Re: Accuracy of 754-compliant recommended functions
On 2013-07-03 11:37:45 +0100, John Pryce wrote:
> The definition of quantum in 754 §2.1.44 certainly looks like an ulp.
> My understanding of the alternative representations for decimal
> numbers is as follows. Suppose we use decimal64, which (754 Table
> 3.2) has 16 digits in the significand. Then the mathematical number
> 1.23456789 can be stored exactly as any of
> 1.234567890000000*10^0 or 0.123456789000000*10^1 or ... or 0.000000123456789*10^7
> (8 possibilities, i.e. one more than the number of trailing zeros in
> the first, normalised, representation.)
> The quantum is 10^(-15) in the first, ... 10^(-8) in the last.
> Am I understanding correctly?
Yes, and as you could see, it is related to the representation,
not to the value (as a real number) itself.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)