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trunk/doc/documentation.pdf Property changes : Added: svn:mime-type ## -0,0 +1 ## +application/pdf \ No newline at end of property Index: trunk/doc/documentation.tex =================================================================== --- trunk/doc/documentation.tex (nonexistent) +++ trunk/doc/documentation.tex (revision 2) @@ -0,0 +1,507 @@ +\documentclass[a4paper, 12pt, notitlepage]{report} + +\usepackage{amsfonts} +\usepackage{graphicx} +\usepackage{fullpage} +\usepackage[pagewise]{lineno} +\usepackage{hyperref} +\usepackage{longtable} +\usepackage{ltxtable} +\usepackage[usenames,dvipsnames]{color} +\usepackage{colortbl} +\usepackage{tabularx, booktabs} +\usepackage{multirow} +\usepackage{dirtree} +\definecolor{tableheadcolor}{gray}{0.8} +\definecolor{darkblue}{rgb}{0,0,.5} +\definecolor{gray}{gray}{0.95} +\definecolor{lightgray}{gray}{0.95} +\newcommand{\file}[1]{\textbf{#1}} +\newcommand{\state}[1]{{\tt\textbf{#1}}} +\newcommand{\signal}[1]{{\textbf{\tt#1}}} +\title{YAC - Yet Another CORDIC Core} +\author{Christian Haettich [feddischson@opencores.org]} +\date{\today} + +\begin{document} + +%%%%%%%%%% PRELIMINARY MATERIAL %%%%%%%%%% +\maketitle +\begin{center} +IP core and C-model documentation +\end{center} +\thispagestyle{empty} + +\tableofcontents + + +\chapter{Organization and Introduction} +\section{History} +\begin{table}[htbp] + \center + \begin{tabular}{@{}llll@{}} + \rowcolor{tableheadcolor}\textbf{Version}& \textbf{Date} & \textbf{Description} & \textbf{Author} \\ + + \multirow{1}{*}{0.01} & 4th March 2014 & Initial document & Christian Haettich\\\midrule + \bottomrule + \end{tabular} + \caption{History} + \label{tab:frqband} +\end{table} + + +\section{Folder and Files} + +\dirtree{% +.1 /. +.2 c\_octave. +.3 cordic\_iterative.c\DTcomment{C-code for bit accurate model}. +.3 cordic\_iterative\_code.m\DTcomment{Script to auto-generate VHDL and C-code}. +.3 cordic\_iterative\_test.m\DTcomment{YAC performance analysis script}. +.2 doc.\DTcomment{Contains files to create this documentation}. +.2 licenses. +.3 lgpl-3.0.txt\DTcomment{LGPL license}. +.2 README.txt\DTcomment{A short read-me file}. +.2 rtl. +.3 vhdl. +.4 cordic\_iterative\_int.vhd\DTcomment{Top-level VHDL file}. +.4 cordic\_iterative\_pkg.vhd\DTcomment{VHDL package file}. +.4 cordic\_iterative\_tb.vhd\DTcomment{VHDL testbench}. +} + +\section{License} +Copyright (c) 2014, Christian Haettich, All rights reserved. \newline\newline +YAC is free software; you can redistribute it and/or +modify it under the terms of the GNU Lesser General Public +License as published by the Free Software Foundation; either +version 3.0 of the License, or (at your option) any later version. \newline\newline +YAC is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +Lesser General Public License for more details. \newline\newline +You should have received a copy of the GNU Lesser General Public +License along with this library. If not, download it from +http://www.gnu.org/licenses/lgpl + + +\section{The CORDIC algorithm} + +The CORDIC algorithm is used to do trigonometric, hyperbolic, multiplication +and division calculations in a hardware-efficient way. This means, that +only bit-shift, addition and subtraction operations in combination +with a lookup-table is required.\newline +Good introductions are available in \cite{survey}\cite{vlsi}\cite{dawid}. +A description on wikibook.org \cite{wikibook} is also useful. +For this reason, no more introduction is given here and the following chapters assume, that +the reader is familiar with the CORDIC algorithm. + + +\chapter{IP-Core Description} + +The two files \file{cordic\_iterative\_int.vhd} and \file{cordic\_iterative\_pkg.vhd} +implements an iterative CORDIC algorithm in fixed-point format. +Iterative means, that the IP-core is started with a set of input data and after +a specific amount of clock cycles, the result is available. No parallel data +can be processed. The +following six modes are supported: +\begin{itemize} + \item trigonometric rotation + \item trigonometric vectoring + \item linear rotation + \item linear vectoring + \item hyperbolic rotation + \item hyperbolic vectoring +\end{itemize} + +\section{Port Description} +\begin{table}[htbp] + \center + \begin{tabular}{@{}lllll@{}} + \rowcolor{tableheadcolor}\textbf{Name}& \textbf{Type} & \textbf{Direction} & \textbf{Size} & \textbf{Description} \\ + + \multirow{1}{*}{clk} & std\_logic & input & 1 & clock \\\midrule + \multirow{1}{*}{rst} & std\_logic & input & 1 & synchronous reset \\\midrule + \multirow{1}{*}{en} & std\_logic & input & 1 & clock-enable \\\midrule + \multirow{1}{*}{start} & std\_logic & input & 1 & start trigger \\\midrule + \multirow{1}{*}{done} & std\_logic & output & 1 & done indicator \\\midrule + \multirow{1}{*}{mode} & std\_logic\_vector & input & 4 & mode configuration \\\midrule + \multirow{1}{*}{x\_i} & std\_logic\_vector & input & XY\_WIDTH & X input vector \\\midrule + \multirow{1}{*}{y\_i} & std\_logic\_vector & input & XY\_WIDTH & Y input vector \\\midrule + \multirow{1}{*}{a\_i} & std\_logic\_vector & input & A\_WIDTH + 2 & angular input vector \\\midrule + \multirow{1}{*}{x\_o} & std\_logic\_vector & input & XY\_WIDTH + GUARD\_BITS & X output vector \\\midrule + \multirow{1}{*}{y\_o} & std\_logic\_vector & input & XY\_WIDTH + GUARD\_BITS & Y output vector \\\midrule + \multirow{1}{*}{a\_o} & std\_logic\_vector & input & A\_WIDTH + 2 & angular output vector \\\midrule + \bottomrule + \end{tabular} + \caption{Port description} + \label{tab:ports} +\end{table} + +\begin{figure}[p] +\centering + \includegraphics{figs/block_symbol.pdf} + \caption{YAC block symbol} + \label{fig:ports} +\end{figure} +Table \ref{tab:ports} and Figure \ref{fig:ports} gives an overview +of the YAC ports. +The three input ports start, done and mode and are used to interact +with an external state machine or with a software driver. +After setting \signal{start} to high, the YAC starts processing. +If all necessary rotations are done, the \signal{done} output is set to +high for one clock cycle. +When starting the YAC, all other inputs must contain valid data. +The mode input is used to select the CORDIC mode. +Table \ref{fig:ports} shows all input and output ports and Figure +\ref{fig:ports} shows a CORDIC block symbol: $x_i, y_i, a_i, x_o, y_o, a_o$ +are data ports whereas start, done and mode are configuration signals. + + + + + + +\section{Parameter Description} +\begin{table}[htbp] + \center + \begin{tabular}{@{}lllll@{}} + \rowcolor{tableheadcolor}\textbf{Name}& \textbf{type} & \textbf{size} & \textbf{Description} \\ + + \multirow{1}{*}{XY\_WIDTH} & natural & defines the size of x and y input and output vectors \\\midrule + \multirow{1}{*}{A\_WIDTH} & natural & defines the size of the angular input and output vectors \\\midrule + \multirow{1}{*}{GUARD\_BITS} & natural & defines the number of guard bits \\\midrule + \multirow{1}{*}{RM\_GAIN} & natural & defines the precision of the CORDIC gain removal \\\midrule + \bottomrule + \end{tabular} + \caption{Parameter description} + \label{tab:params} +\end{table} +Table \ref{tab:params} shows the four parameter, which can be used to parameterize +the YAC. + + +\section{Mode description} +With the mode-input, it is possible to select between circular, linear and hyperbolic +operation as well as between rotation and vectoring operations: +\begin{itemize} +\item mode(1:0) = "00" selects circular operation +\item mode(1:0) = "01" selects linear operation +\item mode(1:0) = "10" selects hyperbolic operation +\item mode(1:0) = "11" is reserved +\item mode(3) = '0' selects rotation +\item mode(3) = '1' selects vectoring +\end{itemize} +The package cordic\_iterative\_int.vhd contains the following defines to +setup the mode: +\begin{itemize} + \item VAL\_MODE\_CIRC = "00" + \item VAL\_MODE\_LIN = "01" + \item VAL\_MODE\_HYP = "10" + \item I\_FLAG\_VEC\_ROT = 3 (bit index) +\end{itemize} +For example if a hyperbolic rotation mode is required, the mode input is "0010", +and for the linear vector operation, the mode input is "1001". +Please note, that bit number 2 is reserved for future implementations.\newline +Table \ref{tab:modes} defines the behaviour of the YAC +for different mode configurations. +\begin{table}[htbp] + \center + \begin{tabular}{@{}ll@{}} + \rowcolor{tableheadcolor}\textbf{Setup}& \textbf{Description} \\ + + \multirow{2}{*}{mode =( FLAG\_VEC\_ROT = 1, VAL\_MODE\_CIR ) } & $a_o = \textrm{atan2}( y_i, x_i ) \cdot \beta, $\\ + & $x_o = \sqrt{ x_i^2+y_i^2 } $ \\\midrule + \multirow{2}{*}{mode =( FLAG\_VEC\_ROT = 0, VAL\_MODE\_CIR ) } & $x_o = \cos( a_i / \beta ) \cdot \alpha $\\ + & $y_o = \sin( a_i / \beta ) \cdot \alpha $\\\midrule + \multirow{1}{*}{mode =( FLAG\_VEC\_ROT = 1, VAL\_MODE\_LIN ) } & $a_o = z + y/x $\\\midrule + \multirow{1}{*}{mode =( FLAG\_VEC\_ROT = 0, VAL\_MODE\_LIN ) } & $a_o = y + x\cdot z $ $ $\\\midrule + \multirow{2}{*}{mode =( FLAG\_VEC\_ROT = 1, VAL\_MODE\_HYP ) } & $a_o = \textrm{tanh}( y_i / x_i ) \cdot \beta, $\\ + & $x_o = \sqrt{ x_i^2-y_i^2 } $\\\midrule + \multirow{2}{*}{mode =( FLAG\_VEC\_ROT = 0, VAL\_MODE\_HYP ) } & $x_o = \cosh( a_i / \beta ) \cdot \alpha$\\ + & $y_o = \sinh( a_i / \beta ) \cdot \alpha$\\ + \bottomrule + \end{tabular} + \caption{Mode description (see equation \ref{eqn:alpha} and \ref{eqn:beta} for $\alpha$ and $\beta$)} + \label{tab:modes} +\end{table} + + +\section{Data Range and Limitations} + + Both, the $x_i$ and $y_i$ inputs are defined with a size of $XY\_WIDTH$ and therefore, + the maximum positive value in the two's complement format is + \begin{eqnarray} + \alpha & = & 2^{XY\_WIDTH-1}-1 + \label{eqn:alpha} + \end{eqnarray} + The angle input $a_i$ is defined with a size of $A\_WIDTH+2$. + The value $\beta$ is defined with + \begin{eqnarray} + \beta & = & 2^{A\_WIDTH-1} -1 + \label{eqn:beta} + \end{eqnarray} + + \subsection{Circular Vectoring Mode} + + The valid input range for $x_i$ and $y_i$ is $-\alpha ... +\alpha$. + The angular input $a_i$ is ignored. + + \subsection{Circular Rotation Mode} + The valid input range for $x_i$ and $y_i$ is $-\alpha ... +\alpha$. + For the angular input $a_i$, values between $-\beta\pi$ and $+\beta\pi$ are valid. + For calculating a complex rotation of a complex vector, all three inputs + are required. For calculating $\sin$ and $\cos$, $x_i$ is set to $\alpha$ + and $y_i$ to 0, the angle input $a_i$ gets the angle. + + \subsection{Linear Vectoring Mode} + The linear vectoring mode is used to calculate $y_i / x_i$. The limitation + of this operation is the following: + \begin{eqnarray} + \frac{y_i}{x_i} \le 2 + \end{eqnarray} + The valid input values for $x_i$ and $y_i$ are $-\alpha ... +\alpha$. + + \subsection{Linear Rotation Mode} + The two inputs $x_i$ and $y_i$ have a valid data range between $-\alpha$ and $+\alpha$. + + + \subsection{Hyperbolic Vectoring Mode} + The data-range for $x_i$ and $y_i$ is $-0.79 \cdot \alpha$ to $0.79 \cdot \alpha$. + + + \subsection{Hyperbolic Rotation Mode} + The data-range for $a_i$ is $-\beta ... \beta$. Typically, $x_i$ is set to + $\alpha$ and $y_i$ to 0. + +\section{Internal Operation} +\begin{figure}[p] +\centering + \includegraphics[width=200pt]{figs/state_diagram.pdf} + \caption{State diagram} + \label{fig:states} +\end{figure} +Five states are used do to the CORDIC algorithm. The five states are visualized in a +state diagram in Figure \ref{fig:states}. +After reset, the YAC goes into the \state{ST\_IDLE} state. Only in this state, the +start signal is accepted. After starting the YAC, the state switches from +the \state{ST\_IDLE} state to the \state{ST\_INIT} state. The init state does some initial +rotations/flipping. +After initialization, the main rotation starts with the \state{ST\_ROTATION} state +(there are a few cases, where no further rotations are required, see next sections). +Every rotation step is done within two clock cycles: in the first cycle, +the angular value is loaded from the lookup-table and shifted. In addition, +the x and y values are shifted. In the second +clock cycle, the results are added according to the CORDIC algorithm. +After all required iterations are done, the state switches to +the \state{RM\_GAIN} state, where the CORDIC gain is removed (depending on +the mode). The last state \state{ST\_DONE} is only used to set the done flag to +'1' for one clock cycle. After this, the YAC returns to the \state{ST\_IDLE} state. + + + + \subsection{Initialization} + During the initialization state ST\_INIT, pre-rotations are done, depending on + the selected mode. + + + \subsubsection{Circular Vectoring Mode} + Because we support atan2 and not atan, we do the following pre-rotations. + Some specific input values don't need a further processing, for + example $atan( 0, 0 )$.\newline\newline + \begin{tabular}{@{}lp{380pt}@{}} + \rowcolor{tableheadcolor}\textbf{Input} &\textbf{ Description } \\ + + $x_i = 0, y_i = 0$ & Fixed result: $x_o = 0, a_o = 0$, + to support cartesian to polar coordinate transformations, + further processing is skipped \\ \midrule + + $x_i = 0, y_i > 0 $ & Fixed result: $x_o = y_i, a_o = \pi/2$, + further processing is skipped \\ \midrule + + $x_i = 0, y_i < 0 $ & Fixed result: $x_o = -y_i, a_o = -\pi/2$, + further processing is skipped \\ \midrule + + + $x_i < 0, y_i < 0 $ & Pre-rotation from the third to the first quadrant, + the angular register is initialized with $-\pi$ and + the sign of the $x$ and $y$ register is flipped. \\ \midrule + + $x_i < 0, y_i \ge 0 $ & Pre-rotation from the second to the fourth quadrant, + the angular register is initialized with $\pi$ and + the sign of the $x$ and $y$ register is flipped. \\ \midrule + + + $x_i = + \alpha, y_i = + \alpha $ & Fixed result: $x_o = \sqrt{2} \cdot \alpha, a_o = \frac{\pi}{4} \cdot \beta$ , + further processing is skipped \\ \midrule + + $x_i = + \alpha, y_i = - \alpha $ & Fixed result: $x_o = \sqrt{2} \cdot \alpha, a_o = - \frac{\pi}{4} \cdot \beta$, + further processing is skipped \\ \midrule + + $x_i = - \alpha, y_i = + \alpha $ & Fixed result: $x_o = \sqrt{2} \cdot \alpha, a_o = \frac{3 \pi}{4} \cdot \beta$, + further processing is skipped \\ \midrule + + $x_i = - \alpha, y_i = - \alpha $ & Fixed result: $x_o = \sqrt{2} \cdot \alpha, a_o = - \frac{3 \pi }{4} \cdot \beta$ , + further processing is skipped \\ + \bottomrule + \end{tabular} + + \subsubsection{Circular Rotation Mode} + The following pre-rotations are done:\newline\newline + \begin{tabular}{@{}lp{380pt}@{}} + \rowcolor{tableheadcolor}\textbf{Input} &\textbf{ Description } \\ + + $a_i < - \frac{\pi}{2}$ & Pre-rotation from the third to the first quadrant, + the sign of the $x$ and $y$ register is flipped, + the angular register is initialized with $\pi$ \\ \midrule + + $a_i > \frac{\pi}{2}$ & Pre-rotation from the second to the fourth quadrant, + the sign of the $x$ and $y$ register is flipped, + the angular register is initialized with $-\pi$ \\ + \bottomrule + \end{tabular} + + \subsubsection{Linear Vectoring Mode} + The following pre-rotations are done:\newline\newline + \begin{tabular}{@{}lp{380pt}@{}} + \rowcolor{tableheadcolor}\textbf{Input} &\textbf{ Description } \\ + + $x_i < 0$ & Pre-rotation from the left half to the right half, thus + the sign of the $x$ and $y$ register is flipped \\ + \bottomrule + \end{tabular} + + + \subsection{Rotation} + + \subsubsection{Hyperbolic Repetitions} + The following iteration steps are repeated for convergence of the hyperbolic mode: + \begin{eqnarray} + 4, 13, 40, 121, ..., 3i+1 + \end{eqnarray} + + + +\section{Testbench} +A VHDL testbench (cordic\_iterative\_tb.vhd) is available which reads from an input file +data. This data is fed into the YAC. In addition, the input file must +provide the output data, which is expected from the YAC processing. +The following format is used in the testbench input-file: +\begin{verbatim} +x_i y_i a_i x_o y_o a_o mode + +1234 1234 1234 1234 1234 1234 111 \ +2345 2345 2345 2345 2345 2345 222 | 7 columns: +3456 3456 3456 3456 3456 3456 333 | 3 input, 3 output and one mode +... ... | +... | +... +\end{verbatim} +The data must be in the two's complement with a base of 10. +After processing all lines, the testbench prints some info, how much +tests failed.\newline +For generating the test-patterns, the C-model with octave is used. By running +the script \file{cordic\_iterative\_test.m}, an entry +in the testbech data file is done for every cordic calculation. + + +\chapter{Using the C-Model with Octave or Matlab} +For using the C-model, open octave or Matlab and compile the C-Model +with \newline +\textit{mex cordic\_iterative.c} +Afterwards, the C-model can be used in Octave/Matlab with the function call\newline +{\tt [ x\_o, y\_o, a\_o, it ] = cordic\_iterative( x\_i, y\_i, a\_i, mode, XY\_WIDTH, ANGLE\_WIDTH, +GUARD\_BITS, RM\_GAIN )}.\newline +The input and output arguments reflect almost the ports and parameters of the +VHDL toplevel implementation, except that there is no done, start clk and rst port +in the C-model. In addition, the last argument provides the number of iterations, +which are done.\newline \newline +The input arguments x\_i, y\_i, and a\_i can be 1xN vectors with N elements. +In this case, this three input arguments must have the same size. All +output arguments will also have the same size 1xN. + + + +\section{Guard-Bits -- Input and output sizes} +It is possible to define MSB guard bits. +The need of MSB guard bits have several reasons. On the one hand, +they are required to handle the data growth of the cordic gain within the rotation state. +(which is compensated later). A nother reason is the data growth caused by the choise of +input data. For example +\begin{eqnarray} + \sqrt{ \alpha^2 + \alpha^2 } = \sqrt{2} \alpha +\end{eqnarray} +and therefore, a growth by the factor $\sqrt{2}$ happens, if an absolute calculation +of the two maximum input values is processed.\newline +\newline +Another point is the input and output size of the angular values ($a_i$ and $a_o$) +Because within this YAC, $\beta$ represents the angle 1, the input and output with +of $a_i$ and $a_o$ is A\_WIDTH+2, which allows to process angle values within +$-\pi ... \pi$ + + +\subsection{Input data width versus iterations} +The number of iterations depends on the width of the input data. +Input data with $X$ bit require $X+1$ rotations \cite{dawid}. +This requires, that the number of iterations are adapted. One solution might +be to detect the size of the input data and use this information for the CORDIC processing. +In YAC, a different sheme was chosen: the rotations are done until +\begin{itemize} + \item the angular register is 0 or doesn't change (in case of the rotation mode) + \item the y register is 0 or doesn't change (in case of the vecotring mode). +\end{itemize} +This results in a dynamic iterations adaption, depending the the input data width. + +\chapter{Performance} +The performance is evaluated through the matlab script \file{cordic\_iterative\_test.m}. + + +\chapter{Open issues and future work} + + \section{Next steps} + \begin{itemize} + \item Add YAC to a FPGA based System-on-Chip to prove + FPGA feasibility + \item Performance optimization + \item circuit optimizations + \item numerical optimizations + \end{itemize} + + \section{Future plans} + \begin{itemize} + \item Hyperbolic range extension + \item Floating point CORDIC + \end{itemize} + + + +%%%%%%%%%% BIBLIOGRAPHY %%%%%%%%%% +\begin{thebibliography}{9} + +\bibitem{survey} + Andraka, Ray; \textit{A survey of CORDIC algorithms for FPGA based computers} + +\bibitem{vlsi} + Hu, Yu Hen; \textit{CORDIC-Based VLSI Architectures for Digital Signal Processing} + +\bibitem{wikibook} + CORDIC on wikibook: \url{http://en.wikibooks.org/wiki/Digital_Circuits/CORDIC} + +\bibitem{dawid} + David, Herbert; Meyr, Heinricht; \textit{CORDIC Algorithms and Architectures} + \url{http://www.eecs.berkeley.edu/newton/Classes/EE290sp99/lectures/ee290aSp996_1/cordic_chap24.pdf} +\end{thebibliography} +\end{document} + + +% +% +% Opencores Description +% +% For this project GIT is preferred as revision control and therefore, the files under development are located on https://github.com/feddischson/yac. +% Nevertheless, stable intermediate steps are place here on SVN. +% +% +% +% +% +% Index: trunk/licenses/lgpl-3.0.txt =================================================================== --- trunk/licenses/lgpl-3.0.txt (nonexistent) +++ trunk/licenses/lgpl-3.0.txt (revision 2) @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. 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If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. Index: trunk/README.txt =================================================================== --- trunk/README.txt (nonexistent) +++ trunk/README.txt (revision 2) @@ -0,0 +1,120 @@ +---------------------------------------------------------------------------- +---- ---- +---- Copyright Notice ---- +---- ---- +---- This file is part of YAC - Yet Another CORDIC Core ---- +---- Copyright (c) 2014, Author(s), All rights reserved. ---- +---- ---- +---- YAC is free software; you can redistribute it and/or ---- +---- modify it under the terms of the GNU Lesser General Public ---- +---- License as published by the Free Software Foundation; either ---- +---- version 3.0 of the License, or (at your option) any later version. ---- +---- ---- +---- YAC is distributed in the hope that it will be useful, ---- +---- but WITHOUT ANY WARRANTY; without even the implied warranty of ---- +---- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ---- +---- Lesser General Public License for more details. ---- +---- ---- +---- You should have received a copy of the GNU Lesser General Public ---- +---- License along with this library. If not, download it from ---- +---- http://www.gnu.org/licenses/lgpl ---- +---- ---- +---------------------------------------------------------------------------- + + + + Author(s): Christian Haettich + Email feddischson@opencores.org + + + + + + +Description +------------------ + +CORDIC is the acronym for COordinate Rotation DIgital Computer and +allows a hardware efficient calculation of various functions +like - atan, sin, cos - atanh, sinh, cosh, - division, multiplication. +Hardware efficient means, that only shifting, additions and +subtractions in combination with table-lookup is required. This makes +it suitable for a realization in digital hardware. Good +introductions can be found in [1][2][3][5]. + + + +The following six CORDIC modes are supported: +- trigonometric rotation +- trigonometric vectoring +- linear rotation +- linear vectoring +- hyperbolic rotation +- hyperbolic vectoring + + +Furthermore, the CORDIC algorithm is implemented for iterative +processing which means, that the IP-core is started +with a set of input data and after a specific amount of +clock cycles, the result is +available. No parallel data can be processed. + +In addition to an IP-core written in VHDL, a bit-accurate C-model +is provided. This C-model can be compiled as mex for a usage with Octave or +Matlab. Therefore, this C-model allows a bit-accurate analysis +of the CORDIC performance on a higher level. + + +For a more detailed documentation, see ./doc/documentation.pdf + + + + + +Status +---------------------- +- C-model implementation is done +- RTL model implementation is done +- RTL model is verified against C-model + + + + + +Next-Steps +----------------------- +- Prove of FPGA feasibility +- Circuit optimizations +- Numerical optimizations + + + + + +Files and folders: +------------------ + + ./c_octave : contains a bit-accurate C-implementation of the YAC. + This C-implementation is used for analyzing the performance + and to generate RTL testbench stimulus + (cordic_iterative_test.m). + The file cordic_iterative_code.m is used to create some + VHDL/C-code automatically. + + ./rtl/vhdl : Contains the VHDL implementation files + + ./doc : Will contain a detailed documentation in future. + + + + + + +[1] Andraka, Ray; A survey of CORDIC algorithms for FPGA based computers, 1989 +[2] Hu, Yu Hen; CORDIC-Based VLSI Architectures for Digital Signal Processing, 1992 +[3] CORDIC on wikibook: http://en.wikibooks.org/wiki/Digital_Circuits/CORDIC +[4] CORDIC on wikipedia:http://en.wikipedia.org/wiki/CORDIC +[5] David, Herbert; Meyr, Heinricht; CORDIC Algorithms and Architectures + http://www.eecs.berkeley.edu/newton/Classes/EE290sp99/lectures/ee290aSp996_1/cordic_chap24.pdf + +

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