On 24/03/2013 15:01, Duncan Murdoch wrote:
On 13-03-23 10:20 AM, Matthew Dowle wrote:
On 23.03.2013 12:01, Prof Brian Ripley wrote:
On 20/03/2013 12:56, Matthew Dowle wrote:
Hi,
Please consider the following :
x = as.integer(2^30-1)
[1] 1073741823
sum(c(rep(x, 10000000), rep(-x,9999999)))
[1] 1073741824
Tested on 2.15.2 and a recent R-devel (r62132).
I'm wondering if s in isum could be LDOUBLE instead of double, like
rsum, to fix this edge case?
No, because there is no guarantee that LDOUBLE differs from double
(and platform on which it does not).
That's a reason for not using LDOUBLE at all isn't it? Yet src/main/*.c
has 19 lines using LDOUBLE e.g. arithmetic.c and cum.c as well as
summary.c.
I'd assumed LDOUBLE was being used by R to benefit from long double (or
equivalent) on platforms that support it (which is all modern Unix, Mac
and Windows as far as I know). I do realise that the edge case wouldn't
Actually, you don't know. Really only on almost all Intel ix86: most
other current CPUs do not have it in hardware. C99/C11 require long
double, but does not require the accuracy that you are thinking of and
it can be implemented in software.
Note that even on ix86 this is something that can be switched on or off
in the CPU: last time I looked (years ago) it was off by default in
Microsoft compilers.
All C99 requires is that long double is at least as precise as double.
C11 recommends in §F.2
Recommended practice
2 The long double type should match an IEC 60559 extended format.
Notice the 'an': there are two such formats, and both are in use on R
platforms. But then some OS/compiler suppliers have never paid any heed
to ISO standards.
be fixed on platforms where LDOUBLE is defined as double.
I think the problem is that there are two opposing targets in R: we
want things to be as accurate as possible, and we want them to be
consistent across platforms. Sometimes one goal wins, sometimes the
other. Inconsistencies across platforms give false positives in tests
that tend to make us miss true bugs. Some people think we should never
use LDOUBLE because of that. In other cases, the extra accuracy is so
helpful that it's worth it. So I think you'd need to argue that the
case you found is something where the benefit outweighs the costs. Since
almost all integer sums are done exactly with the current code, is it
really worth introducing inconsistencies in the rare inexact cases?
But as I said lower down, a 64-bit integer accumulator would be helpful,
C99/C11 requires one at least that large and it is implemented in
hardware on all known R platforms. So there is a way to do this pretty
consistently across platforms.
Duncan Murdoch
What have I misunderstood?
Users really need to take responsibility for the numerical stability
of calcuations they attempt. Expecting to sum 20 million large
numbers exactly is unrealistic.
Trying to take responsibility, but you said no. Changing from double to
LDOUBLE would mean that something that wasn't realistic, was then
realistic (on platforms that support long double).
And it would bring open source R into line with TERR, which gets the
answer right, on 64bit Windows at least. But I'm not sure I should be as
confident in TERR as I am in open source R because I can't see its
source code.
There are cases where 64-bit integer accumulators would be
beneficial, and this is one. Unfortunately C11 does not require them
but some optional moves in that direction are planned.
https://svn.r-project.org/R/trunk/src/main/summary.c
Thanks,
Matthew
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--
Brian D. Ripley, rip...@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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