Related
I am writing some numeric code in C++ and I want to be able to swap between using double and float. I have therefore added a #define MYFLT which I can make either a float or a double as needed. However, how do I deal with the various numeric literals.
For example
MYFLT someNumber = 1.2;
MYFLT someOtherNumber = 1.5f;
gives compiler warnings for the first line when MYFLT is a float and for the second line when MYFLT is a double. I know this is a trivial example, but there are other cases where I have longer expresions with literals in and floats can end up being converted to doubles then the result back to floats which I think is costing me significant performance. How should I deal with this?
I could do things like
MYFLT someNumber = MYFLT(1.2);
MYFLT someOtherNumber = MYFLT(1.5);
but this is quite tedious. I'm assuming that in that if I do this the compiler is clever enough to just use a float when needed (can anyone confirm that?). What would be better would be if there was a MSVC++ compiler switch or #define that will tell the compiler to treat all floating point literals as floats instead of doubles. Does such a switch exist?
Even when I wrap all my literals as above my code runs 50% slower when I use float rather than double. I was expecting a performance boost through simd type operations, not a penalty!
Phil
What you'd want is #define MYFLTCONST(x) x##f or #define MYFLTCONST(x) x depending on whether you want a f suffix for float appended.
This is a (not quite complete) answer to my own question.
I found that a small function that was called many times (a fast approximation to sin) didn't have its literals cast as MYFLT. The extra computational hit of this also meant that the compiler wasn't inlining it. This function accounted for most of the difference. Some further profiling seemed to indicate that accessing std::vector<float> was slower than std::vector<double> ( I am using [] to do the access if it matters ). Replacing std::vectors with raw fixed sized arrays sped up the double implementation a little and closed the gap significantly for the float implementation. The float version is now only about 10% slower than the double version. But definitely no speed increase due to either RAM access nor vectorization. I guess I need to think more carefully about my loops to get any benefit there.
I guess the conclusion here (yet again) is that the compiler is pretty good at optimising code - it's much better to work with it and do careful profiling than it is to try and do your own blind "optimisations" which might actually have negative effects, like stopping the compiler performing good inlining.
I defined function
double builtin_test(double y)
{
double x = __builtin_sin(y);
return x;
}
thought it should work, but when coompiling
C:\DOCUME~1\ADMINI~1\USTAWI~1\Temp\ccNuVeYz.o:test6.c:(.text+0x5): undefined ref
erence to `sin'
how to make it work?
This is not REALLY an answer (but then, the question isn't exactly clear either) - it just got too long for a comment, and I don't want to chain 2-3 comments...
It is important to understand that the MAIN reason for __builtin_* functions is to support things that the compiler knows how to do - and sometimes, that turns into simply calling the relevant standard library function, rather than actually doing anything special.
If we take sin as an example, in x87, there is a fsin instruction that can be generated. But if the compiler just sees a bunch of math, it won't know that the code does sin, so won't produce the fsin instruction, just do a bunch of multiply, subtract, add, etc to perform that calculation. So using __builtin_sin inside the standard library or header, for example like this:
double sin(double x)
{
return __builtin_sin(x);
}
will generate a fsin instruction.
I ran some experiments with gcc and clang on my machine, and I was not able to convince the compiler to actually calculate sin at runtime and NOT call the sin function. The clang version of the code decided to calculate my entire loops worth of sin values into a constant - which is of course a good win over doing 100 calculations, but not exactly what we're looking for.
Note that the fsin instruction is quite slow, and to perform individual calculation steps using simple instructions is quite possibly equally fast - but we don't want to inline that every time sin is used (and certainly don't want the compiler to "know" how to do that).
We have some code that looks like this:
inline int calc_something(double x) {
if (x > 0.0) {
// do something
return 1;
} else {
// do something else
return 0;
}
}
Unfortunately, when using the flag /fp:fast, we get calc_something(0)==1 so we are clearly taking the wrong code path. This only happens when we use the method at multiple points in our code with different parameters, so I think there is some fishy optimization going on here from the compiler (Microsoft Visual Studio 2008, SP1).
Also, the above problem goes away when we change the interface to
inline int calc_something(const double& x) {
But I have no idea why this fixes the strange behaviour. Can anyone explane this behaviour? If I cannot understand what's going on we will have to remove the /fp:fastswitch, but this would make our application quite a bit slower.
I'm not familiar enough with FPUs to comment with any certainty, but my guess would be that the compiler is letting an existing value that it thinks should be equal to x sit in on that comparison. Maybe you go y = x + 20.; y = y - 20; y is already on the FP stack, so rather than load x the compiler just compares against y. But due to rounding errors, y isn't quite 0.0 like it is supposed to be, and you get the odd results you see.
For a better explanation: Why is cos(x) != cos(y) even though x == y? from the C++FAQ lite. This is part of what I'm trying to get across, I just couldn't remember where exactly I had read it until just now.
Changing to a const reference fixes this because the compiler is worried about aliasing. It forces a load from x because it can't assume its value hasn't changed at some point after creating y, and since x is actually exactly 0.0 [which is representable in every floating point format I'm familiar with] the rounding errors vanish.
I'm pretty sure MS provides a pragma that allows you to set the FP flags on a per-function basis. Or you could move this routine to a separate file and give that file custom flags. Either way, it could prevent your whole program from suffering just to keep that one routine happy.
what are the results of calc_something(0L), or calc_something(0.0f) ? It could be linked to the size of the types before casting. An integer is 4 bytes, a double is 8.
Have you tried looking at the asembled code, to see how the aforementioned conversion is done ?
Googling for 'fp fast', I found this post [social.msdn.microsoft.com]
As I've said in other question, compilers suck at generating floating point code. The article Dennis links to explains the problems well. Here's another: An MSDN article.
If the performance of the code is important, you can easily1 out-perform the compiler by writing your own assembler code. If your algoritm is vectorisable then you can make use of SIMD too (with a slight loss of precision though).
Assuming you understand the way the FPU works.
inline int calc_something(double x) will (probably) use an 80 bits register. inline int calc_something(const double& x) would store the double in memory, where it takes 64 bits. That at least explains the difference between the two.
However, I find your test quite fishy to begin with. The results of calc_something are extremely sensitive to rounding of its input. Your FP algorithms should be robust to rounding. calc_something(1.0-(1.0/3.0)*3) should be the same as calc_something(0.0).
I think the behavior is correct.
You never compare a floating point number up to less than the holding type's precision.
Something that comes from zero may be equal, greater or less than another zero.
See http://floating-point-gui.de/
I am writing a C++ number crunching application, where the bottleneck is a function that has to calculate for double:
template<class T> inline T sqr(const T& x){return x*x;}
and another one that calculates
Base dist2(const Point& p) const
{ return sqr(x-p.x) + sqr(y-p.y) + sqr(z-p.z); }
These operations take 80% of the computation time. I wonder if you can suggest approaches to make it faster, even if there is some sort of accuracy loss
Thanks
First, make sure dist2 can be inlined (it's not clear from your post whether or not this is the case), having it defined in a header file if necessary (generally you'll need to do this - but if your compiler generates code at link time, then that's not necessarily the case).
Assuming x86 architecture, be sure to allow your compiler to generate code using SSE2 instructions (an example of an SIMD instruction set) if they are available on the target architecture. To give the compiler the best opportunity to optimize these, you can try to batch your sqr operations together (SSE2 instructions should be able to do up to 4 float or 2 double operations at a time depending on the instruction.. but of course it can only do this if you have the inputs to more than one operation on the ready). I wouldn't be too optimistic about the compiler's ability to figure out that it can batch them.. but you can at least set up your code so that it would be possible in theory.
If you're still not satisfied with the speed and you don't trust that your compiler is doing it best, you should look into using compiler intrinsics which will allow you to write potential parallel instructions explicitly.. or alternatively, you can go right ahead and write architecture-specific assembly code to take advantage of SSE2 or whichever instructions are most appropriate on your architecture. (Warning: if you hand-code the assembly, either take extra care that it still gets inlined, or make it into a large batch operation)
To take it even further, (and as glowcoder has already mentioned) you could perform these operations on a GPU. For your specific case, bear in mind that GPU's often don't support double precision floating point.. though if it's a good fit for what you're doing, you'll get orders of magnitude better performance this way. Google for GPGPU or whatnot and see what's best for you.
What is Base?
Is it a class with a non-explicit constructor? It's possible that you're creating a fair amount of temporary Base objects. That could be a big CPU hog.
template<class T> inline T sqr(const T& x){return x*x;}
Base dist2(const Point& p) const {
return sqr(x-p.x) + sqr(y-p.y) + sqr(z-p.z);
}
If p's member variables are of type Base, you could be calling sqr on Base objects, which will be creating temporaries for the subtracted coordinates, in sqr, and then for each added component.
(We can't tell without the class definitions)
You could probably speed it up by forcing the sqr calls to be on primitves and not using Base until you get to the return type of dist2.
Other performance improvement opportunities are to:
Use non-floating point operations, if you're ok with less precision.
Use algorithms which don't need to call dist2 so much, possibly caching or using the transitive property.
(this is probably obvious, but) Make sure you're compiling with optimization turned on.
I think optimising these functions might be difficult, you might be better off optimising the code that calls these functions to call them less, or to do things differently.
You don't say whether the calls to dist2 can be parallelised or not. If they can, then you could build a thread pool and split this work up into smaller chunks per thread.
What does your profiler tell you is happening inside dist2. Are you actually using 100% CPU all the time or are you cache missing and waiting for data to load?
To be honest, we really need more details to give you a definitive answer.
If sqr() is being used only on primitive types, you might try taking the argument by value instead of reference. That would save you an indirection.
If you can organise your data suitably then you may well be able to use SIMD optimisation here. For an efficient implementation you would probably want to pad your Point struct so that it has 4 elements (i.e. add a fourth dummy element for padding).
If you have a number of these to do, and you're doing graphics or "graphic like" tasks (thermal modeling, almost any 3d modeling) you might consider using OpenGL and offloading the tasks to a GPU. This would allow the computations to run in parallel, with highly optimized operational capacity. After all, you would expect something like distance or distancesq to have its own opcode on a GPU.
A researcher at a local univeristy offload almost all of his 3d-calculations for AI work to the GPU and achieved much faster results.
There are a lot of answers mentioning SSE already… but since nobody has mentioned how to use it, I'll throw another in…
Your code has most everything a vectorizer needs to work, except two constraints: aliasing and alignment.
Aliasing is the problem of two names referring two the same object. For example, my_point.dist2( my_point ) would operate on two copies of my_point. This messes with the vectorizer.
C99 defines the keyword restrict for pointers to specify that the referenced object is referenced uniquely: there will be no other restrict pointer to that object in the current scope. Most decent C++ compilers implement C99 as well, and import this feature somehow.
GCC calls it __restrict__. It may be applied to references or this.
MSVC calls it __restrict. I'd be surprised if support were any different from GCC.
(It is not in C++0x, though.)
#ifdef __GCC__
#define restrict __restrict__
#elif defined _MSC_VER
#define restrict __restrict
#endif
Base dist2(const Point& restrict p) const restrict
Most SIMD units require alignment to the size of the vector. C++ and C99 leave alignment implementation-defined, but C++0x wins this race by introducing [[align(16)]]. As that's still a bit in the future, you probably want your compiler's semi-portable support, a la restrict:
#ifdef __GCC__
#define align16 __attribute__((aligned (16)))
#elif defined _MSC_VER
#define align16 __declspec(align (16))
#endif
struct Point {
double align16 xyz[ 3 ]; // separate x,y,z might work; dunno
…
};
This isn't guaranteed to produce results; both GCC and MSVC implement helpful feedback to tell you what wasn't vectorized and why. Google your vectorizer to learn more.
If you really need all the dist2 values, then you have to compute them. It's already low level and cannot imagine speedups apart from distributing on multiple cores.
On the other side, if you're searching for closeness, then you can supply to the dist2() function your current miminum value. This way, if sqr(x-p.x) is already larger than your current minimum, you can avoid computing the remaining 2 squares.
Furthermore, you can avoid the first square by going deeper in the double representation. Comparing directly on the exponent value with your current miminum can save even more cycles.
Are you using Visual Studio? If so you may want to look at specifying the floating point unit control using /fp fast as a compile switch. Have a look at The fp:fast Mode for Floating-Point Semantics. GCC has a host of -fOPTION floating point optimisations you might want to consider (if, as you say, accuracy is not a huge concern).
I suggest two techniques:
Move the structure members into
local variables at the beginning.
Perform like operations together.
These techniques may not make a difference, but they are worth trying. Before making any changes, print the assembly language first. This will give you a baseline for comparison.
Here's the code:
Base dist2(const Point& p) const
{
// Load the cache with data values.
register x1 = p.x;
register y1 = p.y;
register z1 = p.z;
// Perform subtraction together
x1 = x - x1;
y1 = y - y1;
z1 = z - z2;
// Perform multiplication together
x1 *= x1;
y1 *= y1;
z1 *= z1;
// Perform final sum
x1 += y1;
x1 += z1;
// Return the final value
return x1;
}
The other alternative is to group by dimension. For example, perform all 'X' operations first, then Y and followed by Z. This may show the compiler that pieces are independent and it can delegate to another core or processor.
If you can't get any more performance out of this function, you should look elsewhere as other people have suggested. Also read up on Data Driven Design. There are examples where reorganizing the loading of data can speed up performance over 25%.
Also, you may want to investigate using other processors in the system. For example, the BOINC Project can delegate calculations to a graphics processor.
Hope this helps.
From an operation count, I don't see how this can be sped up without delving into hardware optimizations (like SSE) as others have pointed out. An alternative is to use a different norm, like the 1-norm is just the sum of the absolute values of the terms. Then no multiplications are necessary. However, this changes the underlying geometry of your space by rearranging the apparent spacing of the objects, but it may not matter for your application.
Floating point operations are quite often slower, maybe you can think about modifying the code to use only integer arithmetic and see if this helps?
EDIT: After the point made by Paul R I reworded my advice not to claim that floating point operations are always slower. Thanks.
Your best hope is to double-check that every dist2 call is actually needed: maybe the algorithm that calls it can be refactored to be more efficient? If some distances are computed multiple times, maybe they can be cached?
If you're sure all of the calls are necessary, you may be able to squeeze out a last drop of performance by using an architecture-aware compiler. I've had good results using Intel's compiler on x86s, for instance.
Just a few thoughts, however unlikely that I will add anything of value after 18 answers :)
If you are spending 80% time in these two functions I can imagine two typical scenarios:
Your algorithm is at least polynomial
As your data seem to be spatial maybe you can bring the O(n) down by introducing spatial indexes?
You are looping over certain set
If this set comes either from data on disk (sorted?) or from loop there might be possibility to cache, or use previous computations to calculate sqrt faster.
Also regarding the cache, you should define the required precision (and the input range) - maybe some sort of lookup/cache can be used?
(scratch that!!! sqr != sqrt )
See if the "Fast sqrt" is applicable in your case :
http://en.wikipedia.org/wiki/Fast_inverse_square_root
Look at the context. There's nothing you can do to optimize an operation as simple as x*x.
Instead you should look at a higher level: where is the function called from? How often? Why? Can you reduce the number of calls? Can you use SIMD instructions to perform the multiplication on multiple elements at a time?
Can you perhaps offload entire parts of the algorithm to the GPU?
Is the function defined so that it can be inlined? (basically, is its definition visible at the call sites)
Is the result needed immediately after the computation? If so, the latency of FP operations might hurt you. Try to arrange your code so dependency chains are broken up or interleaved with unrelated instructions.
And of course, examine the generated assembly and see if it's what you expect.
Is there a reason you are implementing your own sqr operator?
Have you tried the one in libm it should be highly optimized.
The first thing that occurs to me is memoization ( on-the-fly caching of function calls ), but both sqr and dist2 it would seem like they are too low level for the overhead associated with memoization to be made up for in savings due to memoization. However at a higher level, you may find it may work well for you.
I think a more detailed analysis of you data is called for. Saying that most of the time in the program is spent executing MOV and JUMp commands may be accurate, but it's not going to help yhou optimise much. The information is too low level. For example, if you know that integer arguments are good enough for dist2, and the values are between 0 and 9, then a pre-cached tabled would be 1000 elements--not to big. You can always use code to generate it.
Have you unrolled loops? Broken down matrix opration? Looked for places where you can get by with table lookup instead of actual calculation.
Most drastic would be to adopt the techniques described in:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.115.8660&rep=rep1&type=pdf
though it is admittedly a hard read and you should get some help from someone who knows Common Lisp if you don't.
I'm curious why you made this a template when you said the computation is done using doubles?
Why not write a standard method, function, or just 'x * x' ?
If your inputs can be predictably constrained and you really need speed create an array that contains all the outputs your function can produce. Use the input as the index into the array (A sparse hash). A function evaluation then becomes a comparison (to test for array bounds), an addition, and a memory reference. It won't get a lot faster than that.
See the SUBPD, MULPD and DPPD instructions. (DPPD required SSE4)
Depends on your code, but in some cases a stucture-of-arrays layout might be more friendly to vectorization than an array-of-structures layout.
I was reading some old game programming books and as some of you might know, back in that day it was usually faster to do bit hacks than do things the standard way. (Converting float to int, mask sign bit, convert back for absolute value, instead of just calling fabs(), for example)
Nowadays is almost always better to just use the standard library math functions, since these tiny things are hardly the cause of most bottlenecks anyway.
But I still want to do a comparison, just for curiosity's sake. So I want to make sure when I profile, I'm not getting skewed results. As such, I'd like to make sure the compiler does not optimize out statements that have no side effect, such as:
void float_to_int(float f)
{
int i = static_cast<int>(f); // has no side-effects
}
Is there a way to do this? As far as I can tell, doing something like i += 10 will still have no side-effect and as such won't solve the problem.
The only thing I can think of is having a global variable, int dummy;, and after the cast doing something like dummy += i, so the value of i is used. But I feel like this dummy operation will get in the way of the results I want.
I'm using Visual Studio 2008 / G++ (3.4.4).
Edit
To clarify, I would like to have all optimizations maxed out, to get good profile results. The problem is that with this the statements with no side-effect will be optimized out, hence the situation.
Edit Again
To clarify once more, read this: I'm not trying to micro-optimize this in some sort of production code.
We all know that the old tricks aren't very useful anymore, I'm merely curious how not useful they are. Just plain curiosity. Sure, life could go on without me knowing just how these old hacks perform against modern day CPU's, but it never hurts to know.
So telling me "these tricks aren't useful anymore, stop trying to micro-optimize blah blah" is an answer completely missing the point. I know they aren't useful, I don't use them.
Premature quoting of Knuth is the root of all annoyance.
Assignment to a volatile variable shold never be optimized away, so this might give you the result you want:
static volatile int i = 0;
void float_to_int(float f)
{
i = static_cast<int>(f); // has no side-effects
}
So I want to make sure when I profile, I'm not getting skewed results. As such, I'd like to make sure the compiler does not optimize out statements
You are by definition skewing the results.
Here's how to fix the problem of trying to profile "dummy" code that you wrote just to test: For profiling, save your results to a global/static array and print one member of the array to the output at the end of the program. The compiler will not be able to optimize out any of the computations that placed values in the array, but you'll still get any other optimizations it can put in to make the code fast.
In this case I suggest you make the function return the integer value:
int float_to_int(float f)
{
return static_cast<int>(f);
}
Your calling code can then exercise it with a printf to guarantee it won't optimize it out. Also make sure float_to_int is in a separate compilation unit so the compiler can't play any tricks.
extern int float_to_int(float f)
int sum = 0;
// start timing here
for (int i = 0; i < 1000000; i++)
{
sum += float_to_int(1.0f);
}
// end timing here
printf("sum=%d\n", sum);
Now compare this to an empty function like:
int take_float_return_int(float /* f */)
{
return 1;
}
Which should also be external.
The difference in times should give you an idea of the expense of what you're trying to measure.
What always worked on all compilers I used so far:
extern volatile int writeMe = 0;
void float_to_int(float f)
{
writeMe = static_cast<int>(f);
}
note that this skews results, boith methods should write to writeMe.
volatile tells the compiler "the value may be accessed without your notice", thus the compiler cannot omit the calculation and drop the result. To block propagiation of input constants, you might need to run them through an extern volatile, too:
extern volatile float readMe = 0;
extern volatile int writeMe = 0;
void float_to_int(float f)
{
writeMe = static_cast<int>(f);
}
int main()
{
readMe = 17;
float_to_int(readMe);
}
Still, all optimizations inbetween the read and the write can be applied "with full force". The read and write to the global variable are often good "fenceposts" when inspecting the generated assembly.
Without the extern the compiler may notice that a reference to the variable is never taken, and thus determine it can't be volatile. Technically, with Link Time Code Generation, it might not be enough, but I haven't found a compiler that agressive. (For a compiler that indeed removes the access, the reference would need to be passed to a function in a DLL loaded at runtime)
Compilers are unfortunately allowed to optimise as much as they like, even without any explicit switches, if the code behaves as if no optimisation takes place. However, you can often trick them into not doing so if you indicate that value might be used later, so I would change your code to:
int float_to_int(float f)
{
return static_cast<int>(f); // has no side-effects
}
As others have suggested, you will need to examine the assemnler output to check that this approach actually works.
You just need to skip to the part where you learn something and read the published Intel CPU optimisation manual.
These quite clearly state that casting between float and int is a really bad idea because it requires a store from the int register to memory followed by a load into a float register. These operations cause a bubble in the pipeline and waste many precious cycles.
a function call incurs quite a bit of overhead, so I would remove this anyway.
adding a dummy += i; is no problem, as long as you keep this same bit of code in the alternate profile too. (So the code you are comparing it against).
Last but not least: generate asm code. Even if you can not code in asm, the generated code is typically understandable since it will have labels and commented C code behind it. So you know (sortoff) what happens, and which bits are kept.
R
p.s. found this too:
inline float pslNegFabs32f(float x){
__asm{
fld x //Push 'x' into st(0) of FPU stack
fabs
fchs //change sign
fstp x //Pop from st(0) of FPU stack
}
return x;
}
supposedly also very fast. You might want to profile this too. (although it is hardly portable code)
Return the value?
int float_to_int(float f)
{
return static_cast<int>(f); // has no side-effects
}
and then at the call site, you can sum all the return values up, and print out the result when the benchmark is done. The usual way to do this is to somehow make sure you depend on the result.
You could use a global variable instead, but it seems like that'd generate more cache misses. Usually, simply returning the value to the caller (and making sure the caller actually does something with it) does the trick.
If you are using Microsoft's compiler - cl.exe, you can use the following statement to turn optimization on/off on a per-function level [link to doc].
#pragma optimize("" ,{ on |off })
Turn optimizations off for functions defined after the current line:
#pragma optimize("" ,off)
Turn optimizations back on:
#pragma optimize("" ,on)
For example, in the following image, you can notice 3 things.
Compiler optimizations flag is set - /O2, so code will get optimized.
Optimizations are turned off for first function - square(), and turned back on before square2() is defined.
Amount of assembly code generated for 1st function is higher. In second function there is no assembly code generated for int i = num; statement in code.
Thus while 1st function is not optimized, the second function is.
See https://godbolt.org/z/qJTBHg for link to this code on compiler explorer.
A similar directive exists for gcc too - https://gcc.gnu.org/onlinedocs/gcc/Function-Specific-Option-Pragmas.html
A micro-benchmark around this statement will not be representative of using this approach in a genuine scenerio; the surrounding instructions and their affect on the pipeline and cache are generally as important as any given statement in itself.
GCC 4 does a lot of micro-optimizations now, that GCC 3.4 has never done. GCC4 includes a tree vectorizer that turns out to do a very good job of taking advantage of SSE and MMX. It also uses the GMP and MPFR libraries to assist in optimizing calls to things like sin(), fabs(), etc., as well as optimizing such calls to their FPU, SSE or 3D Now! equivalents.
I know the Intel compiler is also extremely good at these kinds of optimizations.
My suggestion is to not worry about micro-optimizations like this - on relatively new hardware (anything built in the last 5 or 6 years), they're almost completely moot.
Edit: On recent CPUs, the FPU's fabs instruction is far faster than a cast to int and bit mask, and the fsin instruction is generally going to be faster than precalculating a table or extrapolating a Taylor series. A lot of the optimizations you would find in, for example, "Tricks of the Game Programming Gurus," are completely moot, and as pointed out in another answer, could potentially be slower than instructions on the FPU and in SSE.
All of this is due to the fact that newer CPUs are pipelined - instructions are decoded and dispatched to fast computation units. Instructions no longer run in terms of clock cycles, and are more sensitive to cache misses and inter-instruction dependencies.
Check the AMD and Intel processor programming manuals for all the gritty details.