dgh@dgh.UUCP (05/21/88)
noalias may be non-negotiable, but it may be non-negligible, as I found
out somewhat to my surprise this week.
At various times I've needed a version of The Linpack Benchmark
written in C, usually because a Fortran compiler was not available;
The Linpack Benchmark is very useful for lots of surprising purposes,
like debugging caches and virtual memory systems. Of course, The Linpack
Benchmark is by definition written entirely in Fortran, so for benchmarking
purposes a C translation is more or less useless. This despite an
observation by one of my colleagues, viewing the C version, that
it appeared to still be written in Fortran. But faithful preservation of
Fortran semantics, including memory access patterns, was one of the goals
of the translation.
My new manager wanted to tackle a small technical job keep in shape,
and so I suggested this translation. It was not quite as small a job
as we expected, but eventually she got it to produce identical numerical
results as the Fortran version, but she never could get comparable performance.
The results for double precision linpack on Sun-4 using SunOS 4.0 and
Fortran 1.1 were:
Rolled Source Unrolled Source
Fortran 1080 KFLOPS 875 KFLOPS
C 850 KFLOPS 875 KFLOPS
Why was C slower than Fortran in the rolled case?
It turns out that almost all The Linpack Benchmark does is execute
a short subroutine of the following simplified Fortran forms:
subroutine daxpy(n,da,dx,dy)
doubleprecision dx(1),dy(1),da
integer i,n
do 30 i = 1,n,4
dy(i) = dy(i) + da*dx(i)
dy(i+1) = dy(i+1) + da*dx(i+1)
dy(i+2) = dy(i+2) + da*dx(i+2)
dy(i+3) = dy(i+3) + da*dx(i+3)
30 continue
return
end
OR
subroutine daxpy(n,da,dx,dy)
doubleprecision dx(1),dy(1),da
integer i,n
do 30 i = 1,n
dy(i) = dy(i) + da*dx(i)
30 continue
return
end
The first of these is the standard UNROLLED form of the program;
the second is a questionably legal modification called the ROLLED form. The
original Fortran was written with unrolled source because that generated
more efficient code ten years ago when most compilers didn't unroll
loops for you automatically. Nowadays many Fortran compilers,
including Sun's, can get better
performance by unrolling the loops themselves than by attempting to
figure out unrolled source code.
Most of the benefit of loop unrolling in high-performance systems derives
from the possibilities it opens up for instruction scheduling across
independent iterations. The current multiplication can overlap the
previous addition, or current computation can overlap previous stores
and subsequent loads; what is worthwhile varies among implementations.
The corresponding rolled C code could be written with a for loop
daxpy(n, da, dx, dy )
double dx[], dy[], da;
int n;
{
int i;
for (i = 0; i < n; i++) {
dy[i] = dy[i] + da * dx[i];
}
}
but Sun compilers catch a red herring: for loops are compiled into two
basic blocks and the unroller won't unroll loops with more than one basic
block. So to bypass that issue, rewrite a little bit more in the form
daxpy(n, da, dx, dy )
double dx[], dy[], da;
int n;
{
int i;
i = 0;
do {
dy[i] = dy[i] + da * dx[i];
} while (i++ < n);
}
In this form the optimizer still won't unroll it,
and consequently the performance is less than Fortran. If the source
form is unrolled, however, the optimizer can't do as much with Fortran,
and C performance is the same.
Investigation revealed that the reason had to do with noalias: all Fortran
pointer variables (which happen to be exactly the set of procedure parameters)
are defined by the Fortran standard to be "noalias", meaning a compiler
may optimize code based on the assumption that the pointers never reference
the same memory. Alleged Fortran programs which break under such optimization
are declared by the Fortran standard to be non-standard. Very neat.
C, in contrast, has other kinds of pointer variables than procedure
parameters, and many people believe that a global decree of the Fortran type
would
break a lot of existing C programs. So the default is that optimization
must assume that any two pointers may be pointing to the same thing unless
it can prove otherwise. For a while X3J11 had a local "noalias" attribute
that you could attach to pointers, but later recanted in consideration to
assertions like 1) nobody had done it before, which is probably true,
2) nobody could agree on exactly what it meant, which appeared to be
true, and 3) optimizing compilers should be able to figure out if aliasing
exists, which is definitely false in a separate compilation environment
(unless you want the linker to recompile everything, in which case the
linker is the compiler, and you're back to no separate compilation).
Anyway there is no
portable way in draft ANSI C to say "this pointers are guaranteed
to have no aliases".
Thus the first part of the C compiler does NOT tell the optimizer that any
pointers are guaranteed unaliased; the optimizer won't unroll anything if
there are potential aliasing problems: you don't dare load dx[i+1] before
you store dy[i] if there is any danger that they point to the same place.
The Fortran compiler need have no such qualms.
What is to be done? I submitted extensive commentary to X3J11 during the
last public review period about numerical issues, but didn't mention noalias
because it was such a hot potato and I didn't think it mattered much, not
having investigated the possibilities. Even if noalias could be proved
to be unquestionably a good idea, I doubt X3J11 would want to change its draft
again, since such proofs seem so easy to overturn. Perhaps what will happen
is that high-performance
C compilers will adopt the questionable CDC/Cray Fortran practice
of providing "unsafe" optimization levels that, for instance,
assume all pointers are unaliased.
David Hough
dhough@sun.com
na.hough@na-net.stanford.edu
{ucbvax,decvax,decwrl,seismo}!sun!dhoughgwyn@brl-smoke.ARPA (Doug Gwyn ) (05/21/88)
In article <54080@sun.uucp> dgh%dgh@Sun.COM (David Hough) writes: >Perhaps what will happen is that high-performance >C compilers will adopt the questionable CDC/Cray Fortran practice >of providing "unsafe" optimization levels that, for instance, >assume all pointers are unaliased. David's article did an excellent job of illustrating why many X3J11 members thought something like "noalias" would have been useful. He correctly points out that ANSI C as it now stands requires that aliasing be handled "right", and that this interferes with some forms of optimization. I think one of two possible "solutions" will be implemented by vendors who care about this issue (for example, on vector hardware). One is to adopt essentially "noalias", i.e. a type qualifier that makes an appropriate guarantee so the optimizer is free to do its thing (it would be best if this were "__noalias" or some other non- conflicting extension to ANSI C). The other approach is to provide a compiler switch to enable such optimization globally on a per- source file basis. Both approaches are known to be viable; the first is more general but requires more work on the part of the programmer, and the resulting code is not strictly conforming. It is even possible to support both methods simultaneously.
ark@alice.UUCP (05/22/88)
In article <54080@sun.uucp>, dgh@dgh.UUCP writes: > What is to be done? Before writing off C for lacking noalias, try working on the program a little harder. Here is the original program: daxpy(n, da, dx, dy ) double dx[], dy[], da; int n; { int i; i = 0; do { dy[i] = dy[i] + da * dx[i]; } while (i++ < n); } I don't really think there's much here that noalias would help: the object code has to fetch dy[i], add da, multiply by dx[i], and store it in dy[i] and aliasing is irrelevant to each of these operations. Four things could speed it up, though, on many C implementations: 1. Make `i', `n', and `da' into register variables. 2. Use pointers instead of subscripts. 3. Use the += operator to avoid fetching and then storing dy[i]. 4. Replace i++<n by the faster, but equivalent, ++i<=n. Doing all these things gives the following revised program: daxpy(n, da, dx, dy) register double *dx, *dy, da; int n; { register double *dylim = dy + n; do *dy += da * *dx++; while (++dy <= dylim); } Why not try this and let us know the results?
henry@utzoo.uucp (Henry Spencer) (05/23/88)
Everyone agrees that the problem needs attention; unfortunately, there is no well-proven solution to it for C, and thus it is inappropriate to try to deal with it as part of standardization of the existing language. > ... Perhaps what will happen is that high-performance > C compilers will adopt the questionable CDC/Cray Fortran practice > of providing "unsafe" optimization levels that, for instance, > assume all pointers are unaliased. High-performance compilers will have to have *SOME WAY* to find out about aliasing or lack thereof. The obvious way is to have some sort of magic cookie in the source to selectively indicate when promises are made about aliasing. A compile-time option that covers a whole file isn't really a good idea, considering how pervasive pointers are in C and how common aliasing is. The obvious type of cookie is #pragma. (It is claimed, probably correctly, that #pragma technically is not allowed to change the semantics of the language, but that's not the way it will happen in the real world.) -- NASA is to spaceflight as | Henry Spencer @ U of Toronto Zoology the Post Office is to mail. | {ihnp4,decvax,uunet!mnetor}!utzoo!henry
tim@amdcad.AMD.COM (Tim Olson) (05/23/88)
In article <7879@alice.UUCP> ark@alice.UUCP writes: | I don't really think there's much here that noalias would help: | the object code has to fetch dy[i], add da, multiply by | dx[i], and store it in dy[i] and aliasing is irrelevant to | each of these operations. But that forces each iteration of the loop to be performed sequentially. I believe the original intent was to guarantee non-overlapping arrays to allow vector machines to compute the loop iterations in parallel. -- Tim Olson Advanced Micro Devices (tim@amdcad.amd.com)
njk@diku.dk (Niels J|rgen Kruse) (05/26/88)
In article <54080@sun.uucp>, dgh%dgh@Sun.COM (David Hough) writes: >(...) > it appeared to still be written in Fortran. But faithful preservation of > Fortran semantics, including memory access patterns, was one of the goals > of the translation. Since nobody else commented on this ... If you didn't want to preserve memory access patterns so badly, you could have done some hand scheduling on the unrolled loop : (similarly simplified) daxpy(n, da, dx, dy ) double dx[], dy[], da; int n; { int i; double a,b,c,d; for (i = 0; i < n; i++) { /* * Compute 4 independent expressions into * registers a,b,c,d. */ a = dy[i] + da * dx[i]; b = dy[i+1] + da * dx[i+1]; c = dy[i+2] + da * dx[i+2]; d = dy[i+3] + da * dx[i+3]; /* * Store results back. */ dy[i] = a, dy[i+1] = b, dy[i+2] = c, dy[i+3] = d; } } This alleviates the constraints imposed on scheduling by potential aliasing. The first store can be scheduled as soon as the last load has completed. Given that a sufficient number of registers are available for scheduling loads into, enough time should be left before computations terminate to catch up on the stores. If the fortran compiler doesn't unroll more than 4 times, i see no reason why this should be slower than the rolled fortran version. On the other hand, i see no reason why the unrolled fortran version should be slower than the rolled version either, so what do i know. Niels J|rgen Kruse
bill@proxftl.UUCP (T. William Wells) (06/02/88)
In article <7879@alice.UUCP>, ark@alice.UUCP writes: > daxpy(n, da, dx, dy) > register double *dx, *dy, da; > int n; > { > register double *dylim = dy + n; > > do *dy += da * *dx++; > while (++dy <= dylim); > } If you go this far, you should do this: daxpy(n, da, dx, dy) register double *dx, *dy, da; int n; { register double *dylim = dy + n; do *dy++ += da * *dx++; while (dy <= dylim); } [If n is the number of elements in dy, shouldn't the test be a <, not a <=?] The only difference is moving the ++ from the test condition to the assignment. For some machines (680?0 ?, VAX ?), this might give slightly better results because it may be possible to use an addressing mode to accomplish the increment. Also, the register variables should be ordered dy and dx instead of dx and dy, this might not make any difference here, but had these register variables been the second and third, this would have made a minor difference (on an 80?86, for example).
ssd@sugar.UUCP (Scott Denham) (06/04/88)
In article <21727@amdcad.AMD.COM>, tim@amdcad.AMD.COM (Tim Olson) writes: > In article <7879@alice.UUCP> ark@alice.UUCP writes: > | I don't really think there's much here that noalias would help: > | the object code has to fetch dy[i], add da, multiply by > | dx[i], and store it in dy[i] and aliasing is irrelevant to > | each of these operations. > > But that forces each iteration of the loop to be performed sequentially. > I believe the original intent was to guarantee non-overlapping arrays to > allow vector machines to compute the loop iterations in parallel. > > -- Tim Olson There is a real need to be able to assure the compiler that there is no recursion present in an expression in which it is impossible for the compiler to decide this for itself from the information available in the code. This is particularly true in subroutines - the designer can know things about the values of arguments that the compile could never guess, and in the case of any doubt, the compiler must play it "safe". IBM made a serious misjudgement in their first attempt at a vector Fortran compiler and included no such facility - and it took some very nasty coding to "fool" the compiler into vectorizing code that when written in a straightforward way left open the possiblity that the loop would not give consistent results if pipelined or split into parallel tasks.