What is the limit of optimization using SIMD? - c

I need to optimize some C code, which does lots of physics computations, using SIMD extensions on the SPE of the Cell Processor. Each vector operator can process 4 floats at the same time. So ideally I would expect a 4x speedup in the most optimistic case.
Do you think the use of vector operators could give bigger speedups?
Thanks

The best optimization occurs in rethinking the algorithm. Eliminate unnecessary steps. Find more a direct way of accomplishing the same result. Compute the solution in a domain more relevant to the problem.
For example, if the vector array is a list of n which are all on the same line, then it is sufficient to transform the end points only and interpolate the intermediate points.

It CAN give better speeds up than 4 times over straight floating point as the SIMD instructions could be less exact (Not so much as to give too many problems though) and so take fewer cycles to execute. It really depends.
Best plan is to learn as much about the processor you are optimising for as possible. You may find it can give you far better than 4x improvements. You may find out you can't. We can't say though without knowing more about the algorithm you are optimising and what CPU you are targetting.

On their own, no. But if the process of re-writing your algorithms to support them also happens to improve, say, cache locality or branching behaviour, then you could find unrelated speed-ups. However, this is true of any re-write...

This is entirely possible.
You can do more clever instruction-level micro optimizations than a compiler, if you know what you're doing.
Most SIMD instruction sets offers several powerful operations that don't have any equivalent in normal scalar FPU/ALU code (e.g. PAVG/PMIN etc. in SSE2). Even if these don't fit your problem exactly, you can often combine these instructions for great effect.
Not sure about Cell, but most SIMD instruction sets have features to optimize memory access, for example to prefetch data into cache. I've had very good results with these.
Now this isn't Cell or PPC at all, but a simple image convolution filter of mine got a 20x speedup (C vs. SSE2) on Atom, which is higher than the level of parallelity (16 pixels at a time).

It depends on the architecture.. For the moment I assume x86 architecture (aka SSE).
You can get factor four on tight loops easily. Just replace your existing math with SSE instruction and you're done.
You can even get a little more than that because if you use SSE you do the math in registers which are usually not used by the compiler. This frees up the general purpose register for other task such as loop control and address calculation. In short the code that surrounds the SSE instruction will be more compact and execute faster.
And then there is the option to hint the memory controller how you want to access the memory, e.g. if you want to store data in a way that it bypasses the cache or not. For bandwidth hungry algorithms that may give you some more extra speed ontop of that.

Related

C- Why is for loop pointer indexing faster? [duplicate]

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.
Closed 10 years ago.
Some years ago I was on a panel that was interviewing candidates for a relatively senior embedded C programmer position.
One of the standard questions that I asked was about optimisation techniques. I was quite surprised that some of the candidates didn't have answers.
So, in the interests of putting together a list for posterity - what techniques and constructs do you normally use when optimising C programs?
Answers to optimisation for speed and size both accepted.
First things first - don't optimise too early. It's not uncommon to spend time carefully optimising a chunk of code only to find that it wasn't the bottleneck that you thought it was going to be. Or, to put it another way "Before you make it fast, make it work"
Investigate whether there's any option for optimising the algorithm before optimising the code. It'll be easier to find an improvement in performance by optimising a poor algorithm than it is to optimise the code, only then to throw it away when you change the algorithm anyway.
And work out why you need to optimise in the first place. What are you trying to achieve? If you're trying, say, to improve the response time to some event work out if there is an opportunity to change the order of execution to minimise the time critical areas. For example when trying to improve the response to some external interrupt can you do any preparation in the dead time between events?
Once you've decided that you need to optimise the code, which bit do you optimise? Use a profiler. Focus your attention (first) on the areas that are used most often.
So what can you do about those areas?
minimise condition checking. Checking conditions (eg. terminating conditions for loops) is time that isn't being spent on actual processing. Condition checking can be minimised with techniques like loop-unrolling.
In some circumstances condition checking can also be eliminated by using function pointers. For example if you are implementing a state machine you may find that implementing the handlers for individual states as small functions (with a uniform prototype) and storing the "next state" by storing the function pointer of the next handler is more efficient than using a large switch statement with the handler code implemented in the individual case statements. YMMV.
minimise function calls. Function calls usually carry a burden of context saving (eg. writing local variables contained in registers to the stack, saving the stack pointer), so if you don't have to make a call this is time saved. One option (if you're optimising for speed and not space) is to make use of inline functions.
If function calls are unavoidable minimise the data that is being passed to the functions. For example passing pointers is likely to be more efficient than passing structures.
When optimising for speed choose datatypes that are the native size for your platform. For example on a 32bit processor it is likely to be more efficient to manipulate 32bit values than 8 or 16 bit values. (side note - it is worth checking that the compiler is doing what you think it is. I've had situations where I've discovered that my compiler insisted on doing 16 bit arithmetic on 8 bit values with all of the to and from conversions to go with them)
Find data that can be precalculated, and either calculate during initialisation or (better yet) at compile time. For example when implementing a CRC you can either calculate your CRC values on the fly (using the polynomial directly) which is great for size (but dreadful for performance), or you can generate a table of all of the interim values - which is a much faster implementation, to the detriment of the size.
Localise your data. If you're manipulating a blob of data often your processor may be able to speed things up by storing it all in cache. And your compiler may be able to use shorter instructions that are suited to more localised data (eg. instructions that use 8 bit offsets instead of 32 bit)
In the same vein, localise your functions. For the same reasons.
Work out the assumptions that you can make about the operations that you're performing and find ways of exploiting them. For example, on an 8 bit platform if the only operation that at you're doing on a 32 bit value is an increment you may find that you can do better than the compiler by inlining (or creating a macro) specifically for this purpose, rather than using a normal arithmetic operation.
Avoid expensive instructions - division is a prime example.
The "register" keyword can be your friend (although hopefully your compiler has a pretty good idea about your register usage). If you're going to use "register" it's likely that you'll have to declare the local variables that you want "register"ed first.
Be consistent with your data types. If you are doing arithmetic on a mixture of data types (eg. shorts and ints, doubles and floats) then the compiler is adding implicit type conversions for each mismatch. This is wasted cpu cycles that may not be necessary.
Most of the options listed above can be used as part of normal practice without any ill effects. However if you're really trying to eke out the best performance:
- Investigate where you can (safely) disable error checking. It's not recommended, but it will save you some space and cycles.
- Hand craft portions of your code in assembler. This of course means that your code is no longer portable but where that's not an issue you may find savings here. Be aware though that there is potentially time lost moving data into and out of the registers that you have at your disposal (ie. to satisfy the register usage of your compiler). Also be aware that your compiler should be doing a pretty good job on its own. (of course there are exceptions)
As everybody else has said: profile, profile profile.
As for actual techniques, one that I don't think has been mentioned yet:
Hot & Cold Data Separation: Staying within the CPU's cache is incredibly important. One way of helping to do this is by splitting your data structures into frequently accessed ("hot") and rarely accessed ("cold") sections.
An example: Suppose you have a structure for a customer that looks something like this:
struct Customer
{
int ID;
int AccountNumber;
char Name[128];
char Address[256];
};
Customer customers[1000];
Now, lets assume that you want to access the ID and AccountNumber a lot, but not so much the name and address. What you'd do is to split it into two:
struct CustomerAccount
{
int ID;
int AccountNumber;
CustomerData *pData;
};
struct CustomerData
{
char Name[128];
char Address[256];
};
CustomerAccount customers[1000];
In this way, when you're looping through your "customers" array, each entry is only 12 bytes and so you can fit many more entries in the cache. This can be a huge win if you can apply it to situations like the inner loop of a rendering engine.
My favorite technique is to use a good profiler. Without a good profile telling you where the bottleneck lies, no tricks and techniques are going to help you.
most common techniques I encountered are:
loop unrolling
loop optimization for better cache prefetch
(i.e. do N operations in M cycles instead of NxM singular operations)
data aligning
inline functions
hand-crafted asm snippets
As for general recommendations, most of them are already sounded:
choose better algos
use profiler
don't optimize if it doesn't give 20-30% performance boost
For low-level optimization:
START_TIMER/STOP_TIMER macros from ffmpeg (clock-level accuracy for measurement of any code).
Oprofile, of course, for profiling.
Enormous amounts of hand-coded assembly (just do a wc -l on x264's /common/x86 directory, and then remember most of the code is templated).
Careful coding in general; shorter code is usually better.
Smart low-level algorithms, like the 64-bit bitstream writer I wrote that uses only a single if and no else.
Explicit write-combining.
Taking into account important weird aspects of processors, like Intel's cacheline split issue.
Finding cases where one can losslessly or near-losslessly make an early termination, where the early-termination check costs much less than the speed one gains from it.
Actually inlined assembly for tasks which are far more suited to the x86 SIMD unit, such as median calculations (requires compile-time check for MMX support).
First and foremost, use a better/faster algorithm. There is no point optimizing code that is slow by design.
When optimizing for speed, trade memory for speed: lookup tables of precomputed values, binary trees, write faster custom implementation of system calls...
When trading speed for memory: use in-memory compression
Avoid using the heap. Use obstacks or pool-allocator for identical sized objects. Put small things with short lifetime onto the stack. alloca still exists.
Pre-mature optimization is the root of all evil!
;)
As my applications usually don't need much CPU time by design, I focus on the size my binaries on disk and in memory. What I do mostly is looking out for statically sized arrays and replacing them with dynamically allocated memory where it's worth the additional effort of free'ing the memory later. To cut down the size of the binary, I look for big arrays that are initialized at compile time and put the initializiation to runtime.
char buf[1024] = { 0, };
/* becomes: */
char buf[1024];
memset(buf, 0, sizeof(buf));
This will remove the 1024 zero-bytes from the binaries .DATA section and will instead create the buffer on the stack at runtime and the fill it with zeros.
EDIT: Oh yeah, and I like to cache things. It's not C specific but depending on what you're caching, it can give you a huge boost in performance.
PS: Please let us know when your list is finished, I'm very curious. ;)
If possible, compare with 0, not with arbitrary numbers, especially in loops, because comparison with 0 is often implemented with separate, faster assembler commands.
For example, if possible, write
for (i=n; i!=0; --i) { ... }
instead of
for (i=0; i!=n; ++i) { ... }
Another thing that was not mentioned:
Know your requirements: don't optimize for situations that will unlikely or never happen, concentrate on the most bang for the buck
basics/general:
Do not optimize when you have no problem.
Know your platform/CPU...
...know it thoroughly
know your ABI
Let the compiler do the optimization, just help it with the job.
some things that have actually helped:
Opt for size/memory:
Use bitfields for storing bools
re-use big global arrays by overlaying with a union (be careful)
Opt for speed (be careful):
use precomputed tables where possible
place critical functions/data in fast memory
Use dedicated registers for often used globals
count to-zero, zero flag is free
Difficult to summarize ...
Data structures:
Splitting of a data structure depending on case of usage is extremely important. It is common to see a structure that holds data that is accessed based on a flow control. This situation can lower significantly the cache usage.
To take into account cache line size and prefetch rules.
To reorder the members of the structure to obtain a sequential access to them from your code
Algorithms:
Take time to think about your problem and to find the correct algorithm.
Know the limitations of the algorithm you choose (a radix-sort/quick-sort for 10 elements to be sorted might not be the best choice).
Low level:
As for the latest processors it is not recommended to unroll a loop that has a small body. The processor provides its own detection mechanism for this and will short-circuit whole section of its pipeline.
Trust the HW prefetcher. Of course if your data structures are well designed ;)
Care about your L2 cache line misses.
Try to reduce as much as possible the local working set of your application as the processors are leaning to smaller caches per cores (C2D enjoyed a 3MB per core max where iCore7 will provide a max of 256KB per core + 8MB shared to all cores for a quad core die.).
The most important of all: Measure early, Measure often and never ever makes assumptions, base your thinking and optimizations on data retrieved by a profiler (please use PTU).
Another hint, performance is key to the success of an application and should be considered at design time and you should have clear performance targets.
This is far from being exhaustive but should provide an interesting base.
These days, the most important things in optimzation are:
respecting the cache - try to access memory in simple patterns, and don't unroll loops just for fun. Use arrays instead of data structures with lots of pointer chasing and it'll probably be faster for small amounts of data. And don't make anything too big.
avoiding latency - try to avoid divisions and stuff that's slow if other calculations depend on them immediately. Memory accesses that depend on other memory accesses (ie, a[b[c]]) are bad.
avoiding unpredictabilty - a lot of if/elses with unpredictable conditions, or conditions that introduce more latency, will really mess you up. There's a lot of branchless math tricks that are useful here, but they increase latency and are only useful if you really need them. Otherwise, just write simple code and don't have crazy loop conditions.
Don't bother with optimizations that involve copy-and-pasting your code (like loop unrolling), or reordering loops by hand. The compiler usually does a better job than you at doing this, but most of them aren't smart enough to undo it.
Collecting profiles of code execution get you 50% of the way there. The other 50% deals with analyzing these reports.
Further, if you use GCC or VisualC++, you can use "profile guided optimization" where the compiler will take info from previous executions and reschedule instructions to make the CPU happier.
Inline functions! Inspired by the profiling fans here I profiled an application of mine and found a small function that does some bitshifting on MP3 frames. It makes about 90% of all function calls in my applcation, so I made it inline and voila - the program now uses half of the CPU time it did before.
On most of embedded system i worked there was no profiling tools, so it's nice to say use profiler but not very practical.
First rule in speed optimization is - find your critical path.
Usually you will find that this path is not so long and not so complex. It's hard to say in generic way how to optimize this it's depend on what are you doing and what is in your power to do. For example you want usually avoid memcpy on critical path, so ever you need to use DMA or optimize, but what if you hw does not have DMA ? check if memcpy implementation is a best one if not rewrite it.
Do not use dynamic allocation at all in embedded but if you do for some reason don't do it in critical path.
Organize your thread priorities correctly, what is correctly is real question and it's clearly system specific.
We use very simple tools to analyze the bottle-necks, simple macro that store the time-stamp and index. Few (2-3) runs in 90% of cases will find where you spend your time.
And the last one is code review a very important one. In most case we avoid performance problem during code review very effective way :)
Measure performance.
Use realistic and non-trivial benchmarks. Remember that "everything is fast for small N".
Use a profiler to find hotspots.
Reduce number of dynamic memory allocations, disk accesses, database accesses, network accesses, and user/kernel transitions, because these often tend to be hotspots.
Measure performance.
In addition, you should measure performance.
Sometimes you have to decide whether it is more space or more speed that you are after, which will lead to almost opposite optimizations. For example, to get the most out of you space, you pack structures e.g. #pragma pack(1) and use bit fields in structures. For more speed you pack to align with the processors preference and avoid bitfields.
Another trick is picking the right re-sizing algorithms for growing arrays via realloc, or better still writing your own heap manager based on your particular application. Don't assume the one that comes with the compiler is the best possible solution for every application.
If someone doesn't have an answer to that question, it could be they don't know much.
It could also be that they know a lot. I know a lot (IMHO :-), and if I were asked that question, I would be asking you back: Why do you think that's important?
The problem is, any a-priori notions about performance, if they are not informed by a specific situation, are guesses by definition.
I think it is important to know coding techniques for performance, but I think it is even more important to know not to use them, until diagnosis reveals that there is a problem and what it is.
Now I'm going to contradict myself and say, if you do that, you learn how to recognize the design approaches that lead to trouble so you can avoid them, and to a novice, that sounds like premature optimization.
To give you a concrete example, this is a C application that was optimized.
Great lists. I will just add one tip I didn't saw in the above lists that in some case can yield huge optimisation for minimal cost.
bypass linker
if you have some application divided in two files, say main.c and lib.c, in many cases you can just add a \#include "lib.c" in your main.c That will completely bypass linker and allow for much more efficient optimisation for compiler.
The same effect can be achieved optimizing dependencies between files, but the cost of changes is usually higher.
Sometimes Google is the best algorithm optimization tool. When I have a complex problem, a bit of searching reveals some guys with PhD's have found a mapping between this and a well-known problem and have already done most of the work.
I would recommend optimizing using more efficient algorithms and not do it as an afterthought but code it that way from the start. Let the compiler work out the details on the small things as it knows more about the target processor than you do.
For one, I rarely use loops to look things up, I add items to a hashtable and then use the hashtable to lookup the results.
For example you have a string to lookup and then 50 possible values. So instead of doing 50 strcmps, you add all 50 strings to a hashtable and give each a unique number ( you only have to do this once ). Then you lookup the target string in the hashtable and have one large switch with all 50 cases ( or have functions pointers ).
When looking up things with common sets of input ( like css rules ), I use fast code to keep track of the only possible solitions and then iterate thought those to find a match. Once I have a match I save the results into a hashtable ( as a cache ) and then use the cache results if I get that same input set later.
My main tools for faster code are:
hashtable - for quick lookups and for caching results
qsort - it's the only sort I use
bsp - for looking up things based on area ( map rendering etc )

Bitwise operation over a simple piece of code

Recently I came across a code that can compute the largest number given two numbers using XOR. While this looks nifty, the same thing can be achieved by a simple ternary operator or an if else. Not pertaining to just this example, but do bitwise operations have any advantage over normal code? If so, is this advantage in speed of computation or memory usage? I am assuming in bitwise operations the assembly code will look much simpler than normal code. On a related note, while programming embedded systems which is more efficient?
*Normal code refers to how you'd normally do it. For example a*2 is normal code and I can achieve the same thing with a<<1
do bitwise operations have any advantage over normal code?
Bitwise operations are normal code. Most compilers these days have optimizers that generate the same instruction for a << 1 as for a * 2. On some hardware, especially on low-powered microprocessors, shift operations take fewer CPU cycles than multiplication, but there is hardware on which this makes no difference.
In your specific case there is an advantage, though: the code with XOR avoids branching, which has a great potential of speeding up the code. When there is no branching, CPU can use pipelining to perform the same operations much faster.
when programming embedded systems which is more efficient?
Embedded systems often have less powerful CPUs, so bitwise operations do have an advantage. For example, on 68HC11 CPU multiplication takes 10 cycles, while shifting left takes only 3.
Note, however, that it does not mean that you should be using bitwise operations explicitly. Most compilers, including embedded ones, will convert multiplication by a constant to a sequence of shifts and additions in case it saves CPU cycles.
Bitwise operators generally have the advantage of being constant time, regardless of input values. Conditional moves and branches may be the target of timing attacks in certain applications, such as crypto libraries, while bitwise operations are not subject to such attacks. (Disregarding cache timing attacks, etc.)
Generally, if a processor is capable of pipelining, it would be more efficient to use bitwise operations than conditional moves or branches, bypassing the entire branch prediction problem. This may or may not speed up your resulting code.
You do have to be careful, though, as some operations constitute undefined behavior in C, such as shifting signed integers, etc. For this reason, it may be to your advantage to do things the "normal" way.
On some platforms branches are expensive, so finding a way to get the min(x,y) without branching has some merit. I think this is particularly useful in CUDA, where the pipelines in the hardware are long.
Of course, on other platforms (like ARM) with conditional execution and compilers that emit those op-codes, it boils down to a compare and a conditional move (two instructions) with no pipeline bubble. Almost certainly better than a compare, and a few logical operations.
Since the poster asks it with the Embedded tag listed, I will try to reflect primarily that in my answer.
In short, usually you shouldn't try to be "creative" with your coding, since it becomes harder to understand later! (The old saying, "premature optimization is the root of all evils")
So only do anything alike when you know what you are doing, precisely, and in any other case, try to write the most understandable C code.
Well, this was the general part, now lets get on what such tricks could do, how they could affect the execution time.
First thing, in embedded, it is good to check the disassembly listing. If you use a variant of GCC with -O2 optimizations, you can usually assume it is quite clever understanding what the code is meant to do, and will produce the result which is likely fine. It can even use such tricks by itself figuring out the code, if it "sees" that it will be faster on the target CPU, so you don't need to ruin the understandability of your code with tricks. With other compilers, results may vary, in doubt, the assembly listing should be observed to see if execution times could be improved utilizing such bit hack tricks.
On the usual embedded platform, especially at 8 bits, you don't need to care that much about pipeline (and related, branch mispredictions) since it is short (or nonexistent). So you usually gain nothing by eliminating a conditional at the cost of an arithmetic operation, and could actually ruin performance by utilizing some elaborate hacks.
On faster 32 bit CPUs usually there is a longer pipeline and branch predictor to eliminate flushes (costing many cycles), so eliminating conditionals may pay off. But only if they are of such nature that the branch predictor can not guess them right (such as comparisons on "random" data), otherwise the conditionals may still be the better, taking the most minimal time (single cycle or even "less" if the CPU is capable to process more than one operation per cycle) when they were predicted right.

Programming without jumps

I try to find articles, books or anything about programming without jumps (x86 arch). I know that generally it is impossible but I try to avoid jumps but gcc even with inline func uses jumps many times. Coding only in Assembly is some sort of solution, but writing equivalent of 1000 lines in C is like hell party to my eyes..
Unless your jumps are really random, branch prediction should eliminate most of overhead involved.
I would dedicate more effort to optimizing memory access patterns in order to improve locality and reduce cache misses. These days, memory latency is the major bottleneck to performance.
Another good direction is improving parallelism (using both vectorized SIMD instructions and, if possible, more than one core).
Optimize only performance critical code, and only once you really know it is performance critical. Do not try to optimize jumps only because you read they case a performance hit. Everything causes a performance hit, and the fastest possible code is the code which does nothing. There are other things much worse than jumps.
If you will show a particular example of a jump in the generated code, chance is there will be some way to avoid it, but it is more likely the code you will show will still contain more serious issues.
One particular way how to avoid branches is to use "conditional move" instructions. They can be used e.g. to compute max or min. If you allow the compiler to use SSE architecture, it assumes the CPU also supports CMOV/FCOMI/FCOMIP/FUCOMI/FUCOMIP instructions and will use them (beware: sometimes it may be tricky to make the compiler to do what you want, see e.g. this gamedev.net discussion).
I think you may mean branching. In C there are bit twiddling tricks to use to speed up certain operations
See bit hacks:
http://www-graphics.stanford.edu/~seander/bithacks.html
It is not impossible to code without jumps but it seems pointless to try.
In the end if you need to do something more than once then your choices are:
Loop unrolling (i.e. repeating the code instead of looping).
Somehow get the instruction pointer to visit the same code more than once.
The first approach requiers knowing the number of iterations in advance and doesn't scale and the second involves some sort of jump.
Not knowing what your code looks like, it's hard to give any advice. But I will give it a try.
Before you start optimizing, run a profiling tool to locate the problem areas. After optimizing, run the profiling tool again to see if you actually made it faster.
It's hard to actually remove branches, but you can minimize them by doing loop unrolling.
Someone mentioned conditional move instructions, there's plenty of conditional instructions on the ARM architecture, but if they're not executed they will translate to a NOP and take one cycle each. Not sure how they work on x86. It might actually get slower then using a simple branch depending on how long the pipeline is.
There's a lot of other optimizing tricks you could try before removing branches.

What is the maximum theoretical speed-up due to SSE for a simple binary subtraction?

In trying to figure out whether or not my code's inner loop is hitting a hardware design barrier or a lack of understanding on my part barrier. There's a bit more to it, but the simplest question I can come up with to answer is as follows:
If I have the following code:
float px[32768],py[32768],pz[32768];
float xref, yref, zref, deltax, deltay, deltaz;
initialize_with_random(px);
initialize_with_random(py);
initialize_with_random(pz);
for(i=0;i<32768-1;i++) {
xref=px[i];
yref=py[i];
zref=pz[i];
for(j=0;j<32768-1;j++ {
deltx=xref-px[j];
delty=yref-py[j];
deltz=zref-pz[j];
} }
What type of maximum theoretical speed up would I be able to see by going to SSE instructions in a situation where I have complete control over code (assembly, intrinsics, whatever) but no control over runtime environment other than architecture (i.e. it's a multi-user environment so I can't do anything about how the OS kernel assigns time to my particular process).
Right now I'm seeing a speed up of 3x with my code, when I would have thought using SSE would give me much more vector depth than the 3x speed up is indicating (presumably the 3x speed up tells me I have a 4x maximum theoretical throughput). (I've tried things such as letting deltx/delty/deltz be arrays in case the compiler wasn't smart enough to auto-promote them, but I still see only 3x speed up.) I'm using the intel C compiler with the appropriate compiler flags for vectorization, but no intrinsics obviously.
It depends on the CPU. But the theoretical max won't get above 4x. I don't know of a CPU which can execute more than one SSE instruction per clock cycle, which means that it can at most compute 4 values per cycle.
Most CPU's can do at least one floating point scalar instruction per cycle, so in this case you'd see a theoretical max of a 4x speedup.
But you'll have to look up the specific instruction throughput for the CPU you're running on.
A practical speedup of 3x is pretty good though.
I think you'd probably have to interleave the inner loop somehow. The 3-component vector is getting done at once, but that's only 3 operations at once. To get to 4, you'd do 3 components from the first vector, and 1 from the next, then 2 and 2, and so on. If you established some kind of queue that loads and processes the data 4 components at a time, then separate it after, that might work.
Edit: You could unroll the inner loop to do 4 vectors per iteration (assuming the array size is always a multiple of 4). That would accomplish what I said above.
Consider: How wide is a float? How wide is the SSEx instruction? The ratio should should give you some kind of reasonable upper bound.
It's also worth noting that out-of-order pipes play havok with getting good estimates of speedup.
You should consider loop tiling - the way you are accessing values in the inner loop is probably causing a lot of thrashing in the L1 data cache. It's not too bad, because everything probably still fits in the L2 at 384 KB, but there is easily an order of magnitude difference between an L1 cache hit and an L2 cache hit, so this could make a big difference for you.

Practical use of automatic vectorization?

Has anyone taken advantage of the automatic vectorization that gcc can do? In the real world (as opposed to example code)? Does it take restructuring of existing code to take advantage? Are there a significant number of cases in any production code that can be vectorized this way?
I have yet to see either GCC or Intel C++ automatically vectorize anything but very simple loops, even when given the code of algorithms that can (and were, after I manually rewrote them using SSE intrinsics) be vectorized.
Part of this is being conservative - especially when faced with possible pointer aliasing, it can be very difficult for a C/C++ compiler to 'prove' to itself that a vectorization would be safe, even if you as the programmer know that it is. Most compilers (sensibly) prefer to not optimize code rather than risking miscompiling it. This is one area where higher level languages have a real advantage over C, at least in theory (I say in theory since I'm not actually aware of any automatically vectorizing ML or Haskell compilers).
Another part of it is simply analytical limitations - most research in vectorization, I understand, is related to optimizing classical numerical problems (fluid dynamics, say) which was the bread and butter of most vector machines before a few years ago (when, between CUDA/OpenCL, Altivec/SSE, and the STI Cell, vector programming in various forms became widely available in commercial systems).
It's fairly unlikely that code written for a scalar processor in mind will be easy for a compiler to vectorize. Happily, many things you can do to make it easier for a compiler to understand how to vectorize it, like loop tiling and partial loop unrolling, also (tend to) help performance on modern processors even if the compiler doesn't figure out how to vectorize it.
It is hard to use in any business logic, but gives speed ups when you are processing volumes of data in the same way.
Good example is sound/video processing where you apply the same operation to every sample/pixel.
I have used VisualDSP for this, and you had to check the results after compiling - if it is really used where it should.
Vectorized instructions are not limited to Cell processors - most modern workstations-like CPU have them (PPC, x86 since pentium 3, Sparc, etc...). When used well for floating points operations, it can help quite a lot for very computing intensive tasks (filters, etc...). In my experience, automatic vectorization does not work so well.
You may have noticed that pretty much no-one actually knows how to make good use of GCC's Automatic Vectorization. If you search around the web to see people's comments, it always come to the idea that GCC allows you to enable automatic vectorization, but it extremely rarely makes actual use of it, and so if you want to use SIMD acceleration (eg: MMX, SSE, AVX, NEON, AltiVec), then you basically haveto figure out how to write it using compiler intrinsics or Assembly language code.
But the problem with intrinsics is that you effectively need to understand the Assembly language side of it and then also learn the Intrinsics method of describing what you want, which is likely to result in much less efficient code than if you wrote it in Assembly code (such as by a factor of 10x), because the compiler is still going to have trouble making good use of your intrinsic instructions!
For example, you might be using SIMD Intrinsics so that many operations can be performed in parallel at the same time, but your compiler will probably generate Assembly code that transfers the data between the SIMD registers and the normal CPU registers and back, effectively making your SIMD code run at a similar speed (or even slower) than normal code!
So basically:
If you want upto 100% speedups (2x
speed), then either buy the
official Intel/ARM compilers or convert some of your code to use SIMD C/C++ Intrinsics.
If you
want 1000% speedups (10x speed), then
write it in Assembly code using SIMD instructions by hand. Or if available on your hardware, use GPU acceleration instead such as OpenCL or Nvidia's CUDA SDK, since they can provide similar speedups in the GPU as SIMD does in the CPU.

Resources