If in existing code there are calls to DCONJG(Z) where Z is declared to be COMPLEX*16. Can the DCONJG call be replaced with CONJG when the -fdefault-real-8 flag is added?
If Z is defined as double complex does this still apply?
In the existing code double complex and complex*16 have both been used to increase precision (and should be equivalent). With the -fdefault-real-8 flag applied, do double complex map to complex*32?
Can the DCONJG call be replaced with CONJG when the -fdefault-real-8
flag is added?
Yes, the standard conjg will return a value of the same kind as its argument, irrespective of the compilation settings. Kind-specific variants of intrinsic functions, such as dconjg, are generally deprecated precisely because they are not kind-indifferent.
If Z is defined as double complex does this still apply?
Yes.
And is double complex equivalent to complex with the flag applied
(same for double precision and real)?
If you mean does that compilation flag also affect the size of the real and imaginary components of a complex value then yes, it does.
EDIT
I don't know what gfortran means by the non-standard (never was, isn't, and probably never will be) kind specification complex*32. But the compiler is reasonably well documented so have a scout yourself. Personally I'd stick to one of the standard ways of specifying a complex number's kind, in which case the standard assures you that the kind specified, e.g. complex(real64), means the kind of each component of the complex number.
When creating custom typedefs for integers, is it possible for compiler to warn when you when using a default numeric type?
For example,
typedef int_fast32_t kint;
int_fast32_t test=0;//Would be ok
kint test=0; //Would be ok
int test=0; //Would throw a warning or error
We're converting a large project and the default int size on platform is 32767 which is causing some issues. This warning would warn a user to not use ints in the code.
If possible, it would be great if this would work on GCC and VC++2012.
I'm reasonably sure gcc has no such option, and I'd be surprised if VC did.
I suggest writing a program that detects references to predefined types in source code, and invoking that tool automatically as part of your build process. It would probably suffice to search for certain keywords.
Be sure you limit this to your own source files; predefined and third-party headers are likely to make extensive use of predefined types.
But I wouldn't make the prohibition absolute. There are a number of standard library functions that use predefined types. For example, in c = getchar() it makes no sense to declare c as anything other than int. And there's no problem for something like for (int i = 0; i <= 100; i ++) ...
Ideally, the goal should be to use predefined types properly. The language has never guaranteed that an int can exceed 32767. (But "proper" use is difficult or impossible to verify automatically.)
I'd approach this by doing a replace-all first and then documenting this thoroughly.
You can use a preprocessor directive:
#define int use kint instead
Note that technically this is undefined behavior and you'll run into trouble if you do this definition before including third-party headers.
I would recommend to make bulk replacement int -> old_int_t at the very beginning of your porting. This way you can continue modifying your code without facing major restrictions and at the same time have access to all places that are not yet updated.
Eventually, at the end of your work, all occurencies of old_int_t should go away.
Even if one could somehow undefine the keyword int, that would do nothing to prevent usage of that type, since there are many cases where the compiler will end up using that type. Beyond the obvious cases of integer literals, there are some more subtle cases involving integer promotion. For example, if int happens to be 64 bits, operations between two variables of type uint32_t will be performed using type int rather than uint32_t. As nice as it would be to be able to specify that some variables represent numbers (which should be eagerly promoted when practical) while others represent members of a wrapping algebraic ring (which should not be promoted), I know of no facility to do such a thing. Consequently, int is unavoidable.
Let say I have a snippet of code like this:
typedef double My_fp_t;
My_fp_t my_fun( My_fp_t input )
{
// some fp computation, it uses operator+, operator- and so on for type My_fp_t
}
My_fp_t input = 0.;
My_fp_t output = my_fun( input );
Is it possible to retrofit my existing code with a floating point arbitrary precision C++ library?
I would like to simple add #include <cpp_arbitrary_precision_fp>, change my typedef double My_fp_t; into typedef arbitrary_double_t My_fp_t; and let the operator overloading of C++ doing its job...
My main problem is that actually my code do NOT have the typedef :-( and so maybe my plan is doomed to failure.
Assuming that my code had the typedef, what other problems would I face?
This might be tough. I used a template approach in my PhD thesis code do deal with different numerical types. You might want to take a look at it to see the problems I encountered.
The thing is you are fine if all you do with your numbers is use the standard arithmetic operators. However, as soon as you use a square root or some other non operator function you need to create helper objects to detect your object's type (at compile time as it is too slow to do this at run time; see the boost metaprogramming library for help on that) and then call the correct function and return it as the correct type. It is all totally doable, but is likely to take longer than you think and will add considerably to the complexity of your code.
In my experience, (I was using GMP which must be the fastest arbitrary precision library available for C++) after all of the effort and complexity I had introduced, I found that GMP was just too slow for the sorts of computation that I was doing; so it was academically interesting, but practically useless. Before you start on this do some speed tests to see whether your library will still be usable if you use arbitrary precision arithmetic.
If the library defines a type that correctly overloads the operators you use, I don't see any problem...
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 have double (or float) variables that might be "empty", as in holding no valid value. How can I represent this condition with the built in types float and double?
One option would be a wrapper that has a float and a boolean, but that can´t work, as my libraries have containers that store doubles and not objects that behave as doubles. Another would be using NaN (std::numeric_limits). But I see no way to check for a variable being NaN.
How can I solve the problem of needing a "special" float value to mean something other than the number?
We have done that by using NaN:
double d = std::numeric_limits<double>::signaling_NaN();
bool isNaN = (d != d);
NaN values compared for equality against itself will yield false. That's the way you test for NaN, but which seems to be only valid if std::numeric_limits<double>::is_iec559 is true (if so, it conforms to ieee754 too).
In C99 there is a macro called isnan for this in math.h, which checks a floating point number for a NaN value too.
In Visual C++, there is a non-standard _isnan(double) function that you can import through float.h.
In C, there is a isnan(double) function that you can import through math.h.
In C++, there is a isnan(double) function that you can import through cmath.
As others have pointed out, using NaN's can be a lot of hassle. They are a special case that has to be dealt with like NULL pointers. The difference is that a NaN will not usually cause core dumps and application failures, but they are extremely hard to track down. If you decide to use NaN's, use them as little as possible. Overuse of NaN's is an offensive coding practice.
It's not a built-in type, but I generally use boost::optional for this kind of thing. If you absolutely can't use that, perhaps a pointer would do the trick -- if the pointer is NULL, then you know the result doesn't contain a valid value.
One option would be a wrapper that has a float ad a boolean, but that can´t work, as my libraries have containers that store doubles and not objects that behave as doubles.
That's a shame. In C++ it's trivial to create a templated class that auto-converts to the actual double (reference) attribute. (Or a reference to any other type for that matter.) You just use the cast operator in a templated class. E.g.: operator TYPE & () { return value; } You can then use a HasValue<double>anywhere you'd normally use a double.
Another would be using NaN (std::numeric_limits). But i see no way to check for a variable being NaN.
As litb and James Schek also remarked, C99 provides us with isnan().
But be careful with that! Nan values make math & logic real interesting! You'd think a number couldn't be both NOT>=foo and NOT<=foo. But with NaN, it can.
There's a reason I keep a WARN-IF-NAN(X) macro in my toolbox. I've had some interesting problems arise in the past.