General CORDIC Description

• 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 Simulations

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

Fixed Point Software Implementations

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

FPGA Hardware Implementations

• 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

• Lookahead CORDIC Literature Note (pdf)

Redundant CORDIC

• 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)

Angle Recoding CORDIC

• 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

• 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)

Binary Angular Measurement

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

Scaling-free CORDIC

CORDIC as a Search Algorithm

• CORDIC as a Search Idea.3.A (pdf)

5. Search (pdf)

Quad Angle Tree Based CORDIC

• CORDIC Quad Tree Angles (pdf)

6 Lookahead Idea (pdf)

Minimizing Latency

• Latency Minimizing Idea.2.A (pdf)

7. Backtrack (pdf)

Maximizing Throughput

• Throughput Maximizing Idea.1.A (pdf)

8. Serialize (pdf)

Bit-Serial & Bit-Parallel Trade-offs

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

9. Precision (pdf)

Bit-serial Redundant CORDIC (pdf)

Implementation Technical Background

- [ Understanding VLSI Design ]

- [ Understanding Low Power Design ]

- [ Understanding Arithmetic Circuits ]

- [ Understanding FPGA Design ]

Fixed Point Simulation

-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

Resource Sharing

- Area, Speed, Power Trade-offs between architectures

CORDIC Sensor Characteristics

• Accuracy
• Preceision
• Sensitivity
• Linearity
• Resoltion

Binary Angle Tree Approaches (C++, gnuplot)

General Angle Tree Approaches (C, R)

Functional Programming Approach

Background (pdf)

Binary Tree in Prolog

Background (pdf)

Rotating Vector Plotting

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

Symbolic Computation of CORDIC Equations

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

Simulation in C, C++, Octave

• 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)

Simulation using Multiple Precision Libraries (GMP, MPFR)

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

SystemC Model

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

VHDL Behavioral Model

• 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

• 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

CMOS CORDIC Design Examples

FPGA CORDIC Design Examples

Old CORDIC Background