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Change @verbatim to @example. 

Add link near hexadecimal floating constants to
the node that documents them.
Change http links to https.
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Richard Stallman 2022-09-15 17:25:33 -04:00
parent ff0c64366f
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1 changed files with 17 additions and 16 deletions
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@ -914,11 +914,11 @@ the other.
In GNU C, you can create a value of negative Infinity in software like In GNU C, you can create a value of negative Infinity in software like
this: this:
@verbatim @example
double x; double x;
x = -1.0 / 0.0; x = -1.0 / 0.0;
@end verbatim @end example
GNU C supplies the @code{__builtin_inf}, @code{__builtin_inff}, and GNU C supplies the @code{__builtin_inf}, @code{__builtin_inff}, and
@code{__builtin_infl} macros, and the GNU C Library provides the @code{__builtin_infl} macros, and the GNU C Library provides the
@ -1303,13 +1303,14 @@ eps_pos = nextafter (x, +inf() - x);
@noindent @noindent
In such cases, if @var{x} is Infinity, then @emph{the @code{nextafter} In such cases, if @var{x} is Infinity, then @emph{the @code{nextafter}
functions return @var{y} if @var{x} equals @var{y}}. Our two functions return @var{y} if @var{x} equals @var{y}}. Our two
assignments then produce @code{+0x1.fffffffffffffp+1023} (about assignments then produce @code{+0x1.fffffffffffffp+1023} (that is a
1.798e+308) for @var{eps_neg} and Infinity for @var{eps_pos}. Thus, hexadecimal floating point constant and its value is around
the call @code{nextafter (INFINITY, -INFINITY)} can be used to find 1.798e+308; see @ref{Floating Constants}) for @var{eps_neg}, and
the largest representable finite number, and with the call Infinity for @var{eps_pos}. Thus, the call @code{nextafter (INFINITY,
@code{nextafter (0.0, 1.0)}, the smallest representable number (here, -INFINITY)} can be used to find the largest representable finite
@code{0x1p-1074} (about 4.491e-324), a number that we saw before as number, and with the call @code{nextafter (0.0, 1.0)}, the smallest
the output from @code{macheps (0.0)}). representable number (here, @code{0x1p-1074} (about 4.491e-324), a
number that we saw before as the output from @code{macheps (0.0)}).
@c ===================================================================== @c =====================================================================
@ -1657,7 +1658,7 @@ a substantial portion of the functions described in the famous
@cite{NIST Handbook of Mathematical Functions}, Cambridge (2018), @cite{NIST Handbook of Mathematical Functions}, Cambridge (2018),
ISBN 0-521-19225-0. ISBN 0-521-19225-0.
See See
@uref{http://www.math.utah.edu/pub/mathcw} @uref{https://www.math.utah.edu/pub/mathcw}
for compilers and libraries. for compilers and libraries.
@item @c sort-key: Clinger-1990 @item @c sort-key: Clinger-1990
@ -1669,13 +1670,13 @@ See also the papers by Steele & White.
@item @c sort-key: Clinger-2004 @item @c sort-key: Clinger-2004
William D. Clinger, @cite{Retrospective: How to read floating William D. Clinger, @cite{Retrospective: How to read floating
point numbers accurately}, ACM SIGPLAN Notices @b{39}(4) 360--371 (April 2004), point numbers accurately}, ACM SIGPLAN Notices @b{39}(4) 360--371 (April 2004),
@uref{http://doi.acm.org/10.1145/989393.989430}. Reprint of 1990 paper, @uref{https://doi.acm.org/10.1145/989393.989430}. Reprint of 1990 paper,
with additional commentary. with additional commentary.
@item @c sort-key: Goldberg-1967 @item @c sort-key: Goldberg-1967
I. Bennett Goldberg, @cite{27 Bits Are Not Enough For 8-Digit Accuracy}, I. Bennett Goldberg, @cite{27 Bits Are Not Enough For 8-Digit Accuracy},
Communications of the ACM @b{10}(2) 105--106 (February 1967), Communications of the ACM @b{10}(2) 105--106 (February 1967),
@uref{http://doi.acm.org/10.1145/363067.363112}. This paper, @uref{https://doi.acm.org/10.1145/363067.363112}. This paper,
and its companions by David Matula, address the base-conversion and its companions by David Matula, address the base-conversion
problem, and show that the naive formulas are wrong by one or problem, and show that the naive formulas are wrong by one or
two digits. two digits.
@ -1692,7 +1693,7 @@ and then rereading from time to time.
@item @c sort-key: Juffa @item @c sort-key: Juffa
Norbert Juffa and Nelson H. F. Beebe, @cite{A Bibliography of Norbert Juffa and Nelson H. F. Beebe, @cite{A Bibliography of
Publications on Floating-Point Arithmetic}, Publications on Floating-Point Arithmetic},
@uref{http://www.math.utah.edu/pub/tex/bib/fparith.bib}. @uref{https://www.math.utah.edu/pub/tex/bib/fparith.bib}.
This is the largest known bibliography of publications about This is the largest known bibliography of publications about
floating-point, and also integer, arithmetic. It is actively floating-point, and also integer, arithmetic. It is actively
maintained, and in mid 2019, contains more than 6400 references to maintained, and in mid 2019, contains more than 6400 references to
@ -1708,7 +1709,7 @@ base-conversion problem.
@item @c sort-key: Kahan @item @c sort-key: Kahan
William Kahan, @cite{Branch Cuts for Complex Elementary Functions, or William Kahan, @cite{Branch Cuts for Complex Elementary Functions, or
Much Ado About Nothing's Sign Bit}, (1987), Much Ado About Nothing's Sign Bit}, (1987),
@uref{http://people.freebsd.org/~das/kahan86branch.pdf}. @uref{https://people.freebsd.org/~das/kahan86branch.pdf}.
This Web document about the fine points of complex arithmetic This Web document about the fine points of complex arithmetic
also appears in the volume edited by A. Iserles and also appears in the volume edited by A. Iserles and
M. J. D. Powell, @cite{The State of the Art in Numerical M. J. D. Powell, @cite{The State of the Art in Numerical
@ -1775,7 +1776,7 @@ Michael Overton, @cite{Numerical Computing with IEEE Floating
Point Arithmetic, Including One Theorem, One Rule of Thumb, and Point Arithmetic, Including One Theorem, One Rule of Thumb, and
One Hundred and One Exercises}, SIAM (2001), ISBN 0-89871-482-6 One Hundred and One Exercises}, SIAM (2001), ISBN 0-89871-482-6
(xiv + 104 pages), (xiv + 104 pages),
@uref{http://www.ec-securehost.com/SIAM/ot76.html}. @uref{https://www.ec-securehost.com/SIAM/ot76.html}.
This is a small volume that can be covered in a few hours. This is a small volume that can be covered in a few hours.
@item @c sort-key: Steele-1990 @item @c sort-key: Steele-1990
@ -1789,7 +1790,7 @@ See also the papers by Clinger.
Guy L. Steele Jr. and Jon L. White, @cite{Retrospective: How to Guy L. Steele Jr. and Jon L. White, @cite{Retrospective: How to
Print Floating-Point Numbers Accurately}, ACM SIGPLAN Notices Print Floating-Point Numbers Accurately}, ACM SIGPLAN Notices
@b{39}(4) 372--389 (April 2004), @b{39}(4) 372--389 (April 2004),
@uref{http://doi.acm.org/10.1145/989393.989431}. Reprint of 1990 @uref{https://doi.acm.org/10.1145/989393.989431}. Reprint of 1990
paper, with additional commentary. paper, with additional commentary.
@item @c sort-key: Sterbenz @item @c sort-key: Sterbenz