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NIST
3 Numerical MethodsAreas3.1 Arithmetics and Error Measures

Figure 3.1.1 (See in context.)

\begin{picture}(152.0,38.0)(-1.0,-1.0)\put(0.0,31.0){\makebox(2.0,6.0){\small 1%
}}
\put(0.0,26.0){\framebox(2.0,6.0){$s$}}
\put(3.0,31.0){\makebox(8.0,6.0){\small 8}}
\put(3.0,26.0){\framebox(8.0,6.0){$E$}}
\put(12.0,31.0){\makebox(23.0,6.0){\small 23 bits}}
\put(12.0,26.0){\framebox(23.0,6.0){$f$}}
\put(133.0,31.0){$N=32$,}
\put(135.0,27.0){$p=24$}
\put(0.0,18.0){\makebox(2.0,6.0){\small 1}}
\put(0.0,13.0){\framebox(2.0,6.0){$s$}}
\put(3.0,18.0){\makebox(11.0,6.0){\small 11}}
\put(3.0,13.0){\framebox(11.0,6.0){$E$}}
\put(15.0,18.0){\makebox(52.0,6.0){\small 52 bits}}
\put(15.0,13.0){\framebox(52.0,6.0){$f$}}
\put(133.0,17.0){$N=64$,}
\put(135.0,13.0){$p=53$}
\put(0.0,5.0){\makebox(2.0,6.0){\small 1}}
\put(0.0,0.0){\framebox(2.0,6.0){$s$}}
\put(3.0,5.0){\makebox(15.0,6.0){\small 15}}
\put(3.0,0.0){\framebox(15.0,6.0){$E$}}
\put(19.0,5.0){\makebox(112.0,6.0){\small 112 bits}}
\put(19.0,0.0){\framebox(112.0,6.0){$f$}}
\put(133.0,4.0){$N=128$,}
\put(135.0,0.0){$p=113$}
\end{picture}
Figure 3.1.1: Floating-point arithmetic. Representation of data in the binary interchange formats for binary32, binary64 and binary128 (previously single, double and quad precision). Magnify