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Diffstat (limited to 'systems/doc/metapost/source-manual/mpman-app-numbersystems.tex')
-rw-r--r-- | systems/doc/metapost/source-manual/mpman-app-numbersystems.tex | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex b/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex index 23d3dce7cf..4839943fb1 100644 --- a/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex +++ b/systems/doc/metapost/source-manual/mpman-app-numbersystems.tex @@ -1,4 +1,4 @@ -\svnInfo $Id: mpman-app-numbersystems.tex 2023 2014-05-21 08:47:19Z stephanhennig $ +\svnInfo $Id: mpman-app-numbersystems.tex 2163 2020-12-31 19:51:53Z luigi.scarso@gmail.com $ \section{High-precision arithmetic with MetaPost} \label{hparith} @@ -21,7 +21,7 @@ Assigning a value to this variable at run-time triggers an error. The \texttt{scaled}\index{scaled?\texttt{scaled}} number system refers to 32~bit fixed-point arithmetics described in Section~\ref{datatypes}. -This is the default number system. Precision is ca. 10~decimal digits, +This is the default number system. Precision is ca.~10~decimal digits, 5 digits before and after the comma. All arithmetic operations are done in software. @@ -31,9 +31,9 @@ precision. In the internal representation, double floating-point numbers use $52+1$~bits for the mantissa, which determines precision, 11~bits for the exponent, which determines the valid range of numbers, and one bit for the sign. The smallest absolute value that can be -represented is ca. $2.2\cdot10^{-308}$, the largest value is -ca. $1.8\cdot10^{308}$. The 53~bit mantissa makes for a precision of -ca. 15 decimal digits. The smallest possible difference between two +represented is ca.~$2.2\cdot10^{-308}$, the largest value is +ca.~$1.8\cdot10^{308}$. The 53~bit mantissa makes for a precision of +ca.~15 decimal digits. The smallest possible difference between two distinct numbers in double floating-point number representation is $2^{-53} \approx 1.1\cdot10^{-16}$. The largest integer value that can be represented exactly is $2^{53}-1 \approx 9,0\cdot10^{15}$. Variable @@ -53,7 +53,7 @@ Precision is determined by an internal variable in decimal digits. Valid numbers are in the range 1 to 1000. Higher values make for better precision at the expense of performance of arithmetic operations. Default precision is 34~decimal digits -(ca. 113~bits in the mantissa). Exponent in the internal representation +(ca.~113~bits in the mantissa). Exponent in the internal representation is an integer in the range $[-9,999,999; +9,999,999]$. All arithmetic operations are done in software using the MPFR library~\cite{lib:mpfr} and are usually orders of magnitude slower than in \texttt{double} mode. |