Change @verbatim to @example.

Add link near hexadecimal floating constants to
the node that documents them.
Change http links to https.
This commit is contained in:
Richard Stallman 2022-09-15 17:25:33 -04:00
parent ff0c64366f
commit b79376cac2
1 changed files with 17 additions and 16 deletions

33
fp.texi
View File

@ -914,11 +914,11 @@ the other.
In GNU C, you can create a value of negative Infinity in software like
this:
@verbatim
@example
double x;
x = -1.0 / 0.0;
@end verbatim
@end example
GNU C supplies the @code{__builtin_inf}, @code{__builtin_inff}, and
@code{__builtin_infl} macros, and the GNU C Library provides the
@ -1303,13 +1303,14 @@ eps_pos = nextafter (x, +inf() - x);
@noindent
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
assignments then produce @code{+0x1.fffffffffffffp+1023} (about
1.798e+308) for @var{eps_neg} and Infinity for @var{eps_pos}. Thus,
the call @code{nextafter (INFINITY, -INFINITY)} can be used to find
the largest representable finite number, and with the call
@code{nextafter (0.0, 1.0)}, the smallest representable number (here,
@code{0x1p-1074} (about 4.491e-324), a number that we saw before as
the output from @code{macheps (0.0)}).
assignments then produce @code{+0x1.fffffffffffffp+1023} (that is a
hexadecimal floating point constant and its value is around
1.798e+308; see @ref{Floating Constants}) for @var{eps_neg}, and
Infinity for @var{eps_pos}. Thus, the call @code{nextafter (INFINITY,
-INFINITY)} can be used to find the largest representable finite
number, and with the call @code{nextafter (0.0, 1.0)}, the smallest
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 =====================================================================
@ -1657,7 +1658,7 @@ a substantial portion of the functions described in the famous
@cite{NIST Handbook of Mathematical Functions}, Cambridge (2018),
ISBN 0-521-19225-0.
See
@uref{http://www.math.utah.edu/pub/mathcw}
@uref{https://www.math.utah.edu/pub/mathcw}
for compilers and libraries.
@item @c sort-key: Clinger-1990
@ -1669,13 +1670,13 @@ See also the papers by Steele & White.
@item @c sort-key: Clinger-2004
William D. Clinger, @cite{Retrospective: How to read floating
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.
@item @c sort-key: Goldberg-1967
I. Bennett Goldberg, @cite{27 Bits Are Not Enough For 8-Digit Accuracy},
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
problem, and show that the naive formulas are wrong by one or
two digits.
@ -1692,7 +1693,7 @@ and then rereading from time to time.
@item @c sort-key: Juffa
Norbert Juffa and Nelson H. F. Beebe, @cite{A Bibliography of
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
floating-point, and also integer, arithmetic. It is actively
maintained, and in mid 2019, contains more than 6400 references to
@ -1708,7 +1709,7 @@ base-conversion problem.
@item @c sort-key: Kahan
William Kahan, @cite{Branch Cuts for Complex Elementary Functions, or
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
also appears in the volume edited by A. Iserles and
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
One Hundred and One Exercises}, SIAM (2001), ISBN 0-89871-482-6
(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.
@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
Print Floating-Point Numbers Accurately}, ACM SIGPLAN Notices
@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.
@item @c sort-key: Sterbenz