On Friday, 7 October 2016 at 17:02:02 UTC, Andrei Alexandrescu
wrote:
On 10/07/2016 03:42 AM, Ilya Yaroshenko wrote:
For example, SUM_i of sqrt(fabs(a[i])) can be vectorised using
mir.ndslice.algorithm.
vxorps instruction can be used for fabs.
vsqrtps instruction can be used for sqrt.
LDC's @fastmath allows to re-associate summation elements.
Depend on data cache level this allows to speed up iteration 8
times for
single precision floating point number for AVX (16 times for
AVX512?).
Yah, 8 times is large enough to justify an important change.
Current std.math has following problems:
1. Math funcitons are not templates -> Phobos should be linked.
This is also the case for C++ - most math functions are linked
from the C standard library. How do typical linear algebra
libraries similar in functionality with Mir (such as Eigen)
deal with this situation?
1) BLAS-like API requires only sqrt and fabs. The solutions used
in Eigen depend on compiler. For example, the following code can
be found:
```c++
template<> EIGEN_DEVICE_FUNC inline float4 pabs<float4>(const
float4& a) {
return make_float4(fabsf(a.x), fabsf(a.y), fabsf(a.z),
fabsf(a.w));
}
template<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const
double2& a) {
return make_double2(fabs(a.x), fabs(a.y));
}
```
2) Eigen, uBLAS and other use Expression Templates [1], which are
used to compose few multiplications, additions/subtractions and
maybe some per element operations on matrices and vectors. In the
same time I have never seen that a lambda can be passed. C/C++
high performance libraries uses macroses/templates for type
specification, but lambdas are not used.
This makes upcoming ndslice.algorithm a unique solution, which is
more flexible, fast, and universal comparing with C++ Expression
Templates. It still requires some rework, and LDC based DMD 2.072
for further optimization.
Also, one question is how does the existence of unused
functions impede the working of faster functions provided
separately? Is it a sticky point that std.math is he exact
module used?
Of course a separate module or dub can be provided instead. In
addition, std.math should be splitted into package and reworked.
So, instead of modifying std.math we can start a new math package.
Trying to get a good grip on the matter. Generally you'd have a
very easy time convincing me that templates are a better way to
go :o). But we need to have a good motivation. Do you have a
brief example illustrating one proposed template and how it is
better than the old ways?
Yes, the example can be found at [2].
First template is better for BetterC mode. The example contains
a C program. The last paragraph in this post contains second part
about this example.
The first part:
```c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
float mir_alg_bar(float, float, float);
int main(int argc, char const *argv[])
{
if(argc < 4)
{
puts("Usage: app number_a number_b number_с");
return 1;
}
float a = atof(argv[1]);
float b = atof(argv[2]);
float c = atof(argv[3]);
float d = mir_alg_bar(a, b, c);
printf("%f\n", d);
return 0;
}
```
This program should be linked with BetterC libray:
```sh
clang app.c alg/libmir-alg.a
```
`mir-alg` is a small betterC library, which uses a generic `mir`
dummy (not a normal Mir for example simplicity). It can be linked
as common C library and has extern(C) nothrow @nogc interface.
```d
module alg_bar;
pragma(LDC_no_moduleinfo);
import ldc.attributes : fastmath;
import mir.alg;
extern(C) nothrow @nogc @fastmath:
float mir_alg_bar(float a, float b, float c) { return alg1!bar(a,
b, c); };
```
Mir dummy contains 3 implementations `alg1`, `alg2`, `alg3`.
```d
module mir.alg;
import ldc.intrinsics : llvm_fabs;
import ldc.attributes : fastmath;
pragma(LDC_no_moduleinfo);
@fastmath
{
auto alg1(alias f)(float a, float b, float c)
{
return f(a, llvm_fabs(b), c);
}
auto alg2(alias f)(float a, float b, float c)
{
return f(a, fabs(b), c);
}
auto alg3(alias f)(float a, float b, float c)
{
import std.math;
return f(a, std.math.fabs(b), c);
}
}
@fastmath
auto bar()(float a, float b, float c)
{
return a * b + c;
}
float fabs(float x) @safe pure nothrow @nogc { return
llvm_fabs(x); }
```
`fabs` function declaration is the same as in LDC's Phobos fork.
`alg1` can be linked with C library in any optimization modes.
`alg2` and `alg3` uses function declarations and requir to link
`libmir` dummy or `libphobos2` respectively. Making `fabs`
template solves this problem.
LDC can inline `fabs` for `alg2` and `alg3`, but `O2` flag is
required.
1.a I strongly decided to move forward without DRuntime. A
phobos as
source library is partially OK, but no linking dependencies
should be.
BetterC mode is what required for Mir to replace OpenBLAS and
Eigen.
New
cpuid, threads and mutexes should be provided too. New cpuid
[1] is
already implemented (I just need to replace module constructor
with
explicit initialization function).
Do you think you can integrate the new cpuid implementation
with the existing interface (most likely greatly enhancing it)
without breaking the existing clients?
New cpuid has low level and hight level API. The hight level API
will be reworked to intermediate level API without the module
constructor. This is required for BetterC mode. Current DRuntime
cpuid API can be implemented on top of new cpuid low level
interface. However current DRuntime API can not be used for Mir.
The reasons are:
1. It is not compatible with betterC mode.
2. It performs additional weird computations for cache level
sizes. This makes me crazy to predict what returned value means.
If an engineer asks about Level3 cache size, Level3 cache size
should be returned instead current hell. See also Issue 16028 [3].
3. It can not represent complex CPU topology, which is required
by ARM (especially by server ARM CPUs). CPU information is
protected on ARM CPUs, but it can be predefined by a user of be
fetched from an OS.
Same question for threads.
Same question for mutexes.
Current DRuntime mutexes and threads can be implemented on top of
nothrow @nogc successors.
My strong opinion is that a D library
for D is a wrong direction. A numeric D library should be a
product for
other languages too, like many C libraries does. One my client
is
thinking to invest to nothrow @nogc async I/O for production,
so it may
help to move to betterC direction too.
Sure. A different way to frame this is to make D friendlier
toward linking with other languages. The way I see it, if we
get alternatives for cpuid, threads, and mutexes in Mir, that
would benefit clients interested in linear algebra. If we get
them in DRuntime, that would benefit clients interested in
linear algebra and everything else. Clearly the impact would be
much larger.
We do not need to have DRuntime for the future, but existing
users. Fat runtime (except generic algorithms) is red flag for
software developers if they need to creat something like Eigen or
hight perfromance web server. The number of such libraries is
always small. In the same time these libraries make weather and a
lot of packages will be build on top of them after a while. Dub
allows to overload dependencies versions in dub.selections.json.
This is what is required for continuous development.
Assume you manage a set of integrated infrastructure projects,
which use a set of third sides DUB projects, which depends on
DRuntime. Part of this infrastructure is open source. Consultancy
for clients is main income. And you want to add support for
modern CPU or add new system API for another one appleOS. A
release has time constraints, so you can not wait for new
compiler release. Also clients wants new features and backward
compatability for older compiler in the same time. Plus testing
complex infrastructure with a compiler fork requires additional
efforts and time and clients would not be happy to deploy your
compiler fork into their infrastructure and for their clients. In
addition, you need to update forked DRuntime API usage for the
third side projects. This is a stalemate situation and red flag
for business.
Cpuid, threads, mutexes, event loop, async I/O, and numeric
software as low level DUB packages with good community support
and small release cycle are what we really need. I am not against
hight level API. Furthermore, bindings to other languages is an
option to provide simple and familiar API for users. But low
level API is required.
Users do not care about `std`/`core` or other prefix. They want
good support. Business requires reliability and flexibility, bugs
are not a huge problem if an architecture allows to find and fix
them. Really huge problem is a high level object-oriented
GC-oriented X86-oriented DRuntime, which is dependency almost
everywhere. I would like to see `std.glas` instead of `mir.glas`,
but it should be provided as common dub project.
2.b In context of 1.a, linking multiple binaries compiled
with
different DRuntime/Phobos versions may cause significant
problems.
DRuntime is not so stable like std C lib. One may say that I
am doing
something wrong if I need to link libraries compiled with
different
DRuntimes. But this is what will happen often with D in real
world if D
start to replace C libraries (1.a). So, betterC without
DRuntime /
Phobos linking dependencies is a direction to move forward.
nothrow
@nogc generic Phobos code seems to be OK.
Hmmm... well I seem to recall the C std lib in gcc has large
interoperability issues with its own previous versions, even
across minor releases. This has caused numerous headaches at
Facebook because the breakages always come without warning and
manifest themselves in obscure ways. On the Microsoft side
things are even worse, because they virtually guarantee that a
version of VS is not binary compatible with the previous ones
(I'm not kidding; it's deliberate).
That sets a rather low baseline for us :o). Clearly we'd want
to do better, and we probably can. But I think it would be an
exaggeration to worry too much about such scenarios.
2. Math funcitons are not templates -> They are not inlined ->
No
vectorization + function calls in a loop body. One day this
may be
fixed, but (1.a, 1.b).
How to the likes of Eigen do it? Do they provide their own
templated implementation of <math.h>?
Seems like the recent LDC fixes this problem. Many thanks to our
LDC team!
Eigen code is very weird, it uses templates and macroses in the
same time with specialization for different compilers and clibs
including Intel MKL.
Have you investigated the much hailed link-time inlining?
This probably would not work for loop vectorization.
3. Math funcitons are not aliases for LDC -> LDC's @fastmath
would not
work for them. To enable @fastmath for this functions they
should be
annotated with @fastmath, which is not acceptable. If a
function is an
alias for llvm intrinsics, than @fastmath flag can be applied
to a
function, which calls it.
Not sure I udnerstand this, but it seems to me making the math
functions templates would solve it?
Yes. Templates can be replaced with aliases to the intrinsics for
`version(LDC)`.
For the example above and for all optimization turning on only
the `alg1`, which calls `llvm_fabs` directly, has fused
operations. The reason is that fma composition is in the end of
LLVM optimization pipeline. If one inlined function (bar) and
root function (alg2) have `@fastmath` and another inlined
function (fabs) has not `@fastmath`, the code for root will have
fma, but inlined code for _both_ functions will not have fma. To
perform other optimizations like vectorization LLVM needs to
decompose fma and recompose it later.
Best regards,
Ilya
[1] https://en.wikipedia.org/wiki/Expression_templates
[2]
https://github.com/libmir/temporary_experiments/tree/master/alias_vs_fun
[3] https://issues.dlang.org/show_bug.cgi?id=16028