somehow commited dud versions of mkdocs.sh and running_average.md

docs/mkdocs.sh

@@ -1,6 +1,5 @@
 #!/bin/bash
 set -e
-set -x
 cd `dirname $0`
 
 if [[ "$OSTYPE" == "linux-gnu"* ]]; then
@@ -16,19 +15,15 @@ templates="./pandoc_templates"
 options=$osoptions"--toc -N --toc-depth=5 --wrap=preserve --metadata=lang:en  --include-in-header=$templates/icon.pandoc --include-before-body=$templates/before.pandoc --css=$templates/style.css -o"
 for f in *.md
 do
- echo $f
  len=${#f}
  base=${f:0:($len-3)}
  if [ $f -nt $base.html ];
  then
-   set -x
    katex=""
    mine="--include-after-body=$templates/after.pandoc "
-   for i in 1 2 3 4
+   for i in 1 2 3 4 5 6
    do
-	 set -x
 	 read line
-	 echo $line
 	 if [[ $line =~ katex$ ]];
 	 then
 		 katex=" --katex=./"
@@ -45,13 +40,11 @@ if [[ $line =~ notmine$ ]];
  #  echo "       $base.html up to date"
  fi
 done
-echo normal exit
 cd libraries
 templates="../pandoc_templates"
 options=$osoptions"--toc -N --toc-depth=5 --wrap=preserve --metadata=lang:en --include-in-header=$templates/icondotdot.pandoc --include-before-body=$templates/beforedotdot.pandoc --css=$templates/style.css --include-after-body=$templates/after.pandoc -o"
 for f in *.md
 do
- echo $f
  len=${#f}
  base=${f:0:($len-3)}
  if [ $f -nt $base.html ];
@@ -75,7 +68,6 @@ cd ../..
 templates=docs/pandoc_templates
 for f in *.md
 do
- echo $f
  len=${#f}
  base=${f:0:($len-3)}
  if [ $f -nt $base.html ];

docs/running_average.md

@@ -0,0 +1,32 @@
+---
+# katex
+title: running average
+---
+
+The running average $a_n$ of a series $R_n$
+
+$$a_n =\frac{a\_{n-1}\times u+R_n\times v}{u+v}$$
+
+The larger $u$ and the smaller $v$, the longer the period over which the running average is taken.
+
+We don’t want to do floating point arithmetic, because different peers
+might get different answers.
+
+It is probably harmless if they get different answers, provided that this
+happens rarely, but easier to ensure that this never happens than to try to
+think about all the possible circumstances where this could become a
+problem, where malicious people could contrive inputs to make sure it
+becomes a problem.
+
+Unsigned integer arithmetic is guaranteed to give the same answers on all
+hardware under all compilers. So, when we can, use unsigned integers.
+
+$R_n$is a very small integer where we are worried about very small
+differences, so we rescale to represent arithmetic with eight or so bits after
+the binary point in integer arithmetic.
+
+$\widetilde {a_n}$represents the rescaled running average $a_n$
+
+$$\widetilde {a_n}=\frac{u\widetilde{a_{n-1}} +v{R_n}\times 2^8}{u+v}$$
+
+$$a_n = \bigg\lfloor\frac{{\widetilde {a_n}}+2^7}{2^8}\bigg\rfloor$$