X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground%2FFloats%2FOperations.tex;h=a527c39d319efd05b06846d3b48fae241c7b21f9;hp=1a724f97580290630835a14e7eb38ab385249e18;hb=ae8d5f837db032eb4d9e9666f5026fab7e3e8e4a;hpb=9fcf44a0c34f393689118e913a2d17d907036c85

diff --git a/chapters/Background/Floats/Operations.tex b/chapters/Background/Floats/Operations.tex
index 1a724f9..a527c39 100644
--- a/chapters/Background/Floats/Operations.tex
+++ b/chapters/Background/Floats/Operations.tex
@@ -1,8 +1,12 @@
 
+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}. 
 
-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.
+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?}
 \subsection{Addition and Subtraction}
@@ -26,4 +30,4 @@ 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}