Added Kahan documentation.

simmod/ass1/report.tex

@@ -113,12 +113,12 @@ We've calculated $\sum_{i=1}^{N}\frac{1}{i}$ for $N = 10^8$ and $N = 2 \cdot
 
 \begin{table}[H]
 \begin{tabular}{l|llll}
-Type                   & N              & Forward    & Backward   & Kahan\\
+Type                   & N              & Forward     & Backward    & Kahan\\
 \hline
-\texttt{float}         & $10^8$         & $15.40368$ & $18.80792$ & $18.99790$ \\
-\texttt{float}         & $2 \cdot 10^8$ & $15.40368$ & $18.80792$ & $19.69104$ \\
-\texttt{double}        & $10^8$         & $18.99790$ & $18.99790$ & \\
-\texttt{double}        & $2 \cdot 10^8$ & $19.69104$ & $19.69104$ & \\
+\texttt{float}         & $10^8$         & $15.403683$ & $18.807919$ & $18.997896$ \\
+\texttt{float}         & $2 \cdot 10^8$ & $15.403683$ & $18.807919$ & $19.691044$ \\
+\texttt{double}        & $10^8$         & $18.997896$ & $18.997896$ & \\
+\texttt{double}        & $2 \cdot 10^8$ & $19.691044$ & $19.691044$ & \\
 \end{tabular}
 \caption{Results of various summation approaches on floats and doubles.}
 \end{table}
@@ -150,7 +150,14 @@ Type                   & N              & Forward    & Backward   & Kahan\\
     \frac{1}{2 \cdot 10^8}]$ are also represented as zero and therefore not added
     to the result.
     \item To improve the precision of the \texttt{float} data type summation, we
-    implemented the Kahan summation algorithm.
+    implemented the Kahan summation algorithm. This algorithm basically divides the
+    summation in a higher- and lower-order part. The lower-order part is used to
+    compensate for the error at each summation. See
+    \url{http://en.wikipedia.org/wiki/Kahan\_summation\_algorithm} for more
+    information about this algorithm. The results are in the last column as the
+    table, we can see that the algorithm yields the correct number. We know this
+    because they are equal to the result of the \texttt{double} summations (but
+    rounded to the precision of a \texttt{float}, of course).
 \end{itemize}
 
 % }}}