CORDIC Hardware Implementations

• developing CORDIC architectures similar to DDR (Double Data Rate).

• General.1.A.pdf - Rotation as a complex number multiplication (in CORDIC FAQ)
• General.2.A.pdf - Rotation as a geometric interpretation (in Synthesis of Arithmetic Circuits examples)
• General.3.A.pdf - A set of CORDIC equations (in Andraka's paper )
• General.4.A.pdf - Unified CORDIC

• Software.1.A.pdf - Burkardt's MATLAB implementation
• Software.2.A.pdf - Burkardt's C++ implementation

• Fixed.1.A.pdf - Dr. Dobbs Journal implementation

• FPGA.1.A.pdf - Monash Univ VHDL implementation (architecture and precision)
• FPGA.2.A.pdf - Monash Univ VHDL implementation (VHDL detail )
• FPGA.2.B.pdf - Andraka's paper (FPGA related)

• Lookahead CORDIC Literature Note (pdf)

• Redundant Adders (pdf)
• Redundant CORDIC Note 1 - Tagaki (pdf)
• Redundant CORDIC Note 2 - Ercegovac (pdf)
• Redundant CORDIC Note 3 - Timmermann - A.(pdf) - B.(pdf) - C.(pdf)
• Redundant CORDIC Note 4 - Booth Encoding (pdf)
• Redundant CORDIC Note 5 - Noll (pdf)

• AR CORDIC Note 1 - Hu (pdf)
• AR CORDIC Note 2 - Wu (pdf)

0. Overview (pdf)

1. Conventional CORDIC (pdf)

2. AR (Angle Recoding) (pdf)

3. MVR (Modified Vector Rotation) (pdf)

4. EEAS (Extended Elementary Angle Set) (pdf)

5. Generalized EEAS (Extended Elementary Angle Set) (pdf)

• AR CORDIC Note 3 - Swartzlander (pdf)

• Hybrid CORDIC Note 1 - Sine/Cosine Generator Algorithms (pdf)
• Hybrid CORDIC Note 2 - Sine/Cosine Generator Architecture (pdf)
• Hybrid CORDIC Note 3 - ROM free modified coarse fine approach (pdf)
• Hybrid CORDIC Note 4 - Hybrid CORDIC Alogorithms (pdf)

Let's identify the source of the prevalent statement of "50 % improvement".

An explanation using a uniform framework would be good.

• BAM.1.A.pdf - Angle Recoding CORDIC- Y. H. Hu
• BAM.2.A.pdf - Trellis-based Searching CORDIC - C. S. Wu
• BAM.3.A.pdf - Look-ahead CORDIC - C. C. Kao
• BAM.4.A.pdf - Redundant CORDIC - T. Vladimirova
• BAM.5.A.pdf - Adpative CORDIC - T. K. Rodrigues
• BAM.6.A.pdf - MSE Variance CORDIC - S. Y. Park
• BAM.7.A.pdf - Angle Approx Error & Datapath Rounding Error - C. Dick

• CORDIC as a Search Idea.3.A (pdf)

5. Search (pdf)

• CORDIC Quad Tree Angles (pdf)

6 Lookahead Idea (pdf)

• Latency Minimizing Idea.2.A (pdf)

7. Backtrack (pdf)

• Throughput Maximizing Idea.1.A (pdf)

8. Serialize (pdf)

• Generalized Multi-Byte CORDIC Idea.4.A (pdf)

9. Precision (pdf)

Bit-serial Redundant CORDIC (pdf)

- [ Understanding VLSI Design ]

- [ Understanding Low Power Design ]

- [ Understanding Arithmetic Circuits ]

- [ Understanding FPGA Design ]

-Octave

3. Octave Codes (pdf)

-SystemC

-VHDL Simulation

CORDIC Angle LUT ( scr.pdf, out.pdf)

CORDIC ROM Generation and Initialization ( c6.rom.file.vhdl )

CORDIC BEH Simulation ( cordic_beh.pdf )

CORDIC RTL Simulation ( cordic_rtl.pdf )

CORDIC testbench ( cordic_tb.vhdl )

-VHDL Testcases

- Area, Speed, Power Trade-offs between architectures

• Accuracy
• Preceision
• Sensitivity
• Linearity
• Resoltion

CORDIC.AccPrec (pdf)

CORDIC Source (pdf)

Makefile (pdf)

Core class (pdf)

Angles class (pdf, pdf)

GPData class (pdf)

Figures class (pdf)

Interfacing GHDL CORDIC simulation with C (pdf)

Calling C++ cordic function from C (pdf)

batch run bash file for Angles_tb (pdf)

fig_basic (pdf, note)

fig_tscale (pdf)

fig_uscale (pdf)

cordic testbenches (pdf)

cordic testbench 01 (percent error)

cordic testbench 02 (path error)

cordic testbench 03 (varying tree levels)

fig_basic (pdf)

fig_tscale (pdf)

fig_uscale (pdf)

cordic testbench 04 (coarse-fine)

1. General (pdf)

2. Statistical Analysis (pdf)

3. Octave Fixed Point Simulation (pdf)

4. Scaling K (pdf)

batch run bash file for testbench 01 (pdf)

batch run bash file for testbench 02 (pdf)

Angles_wx using wxWidgets & wxGlade (pdf)

Tree type	Memory bound	Time bound
Binary Tree	code, output	pdf
Ternary Tree	code, output	pdf
Quaternary tree	code, output	pdf
Full Tree	code, output	pdf

Tree type	Memory bound	Time bound
Binary Tree	code, output	pdf
Ternary Tree	code, output	pdf
Quaternary tree	code, output	pdf
Full Tree	code, output	pdf

Tree type	Memory bound	Time bound
Binary Tree	code, output	pdf
Ternary Tree	code, output	pdf
Quaternary tree	code, output	pdf
Full Tree	code, output	pdf

Tree Type	R Script	Output
Binary Tree	pdf	pdf
Ternary Tree	pdf	pdf
Quaternary	pdf	pdf

1. Powers of 2 angles testcase (code, summary)

Tree Type	log file	table	plot
Binary Tree	pdf	pdf	pdf
Ternary Tree	pdf	pdf	pdf
Quaternary	pdf	pdf	pdf

2. Leaf and internal node angles testcase

3. Uniformly distributed angles testcase

4. Subtree angles testcase

Background (pdf)

Background (pdf)

• Scale Space Filtering (Gaussian Smoothing)
• Parallel CORDIC
• Neural Network (Computing Exponential Function)

See Burkardt's C++ Implementations

• Using gnuplot_i package (pdf)
• CORDIC Animation: Java Swing Based CORDIC Simulator

• Using Maxima / wxMaxima (pdf, matrix.pdf)

• CORDIC Octave Simulation ( CORDIC.m.pdf)
• CORDIC C++ Simulation ( CORDIC_cpp.pdf)
• CORDIC C Simulation ( CORDIC.c.pdf, CORDIC_tb.c.pdf)
• CORDIC Fixed Point C Simulation ( CORDIC.fixed.c.pdf)

• CORDIC GMP Simulation ( cordic_gmp.pdf, normerror.pdf)

• SystemC Data Types (my_cnt.systemc, dtype.systemc)
• Fixed point Simulation (cordic.scfix)
• Generating VHDL ROM model (cordic.rom)

• VHDL Behavioral Model and Testbench (cordic_beh in one file, cordic_beh.vhdl, cordic_tb.vhdl, cordic_pkg.vhdl)
• VHDL Data Conversion - some test pieces (test_conv.vhdl)

• VHDL Data Flow Model and Testbench ( cordic_rtl in one file, CORDIC.rtl)

c1.adder.rtl.vhdl, c2.addsub.vhdl, c3.bshift.vhdl, c4.dffreg.vhdl, c5.counter.vhdl, c6.rom.vhdl, c7.mux.vhdl, m1.disp.vhdl,

cordic_rtl.vhdl, cordic_pkg.vhdl, cordic_tb.vhdl

• Background.1.A - CORDIC FAQ (1.A.pdf)
• Background.2.A,B - Andraka's paper (2.A.pdf, 2.B.pdf)
• Background.3.A - Unified CORDIC (3.A.pdf)
• Background.4.A - Synthesis of Arithmetic Circuits examples (4.A.pdf)

• Burkardt's MATLAB implementation (Matlab.1.A) (pdf)
• Burkardt's C++ implementation (C++.1.A) (pdf)

• Dr. Dobbs Journal implementation (fixed.1.A) (pdf)

• Monash Univ VHDL implementation (VHDL.1.A.pdf, VHDL.2.A.pdf )

Some Plots

Threshold=0.0 (pdf)

Threshold=0.001 (pdf)

Quantization Effects (pdf)

Percent Error (pdf)

Residue Statistics (tex file:pdf, pdf)

CORDIC.AccPrec (pdf)

Angles Class Source (pdf)

Angles_wx using wxWidgets & wxGlade (pdf)

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