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Commit 753cfa95 authored by Luigi Scarso's avatar Luigi Scarso
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another small fix to the manual

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......@@ -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.
......
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