Re: IEEE754
 From: "Alf P. Steinbach" <alfps@xxxxxxxx>
 Date: Thu, 23 Aug 2007 20:06:54 +0200
* Roman Töngi:
IEEE754 Arithmetic:
Most real numbers can't be stored exactly on the computer, but there can
be stated the range within which a machine number lies.
For the following example, I assume double precision and the round mode in effect to be 'round to nearest' and that the number lies within the
normalized range:
Definitions:
x := real number
round(x) := correctly rounded normalized number
eps := machine epsilon (2^(52) for double precision)
abs(x) := absolute value of x
That is:
round(x) = x*(1 + delta)
This is not how rounding works.
with delta:
abs(delta) <= 1/2*eps (round to nearest)
i.d. abs(delta) <= 2^(53) (double precision)
abs(delta) corresponds to the relative rounding error.
Now I can state the range including round(x):

x*(12(53)) <= round(x) <= x*(1+2^(53))

Is this the correct range according to my assumptions?
The conclusion is just about right for a positive normalized number, but the derivation of that conclusion does not seem to be sensible.
Directly about your question: "What Every Computer Scientist Should Know About FloatingPoint Arithmetic", <url: http://docs.sun.com/source/8063568/ncg_goldberg.html>. The thing is that although everybody refer to this paper, very few actually read it. It's a way of saying, if you're not doing serious numerical work, then stick to the simple conceptual understanding and /test/ your code.
You might also want to check out (might be more useful!) <url: http://docs.sun.com/source/8063568/ncg_math.html#866>.
And perhaps (almost) the original IEEE 754 standard, with speling corections: <url: http://www.validlab.com/754R/standards/754.pdf>.

A: Because it messes up the order in which people normally read text.
Q: Why is it such a bad thing?
A: Topposting.
Q: What is the most annoying thing on usenet and in email?
.
 References:
 IEEE754
 From: Roman Töngi
 IEEE754
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