| From: "Manoj Dhooria" <manojd(_at_)geometricsoftware(_dot_)com>
| Date: Wed, 24 Jan 2001 17:33:50 +0530
|
| Good overview, Jaffer. Am copying to general list too to draw
| attention to a related issue of which I don't know of an adequate
| internet standard & for which I had to invent my own representation.
|
| I am into distributed engineering software development, & keeping
| precision of floating point values is extremely important for me -
| even when they will be transmitted over the net & across CPU
| architectures. Using printf() format is guaranteed to lose
| precision, even though I can limit the loss by giving lots of
| significant digits. Also, using a large number of significant digits
| increases number of octets to be included in the message.
|
| What I essentially do is transform the source CPU's native
| representation to IEEE floating point representation; then print it
| out as a sequence of hex bytes; then run an optimizer on it to drop
| some of the "unnecessary" octets (guaranteeing that the original hex
| sequence can be reconstructed at the receiver end; no dropping of
| bytes for numbers where I can not guarantee this).
|
| If there are others on the mailing list facing this issue, I would
| like to interact. May be we can have a standard way. I could
| publish my technique as an internet draft, if required. If there is
| already a public spec for it, may be someone would be kind enough to
| share. Thank you.
I think this problem has been solved for IEEE 754-1985 numbers:
[R4RS] William Clinger and Jonathan Rees, editors. The revised^4
report on the algorithmic language Scheme. In "ACM Lisp Pointers"
4(3), pages 1-55, 1991.
which is also
[IEEEScheme] "IEEE Standard 1178-1990. IEEE Standard for the Scheme
Programming Language." IEEE, New York, 1991.
(http://swissnet.ai.mit.edu/~jaffer/r5rs_8.html#SEC56)
specifies that:
The procedure `number->string' takes a number ... and returns as a
string an external representation of the given number ... such that
`string->number' of the string returned by `number->string' will be
equal to the original number.
... the result ... is expressed using the minimum number of digits
(exclusive of exponent and trailing zeroes) needed to make the above
... true [howtoprint], [howtoread]...
Not only is fidelity guaranteed, but using the minimal decimal
representation. I thought there was a C library implementation of these
algorithms; but I can't find it today.
[howtoprint] Robert G. Burger and R. Kent Dybvig. Printing
floating-point numbers quickly and accurately. In "Proceedings of the
ACM SIGPLAN '96 Conference on Programming Language Design and
Implementation", pages 108-116.
http://citeseer.nj.nec.com/cs?profile=976907%2C28233%2C1%2C0.25%2CDownload&rd=http%3A//www.cs.indiana.edu/%7Eburger/FP-Printing-PLDI96.ps.gz
ABSTRACT
This paper presents a fast and accurate algorithm for printing
floating-point numbers in both free- and fixed-format modes. In
free-format mode, the algorithm generates the shortest, correctly
rounded output string that converts to the same number when read back
in, accommodating whatever rounding mode the reader uses. In
fixed-format mode, the algorithm generates a correctly rounded output
string using special # marks to denote insignificant trailing digits.
For both modes, the algorithm employs a fast estimator to scale
floating-point numbers efficiently.
[howtoread] William Clinger. How to read floating point numbers
accurately. In "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation", pages 92-101.
Proceedings published as "SIGPLAN Notices" 25(6), June 1990.
http://citeseer.nj.nec.com/cs?profile=0%2C224562%2C1%2C0.25%2CDownload&rd=ftp%3A//ftp.ccs.neu.edu/pub/people/will/howtoread.ps
ABSTRACT
Consider the problem of converting decimal scientific notation for a
number into the best binary floating point approximation to that
number, for some fixed precision. This problem cannot be solved
using arithmetic of any fixed precision. Hence the IEEE Standard for
Binary Floating-Point Arithmetic does not require the result of such
a conversion to be the best approximation.
This paper presents an efficient algorithm that always finds the best
approximation. The algorithm uses a few extra bits of precision to
compute an IEEE-conforming approximation while testing an
intermediate n result to determine whether the approximation could be
other than the best. If the approximation might not be the best,
then the best approximation is determined by a few simple operations
on multiple-precision integers, where the precision is determined by
the input. When using 64 bits of precision to compute IEEE double
precision results, the algorithm avoids higher-precision arithmetic
over 99% of the time.
The input problem considered by this paper is the inverse of an
output problem considered by Steele and White: Given a binary
floating point number, print a correctly rounded decimal
representation of it using the smallest number of digits that will
allow the number to be read without loss of accuracy. The Steele and
White algorithm assumes that the input problem is solved; an
imperfect solution to the input problem, as allowed by the IEEE
standard and ubiquitous in current practice, defeats the purpose of
their algorithm.
|
| Manoj Dhooria
| Geometric Software [www.geometricsoftware.com]
| Bombay
|
| -----Original Message-----
| From: nsyracus(_at_)cnri(_dot_)reston(_dot_)va(_dot_)us
[mailto:nsyracus(_at_)cnri(_dot_)reston(_dot_)va(_dot_)us]On
| Behalf Of Internet-Drafts(_at_)ietf(_dot_)org
| Sent: Tuesday, January 23, 2001 6:04 PM
| To: IETF-Announce:
| Subject: I-D ACTION:draft-jaffer-metric-interchange-format-02.txt
|
|
| A New Internet-Draft is available from the on-line Internet-Drafts
| directories.
|
|
| Title : Representation of numerical values and SI units in
| character strings for information interchanges
| Author(s) : A. Jaffer
| Filename : draft-jaffer-metric-interchange-format-02.txt
| Pages :
| Date : 22-Jan-01
|
| This document describes a character string encoding for numerical
| values and units which:
| * is unambiguous in all locales;
| * uses only
|
| A URL for this Internet-Draft is:
| http://www.ietf.org/internet-drafts/draft-jaffer-metric-interchange-format-0
| 2.txt
|
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