X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;f=chapters%2FBackground%2FFloats%2FOperations.tex;h=befb9e7859d6efb3b7ddc9c0af259888ab8d497f;hb=a1ede3cfc3ef650aa0f7d3d06e78c6c6ef4cb0cc;hp=1a724f97580290630835a14e7eb38ab385249e18;hpb=9fcf44a0c34f393689118e913a2d17d907036c85;p=ipdf%2Fsam.git

diff --git a/chapters/Background/Floats/Operations.tex b/chapters/Background/Floats/Operations.tex
index 1a724f9..befb9e7 100644
--- a/chapters/Background/Floats/Operations.tex
+++ b/chapters/Background/Floats/Operations.tex
@@ -1,7 +1,14 @@
 
 
-Real values which cannot be represented exactly in a floating point representation must be rounded to the nearest floating point value. The results of a floating point operation will in general be such values and thus there is a rounding error possible in any floating point operation. Referring to Figure \ref{floats.pdf} it can be seen that the largest possible rounding error is half the distance between successive floats; this means that rounding errors increase as the value to be represented increases.
+Real values which cannot be represented exactly in a floating point representation must be rounded to the nearest floating point value. The results of a floating point operation will in general be such values and thus there is a rounding error possible in any floating point operation\cite{HFP,ieee754std2008, goldberg1991whatevery}. 
 
+Referring to Figure \ref{floats.pdf} it can be seen that the largest possible rounding error is half the distance between successive floats; this means that rounding errors increase as the value to be represented increases. For the result of a particular operation, the maximum possible rounding error can be determined and is commonly expressed in ``units in the last place'' (ulp), with 1 ulp equivelant to half the distance between successive floats\cite{goldberg1991whatevery}.
+
+
+
+\begin{comment}
+
+Floating point operations can in principle be performed using integer operations, but specialised Floating Point Units (FPUs) are an almost universal component of modern processors\cite{kelley1997acmos}. The improvement of FPUs remains highly active in several areas including: efficiency\cite{seidel2001onthe}; accuracy of operations\cite{dieter2007lowcost}; and even the adaptation of algorithms originally used in software, such as Kahan's Fast2Sum algorithm\cite{kadric2013accurate}. 
 
 
 {\bf Put this stuff in an Appendix?}
@@ -26,4 +33,4 @@ This is equivelant to shifting the fixed point in $m_2$ by $e_2 - e_1$ to the le
 
 Multiplication and Division are not inverses.
 
-Floating point operations can in principle be performed using integer operations, but specialised Floating Point Units (FPUs) are an almost universal component of modern processors\cite{kelley1997acmos}. The improvement of FPUs remains highly active in several areas including: efficiency\cite{seidel2001onthe}; accuracy of operations\cite{dieter2007lowcost}; and even the adaptation of algorithms originally used in software, such as Kahan's Fast2Sum algorithm\cite{kadric2013accurate}. 
+\end{comment}