Re: Accuracy of 754-compliant recommended functions
Vincent,
Thank you.
OK, now I think I understand, although I'd like to
study 754 a bit more. I'm imagining a "quantum"
in a decimal format to be "language defined" by
the number of digits printed (or input).
With this interpretation, I'm more at ease if
we were to require 754-conformant data types to provide
optimal enclosures for recommended functions, since
the 754-standard itself requires such functions, if
supplied, to be optimally rounded, subject to the
rounding mode in effect.
Best regards,
Baker
On 07/01/2013 11:47 AM, Vincent Lefevre wrote:
On 2013-07-01 09:53:23 -0500, Ralph Baker Kearfott wrote:
Does this mean that, if the functions recommended in 754-2008 are
provided, they must return the nearest floating point number
subject to the rounding mode in effect?
Yes. But whar you had said wasn't clear.
That is what I originally
thought it said. The relevant sections of 754-2008 are
Clause 9.1, in which it says "A conforming
function shall return results correctly rounded for the applicable rounding
direction for all operands
in its domain. The preferred quantum is language-defined," and
the definition of quantum: "2.1.44 quantum: The quantum of a finite
floating-point representation is the value of a
unit in the last position of its significand. This is equal to the radix
raised to the exponent q, which
is used when the significand is regarded as an integer."
Where do you get that a quantum is defined only for decimal?
I think that what Michel meant was that there may be different choices
for the quantum only in decimal (where the representation isn't
necessarily normalized, contrary to binary).
--
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