diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 9abbe53..aef7b71 100644
--- a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ -135210,6 +135210,22 @@ RepeatedDoubling(S):Exports ==Implementation where
 @
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{package REPSQ RepeatedSquaring}
+This code computes $x^n$ by repeated squaring. It takes advantage of the
+law of exponents so that if $n=a*b$ then 
+\[ x^n = x^a x^b \]
+It also takes advantage of the fact that $n$ has a binary representation
+so that a one-bit right-shift of a number divides it by 2. Thus we get
+three cases:
+\[
+\begin{array}{l}
+ n = 1 \rightarrow x^1 \\
+ n \textrm{\ \ odd} \rightarrow \textrm{repeatedsquare}(x*x,n/2)*x \\
+ n \textrm{\ even} \rightarrow \textrm{repeatedsquare}(x*x,n/2) 
+\end{array}
+\]
+
+Since each recursive call divides $n$ by $2$ the algorithm is O(log(n)).
+
 \pagehead{RepeatedSquaring}{REPSQ}
 \pagepic{ps/v104repeatedsquaring.ps}{REPSQ}{1.00}
 
diff --git a/changelog b/changelog
index 6ee8bca..8bbd5f3 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20091218 tpd src/axiom-website/patches.html 20091218.02.tpd.patch
+20091218 tpd books/bookvol10.4 document RepeatedSquaring
 20091218 tpd src/axiom-website/patches.html 20091218.01.tpd.patch
 20091218 tpd src/interp/posit.lisp move functions to bookvol5
 20091218 tpd src/interp/vmlisp.lisp move functions to bookvol5
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 53b13bd..2cf660b 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -2314,5 +2314,7 @@ books/bookvol10.3 rewrite doublefloat to use typed macros<br/>
 books/bookvol5 )describe no longer needs cat, dom, pkg arg<br/>
 <a href="patches/20091218.01.tpd.patch">20091218.01.tpd.patch</a>
 books/bookvol5 tree shake code from cparse, posit, vmlisp<br/>
+<a href="patches/20091218.02.tpd.patch">20091218.02.tpd.patch</a>
+books/bookvol10.4 document RepeatedSquaring<br/>
  </body>
 </html>