r4483 - in developers/werner: . nandpart
werner at docs.openmoko.org
werner at docs.openmoko.org
Wed Jun 11 01:55:42 CEST 2008
Author: werner
Date: 2008-06-11 01:55:41 +0200 (Wed, 11 Jun 2008)
New Revision: 4483
Added:
developers/werner/nandpart/
developers/werner/nandpart/Makefile
developers/werner/nandpart/bb_slack.pl
developers/werner/nandpart/dynpart.fig
developers/werner/nandpart/nand3d.fig
developers/werner/nandpart/nandpart.tex
developers/werner/nandpart/rlatex
developers/werner/nandpart/slackpart.fig
Log:
Document describing old and new NAND partitioning scheme. (Work in progress.)
Added: developers/werner/nandpart/Makefile
===================================================================
--- developers/werner/nandpart/Makefile (rev 0)
+++ developers/werner/nandpart/Makefile 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,88 @@
+#
+# Fairly generic script for paper processing
+#
+
+VERSION=0
+NAME=nandpart
+
+# --- End of user-specific settings -------------------------------------------
+
+
+INC=slack.inc
+WORDS=my.words
+FIGS=nand3d dynpart slackpart
+
+EPS=$(FIGS:=.eps)
+
+
+.SUFFIXES: .fig .eps .dvi .tex .ps .pdf
+
+.PHONY: all spell .personal
+
+all: $(NAME).ps # $(NAME).pdf
+
+$(NAME).dvi: $(EPS) $(NAME).tex $(INC) # bib.inc
+
+slack.inc: bb_slack.pl
+ ./bb_slack.pl 3 20 >slack.inc || { rm -f slack.inc; exit 1; }
+
+
+# --- Spell checking ----------------------------------------------------------
+
+
+#
+# Modern aspell doesn't support personal dictionaries anymore, so we use ispell
+# instead. If we have an old installation, with a correctly working aspell, but
+# a broken ispell-to-aspell wrapper script, we anti-wrap in our own aspell
+# script.
+#
+
+spell: .personal
+ -cat $(INC) $(addsuffix .fig,$(FIGS)) >.tmp
+ PATH=.:$$PATH ispell -t -p ./.personal .tmp
+ rm -f .tmp
+
+.personal: $(WORDS)
+ cat $(WORDS) >.personal || { rm -f .personal; exit 1; }
+
+# modern aspell is broken ?!?
+# rm -f .personal
+# cat $(WORDS) | aspell create personal ./.personal || \
+# { rm -f .personal; exit 1; }
+
+
+# --- Conversion rules --------------------------------------------------------
+
+
+.dvi.ps:
+ dvips -o - $< | \
+ sed '/%%BeginDocument/,/%%EndDocument/s/%%.*//' >$@ || \
+ { rm -f $@; exit 1; }
+
+#.dvi.pdf:
+# dvipdf -o $@ $< || { rm -f $@; exit 1; }
+
+.ps.pdf:
+ ps2pdf $< $@
+
+.tex.dvi:
+ ./rlatex $<
+
+.fig.eps:
+ fig2dev -L eps -m 0.833 $< $@
+
+
+# --- Bibliography ------------------------------------------------------------
+
+
+bib.inc: $(INC) BIBLIOGRAPHY
+ BIBPATH=. perl bibfile.pl kboot.tex >bib.inc || \
+ { rm -f bib.inc; false; }
+
+
+# --- Cleanup -----------------------------------------------------------------
+
+
+clean:
+ rm -f *.dvi *.eps *.pdf *.ps *.aux *.log
+ rm -f .personal .tmp .personal_tmp
Added: developers/werner/nandpart/bb_slack.pl
===================================================================
--- developers/werner/nandpart/bb_slack.pl (rev 0)
+++ developers/werner/nandpart/bb_slack.pl 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,84 @@
+#!/usr/bin/perl
+
+#
+# usage: bb_slack.pl #slack [end_#slack]
+#
+
+#
+# n = minimum number of good blocks needed
+# b = probability that block is bad
+# s = slack
+# p = probability that slack is sufficient
+#
+# s ( n+s )
+# p = sum ( ) * b^i*(1-b)^(n+s-i)
+# i = 0 ( i )
+#
+# Note: this assumes that bad blocks are evenly distributed and don't come in
+# clumps.
+#
+
+$b = 40/2047; # Samsung K5D2G13ACM-D075
+ # (only 2047, since first block is always good)
+
+sub binom
+{
+ local ($n, $k) = @_;
+ local ($b, $i);
+
+ $b = 1;
+ for ($i = $n-$k+1; $i <= $n; $i++) {
+ $b *= $i;
+ }
+ for ($i = 2; $i <= $k; $i++) {
+ $b /= $i;
+ }
+ return $b;
+}
+
+
+sub exp
+{
+ local ($b, $e) = @_;
+
+ return exp(log($b)*$e);
+}
+
+
+sub p_good
+{
+ local ($s) = @_;
+ local ($p, $i);
+
+ $p = 0;
+ for ($i = 0; $i <= $s; $i++) {
+ $p += &binom($n+$s, $i)*&exp($b, $i)*&exp(1-$b, $n+$s-$i);
+ }
+ return $p;
+}
+
+$s0 = $ARGV[0];
+$s1 = defined $ARGV[1] ? $ARGV[1] : $s0;
+
+for ($s = $s0; $s <= $s1; $s++) {
+ $n6 = $n9 = 0;
+
+ $e6 = $e9 = 1;
+ for ($n = $s; $e6 || $e9; $n++) {
+ $p = 1-&p_good($s);
+ if ($p <= 1e-6) {
+ $n6 = $n;
+ }
+ else {
+ $e6 = 0;
+ }
+ if ($p <= 1e-9) {
+ $n9 = $n;
+ }
+ else {
+ $e9 = 0;
+ }
+ }
+
+ print "$s & $n6 & $n9 \\\\\n";
+}
Property changes on: developers/werner/nandpart/bb_slack.pl
___________________________________________________________________
Name: svn:executable
+ *
Added: developers/werner/nandpart/dynpart.fig
===================================================================
--- developers/werner/nandpart/dynpart.fig (rev 0)
+++ developers/werner/nandpart/dynpart.fig 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,99 @@
+#FIG 3.2 Produced by xfig version 3.2.5
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+4 1 0 50 -1 18 12 0.0000 4 165 990 3600 3900 20 blocks\001
+4 1 0 50 -1 18 12 0.0000 4 210 1770 6600 3900 22 blocks (2 bad)\001
Added: developers/werner/nandpart/nand3d.fig
===================================================================
--- developers/werner/nandpart/nand3d.fig (rev 0)
+++ developers/werner/nandpart/nand3d.fig 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,304 @@
+#FIG 3.2 Produced by xfig version 3.2.5
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+4 1 0 55 -1 18 12 0.0000 4 210 3030 10080 8160 (ECC, bad block marker, etc.)\001
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Added: developers/werner/nandpart/nandpart.tex
===================================================================
--- developers/werner/nandpart/nandpart.tex (rev 0)
+++ developers/werner/nandpart/nandpart.tex 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,325 @@
+\documentclass{article}
+\usepackage[obeyspaces]{url}
+\usepackage{fullpage}
+\usepackage{epsfig}
+
+\title{Openmoko NAND Partitioning}
+\author{Werner Almesberger \\
+ \tt werner at openmoko.org}
+\date{June 10, 2008}
+
+\begin{document}
+
+\maketitle
+
+\begin{abstract}
+\noindent
+The Openmoko GTA01 and GTA02 models partition their NAND such that
+partitions grow according to the number of bad blocks they contain.
+This dynamic partitioning complicates production and use of the
+devices. We propose to use static partitions with extra blocks to
+provide a statistical guarantee that bad blocks can be accommodated.
+\end{abstract}
+
+% -----------------------------------------------------------------------------
+
+\section{Structure of a NAND Flash device}
+
+NAND devices are structured in block which in turn contain multiple
+pages. This is illustrated in figure \ref{nand3d}.
+For example, the Samsung K5D2G13ACM-D075 NAND Flash memory in
+the SC32442B54 multi-chip-package (MCP) used in GTA02, contains 2048
+blocks, each containing 64 pages. One page contains 2048 data bytes and
+64 ``spare'' bytes. The latter are used to store meta-data such as bad
+block markers and ECCs.
+
+\begin{figure}[ht]
+\begin{center}
+\includegraphics{nand3d.eps}
+\end{center}
+\caption{Structure of the Samsung K5D2G13ACM-D075 NAND Flash memory.}
+\label{nand3d}
+\end{figure}
+
+The content of each page is protected by an ECC, which can detect any
+single-bit and two-bit error, and correct any single-bit error.
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Initial bad blocks}
+
+Due to the nature of their fabrication process, a NAND device leaves the
+factory with a certain number of defective memory cells that are not
+guaranteed to retain data for the specified amount of time (if at all).
+
+If a block contains one or more defective memory cells, the entire block
+is marked as ``bad'' by setting some of the ``spare'' bytes belonging to
+this block to a specific value.
+
+In the case of the K5D2G13ACM, Samsung guarantee that the first block is
+always ``good''\footnote{Samsung specify that the first block will not
+develop more than one bit error per page within the first 1000
+program/erase cycles. Such a single-bit error can be detected and
+corrected by the ECC.}, and furtermore that no more than 40 of the 2047
+remaining blocks of the device are invalid. This is shown in table
+\ref{badratio}.
+
+\begin{table}[ht]
+\begin{center}
+\begin{tabular}{|c|r|r|}
+ \hline
+ Block number & \multicolumn{1}{c|}{Number of blocks} &
+ \multicolumn{1}{c|}{Maximum ``bad''} \\
+ \hline
+ 0 & 1 & 0 \\
+ 1--2047 & 2047 & 40 \\
+ \hline
+\end{tabular}
+\end{center}
+\caption{When the NAND device leaves the factory, the first NAND block is
+ guaranteed to be ``good'', but several of the other blocks can be marked
+ as invalid and must not be used.}
+\label{badratio}
+\end{table}
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Worn-out blocks}
+
+During use, memory cells of can also lose their content. In particular,
+after a certain the number of program/erase cycles, memory cells may
+no longer be able to retain their content.
+
+Samsung guarantee for the K5D2G13ACM that each block (except for the
+first one and any block that was already marked as invalid during
+production) can be programmed and erased at least 100'000 times before
+more than one bit per page fails. A single-bit failure can be detected and
+corrected by the ECC.
+
+There are various strategies for responding to ECC errors. For example,
+once can just correct them and take no further action, or one can
+correct the error, copy the data to a new block, mark the whole block
+or page as defective, and refrain from making any further use of it.
+
+For the purpose of this paper, we only need to consider than blocks may
+become unusable after production, but are not concerned about what specific
+actions are taken when errors are detected.
+
+% -----------------------------------------------------------------------------
+
+\section{NAND partitions}
+
+NAND devices are usually partitioned. For example, the Openmoko GTA01
+has partitions for the u-boot boot loader, the persistent environment
+of u-boot, a splash screen image, the Linux kernel, and the root file
+system. The GTA02 adds another partition for factory data, such as MAC
+addresses.
+
+Partitions are made up of consecutive blocks and always end and begin
+at a block boundary.\footnote{The reason for this is that only whole
+NAND blocks can be erased. Thus, if blocks were to cross partition
+boundaries, a change to one partition could also affect a neighbouring
+partition, which is undesirable.}
+
+For each partition but the last one, the size of the content is specified
+and the partition must contain good blocks for at least that amount of data.
+The last partition is different in that is simply contains all the
+remaining blocks.
+
+The content size can be an exact value or an estimate of how much space
+once could reasonably expect to need for the respective partition.
+
+% -----------------------------------------------------------------------------
+
+\section{Dynamic partitions}
+
+
+At the time of writing, Openmoko uses the following strategy to
+@@@
+
+\begin{figure}[ht]
+\begin{center}
+\includegraphics{dynpart.eps}
+\end{center}
+\caption{Dynamic sizing of partitions to accommodate bad blocks.}
+\label{dynpart}
+\end{figure}
+
+One important property of this partitioning mechanism is that the
+partition sizes may differ slightly beween devices, depending on
+the number and location of initial bad NAND blocks.
+
+The partition table is stored in the u-boot environment. Since
+partition tables are device-specific, so are therefore also u-boot
+environments.
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Environment updates}
+
+There are two ``correct'' ways to change the
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Production issues}
+
+
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Usage issues}
+
+Most users do not expect the partition table to be device-specific,
+and may actually be unaware that the partition table is stored in the
+u-boot environment.
+
+This sometimes leads to the incorrect assumption that there is a
+``standard'' environment all devices could use. It also leads to the
+assumption that an environment that has been damaged can be restored
+by simply copying the environment of a different device.
+
+If a device receives the environment and thus the partition table of
+a different device, a number of subtle problems may occur. The most
+likely are:
+
+\begin{itemize}
+ \item The beginning of the kernel partition changes, which causes
+ attempts to boot the kernel to fail with a CRC error. This can be
+ ``corrected'' by installing a new kernel through DFU.
+ \item The beginning of the root file system partition changes. Due
+ to the file system (JFFS2) being tolerant to missing blocks, this
+ is often a silent failure, that only causes some checksum errors
+ or the disappearance of some files.
+\end{itemize}
+
+Also, if an incorrect parition table is corrected later, this may cause
+the same type of failures, and possibly files in the rootfs to reappear.
+
+% -----------------------------------------------------------------------------
+
+\section{Partitions with slack}
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Partition structure}
+
+\begin{figure}[ht]
+\begin{center}
+\includegraphics{slackpart.eps}
+\end{center}
+\caption{Static partitions with slack space to accommodate bad blocks.}
+\label{slackpart}
+\end{figure}
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Additional testing}
+
+@@@ additional testing required to verify that slack is indeed sufficient
+
+% -----------------------------------------------------------------------------
+
+\section{Calculating partition sizes}
+
+Assuming that initial bad blocks occur independently, we can calculate the
+probability that adding a certain number of slack blocks to a partition
+will provide enough space to accommodate the bad blocks this partition may
+contain.
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{...}
+
+$X_n$ be the number of bad blocks in a partition containing $n$ blocks.
+Each block is bad with probability $b$. Thus, the probability that this
+partition contains exactly $k$ bad blocks is:
+
+$$
+P(X_n=k)=\left(
+ \hskip-1.5mm
+ \begin{array}{c}
+ k \\
+ n \\
+ \end{array}
+ \hskip-1.5mm
+ \right)
+ b^k(1-b)^{n-k}
+$$
+
+If a partition of size $n$ contains $s$ slack blocks, the probability
+that there will be no more than $s$ bad blocks in this partition is:
+
+$$P(X_n\le s)=\sum_{i=0}^s \left(
+ \hskip-1.5mm
+ \begin{array}{c}
+ i \\
+ n \\
+ \end{array}
+ \hskip-1.5mm
+\right)b^i(1-b)^{n-i}$$
+
+This formula does not apply if a partition contains the the first block,
+which is always good.
+The probability that one or more partitions on a device do not have enough
+slack blocks can be approximated by adding the $1-P(X_n\le s)$ for all
+partitions.
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{Example sizes}
+
+Table \ref{egsizes} shows the number of data blocks a partition can contain
+for a given number of slack blocks, such that the number of bad blocks in
+the partition will be below the number of slack blocks with a given
+probability.
+
+\begin{table}[ht]
+\begin{center}
+\begin{tabular}{|r|r|r|}
+ \hline
+ \multicolumn{1}{|c|}{Slack blocks ($s$)} &
+ \multicolumn{2}{c|}{Maximum data blocks ($n-s$)} \\
+ & $P(X_n)\le 10^{-6}$ & $P(X_n)\le 10^{-9}$ \\
+ \hline
+\input{slack.inc}
+ \hline
+\end{tabular}
+\end{center}
+\caption{}
+\label{egsizes}
+\end{table}
+
+For the first partition, add one to the number of data blocks, since the
+first block is guaranteed to be good.
+
+
+% -----------------------------------------------------------------------------
+
+\section{Example sizes}
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{GTA02}
+
+% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+
+\subsection{GTA03}
+
+
+% -----------------------------------------------------------------------------
+
+\section{Bad block table removal}
+
+% -----------------------------------------------------------------------------
+
+\section{Conclusion}
+
+% -----------------------------------------------------------------------------
+
+\url{http://markmail.org/message/2hbxeemdo5djgnoo}
+\url{http://lists.openmoko.org/pipermail/openmoko-kernel/2008-April/002238.html}
+\url{http://svn.openmoko.org/developers/werner/bb_slack.pl}
+
+\end{document}
+
+* kernel: some will fail before others if we estimate too low
Added: developers/werner/nandpart/rlatex
===================================================================
--- developers/werner/nandpart/rlatex (rev 0)
+++ developers/werner/nandpart/rlatex 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,21 @@
+#!/bin/sh
+while true; do
+ pid=$$
+ export pid
+ rm -f /tmp/rlok$pid
+ (
+ if latex $*; then
+ touch /tmp/rlok$pid
+ fi
+ ) | tee /tmp/rlso$pid
+ if [ ! -f /tmp/rlok$pid ]; then
+ rm -f /tmp/rlso$pid
+ exit 1
+ fi
+ if grep '^LaTeX Warning: Label(s) may' /tmp/rlso$pid >/dev/null; then :
+ else
+ rm -f /tmp/rlso$pid
+ exit 0
+ fi
+ echo "Re-running LaTeX"
+done
Property changes on: developers/werner/nandpart/rlatex
___________________________________________________________________
Name: svn:executable
+ *
Added: developers/werner/nandpart/slackpart.fig
===================================================================
--- developers/werner/nandpart/slackpart.fig (rev 0)
+++ developers/werner/nandpart/slackpart.fig 2008-06-10 23:55:41 UTC (rev 4483)
@@ -0,0 +1,99 @@
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