Floating point issue

Hi,

Taras makes several good points, especially this one:

On Mon, Jul 11, 2022 at 12:31 PM Taras Zakharko <taras.zakharko at uzh.ch>
wrote:
 Available precision can affect numerical properties of algorithms but
should not affect things like decimal to binary or via versa conversion ?
it either produces the accurate enough number or it doesn?t.
This is a key point: there is no need to rely on platform-specific
properties of floating-point representations or operations to get correct
(*) decimal-to-binary or binary-to-decimal conversions.  These tasks can be
done correctly in a way that uses only the guarantees provided by IEEE
floats or doubles, and some additional work using big integers (something
like GNU MP) in some cases.  There are freely-available libraries to do
the conversions in a platform-independent, correct, efficient way.  An even
easier solution in one direction is strtod(): decades ago it was not 100%
correct but I haven't seen any flaws in recent versions of GLIBC or on
Windows.  Certainly strtod can be relied on to do a better job than
"multiply-by-10 and add the next digit".

(*) What is correct?  The easy direction is decimal to binary, staying in
the range of positive normalized numbers.  There are a finite number of
rational numbers that are exactly representable as IEEE doubles.  The
correct double representation of a decimal number (also a rational) is that
IEEE double that is closest.  In the event of a tie, use the round-to-even
rule.

As a side note, I agree with Andre that relying on Intel?s extended
precision in this day an age is not a good idea. This is a legacy feature
from over forty years ago, x86 CPUs have been using SSE instructions for
floating point computation for over a decade. The x87 instructions are slow
and prevent compiler optimisations. Overall, I believe that R would benefit
from dropping this legacy cruft. Not that there are too many places where
it is used from what I see?

Best,

? Taras Zakharko

On 11 Jul 2022, at 13:48, GILLIBERT, Andre <Andre.Gillibert at chu-rouen.fr>
wrote:

From my current experiences, I dare to say that the M1 with all
its speed is just a tad less reliable numerically than the
Intel/AMD floating point implementations..

80 bits floating point (FP) numbers are great, but I think we cannot
rely on it for the future.
I expect, the marketshare of ARM CPUs to grow. It's hard to predict, but
ARM may spread in desktop computers in a timeframe of 10 years, and I would
not expect it to gain extended precision FP.
Moreover, performance of FP80 is not a priority of Intel. FP80 in recent
Intel microprocessors are very slow when using special representations
(NaN, NA, Inf, -Inf) or denormal numbers.
Therefore, it may be wise to update R algorithms to make them work quite
well with 64 bits FP.
--
Sincerely
Andr? GILLIBERT

      [[alternative HTML version deleted]]

______________________________________________
R-devel at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel

______________________________________________
R-devel at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-devel

Steven Dirkse, Ph.D.
GAMS Development Corp.
office: 202.342.0180

	[[alternative HTML version deleted]]

Floating point issue

Thread (25 messages)