Fast and generic use of lambda functions - c++

Motivation
I created a header file which wraps Matlab's mex functionality in c++11 classes; especially for MxNxC images. Two functions I created are forEach, which iterates over each pixel in the image, and also a forKernel, which given a kernel and pixel in the image, iterates over the kernel around that pixel, handling all kinds of nifty, boiler-plate indexing mathematics.
The idea is that one could program sliding-windows like this:
image.forEach([](Image &image, size_t row, size_t col) {
//kr and lc specify which pixel is the center of the kernel
image.forKernel<double>(row, col, kernel, kr, kc, [](Image &image, double w, size_t row, size_t col) {
// w is the weight/coefficient of the kernel, row/col are the corresponding coordinates in the image.
// process ...
});
});
Problem
This provides a nice way to
increase readability: the two function calls are a lot clearer than the corresponding 4 for-loops to do the same,
stay flexible: lambda functions allow you to scope all kinds of variables by value or reference, which are invisible to the implementer of forEach / forKernel, and
increase execution time, unfortunately: this executes around 8x slower than using just for loops.
The latter point is the problem, of course. I was hoping g++ would be able to optimize the lambda-functions out and inline all the code. This does not happen. Hence I created a minimal working example on 1D data:
#include <iostream>
#include <functional>
struct Data {
size_t d_size;
double *d_data;
Data(size_t size) : d_size(size), d_data(new double[size]) {}
~Data() { delete[] d_data; }
double &operator[](size_t i) { return d_data[i]; }
inline void forEach(std::function<void(Data &, size_t)> f) {
for (size_t index = 0; index != d_size; ++index)
f(*this, index);
}
};
int main() {
Data im(50000000);
im.forEach([](Data &im, size_t i) {
im[i] = static_cast<double>(i);
});
double sum = 0;
im.forEach([&sum](Data &im, size_t i) {
sum += im[i];
});
std::cout << sum << '\n';
}
source: http://ideone.com/hviTwx
I'm guessing the compiler is not able to compile the code for forEach per lambda-function, as the lambda function is not a template variable. The good thing is that one can compile once and link to it more often with different lambda functions, but the bad thing is that it is slow.
Moreover, the situation discussed in the motivation already contains templates for the data type (double, int, ...), hence the 'good thing' is overruled anyway.
A fast way to implement the previous would be like this:
#include <iostream>
#include <functional>
struct Data {
size_t d_size;
double *d_data;
Data(size_t size) : d_size(size), d_data(new double[size]) {}
~Data() { delete[] d_data; }
double &operator[](size_t i) { return d_data[i]; }
};
int main() {
size_t len = 50000000;
Data im(len);
for (size_t index = 0; index != len; ++index)
im[index] = static_cast<double>(index);
double sum = 0;
for (size_t index = 0; index != len; ++index)
sum += im[index];
std::cout << sum << '\n';
}
source: http://ideone.com/UajMMz
It is about 8x faster, but also less readable, especially when we consider more complicated structures like images with kernels.
Question
Is there a way to provide the lambda function as a template argument, such that forEach is compiled for each call, and optimized for each specific instance of the lambda function? Can the lambda function be inlined somehow, since lambda functions are typically not recursive this should be trivial, but what is the syntax?
I found some related posts:
Why C++ lambda is slower than ordinary function when called multiple times?
Understanding the overhead of lambda functions in C++11
C++0x Lambda overhead
But they do not give a solution in the form of a minimal working example, and they do not discuss the possibility of inlining a lambda function. The answer to my question should do that: change the Data.forEach member function and it's call such that is as fast as possible / allows for as many running time optimizations (not optimizations at run time, but at compile time that decrease runtime) as possible.
Regarding the suggestion of forEveR
Thank you for creating that fix, it's a huge improvement yet still approximately 2x as slow:
test0.cc: http://ideone.com/hviTwx
test1.cc: http://ideone.com/UajMMz
test2.cc: http://ideone.com/8kR3Mw
Results:
herbert#machine ~ $ g++ -std=c++11 -Wall test0.cc -o test0
herbert#machine ~ $ g++ -std=c++11 -Wall test1.cc -o test1
herbert#machine ~ $ g++ -std=c++11 -Wall test2.cc -o test2
herbert#machine ~ $ time ./test0
1.25e+15
real 0m2.563s
user 0m2.541s
sys 0m0.024s
herbert#machine ~ $ time ./test1
1.25e+15
real 0m0.346s
user 0m0.320s
sys 0m0.026s
herbert#machine ~ $ time ./test2
1.25e+15
real 0m0.601s
user 0m0.575s
sys 0m0.026s
herbert#machine ~ $
I re-ran the code with -O2, which fixes the problem. runtimes of test1 and test2 ar now very similar. Thank you #stijn and #forEveR.
herbert#machine ~ $ g++ -std=c++11 -Wall -O2 test0.cc -o test0
herbert#machine ~ $ g++ -std=c++11 -Wall -O2 test1.cc -o test1
herbert#machine ~ $ g++ -std=c++11 -Wall -O2 test2.cc -o test2
herbert#machine ~ $ time ./test0
1.25e+15
real 0m0.256s
user 0m0.229s
sys 0m0.028s
herbert#machine ~ $ time ./test1
1.25e+15
real 0m0.111s
user 0m0.078s
sys 0m0.033s
herbert#machine ~ $ time ./test2
1.25e+15
real 0m0.108s
user 0m0.076s
sys 0m0.032s
herbert#machine ~ $

Problem is, that you use std::function, that actually use type-erasure and virtual calls.
You can simply use template parameter, instead of std::function. Call of lambda function will be inlined, due n3376 5.1.2/5
The closure type for a lambda-expression has a public inline function
call operator (13.5.4) whose param- eters and return type are
described by the lambda-expression’s parameter-declaration-clause and
trailing- return-type respectively
So, just simply write
template<typename Function>
inline void forEach(Function f) {
for (size_t index = 0; index != d_size; ++index)
f(*this, index);
}
Live example

Related

Why std::for_each is faster than __gnu_parallel::for_each

I'm trying to understand why std::for_each which runs on single thread is ~3 times faster than __gnu_parallel::for_each in the example below:
Time =0.478101 milliseconds
vs
Time =0.166421 milliseconds
Here the code i'm using to benchmark:
#include <iostream>
#include <chrono>
#include <parallel/algorithm>
//The struct I'm using for timming
struct TimerAvrg
{
std::vector<double> times;
size_t curr=0,n;
std::chrono::high_resolution_clock::time_point begin,end;
TimerAvrg(int _n=30)
{
n=_n;
times.reserve(n);
}
inline void start()
{
begin= std::chrono::high_resolution_clock::now();
}
inline void stop()
{
end= std::chrono::high_resolution_clock::now();
double duration=double(std::chrono::duration_cast<std::chrono::microseconds>(end-begin).count())*1e-6;
if ( times.size()<n)
times.push_back(duration);
else{
times[curr]=duration;
curr++;
if (curr>=times.size()) curr=0;}
}
double getAvrg()
{
double sum=0;
for(auto t:times)
sum+=t;
return sum/double(times.size());
}
};
int main( int argc, char** argv )
{
float sum=0;
for(int alpha = 0; alpha <5000; alpha++)
{
TimerAvrg Fps;
Fps.start();
std::vector<float> v(1000000);
std::for_each(v.begin(), v.end(),[](auto v){ v=0;});
Fps.stop();
sum = sum + Fps.getAvrg()*1000;
}
std::cout << "\rTime =" << sum/5000<< " milliseconds" << std::endl;
return 0;
}
This is my configuration:
gcc version 7.3.0 (Ubuntu 7.3.0-21ubuntu1~16.04)
Intel® Core™ i7-7600U CPU # 2.80GHz × 4
htop to check if the program is running in single or multiple threads
g++ -std=c++17 -fomit-frame-pointer -Ofast -march=native -ffast-math -mmmx -msse -msse2 -msse3 -DNDEBUG -Wall -fopenmp benchmark.cpp -o benchmark
The same code doesn't get compiled with gcc 8.1.0. I got that error message:
/usr/include/c++/8/tr1/cmath:1163:20: error: ‘__gnu_cxx::conf_hypergf’ has not been declared
using __gnu_cxx::conf_hypergf;
I already checked couple of posts but either they're very old or not the same issue..
My questions are:
Why is it slower in parallel?
I'm using the wrong functions?
In cppreference it is saying that gcc with Standardization of Parallelism TS is not supported (mentioned with red color in the table) and my code is running in parallel!?
Your function [](auto v){ v=0;} is extremely simple.
The function may be replaced it with a single call to memset or use SIMD instructions for single threaded parallellism. With the knowledge that it overwrites the same state as the vector initially had, the entire loop could be optimised away. It may be easier for the optimiser to replace std::for_each than a parallel implementation.
Furthermore, assuming the parallel loop uses threads, one must remember that creation and eventual synchronisation (in this case there is no need for synchronisation during processing) have overhead, which may be significant in relation to your trivial operation.
Threaded parallellism is often only worth it for computationally expensive tasks. v=0 is one of the least computationally expensive operations there are.
Your benchmark is faulty, I'm even surprised it takes time to run it.
You wrote:
std::for_each(v.begin(), v.end(),[](auto v){ v=0;});
As v is a local argument of the operator() with no reads, I would expect it to become removed by your compiler.
As you now have a loop with a body, that loop can be removed as well as there isn't an observable effect.
And similar to that, the vector can be removed as well as you don't have any readers.
So, without any side effects, this could all be removed. If you would use a parallel algorithm, chances are you have some kind of synchronization, which make optimizing this much harder as there might be side effects in another thread? Proving it doesn't is more complex, not to mention the side effects of the thread management which could exist?
To solve this, a lot of benchmarks have trucks in macros to force the compiler to assume side effects. Use them in the lambda so the compiler doesn't remove it.

Puzzling performance difference between mac and a relatively powerful desktop

My original intention for writing this piece of code is to measure performance difference when an entire array is operated on by a function vs operating individual elements of an array.
i.e. comparing the following two statements:
function_vector(x, y, z, n);
vs
for(int i=0; i<n; i++){
function_scalar(x[i], y[i], z[i]);
}
where function_* does some substantial but identical calculations.
With -ffast-math turned on, the scalar version is roughly 2x faster on multiple machines I have tested on.
However, whats puzzling is the comparison of timings on two different machines, both using gcc 6.3.0:
# on desktop with Intel-Core-i7-4930K-Processor-12M-Cache-up-to-3_90-GHz
g++ loop_test.cpp -o loop_test -std=c++11 -O3
./loop_test
vector time = 12.3742 s
scalar time = 10.7406 s
g++ loop_test.cpp -o loop_test -std=c++11 -O3 -ffast-math
./loop_test
vector time = 11.2543 s
scalar time = 5.70873 s
# on mac with Intel-Core-i5-4258U-Processor-3M-Cache-up-to-2_90-GHz
g++ loop_test.cpp -o loop_test -std=c++11 -O3
./loop_test
vector time = 2.89193 s
scalar time = 1.87269 s
g++ loop_test.cpp -o loop_test -std=c++11 -O3 -ffast-math
./loop_test
vector time = 2.38422 s
scalar time = 0.995433 s
By all means the first machine is superior in terms of cache size, clock speed etc. Still the code runs 5x faster on the second machine.
Question:
Can this be explained? Or am I doing something wrong here?
Link to the code: https://gist.github.com/anandpratap/262a72bd017fdc6803e23ed326847643
Edit
After comments from ShadowRanger, I added the __restrict__ keyword to function_vector and -march=native compilation flag. This gives:
# on desktop with Intel-Core-i7-4930K-Processor-12M-Cache-up-to-3_90-GHz
vector time = 1.3767 s
scalar time = 1.28002 s
# on mac with Intel-Core-i5-4258U-Processor-3M-Cache-up-to-2_90-GHz
vector time = 1.05206 s
scalar time = 1.07556 s
Odds are possible pointer aliasing is limiting optimizations in the vectorized case.
Try changing the declaration of function_vector to:
void function_vector(double *__restrict__ x, double *__restrict__ y, double *__restrict__ z, const int n){
to use g++'s non-standard support for a feature matching C99's restrict keyword.
Without it, function_vector likely has to assume that the writes to x[i] could be modifying values in y or z, so it can't do read-ahead to get the values.

C++ Centralizing SIMD usage

i have a library and a lot of projects depending on that library. I want to optimize certain procedures inside the library using SIMD extensions. However it is important for me to stay portable, so to the user it should be quite abstract.
I say at the beginning that i dont want to use some other great library that does the trick. I actually want to understand if that what i want is possible and to what extent.
My very first idea was to have a "vector" wrapper class, that the usage of SIMD is transparent to the user and a "scalar" vector class could be used in case no SIMD extension is available on the target machine.
The naive thought came to my mind to use the preprocessor to select one vector class out of many depending on which target the library is compiled. So one scalar vector class, one with SSE (something like this basically: http://fastcpp.blogspot.de/2011/12/simple-vector3-class-with-sse-support.html) and so on... all with the same interface.
This gives me good performance but this would mean that i would have to compile the library for any kind of SIMD ISA that i use. I rather would like to evaluate the processor capabilities dynamically at runtime and select the "best" implementation available.
So my second guess was to have a general "vector" class with abstract methods. The "processor evaluator" function would than return instances of the optimal implementation. Obviously this would lead to ugly code, but the pointer to the vector object could be stored in a smart pointer-like container that just delegates the calls to the vector object. Actually I would prefer this method because of its abstraction but I'm not sure if calling the virtual methods actually will kill the performance that i gain using SIMD extensions.
The last option that i figured out would be to do optimizations whole routines and select at runtime the optimal one. I dont like this idea so much because this forces me to implement whole functions multiple times. I would prefer to do this once, using my idea of the vector class i would like to do something like this for example:
void Memcopy(void *dst, void *src, size_t size)
{
vector v;
for(int i = 0; i < size; i += v.size())
{
v.load(src);
v.store(dst);
dst += v.size();
src += v.size();
}
}
I assume here that "size" is a correct value so that no overlapping happens. This example should just show what i would prefer to have. The size-method of the vector object would for example just return 4 in case SSE is used and 1 in case the scalar version is used.
Is there a proper way to implement this using only runtime information without loosing too much performance? Abstraction is to me more important than performance but as this is a performance optimization i wouldn't include it if would not speedup my application.
I also found this on the web: http://compeng.uni-frankfurt.de/?vc
Its open source but i dont understand how the correct vector class is chosen.
Your idea will only compile to efficient code if everything inlines at compile time, which is incompatible with runtime CPU dispatching. For v.load(), v.store(), and v.size() to actually be different at runtime depending on the CPU, they'd have to be actual function calls, not single instructions. The overhead would be killer.
If your library has functions that are big enough to work without being inlined, then function pointers are great for dispatching based on runtime CPU detection. (e.g. make multiple versions of memcpy, and pay the overhead of runtime detection once per call, not twice per loop iteration.)
This shouldn't be visible in your library's external API/ABI, unless your functions are mostly so short that the overhead of an extra (direct) call/ret matters. In the implementation of your library functions, put each sub-task that you want to make a CPU-specific version of into a helper function. Call those helper functions through function pointers.
Start with your function pointers initialized to versions that will work on your baseline target. e.g. SSE2 for x86-64, scalar or SSE2 for legacy 32bit x86 (depending on whether you care about Athlon XP and Pentium III), and probably scalar for non-x86 architectures. In a constructor or library init function, do a CPUID and update the function pointers to the best version for the host CPU. Even if your absolute baseline is scalar, you could make your "good performance" baseline something like SSSE3, and not spend much/any time on SSE2-only routines. Even if you're mostly targetting SSSE3, some of your routines will probably end up only requiring SSE2, so you might as well mark them as such and let the dispatcher use them on CPUs that only do SSE2.
Updating the function pointers shouldn't even require any locking. Any calls that happen from other threads before your constructor is done setting function pointers may get the baseline version, but that's fine. Storing a pointer to an aligned address is atomic on x86. If it's not atomic on any platform where you have a version of a routine that needs runtime CPU detection, use C++ std:atomic (with memory-order relaxed stores and loads, not the default sequential consistency which would trigger a full memory barrier on every load). It matters a lot that there's minimal overhead when calling through the function pointers, and it doesn't matter what order different threads see the changes to the function pointers. They're write-once.
x264 (the heavily-optimized open source h.264 video encoder) uses this technique extensively, with arrays of function pointers. See x264_mc_init_mmx(), for example. (That function handles all CPU dispatching for Motion Compensation functions, from MMX to AVX2). I assume libx264 does the CPU dispatching in the "encoder init" function. If you don't have a function that users of your library are required to call, then you should look into some kind of mechanism for running global constructor / init functions when programs using your library start up.
If you want this to work with very C++ey code (C++ish? Is that a word?) i.e. templated classes & functions, the program using the library will probably have do the CPU dispatching, and arrange to get baseline and multiple CPU-requirement versions of functions compiled.
I do exactly this with a fractal project. It works with vector sizes of 1, 2, 4, 8, and 16 for float and 1, 2, 4, 8 for double. I use a CPU dispatcher at run-time to select the following instructions sets: SSE2, SSE4.1, AVX, AVX+FMA, and AVX512.
The reason I use a vector size of 1 is to test performance. There is already a SIMD library that does all this: Agner Fog's Vector Class Library. He even includes example code for a CPU dispatcher.
The VCL emulates hardware such as AVX on systems that only have SSE (or even AVX512 for SSE). It just implements AVX twice (for four times for AVX512) so in most cases you can just use the largest vector size you want to target.
//#include "vectorclass.h"
void Memcopy(void *dst, void *src, size_t size)
{
Vec8f v; //eight floats using AVX hardware or AVX emulated with SSE twice.
for(int i = 0; i < size; i +=v.size())
{
v.load(src);
v.store(dst);
dst += v.size();
src += v.size();
}
}
(however, writing an efficient memcpy is complicating. For large sizes you should consider non temroal stores and on IVB and above use rep movsb instead). Notice that that code is identical to what you asked for except I changed the word vector to Vec8f.
Using the VLC, as CPU dispatcher, templating, and macros you can write your code/kernel so that it looks nearly identical to scalar code without source code duplication for every different instruction set and vector size. It's your binaries which will be bigger not your source code.
I have described CPU dispatchers several times. You can also see some example using templateing and macros for a dispatcher here: alias of a function template
Edit: Here is an example of part of my kernel to calculate the Mandelbrot set for a set of pixels equal to the vector size. At compile time I set TYPE to float, double, or doubledouble and N to 1, 2, 4, 8, or 16. The type doubledouble is described here which I created and added to the VCL. This produces Vector types of Vec1f, Vec4f, Vec8f, Vec16f, Vec1d, Vec2d, Vec4d, Vec8d, doubledouble1, doubledouble2, doubledouble4, doubledouble8.
template<typename TYPE, unsigned N>
static inline intn calc(floatn const &cx, floatn const &cy, floatn const &cut, int32_t maxiter) {
floatn x = cx, y = cy;
intn n = 0;
for(int32_t i=0; i<maxiter; i++) {
floatn x2 = square(x), y2 = square(y);
floatn r2 = x2 + y2;
booln mask = r2<cut;
if(!horizontal_or(mask)) break;
add_mask(n,mask);
floatn t = x*y; mul2(t);
x = x2 - y2 + cx;
y = t + cy;
}
return n;
}
So my SIMD code for several several different data types and vector sizes is nearly identical to the scalar code I would use. I have not included the part of my kernel which loops over each super-pixel.
My build file looks something like this
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -msse2 -Ivectorclass kernel.cpp -okernel_sse2.o
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -msse4.1 -Ivectorclass kernel.cpp -okernel_sse41.o
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -mavx -Ivectorclass kernel.cpp -okernel_avx.o
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -mavx2 -mfma -Ivectorclass kernel.cpp -okernel_avx2.o
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -mavx2 -mfma -Ivectorclass kernel_fma.cpp -okernel_fma.o
g++ -m64 -c -Wall -g -std=gnu++11 -O3 -fopenmp -mfpmath=sse -mavx512f -mfma -Ivectorclass kernel.cpp -okernel_avx512.o
g++ -m64 -Wall -Wextra -std=gnu++11 -O3 -fopenmp -mfpmath=sse -msse2 -Ivectorclass frac.cpp vectorclass/instrset_detect.cpp kernel_sse2.o kernel_sse41.o kernel_avx.o kernel_avx2.o kernel_avx512.o kernel_fma.o -o frac
Then the dispatcher looks something like this
int iset = instrset_detect();
fp_float1 = NULL;
fp_floatn = NULL;
fp_double1 = NULL;
fp_doublen = NULL;
fp_doublefloat1 = NULL;
fp_doublefloatn = NULL;
fp_doubledouble1 = NULL;
fp_doubledoublen = NULL;
fp_float128 = NULL;
fp_floatn_fma = NULL;
fp_doublen_fma = NULL;
if (iset >= 9) {
fp_float1 = &manddd_AVX512<float,1>;
fp_floatn = &manddd_AVX512<float,16>;
fp_double1 = &manddd_AVX512<double,1>;
fp_doublen = &manddd_AVX512<double,8>;
fp_doublefloat1 = &manddd_AVX512<doublefloat,1>;
fp_doublefloatn = &manddd_AVX512<doublefloat,16>;
fp_doubledouble1 = &manddd_AVX512<doubledouble,1>;
fp_doubledoublen = &manddd_AVX512<doubledouble,8>;
}
else if (iset >= 8) {
fp_float1 = &manddd_AVX<float,1>;
fp_floatn = &manddd_AVX2<float,8>;
fp_double1 = &manddd_AVX2<double,1>;
fp_doublen = &manddd_AVX2<double,4>;
fp_doublefloat1 = &manddd_AVX2<doublefloat,1>;
fp_doublefloatn = &manddd_AVX2<doublefloat,8>;
fp_doubledouble1 = &manddd_AVX2<doubledouble,1>;
fp_doubledoublen = &manddd_AVX2<doubledouble,4>;
}
....
This sets function pointers to each of the different possible datatype vector combination for the instruction set found at runtime. Then I can call whatever function I'm interested.
Thanks Peter Cordes and Z boson. With your both replies I I came to a solution that satisfies me.
I chose the Memcopy just as an example just because of everyone knowing it and its beautiful simplicity (but also slowness) when implemented naively in contrast to SIMD optimizations that are often not well readable anymore but of course much faster.
I have now two classes (more possible of course) a scalar vector and an SSE vector both with inline methods. To the user i show something like:
typedef void(*MEM_COPY_FUNC)(void *, const void *, size_t);
extern MEM_COPY_FUNC memCopyPointer;
I declare my function something like this, as Z boson pointed out:
template
void MemCopyTemplate(void *pDest, const void *prc, size_t size)
{
VectorType v;
byte *pDst, *pSrc;
uint32 mask;
pDst = (byte *)pDest;
pSrc = (byte *)prc;
mask = (2 << v.GetSize()) - 1;
while(size & mask)
{
*pDst++ = *pSrc++;
}
while(size)
{
v.Load(pSrc);
v.Store(pDst);
pDst += v.GetSize();
pSrc += v.GetSize();
size -= v.GetSize();
}
}
And at runtime, when the library is loaded, i use CPUID to do either
memCopyPointer = MemCopyTemplate<ScalarVector>;
or
memCopyPointer = MemCopyTemplate<SSEVector>;
as you both suggested. Thanks a lot.

In which source file should I define a function

Recently I've noticed that in a project where I have several source files (file1.cpp, file2.cpp, ...) it may affect to execution time wether function A, that will be called by another function B, is defined in the same source file than that function B or not.
In my case, when both are defined in the same file1.cpp, function B takes about 90% of execution time, and profiler analysis does not return execution time for function A (called by B).
BUT if they are defined in separated files, then execution times increases in ~150% and function A takes ~65% of time, while B is just ~25 (about 90% in total).
Why has execution time increased? Has function defitinion location an effect on how are they called? I can't figure out.
I should say at this point that I'm using optimization level 3 so function A should be inlined in B in both cases.
EDIT: I'm using Linux Ubuntu 14.04, anf I compile with g++ and the following flags: -O3 -pg -ggdb -Wall -Wextra -std=c++11.
I include also A and B son it can be better understood. As you can she, A is called from B by another C function, but that one seems to not be a problem:
A:
size_t A (const Matrix& P, size_t ID) {
size_t j(0);
while (P[j][0]!=ID) {
++j;
}
return j;
}
B:
Matrix B (const Matrix& P, const Matrix& O, Matrix* pREL, double d, const Vector& f) {`
size_t length (O.size()) ;
Matrix oREL ( *pREL ) ;
for (size_t i(0); i<length; ++i) {
for (size_t j(0); j<=i; ++j) {
double fi(f[O[i][0]-1]);
if (f.size()==1) fi = 0.0;
if (i!=j) {
double gAC, gAD, gBC, gBD, fj(f[O[j][0]-1]);
if (f.size()==1) fj = 0.0;
gAC = C(pREL,P,O,i,j,dcol,dcol);
gAD = C(pREL,P,O,i,j,dcol,scol);
gBC = C(pREL,P,O,i,j,scol,dcol);
gBD = C(pREL,P,O,i,j,scol,scol);
oREL[i][j] = 0.25 * (gAC + gAD + gBC + gBD)
* (1 - d*(fi+fj));
} else if (i==j) oREL[i][i] = 0.5 * ( 1.0+C(pREL,P,O,i,i,dcol,scol) )
* (1.0-2.0*d*fi );
}
}
delete pREL;
return oREL;
}
C:
coefficient C (Matrix * pREL, const Matrix& P, const Matrix& O,
size_t coord1, size_t coord2, unsigned p1, unsigned p2) {
double g;
size_t i, j ;
i = A(P,O[coord1][p1]);
j = A(P,O[coord2][p2]);
if (i<=j) g = (*pREL)[j][i];
if (i>j ) g = (*pREL)[i][j];
return g;
}
Yes. The compiler can only inline a function when it knows the function definition at the point of inlining. It may not know it if you place it in other compilation unit. In your case I'd assume that the compiler is "thinking": he's calling this function but I don't know where it is yet, so I make a normal call and let the linker worry about it later.
For that reason code that should be inlined is very often placed in header files.
First, when you care about performance and benchmarking, you should enable optimizations in your compiler.
I assume you are using GCC on Linux so you compile with g++.
You should compile with g++ -Wall -O2 if you care about performance.
You could enable link time optimizations by compiling and linking with g++ -Wall -O2 -flto
Of course you could use -O3 instead of -O2

What, in short words, does the GCC option -fipa-pta do?

According to the GCC manual, the -fipa-pta optimization does:
-fipa-pta: Perform interprocedural pointer analysis and interprocedural modification and reference analysis. This option can cause excessive
memory and compile-time usage on large compilation units. It is not
enabled by default at any optimization level.
What I assume is that GCC tries to differentiate mutable and immutable data based on pointers and references used in a procedure. Can someone with more in-depth GCC knowledge explain what -fipa-pta does?
I think the word "interprocedural" is the key here.
I'm not intimately familiar with gcc's optimizer, but I've worked on optimizing compilers before. The following is somewhat speculative; take it with a small grain of salt, or confirm it with someone who knows gcc's internals.
An optimizing compiler typically performs analysis and optimization only within each individual function (or subroutine, or procedure, depending on the language). For example, given code like this contrived example:
double *ptr = ...;
void foo(void) {
...
*ptr = 123.456;
some_other_function();
printf("*ptr = %f\n", *ptr);
}
the optimizer will not be able to determine whether the value of *ptr has been changed by the call to some_other_function().
If interprocedural analysis is enabled, then the optimizer can analyze the behavior of some_other_function(), and it may be able to prove that it can't modify *ptr. Given such analysis, it can determine that the expression *ptr must still evaluate to 123.456, and in principle it could even replace the printf call with puts("ptr = 123.456");.
(In fact, with a small program similar to the above code snippet I got the same generated code with -O3 and -O3 -fipa-pta, so I'm probably missing something.)
Since a typical program contains a large number of functions, with a huge number of possible call sequences, this kind of analysis can be very expensive.
As quoted from this article:
The "-fipa-pta" optimization takes the bodies of the called functions into account when doing the analysis, so compiling
void __attribute__((noinline))
bar(int *x, int *y)
{
*x = *y;
}
int foo(void)
{
int a, b = 5;
bar(&a, &b);
return b + 10;
}
with -fipa-pta makes the compiler see that bar does not modify b, and the compiler optimizes foo by changing b+10 to 15
int foo(void)
{
int a, b = 5;
bar(&a, &b);
return 15;
}
A more relevant example is the “slow” code from the “Integer division is slow” blog post
std::random_device entropySource;
std::mt19937 randGenerator(entropySource());
std::uniform_int_distribution<int> theIntDist(0, 99);
for (int i = 0; i < 1000000000; i++) {
volatile auto r = theIntDist(randGenerator);
}
Compiling this with -fipa-pta makes the compiler see that theIntDist is not modified within the loop, and the inlined code can thus be constant-folded in the same way as the “fast” version – with the result that it runs four times faster.