THE FINAL COUNTDOWN

[ipdf/sam.git] / chapters / Background / Standards / Precision.tex

diff --git a/chapters/Background/Standards/Precision.tex b/chapters/Background/Standards/Precision.tex
index 0a9511c..f533b98 100644 (file)
--- a/chapters/Background/Standards/Precision.tex
+++ b/chapters/Background/Standards/Precision.tex
@@ -1,4 +1,6 @@
 
+
+
 \subsection{PostScript}
 The PostScript reference describes a ``Real'' object for representing coordinates and values as follows: ``Real objects approximate mathematical real numbers within a much larger interval, but with limited precision; they are implemented as floating-point numbers''\cite{plrm}. There is no reference to the precision of mathematical operations, but the implementation limits \emph{suggest} a range of $\pm10^{38}$ ``approximate'' and the smallest values not rounded to zero are $\pm10^{-38}$ ``approximate''.
 
@@ -13,11 +15,11 @@ In ``The METAFONT book'' Knuth appears to describe coordinates as fixed point nu
 \subsection{SVG}
 
 The SVG standard specifies a minimum precision equivelant to that of ``single precision floats'' (presumably referring to IEEE-754) with a range of \verb/-3.4e+38F/ to \verb/+3.4e+38F/, and states ``It is recommended that higher precision floating point storage and computation be performed on operations such as
-coordinate system transformations to provide the best possible precision and to prevent round-off errors.''\cite{svg2011-1.1} An SVG Viewer may refer to itself as ``High Quality'' if it uses a minimum of ``double precision'' floats.
+coordinate system transformations to provide the best possible precision and to prevent round-off errors.''\cite{svg2011-1.1} An SVG Viewer may refer to itself as ``High Quality'' if it uses a minimum of ``double precision'' floats for view transformations.
 %\begin{comment}
 \subsection{Javascript}
 We include Javascript here due to its relation with the SVG, HTML5 and PDF standards.
-According to the EMCA-262 standard, ``The Number type has exactly 18437736874454810627 (that is, $2^64-^53+3$) values, 
+According to the EMCA-262 standard, ``The Number type has exactly 18437736874454810627 (that is, $2^{64}-2^{53}+3$) values, 
 representing the double-precision 64-bit format IEEE 754 values as specified in the IEEE Standard for Binary Floating-Point Arithmetic''\cite{ecma-262}. 
 The Number type does differ slightly from IEEE-754 in that there is only a single valid representation of ``Not a Number'' (NaN). The EMCA-262 does not define an ``integer'' representation.
 %\end{comment}