Intel FPGA Integer Arithmetic IP Cores User Guide

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Date 10/05/2020
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Document Table of Contents
Document Table of Contents x
1. Intel FPGA Integer Arithmetic IP Cores 2. LPM_COUNTER (Counter) IP Core 3. LPM_DIVIDE (Divider) Intel FPGA IP Core 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 IP Cores User Guide Document Archives 16. Document Revision History for Intel FPGA Integer Arithmetic 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 (Divider) Intel FPGA IP Core 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 Intel® Cyclone® 10 LP Devices 4.7. Parameters for Intel® Stratix® 10, Intel® Arria® 10, and Intel® Cyclone® 10 GX Devices
4.6. Parameters for Stratix V, Arria V, Cyclone V, and Intel® 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 Intel® Stratix® 10, Intel® Arria® 10, and Intel® 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. Intel FPGA Integer Arithmetic IP Cores
2. LPM_COUNTER (Counter) IP Core
3. LPM_DIVIDE (Divider) Intel FPGA IP Core
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 IP Cores User Guide Document Archives
16. Document Revision History for Intel FPGA Integer Arithmetic 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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