I have a loop written in C++ which is executed for each element of a big integer array. Inside the loop, I mask some bits of the integer and then find the min and max values. I heard that if I use SSE instructions for these operations it will run much faster compared to a normal loop written using bitwise AND , and if-else conditions. My question is should I go for these SSE instructions? Also, what happens if my code runs on a different processor? Will it still work or these instructions are processor specific?
SSE instructions are processor specific. You can look up which processor supports which SSE version on wikipedia.
If SSE code will be faster or not depends on many factors: The first is of course whether the problem is memory-bound or CPU-bound. If the memory bus is the bottleneck SSE will not help much. Try simplifying your integer calculations, if that makes the code faster, it's probably CPU-bound, and you have a good chance of speeding it up.
Be aware that writing SIMD-code is a lot harder than writing C++-code, and that the resulting code is much harder to change. Always keep the C++ code up to date, you'll want it as a comment and to check the correctness of your assembler code.
Think about using a library like the IPP, that implements common low-level SIMD operations optimized for various processors.
SIMD, of which SSE is an example, allows you to do the same operation on multiple chunks of data. So, you won't get any advantage to using SSE as a straight replacement for the integer operations, you will only get advantages if you can do the operations on multiple data items at once. This involves loading some data values that are contiguous in memory, doing the required processing and then stepping to the next set of values in the array.
Problems:
1 If the code path is dependant on the data being processed, SIMD becomes much harder to implement. For example:
a = array [index];
a &= mask;
a >>= shift;
if (a < somevalue)
{
a += 2;
array [index] = a;
}
++index;
is not easy to do as SIMD:
a1 = array [index] a2 = array [index+1] a3 = array [index+2] a4 = array [index+3]
a1 &= mask a2 &= mask a3 &= mask a4 &= mask
a1 >>= shift a2 >>= shift a3 >>= shift a4 >>= shift
if (a1<somevalue) if (a2<somevalue) if (a3<somevalue) if (a4<somevalue)
// help! can't conditionally perform this on each column, all columns must do the same thing
index += 4
2 If the data is not contigous then loading the data into the SIMD instructions is cumbersome
3 The code is processor specific. SSE is only on IA32 (Intel/AMD) and not all IA32 cpus support SSE.
You need to analyse the algorithm and the data to see if it can be SSE'd and that requires knowing how SSE works. There's plenty of documentation on Intel's website.
This kind of problem is a perfect example of where a good low level profiler is essential. (Something like VTune) It can give you a much more informed idea of where your hotspots lie.
My guess, from what you describe is that your hotspot will probably be branch prediction failures resulting from min/max calculations using if/else. Therefore, using SIMD intrinsics should allow you to use the min/max instructions, however, it might be worth just trying to use a branchless min/max caluculation instead. This might achieve most of the gains with less pain.
Something like this:
inline int
minimum(int a, int b)
{
int mask = (a - b) >> 31;
return ((a & mask) | (b & ~mask));
}
If you use SSE instructions, you're obviously limited to processors that support these.
That means x86, dating back to the Pentium 2 or so (can't remember exactly when they were introduced, but it's a long time ago)
SSE2, which, as far as I can recall, is the one that offers integer operations, is somewhat more recent (Pentium 3? Although the first AMD Athlon processors didn't support them)
In any case, you have two options for using these instructions. Either write the entire block of code in assembly (probably a bad idea. That makes it virtually impossible for the compiler to optimize your code, and it's very hard for a human to write efficient assembler).
Alternatively, use the intrinsics available with your compiler (if memory serves, they're usually defined in xmmintrin.h)
But again, the performance may not improve. SSE code poses additional requirements of the data it processes. Mainly, the one to keep in mind is that data must be aligned on 128-bit boundaries. There should also be few or no dependencies between the values loaded into the same register (a 128 bit SSE register can hold 4 ints. Adding the first and the second one together is not optimal. But adding all four ints to the corresponding 4 ints in another register will be fast)
It may be tempting to use a library that wraps all the low-level SSE fiddling, but that might also ruin any potential performance benefit.
I don't know how good SSE's integer operation support is, so that may also be a factor that can limit performance. SSE is mainly targeted at speeding up floating point operations.
If you intend to use Microsoft Visual C++, you should read this:
http://www.codeproject.com/KB/recipes/sseintro.aspx
We have implemented some image processing code, similar to what you describe but on a byte array, In SSE. The speedup compared to C code is considerable, depending on the exact algorithm more than a factor of 4, even in respect to the Intel compiler. However, as you already mentioned you have the following drawbacks:
Portability. The code will run on every Intel-like CPU, so also AMD, but not on other CPUs. That is not a problem for us because we control the target hardware. Switching compilers and even to a 64 bit OS can also be a problem.
You have a steep learning curve, but I found that after you grasp the principles writing new algorithms is not that hard.
Maintainability. Most C or C++ programmers have no knowledge of assembly/SSE.
My advice to you will be to go for it only if you really need the performance improvement, and you can't find a function for your problem in a library like the intel IPP, and if you can live with the portability issues.
I can tell from my experince that SSE brings a huge (4x and up) speedup over a plain c version of the code (no inline asm, no intrinsics used) but hand-optimized assembler can beat Compiler-generated assembly if the compiler can't figure out what the programmer intended (belive me, compilers don't cover all possible code combinations and they never will).
Oh and, the compiler can't everytime layout the data that it runs at the fastest-possible speed.
But you need much experince for a speedup over an Intel-compiler (if possible).
SSE instructions were originally just on Intel chips, but recently (since Athlon?) AMD supports them as well, so if you do code against the SSE instruction set, you should be portable to most x86 procs.
That being said, it may not be worth your time to learn SSE coding unless you're already familiar with assembler on x86's - an easier option might be to check your compiler docs and see if there are options to allow the compiler to autogenerate SSE code for you. Some compilers do very well vectorizing loops in this way. (You're probably not surprised to hear that the Intel compilers do a good job of this :)
Write code that helps the compiler understand what you are doing. GCC will understand and optimize SSE code such as this:
typedef union Vector4f
{
// Easy constructor, defaulted to black/0 vector
Vector4f(float a = 0, float b = 0, float c = 0, float d = 1.0f):
X(a), Y(b), Z(c), W(d) { }
// Cast operator, for []
inline operator float* ()
{
return (float*)this;
}
// Const ast operator, for const []
inline operator const float* () const
{
return (const float*)this;
}
// ---------------------------------------- //
inline Vector4f operator += (const Vector4f &v)
{
for(int i=0; i<4; ++i)
(*this)[i] += v[i];
return *this;
}
inline Vector4f operator += (float t)
{
for(int i=0; i<4; ++i)
(*this)[i] += t;
return *this;
}
// Vertex / Vector
// Lower case xyzw components
struct {
float x, y, z;
float w;
};
// Upper case XYZW components
struct {
float X, Y, Z;
float W;
};
};
Just don't forget to have -msse -msse2 on your build parameters!
Although it is true that SSE is specific to some processors (SSE may be relatively safe, SSE2 much less in my experience), you can detect the CPU at runtime, and load the code dynamically depending on the target CPU.
SIMD intrinsics (such as SSE2) can speed this sort of thing up but take expertise to use correctly. They are very sensitive to alignment and pipeline latency; careless use can make performance even worse than it would have been without them. You'll get a much easier and more immediate speedup from simply using cache prefetching to make sure all your ints are in L1 in time for you to operate on them.
Unless your function needs a throughput of better than 100,000,000 integers per second, SIMD probably isn't worth the trouble for you.
Just to add briefly to what has been said before about different SSE versions being available on different CPUs: This can be checked by looking at the respective feature flags returned by the CPUID instruction (see e.g. Intel's documentation for details).
Have a look at inline assembler for C/C++, here is a DDJ article. Unless you are 100% certain your program will run on a compatible platform you should follow the recommendations many have given here.
I agree with the previous posters. Benefits can be quite large but to get it may require a lot of work. Intel documentation on these instructions is over 4K pages. You may want to check out EasySSE (c++ wrappers library over intrinsics + examples) free from Ocali Inc.
I assume my affiliation with this EasySSE is clear.
I don't recommend doing this yourself unless you're fairly proficient with assembly. Using SSE will, more than likely, require careful reorganization of your data, as Skizz points out, and the benefit is often questionable at best.
It would probably be much better for you to write very small loops and keep your data very tightly organized and just rely on the compiler doing this for you. Both the Intel C Compiler and GCC (since 4.1) can auto-vectorize your code, and will probably do a better job than you. (Just add -ftree-vectorize to your CXXFLAGS.)
Edit: Another thing I should mention is that several compilers support assembly intrinsics, which would probably, IMO, be easier to use than the asm() or __asm{} syntax.
Related
SSE can only be used on x86 x64 CPUs. I have a problem using the SPEEXDSP library on a TI C6678. I've never used the SSE instruction, I've tried many ways and can't get it to work on the DSP.
Is it possible to modify SSE instructions to normal C++ instructions? How to modify it?
Looking forward to your reply.
Example:
static inline double interpolate_product_double(const float* a, const float* b, unsigned int len, const spx_uint32_t oversample, float* frac) {
int i;
double ret;
__m128d sum;
__m128d sum1 = _mm_setzero_pd();
__m128d sum2 = _mm_setzero_pd();
__m128 f = _mm_loadu_ps(frac);
__m128d f1 = _mm_cvtps_pd(f);
__m128d f2 = _mm_cvtps_pd(_mm_movehl_ps(f, f));
__m128 t;
for (i = 0; i < len; i += 2)
{
t = _mm_mul_ps(_mm_load1_ps(a + i), _mm_loadu_ps(b + i * oversample));
sum1 = _mm_add_pd(sum1, _mm_cvtps_pd(t));
sum2 = _mm_add_pd(sum2, _mm_cvtps_pd(_mm_movehl_ps(t, t)));
t = _mm_mul_ps(_mm_load1_ps(a + i + 1), _mm_loadu_ps(b + (i + 1) * oversample));
sum1 = _mm_add_pd(sum1, _mm_cvtps_pd(t));
sum2 = _mm_add_pd(sum2, _mm_cvtps_pd(_mm_movehl_ps(t, t)));
}
sum1 = _mm_mul_pd(f1, sum1);
sum2 = _mm_mul_pd(f2, sum2);
sum = _mm_add_pd(sum1, sum2);
sum = _mm_add_sd(sum, _mm_unpackhi_pd(sum, sum));
_mm_store_sd(&ret, sum);
return ret;
}
Yes, you can use SIMD Everywhere (SIMDe). It provides portable implementations of many intrinsics, including all of the ones in your code. Full disclosure: I am the lead developer.
Edit: replying to phuclv here since it's a bit long for a comment.
SIMDe doesn't currently use the c6x instrinsics to implement functions like we often do for NEON, AltiVec/VSX, WASM SIMD, etc. There is nothing preventing it, and patches are very much welcome, but they're not there yet.
However, every function in SiMDe has fallback implementations all the way back to standard C. Usually things don't get that far, though; even discounting the architecture-specific implementations mentioned above, if the compiler supports it the operations are also implemented using GNU C vector extensions, and even the portable fallbacks are actually annotated with OpenMP SIMD directives. Conversion functions use compiler built-ins like __builtin_convertvector, and functions which require shuffling data around will use __builtin_shuffle / __builtin_shufflevector.
Basically, SIMDe goes to great lengths to get the compiler to vectorize the whenever possible, even if SIMDe doesn't actually know how to do it. The functions above are all pretty straightforward; I don't know enough about c6x SIMD to know what kind of operations are supported in hardware, but GCC and clang (which the TI compilers are based on) generally do a very good job with all the information SIMDe gives them. Honestly, the thing I'm most worried about here is whether the c6x supports double-precision floating point in SIMD (which the code above uses)... there is a pretty good chance it only supports single-precision floats.
Is it possible to modify SSE instructions to normal C++ instructions?
There's no such thing as "C++ instructions" because C++ is a high level language with only statements and no instructions. But yes it's possible to convert SSE intrinsics to C++ expressions because they're simply multiple operations in parallel
SSE is one of the SIMD instruction sets so just convert it to the corresponding SIMD in the target architecture. In your case TI C6678 does have SIMD support:
The C64x+ and C674x DSPs support 2-way SIMD operations for 16-bit data and 4-way SIMD operations for 8-bit data. On the C66x DSP, the vector processing capability is improved by extending the width of the SIMD instructions. C66x DSPs can execute instructions that operate on 128-bit vectors.
The C66x architecture indeed supports a number of SIMD instructions, somewhat comparable to those of Intel's SSE.
You need to be aware of the processor's register set in both architectures and compare the available instructions.
For example, _mm_add_ps performs four simultaneous additions of single-precision floats, contained four by four in the SSE registers. The DSP has a similar DADDSP instruction that only performs two such additions. Hence you will need to translate one _mm_add_ps by two DADDSP.
Read the manuals (these instruction sets are online), understand what the instructions are doing, and find the equivalences. In case of a dead-end, you still have the recourse to good old scalar operations, like C[0]= A[0]+B[0]; C[1]= A[1]+B[1];
I want to implement
void bitwise_and(
char* __restrict__ result,
const char* __restrict__ lhs,
const char* __restrict__ rhs,
size_t length);
or maybe a bitwise_or(), bitwise_xor() or any other bitwise operation. Obviously it's not about the algorithm, just the implementation details - alignment, loading the largest possible element from memory, cache-awareness, using SIMD instructions etc.
I'm sure this has (more than one) fast existing implementations, but I would guess most library implementations would require some fancy container, e.g. std::bitset or boost::dynamic_bit_set - but I don't want to spend the time constructing one of those.
So do I... Copy-paste from an existing library? Find a library which can 'wrap' a raw packed bits array in memory with a nice object? Roll my own implementation anyway?
Notes:
I'm mostly interested in C++ code, but I certainly don't mind a plain C approach.
Obviously, making copies of the input arrays is out of the question - that would probably nearly-double the execution time.
I intentionally did not template the bitwise operator, in case there's some specific optimization for OR, or for AND etc.
Bonus points for discussing operations on multiple vectors at once, e.g. V_out = V_1 bitwise-and V_2 bitwise-and V_3 etc.
I noted this article comparing library implementations, but it's from 5 years ago. I can't ask which library to use since that would violate SO policy I guess...
If it helps you any, assume its uint64_ts rather than chars (that doesn't really matter - if the char array is unaligned we can just treated the heading and trailing chars separately).
This answer is going to assume you want the fastest possible way and are happy to use platform specific things. You optimising compiler may be able to produce similar code to the below from normal C but in my experiance across a few compilers something as specific as this is still best hand-written.
Obviously like all optimisation tasks, never assume anything is better/worse and measure, measure, measure.
If you could lock down you architecture to x86 with at least SSE3 you would do:
void bitwise_and(
char* result,
const char* lhs,
const char* rhs,
size_t length)
{
while(length >= 16)
{
// Load in 16byte registers
auto lhsReg = _mm_loadu_si128((__m128i*)lhs);
auto rhsReg = _mm_loadu_si128((__m128i*)rhs);
// do the op
auto res = _mm_and_si128(lhsReg, rhsReg);
// save off again
_mm_storeu_si128((__m128i*)result, res);
// book keeping
length -= 16;
result += 16;
lhs += 16;
rhs += 16;
}
// do the tail end. Assuming that the array is large the
// most that the following code can be run is 15 times so I'm not
// bothering to optimise. You could do it in 64 bit then 32 bit
// then 16 bit then char chunks if you wanted...
while (length)
{
*result = *lhs & *rhs;
length -= 1;
result += 1;
lhs += 1;
rhs += 1;
}
}
This compiles to ~10asm instructions per 16 bytes (+ change for the leftover and a little overhead).
The great thing about doing intrinsics like this (over hand rolled asm) is that the compiler is still free to do additional optimisations (such as loop unrolling) ontop of what you write. It also handles register allocation.
If you could guarantee aligned data you could save an asm instruction (use _mm_load_si128 instead and the compiler will be clever enough to avoid a second load and use it as an direct mem operand to the 'pand'.
If you could guarantee AVX2+ then you could use the 256 bit version and handle 10asm instructions per 32 bytes.
On arm theres similar NEON instructions.
If you wanted to do multiple ops just add the relevant intrinsic in the middle and it'll add 1 asm instruction per 16 bytes.
I'm pretty sure with a decent processor you dont need any additional cache control.
Don't do it this way. The individual operations will look great, sleek asm, nice performance .. but a composition of them will be terrible. You cannot make this abstraction, nice as it looks. The arithmetic intensity of those kernels is almost the worst possible (the only worse one is doing no arithmetic, such as a straight up copy), and composing them at a high level will retain that awful property. In a sequence of operations each using the result of the previous one, the results are written and read again a lot later (in the next kernel), even though the high level flow could be transposed so that the result the "next operation" needs is right there in a register. Also, if the same argument appears twice in an expression tree (and not both as operands to one operation), they will be streamed in twice, instead of reusing the data for two operations.
It doesn't have that nice warm fuzzy feeling of "look at all this lovely abstraction" about it, but what you should do is find out at a high level how you're combining your vectors, and then try to chop that in pieces that make sense from a performance perspective. In some cases that may mean making big ugly messy loops that will make people get an extra coffee before diving in, that's just too bad then. If you want performance, you often have to sacrifice something else. Usually it's not so bad, it probably just means you have a loop that has an expression consisting of intrinsics in it, instead of an expression of vector-operations that each individually have a loop.
I'm copying elements from one array to another in C++. I found the rep movs instruction in x86 that seems to copy an array at ESI to an array at EDI of size ECX. However, neither the for nor while loops I tried compiled to a rep movs instruction in VS 2008 (on an Intel Xeon x64 processor). How can I write code that will get compiled to this instruction?
Honestly, you shouldn't. REP is sort of an obsolete holdover in the instruction set, and actually pretty slow since it has to call a microcoded subroutine inside the CPU, which has a ROM lookup latency and is nonpipelined as well.
In almost every implementation, you will find that the memcpy() compiler intrinsic both is easier to use and runs faster.
Under MSVC there are the __movsxxx & __stosxxx intrinsics that will generate a REP prefixed instruction.
there is also a 'hack' to force intrinsic memset aka REP STOS under vc9+, as the intrinsic no longer exits, due to the sse2 branching in the crt. this is better that __stosxxx due to the fact the compiler can optimize it for constants and order it correctly.
#define memset(mem,fill,size) memset((DWORD*)mem,((fill) << 24|(fill) << 16|(fill) << 8|(fill)),size)
__forceinline void memset(DWORD* pStart, unsigned long dwFill, size_t nSize)
{
//credits to Nepharius for finding this
DWORD* pLast = pStart + (nSize >> 2);
while(pStart < pLast)
*pStart++ = dwFill;
if((nSize &= 3) == 0)
return;
if(nSize == 3)
{
(((WORD*)pStart))[0] = WORD(dwFill);
(((BYTE*)pStart))[2] = BYTE(dwFill);
}
else if(nSize == 2)
(((WORD*)pStart))[0] = WORD(dwFill);
else
(((BYTE*)pStart))[0] = BYTE(dwFill);
}
of course REP isn't always the best thing to use, imo your way better off using memcpy, it'll branch to either sse2 or REPS MOV based on your system (under msvc), unless you feeling like writing custom assembly for 'hot' areas...
If you need exactly that instruction - use built-in assembler and write that instruction manually. You can't rely on the compiler to produce any specific machine code - even if it emits it in one compilation it can decide to emit some other equivalent during next compilation.
REP and friends was nice once upon a time, when the x86 CPU was a single-pipeline industrial CISC-processor.
But that has changed. Nowadays when the processor encounters any instruction, the first it does is translating it into an easier format (VLIW-like micro-ops) and schedules it for future execution (this is part of out-of-order-execution, part of scheduling between different logical CPU cores, it can be used to simplifying write-after-write-sequences into single-writes, et.c.). This machinery works well for instructions that translates into a few VLIW-like opcodes, but not machine-code that translates into loops. Loop-translated machine code will probably cause the execution pipeline to stall.
Rather than spending hundreds of thousands of transistors into building CPU-circuitry for handling looping portions of the micro-ops in the execution pipeline, they just handle it in some sort of crappy legacy-mode that stutterly stalls the pipeline, and ask modern programmers to write your own damn loops!
Therefore it is seldom used when machines write code. If you encounter REP in a binary executable, its probably a human assembly-muppet who didn't know better, or a cracker that really needed the few bytes it saved to use it instead of an actual loop, that wrote it.
(However. Take everything I just wrote with a grain of salt. Maybe this is not true anymore. I am not 100% up to date with the internals of x86 CPUs anymore, I got into other hobbies..)
I use the rep* prefix variants with cmps*, movs*, scas* and stos* instruction variants to generate inline code which minimizes the code size, avoids unnecessary calls/jumps and thereby keeps down the work done by the caches. The alternative is to set up parameters and call a memset or memcpy somewhere else which may overall be faster if I want to copy a hundred bytes or more but if it's just a matter of 10-20 bytes using rep is faster (or at least was the last time I measured).
Since my compiler allows specification and use of inline assembly functions and includes their register usage/modification in the optimization activities it is possible for me to use them when the circumstances are right.
On a historic note - not having any insight into the manufacturer's strategies - there was a time when the "rep movs*" (etc) instructions were very slow. I think it was around the time of the Pentium/Pentium MMX. A colleague of mine (who had more insight than I) said that the manufacturers had decreased the chip area (<=> fewer transistors/more microcode) allocated to the rep handling and used it to make other, more used instructions faster.
In the fifteen years or so since rep has become relatively speaking faster again which would suggest more transistors/less microcode.
Given the arrays:
int canvas[10][10];
int addon[10][10];
Where all the values range from 0 - 100, what is the fastest way in C++ to add those two arrays so each cell in canvas equals itself plus the corresponding cell value in addon?
IE, I want to achieve something like:
canvas += another;
So if canvas[0][0] =3 and addon[0][0] = 2 then canvas[0][0] = 5
Speed is essential here as I am writing a very simple program to brute force a knapsack type problem and there will be tens of millions of combinations.
And as a small extra question (thanks if you can help!) what would be the fastest way of checking if any of the values in canvas exceed 100? Loops are slow!
Here is an SSE4 implementation that should perform pretty well on Nehalem (Core i7):
#include <limits.h>
#include <emmintrin.h>
#include <smmintrin.h>
static inline int canvas_add(int canvas[10][10], int addon[10][10])
{
__m128i * cp = (__m128i *)&canvas[0][0];
const __m128i * ap = (__m128i *)&addon[0][0];
const __m128i vlimit = _mm_set1_epi32(100);
__m128i vmax = _mm_set1_epi32(INT_MIN);
__m128i vcmp;
int cmp;
int i;
for (i = 0; i < 10 * 10; i += 4)
{
__m128i vc = _mm_loadu_si128(cp);
__m128i va = _mm_loadu_si128(ap);
vc = _mm_add_epi32(vc, va);
vmax = _mm_max_epi32(vmax, vc); // SSE4 *
_mm_storeu_si128(cp, vc);
cp++;
ap++;
}
vcmp = _mm_cmpgt_epi32(vmax, vlimit); // SSE4 *
cmp = _mm_testz_si128(vcmp, vcmp); // SSE4 *
return cmp == 0;
}
Compile with gcc -msse4.1 ... or equivalent for your particular development environment.
For older CPUs without SSE4 (and with much more expensive misaligned loads/stores) you'll need to (a) use a suitable combination of SSE2/SSE3 intrinsics to replace the SSE4 operations (marked with an * above) and ideally (b) make sure your data is 16-byte aligned and use aligned loads/stores (_mm_load_si128/_mm_store_si128) in place of _mm_loadu_si128/_mm_storeu_si128.
You can't do anything faster than loops in just C++. You would need to use some platform specific vector instructions. That is, you would need to go down to the assembly language level. However, there are some C++ libraries that try to do this for you, so you can write at a high level and have the library take care of doing the low level SIMD work that is appropriate for whatever architecture you are targetting with your compiler.
MacSTL is a library that you might want to look at. It was originally a Macintosh specific library, but it is cross platform now. See their home page for more info.
The best you're going to do in standard C or C++ is to recast that as a one-dimensional array of 100 numbers and add them in a loop. (Single subscripts will use a bit less processing than double ones, unless the compiler can optimize it out. The only way you're going to know how much of an effect there is, if there is one, is to test.)
You could certainly create a class where the addition would be one simple C++ instruction (canvas += addon;), but that wouldn't speed anything up. All that would happen is that the simple C++ instruction would expand into the loop above.
You would need to get into lower-level processing in order to speed that up. There are additional instructions on many modern CPUs to do such processing that you might be able to use. You might be able to run something like this on a GPU using something like Cuda. You could try making the operation parallel and running on several cores, but on such a small instance you'll have to know how caching works on your CPU.
The alternatives are to improve your algorithm (on a knapsack-type problem, you might be able to use dynamic programming in some way - without more information from you, we can't tell you), or to accept the performance. Tens of millions of operations on a 10 by 10 array turn into hundreds of billions of operations on numbers, and that's not as intimidating as it used to be. Of course, I don't know your usage scenario or performance requirements.
Two parts: first, consider your two-dimensional array [10][10] as a single array [100]. The layout rules of C++ should allow this. Second, check your compiler for intrinsic functions implementing some form of SIMD instructions, such as Intel's SSE. For example Microsoft supplies a set. I believe SSE has some instructions for checking against a maximum value, and even clamping to the maximum if you want.
Here is an alternative.
If you are 100% certain that all your values are between 0 and 100, you could change your type from an int to a uint8_t. Then, you could add 4 elements together at once of them together using uint32_t without worrying about overflow.
That is ...
uint8_t array1[10][10];
uint8_t array2[10][10];
uint8_t dest[10][10];
uint32_t *pArr1 = (uint32_t *) &array1[0][0];
uint32_t *pArr2 = (uint32_t *) &array2[0][0];
uint32_t *pDest = (uint32_t *) &dest[0][0];
int i;
for (i = 0; i < sizeof (dest) / sizeof (uint32_t); i++) {
pDest[i] = pArr1[i] + pArr2[i];
}
It may not be the most elegant, but it could help keep you from going to architecture specific code. Additionally, if you were to do this, I would strongly recommend you comment what you are doing and why.
You should check out CUDA. This kind of problem is right up CUDA's street. Recommend the Programming Massively Parallel Processors book.
However, this does require CUDA capable hardware, and CUDA takes a bit of effort to get setup in your development environment, so it would depend how important this really is!
Good luck!
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.