Parameters
6. LPM_COMPARE (Comparator) x
6.1. Features 6.2. Verilog HDL Prototype 6.3. VHDL Component Declaration 6.4. VHDL LIBRARY_USE Declaration 6.5. Ports 6.6. Parameters
7. ALTECC (Error Correction Code: Encoder/Decoder) IP Core x
7.1. ALTECC Encoder Features 7.2. Verilog HDL Prototype (ALTECC_ENCODER) 7.3. Verilog HDL Prototype (ALTECC_DECODER) 7.4. VHDL Component Declaration (ALTECC_ENCODER) 7.5. VHDL Component Declaration (ALTECC_DECODER) 7.6. VHDL LIBRARY_USE Declaration 7.7. Encoder Ports 7.8. Decoder Ports 7.9. Encoder Parameters 7.10. Decoder Parameters
8. Intel FPGA Multiply Adder IP Core x
8.1. Features 8.2. Verilog HDL Prototype 8.3. VHDL Component Declaration 8.4. VHDL LIBRARY_USE Declaration 8.5. Signals 8.6. Parameters
8.1. Features x
8.1.1. Pre-adder 8.1.2. Systolic Delay Register 8.1.3. Pre-load Constant 8.1.4. Double Accumulator
8.1.1. Pre-adder x
8.1.1.1. Pre-adder Simple Mode 8.1.1.2. Pre-adder Coefficient Mode 8.1.1.3. Pre-adder Input Mode 8.1.1.4. Pre-adder Square Mode 8.1.1.5. Pre-adder Constant Mode
8.6. Parameters x
8.6.1. General Tab 8.6.2. Extra Modes Tab 8.6.3. Multipliers Tab 8.6.4. Preadder Tab 8.6.5. Accumulator Tab 8.6.6. Systolic/Chainout Tab 8.6.7. Pipelining Tab
9. ALTMEMMULT (Memory-based Constant Coefficient Multiplier) IP Core x
9.1. Features 9.2. Verilog HDL Prototype 9.3. VHDL Component Declaration 9.4. Ports 9.5. Parameters
10. ALTMULT_ACCUM (Multiply-Accumulate) IP Core x
10.1. Features 10.2. Verilog HDL Prototype 10.3. VHDL Component Declaration 10.4. VHDL LIBRARY_USE Declaration 10.5. Ports 10.6. Parameters
11. ALTMULT_ADD (Multiply-Adder) IP Core x
11.1. Features 11.2. Verilog HDL Prototype 11.3. VHDL Component Declaration 11.4. VHDL LIBRARY_USE Declaration 11.5. Ports 11.6. Parameters
12. ALTMULT_COMPLEX (Complex Multiplier) IP Core x
12.1. Complex Multiplication 12.2. Canonical Representation 12.3. Conventional Representation 12.4. Features 12.5. Verilog HDL Prototype 12.6. VHDL Component Declaration 12.7. VHDL LIBRARY_USE Declaration 12.8. Signals 12.9. Parameters
13. ALTSQRT (Integer Square Root) IP Core x
13.1. Features 13.2. Verilog HDL Prototype 13.3. VHDL Component Declaration 13.4. VHDL LIBRARY_USE Declaration 13.5. Ports 13.6. Parameters
14. PARALLEL_ADD (Parallel Adder) IP Core x
14.1. Feature 14.2. Verilog HDL Prototype 14.3. VHDL Component Declaration 14.4. VHDL LIBRARY_USE Declaration 14.5. Ports 14.6. Parameters
1. Integer Arithmetic Intel® FPGA IP Cores
2. LPM_COUNTER (Counter) IP Core
3. LPM_DIVIDE Intel® FPGA IP Core References
4. LPM_MULT (Multiplier) IP Core
5. LPM_ADD_SUB (Adder/Subtractor)
6. LPM_COMPARE (Comparator)
7. ALTECC (Error Correction Code: Encoder/Decoder) IP Core
8. Intel FPGA Multiply Adder IP Core
9. ALTMEMMULT (Memory-based Constant Coefficient Multiplier) IP Core
10. ALTMULT_ACCUM (Multiply-Accumulate) IP Core
11. ALTMULT_ADD (Multiply-Adder) IP Core
12. ALTMULT_COMPLEX (Complex Multiplier) IP Core
13. ALTSQRT (Integer Square Root) IP Core
14. PARALLEL_ADD (Parallel Adder) IP Core
15. Integer Arithmetic Intel® FPGA IP Cores User Guide Document Archives
16. Document Revision History for Integer Arithmetic Intel® FPGA IP Cores User Guide

12.1. 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:√-1
Two complex numbers, x = a + ib and y = c + id are multiplied, as shown in the following equations.
Figure 25. Equation for Two Complex Numbers Multiplication


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