There are several issues here, and a good knowledge of the R Internals
manual seems a prerequisite (and, considering where this started, of the
relevant help pages!).
R uses its integer type for indexing vectors and arrays (which can be
indexed as vectors or via an appropriate number of indices). So if we
allow more than 2^31-1 elements we need a way to index them in R. One
idea would be to make R's integer type int64 on suitable platforms, but
that would have really extensive ramifications (in the R sources and in
packages). Another idea (I think suggested by Luke Tierney) is to allow
double() indices which might be less disruptive. Adding a new type would
be a very serious amount of work (speaking as someone who has done it).
Another issue is the use of Fortran for matrix algebra. That is likely to
cause portability issues, and there's no point in doing it unless one has
an efficient implementation of e.g. BLAS/LAPACK, the reference
implementation being slow at even 100 million. (That's probably not an
empty set, as I see ACML has a int64 BLAS.)
There are lots of portability issues -- e.g. the current save() format is
the same on all systems and we have complete interoperability. (That
cannot be the case if we allow big vectors to be saved.)
But at present I don't see a significant number of applications any time
soon. 2 billion items in a homogenous group is a *lot* of data. I know
there are applications with 2 billion items of data already, but is it
appropriate to store them in a single vector or matrix rather than say a
data frame or DBMS tables? And will there 'ever' be more than a tiny
demand for such applications? (I am excluding mainly-zero vectors, and
Martin has already pointed out that we have ways to deal with those.)
It is three or four years since we first discussed some of the options,
and at the time we thought it would be about five years before suitably
large machines became available to more than a handful of R users. That
still seems about right: >=128GB systems (which is about what you need
for larger than 16GB objects) may start to become non-negligible in a year
or two.
R is a volunteer project with limited resources -- there are AFAIK less
than a handful of people with the knowledge of R internals to tackle these
issues. Only if one of them has a need to work with larger datasets is
this likely to be worked on.
"VK" == Vadim Kutsyy <[EMAIL PROTECTED]>
on Fri, 01 Aug 2008 10:22:43 -0700 writes:
VK> Martin Maechler wrote:
>> [[Topic diverted from R-help]]
>>
>> Well, fortunately, reasonable compilers have indeed kept
>> 'long' == 'long int' to mean 32-bit integers ((less
>> reasonable compiler writers have not, AFAIK: which leads
>> of course to code that no longer compiles correctly when
>> originally it did)) But of course you are right that
>> 64-bit integers (typically == 'long long', and really ==
>> 'int64') are very natural on 64-bit architectures. But
>> see below.
... I wrote complete rubbish,
and I am embarrassed ...
>>
VK> well in 64bit Ubunty, /usr/include/limits.h defines:
VK> /* Minimum and maximum values a `signed long int' can hold. */
VK> # if __WORDSIZE == 64
VK> # define LONG_MAX 9223372036854775807L
VK> # else
VK> # define LONG_MAX 2147483647L
VK> # endif
VK> # define LONG_MIN (-LONG_MAX - 1L)
VK> and using simple code to test
VK> (http://home.att.net/~jackklein/c/inttypes.html#int) my desktop, which
VK> is standard Intel computer, does show.
VK> Signed long min: -9223372036854775808 max: 9223372036854775807
yes. I am really embarrassed.
What I was trying to say was that
the definition of int / long /... should not change when going
from 32bit architecture to 64bit
and that the R internal structures consequently should also be
the same on 32-bit and 64-bit platforms
>> If you have too large a numeric matrix, it would be larger than
>> 2^31 * 8 bytes ~= 2^34 / 2^20 ~= 16'000 Megabytes.
>> If that is is 10% only for you, you'd have around 160 GB of
>> RAM. That's quite a impressive.
>>
>> cat /proc/meminfo | grep MemTotal
VK> MemTotal: 145169248 kB
VK> We have "smaller" SGI NUMAflex to play with, where the memory can
VK> increased to 512Gb ("larger" version doesn't have this "limitation").
VK> But with even commodity hardware you can easily get 128Gb for reasonable
VK> price (i.e. Dell PowerEdge R900)
>> Note that R objects are (pointers to) C structs that are
>> "well-defined" platform independently, and I'd say that this
>> should remain so.
>>
VK> I forgot that R stores two dimensional array in a single dimensional C
VK> array. Now I understand why there is a limitation on total number of
VK> elements. But this is a big limitations.
Yes, maybe
>> One of the last times this topic came up (within R-core),
>> we found that for all the matrix/vector operations,
>> we really would need versions of BLAS / LAPACK that would also
>> work with these "big" matrices, ie. such a BLAS/Lapack would
>> also have to internally use "longer int" for indexing.
>> At that point in time, we had decied we would at least wait to
>> hear about the development of such BLAS/LAPACK libraries
VK> BLAS supports two dimensional metrics definition, so if we would store
VK> matrix as two dimensional object, we would be fine. But than all R code
VK> as well as all packages would have to be modified.
exactly. And that was what I meant when I said "Compatibility".
But rather than changing the
"matrix = colmunwise stored as long vector" paradigm, should
rather change from 32-bit indexing to longer one.
The hope is that we eventually make up a scheme
which would basically allow to just recompile all packages :
In src/include/Rinternals.h,
we have had the following three lines for several years now:
------------------------------------------------------------------------------------
/* type for length of vectors etc */
typedef int R_len_t; /* will be long later, LONG64 or ssize_t on Win64 */
#define R_LEN_T_MAX INT_MAX
------------------------------------------------------------------------------------
and you are right, that it may be time to experiment a bit more
with replacing 'int' with long (and also the corresponding _MAX)
setting there,
and indeed, in the array.c code you cited, should repalce
INT_MAX by R_LEN_T_MAX
This still does not solve the problem that we'd have to get to
a BLAS / Lapack version that correctly works with "long indices"...
which may (or may not) be easier than I had thought.
Martin
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