Can I use SIMD for speeding up string manipulation? - c++

Are SIMD instructions built for vector numerical calculations only? Or does it lend itself well to a class of string manipulation tasks like, writing rows of data to a text file where the order of the rows does not matter? If so which APIs or libraries should I start with?

Yes! And this is actually done in high performance parsing libraries. One example: simdjson- a parser than can parse gigabytes of JSON per second. There's an About simdjson section in the readme, which has a link to a talk that goes over some of the implementation details.
SIMD instructions operate on numeric values, but once you're at that level, "text" is just numeric values, e.g. UTF-8 codepoints are just unsigned 8-bit integers, with plenty of SIMD support. Processing bitmaps is full of operations on multiple 8-bit unsigned integers in parallel, and it just so conveniently happens that this is so common that SIMD instruction sets cover these operations, and plenty of them are thus also usable for text processing.
I/O is so many orders of magnitude slower than the CPU
Not really. It is slower, but when the CPU has to do tasks that kill the streaming performance, such as branch mispredictions, cache misses, or wasting lots of speculative execution resources on dead-ends, the CPU can very easily not keep up with I/O. Modern network cards used for fast storage access or multi-machine communications can saturate the CPU's memory ports. All of them. And keep them that way. But that's state of the art and quite expensive at the moment (bonded 50 GBit links and such). Sequential, byte-at-a-time parser code is way slower than that.

Yes, especially for ASCII e.g. Convert a String In C++ To Upper Case. Or checking for valid UTF-8 (https://lemire.me/blog/2020/10/20/ridiculously-fast-unicode-utf-8-validation/), or checking if a string happens to be the ASCII subset of UTF-8. (If so, you know you have fixed-width characters which is very useful for other things.)
As Daniel Lemire reported, an early attempt at UTF-8 validation gave "a few CPU cycles per character." But with SIMD, he and collaborators were able to achieve ~1 instruction per byte, for net speeds of ~12GB/s. (vs. DRAM bandwidth of a Haswell desktop being ~25GB/s, or Skylake at 34GB/s with DDR4-2133).
Of course, most C libraries already have hand-written asm implementations of functions like strlen, strcpy, strcasecmp, strstr, etc. that use SIMD if it's a win (like on x86-64 where pmovmskb allows relatively efficient compare/branch on any/all SIMD compare results being true or false.) The first part of my answer on Why does glibc's strlen need to be so complicated to run quickly? has some links to hand-optimized asm that glibc actually uses on mainstream platforms, instead of the portable plain C fallback the question is asking about.
https://github.com/WojciechMula/sse4-strstr has a variety of strstr implementations. Substring searching is a much harder problem, with non-trivial algorithm choices as well as just brute-force. The SSE4.2 "string" instructions may help for that, but if not then SIMD vector compares definitely can for better brute-force building blocks.
(SSE4.2 "string" instructions like pcmpistri are definitely worse for memcmp / strcmp and strlen where plain SSE2 (or AVX2) is better. See How much faster are SSE4.2 string instructions than SSE2 for memcmp? and https://www.strchr.com/strcmp_and_strlen_using_sse_4.2)
You can even do cool tricks with looking up a shuffle control vector based on a vector compare bitmap, e.g. Fastest way to get IPv4 address from string or How to implement atoi using SIMD?.
Although I'm not sure the SIMD atoi is a win vs. scalar, especially for short numbers.
Naively I would say SIMD would not help since for long strings memory bandwidth would be the bottleneck. Why is this not the case?
DRAM bandwidth is really pretty good compared to modern CPU speeds, especially when the data comes in byte chunks, not 8-byte double chunks. And data is often hot in L3 cache after copying (e.g. from a read system call).
Even if data has to come from DRAM, modern desktop / laptop CPUs can load about 8 bytes per core clock cycle, within a factor of 2 of that anyway, especially if this core isn't competing with other bandwidth-intensive code on other cores. Good luck keeping up with that with byte-at-a-time scalar loops.
Besides, if you just did a read() system call to get the kernel to memcpy some data from a network buffer or pagecache into your process's memory, the data might still be hot in L3 cache, or even L2. Xeon CPUs can even DMA into L3 cache, or something like that. Aiming for memory bandwidth is a pretty low / unambitious goal, and a poor excuse for not fully optimizing a function if it actually gets use a lot.
Fewer instructions to process the same data lets out-of-order exec "see" farther ahead, and start demand-loads for later pages / cache lines earlier in cases where HW prefetch wouldn't (e.g. across page boundaries). And also better overlap the string processing with earlier / later independent work.
It can also be more hyperthreading-friendly, leaving the HT sibling core with better throughput if anything's running on it. (Maybe nothing if there aren't a lot of threads active). Also, if SIMD is efficient enough, it may save energy: tracking instructions through the pipeline is a large part of the cost, not the integer execution units themselves. Higher power while running, but finishing sooner, is good: race to sleep. CPUs save much more power when fully idle than when just running "cheap" instructions.

SIMD instructions are used on a very low level. Writing data to a text file is a much higher level, involving buffered I/O etc.
You might use SIMD, e.g., to convert a string from lower case to upper case. Wrapping SIMD into a library would be moot. You write the instructions yourself. Which also means that they are processor-specific (e.g. SSE variants on x86/AMD64).
For processing several rows of text in parallel, you might use micro-parallelization instead, e.g. offered by OpenMP or TBB.
However, if you stick to the example of writing to a the text file, we get to another territory of performance optimizations (I/O instead of computation).

Related

Can modern x86 hardware not store a single byte to memory?

Speaking of the memory model of C++ for concurrency, Stroustrup's C++ Programming Language, 4th ed., sect. 41.2.1, says:
... (like most modern hardware) the machine could not load or store anything smaller than a word.
However, my x86 processor, a few years old, can and does store objects smaller than a word. For example:
#include <iostream>
int main()
{
char a = 5;
char b = 25;
a = b;
std::cout << int(a) << "\n";
return 0;
}
Without optimization, GCC compiles this as:
[...]
movb $5, -1(%rbp) # a = 5, one byte
movb $25, -2(%rbp) # b = 25, one byte
movzbl -2(%rbp), %eax # load b, one byte, not extending the sign
movb %al, -1(%rbp) # a = b, one byte
[...]
The comments are by me but the assembly is by GCC. It runs fine, of course.
Obviously, I do not understand what Stroustrup is talking about when he explains that hardware can load and store nothing smaller than a word. As far as I can tell, my program does nothing but load and store objects smaller than a word.
The thoroughgoing focus of C++ on zero-cost, hardware-friendly abstractions sets C++ apart from other programming languages that are easier to master. Therefore, if Stroustrup has an interesting mental model of signals on a bus, or has something else of this kind, then I would like to understand Stroustrup's model.
What is Stroustrup talking about, please?
LONGER QUOTE WITH CONTEXT
Here is Stroustrup's quote in fuller context:
Consider what might happen if a linker allocated [variables of char type like] c and b in the same word in memory and (like most modern hardware) the machine could not load or store anything smaller than a word.... Without a well-defined and reasonable memory model, thread 1 might read the word containing b and c, change c, and write the word back into memory. At the same time, thread 2 could do the same with b. Then, whichever thread managed to read the word first and whichever thread managed to write its result back into memory last would determine the result....
ADDITIONAL REMARKS
I do not believe that Stroustrup is talking about cache lines. Even if he were, as far as I know, cache coherency protocols would transparently handle that problem except maybe during hardware I/O.
I have checked my processor's hardware datasheet. Electrically, my processor (an Intel Ivy Bridge) seems to address DDR3L memory by some sort of 16-bit multiplexing scheme, so I don't know what that's about. It is not clear to me that that has much to do with Stroustrup's point, though.
Stroustrup is a smart man and an eminent scientist, so I do not doubt that he is taking about something sensible. I am confused.
See also this question. My question resembles the linked question in several ways, and the answers to the linked question are also helpful here. However, my question goes also to the hardware/bus model that motivates C++ to be the way it is and that causes Stroustrup to write what he writes. I do not seek an answer merely regarding that which the C++ standard formally guarantees, but also wish to understand why the C++ standard would guarantee it. What is the underlying thought? This is part of my question, too.
TL:DR: On every modern ISA that has byte-store instructions (including x86), they're atomic and don't disturb surrounding bytes. (I'm not aware of any older ISAs where byte-store instructions could "invent writes" to neighbouring bytes either.)
The actual implementation mechanism (in non-x86 CPUs) is sometimes an internal RMW cycle to modify a whole word in a cache line, but that's done "invisibly" inside a core while it has exclusive ownership of the cache line so it's only ever a performance problem, not correctness. (And merging in the store buffer can sometimes turn byte-store instructions into an efficient full-word commit to L1d cache.)
About Stroustrup's phrasing
I don't think it's a very accurate, clear or useful statement. It would be more accurate to say that modern CPUs can't load or store anything smaller than a cache line. (Although that's not true for uncacheable memory regions, e.g. for MMIO.)
It probably would have been better just to make a hypothetical example to talk about memory models, rather than implying that real hardware is like this. But if we try, we can maybe find an interpretation that isn't as obviously or totally wrong, which might have been what Stroustrup was thinking when he wrote this to introduce the topic of memory models. (Sorry this answer is so long; I ended up writing a lot while guessing what he might have meant and about related topics...)
Or maybe this is another case of high-level language designers not being hardware experts, or at least occasionally making mis-statements.
I think Stroustrup is talking about how CPUs work internally to implement byte-store instructions. He's suggesting that a CPU without a well-defined and reasonable memory model might implement a byte-store with a non-atomic RMW of the containing word in a cache line, or in memory for a CPU without cache.
Even this weaker claim about internal (not externally visible) behaviour is not true for high-performance x86 CPUs. Modern Intel CPUs have no throughput penalty for byte stores, or even unaligned word or vector stores that don't cross a cache-line boundary. AMD is similar.
If byte or unaligned stores had to do a RMW cycle as the store committed to L1D cache, it would interfere with store and/or load instruction/uop throughput in a way we could measure with performance counters. (In a carefully designed experiment that avoids the possibility of store coalescing in the store buffer before commit to L1d cache hiding the cost, because the store execution unit(s) can only run 1 store per clock on current CPUs.)
However, some high performance designs for non-x86 ISAs do use an atomic RMW cycle to internally commit stores to L1d cache. Are there any modern CPUs where a cached byte store is actually slower than a word store? The cache line stays in MESI Exclusive/Modified state the whole time, so it can't introduce any correctness problems, only a small performance hit. This is very different from doing something that could step on stores from other CPUs. (The arguments below about that not happening still apply, but my update may have missed some stuff that still argues that atomic cache-RMW is unlikely.)
(On many non-x86 ISAs, unaligned stores are not supported at all, or are used more rarely than in x86 software. And weakly-ordered ISAs allow more coalescing in store buffers, so not as many byte store instructions actually result in single-byte commit to L1d. Without these motivations for fancy (power hungry) cache-access hardware, word RMW for scattered byte stores is an acceptable tradeoff in some designs.)
Alpha AXP, a high-performance RISC design from 1992, famously (and uniquely among modern non-DSP ISAs) omitted byte load/store instructions until Alpha 21164A (EV56) in 1996. Apparently they didn't consider word-RMW a viable option for implementing byte stores, because one of the cited advantages for implementing only 32-bit and 64-bit aligned stores was more efficient ECC for the L1D cache. "Traditional SECDED ECC would require 7 extra bits over 32-bit granules (22% overhead) versus 4 extra bits over 8-bit granules (50% overhead)." (#Paul A. Clayton's answer about word vs. byte addressing has some other interesting computer-architecture stuff.) If byte stores were implemented with word-RMW, you could still do error detection/correction with word-granularity.
Current Intel CPUs only use parity (not ECC) in L1D for this reason. (At least some older Xeons could run with L1d in ECC mode at half capacity instead of the normal 32KiB, as discussed on RWT. It's not clear if anything's changed, e.g. in terms of Intel now using ECC for L1d). See also this Q&A about hardware (not) eliminating "silent stores": checking the old contents of cache before the write to avoid marking the line dirty if it matched would require a RMW instead of just a store, and that's a major obstacle.
It turns out some high-perf pipelined designs do use atomic word-RMW to commit to L1d, despite it stalling the memory pipeline, but (as I argue below) it's much less likely that any do an externally-visible RMW to RAM.
Word-RMW isn't a useful option for MMIO byte stores either, so unless you have an architecture that doesn't need sub-word stores for IO, you'd need some kind of special handling for IO (like Alpha's sparse I/O space where word load/stores were mapped to byte load/stores so it could use commodity PCI cards instead of needing special hardware with no byte IO registers).
As #Margaret points out, DDR3 memory controllers can do byte stores by setting control signals that mask out other bytes of a burst. The same mechanisms that get this information to the memory controller (for uncached stores) could also get that information passed along with a load or store to MMIO space. So there are hardware mechanisms for really doing
a byte store even on burst-oriented memory systems, and it's highly likely that modern CPUs will use that instead of implementing an RMW, because it's probably simpler and is much better for MMIO correctness.
How many and what size cycles will be needed to perform longword transferred to the CPU shows how a ColdFire microcontroller signals the transfer size (byte/word/longword/16-byte line) with external signal lines, letting it do byte loads/stores even if 32-bit-wide memory was hooked up to its 32-bit data bus. Something like this is presumably typical for most memory bus setups (but I don't know). The ColdFire example is complicated by also being configurable to use 16 or 8-bit memory, taking extra cycles for wider transfers. But nevermind that, the important point is that it has external signaling for the transfer size, to tell the memory HW which byte it's actually writing.
Stroustrup's next paragraph is
"The C++ memory model guarantees that two threads of execution can update and access separate memory locations without interfering with each other. This is exactly what we would naively expect. It is the compiler’s job to protect us from the sometimes very strange and subtle behaviors of modern hardware. How a compiler and hardware combination achieves that is up to the compiler. ..."
So apparently he thinks that real modern hardware may not provide "safe" byte load/store. The people who design hardware memory models agree with the C/C++ people, and realize that byte store instructions would not be very useful to programmers / compilers if they could step on neighbouring bytes.
All modern (non-DSP) architectures except early Alpha AXP have byte store and load instructions, and AFAIK these are all architecturally defined to not affect neighbouring bytes. However they accomplish that in hardware, software doesn't need to care about correctness. Even the very first version of MIPS (in 1983) had byte and half-word loads/stores, and it's a very word-oriented ISA.
However, he doesn't actually claim that most modern hardware needs any special compiler support to implement this part of the C++ memory model, just that some might. Maybe he really is only talking about word-addressable DSPs in that 2nd paragraph (where C and C++ implementations often use 16 or 32-bit char as exactly the kind of compiler workaround Stroustrup was talking about.)
Most "modern" CPUs (including all x86) have an L1D cache. They will fetch whole cache lines (typically 64 bytes) and track dirty / not-dirty on a per-cache-line basis. So two adjacent bytes are pretty much exactly the same as two adjacent words, if they're both in the same cache line. Writing one byte or word will result in a fetch of the whole line, and eventually a write-back of the whole line. See Ulrich Drepper's What Every Programmer Should Know About Memory. You're correct that MESI (or a derivative like MESIF/MOESI) makes sure this isn't a problem. (But again, this is because hardware implements a sane memory model.)
A store can only commit to L1D cache while the line is in the Modified state (of MESI). So even if the internal hardware implementation is slow for bytes and takes extra time to merge the byte into the containing word in the cache line, it's effectively an atomic read modify write as long as it doesn't allow the line to be invalidated and re-acquired between the read and the write. (While this cache has the line in Modified state, no other cache can have a valid copy). See #old_timer's comment making the same point (but also for RMW in a memory controller).
This is easier than e.g. an atomic xchg or add from a register that also needs an ALU and register access, since all the HW involved is in the same pipeline stage, which can simply stall for an extra cycle or two. That's obviously bad for performance and takes extra hardware to allow that pipeline stage to signal that it's stalling. This doesn't necessarily conflict with Stroustrup's first claim, because he was talking about a hypothetical ISA without a memory model, but it's still a stretch.
On a single-core microcontroller, internal word-RMW for cached byte stores would be more plausible, since there won't be Invalidate requests coming in from other cores that they'd have to delay responding to during an atomic RMW cache-word update. But that doesn't help for I/O to uncacheable regions. I say microcontroller because other single-core CPU designs typically support some kind of multi-socket SMP.
Many RISC ISAs don't support unaligned-word loads/stores with a single instruction, but that's a separate issue (the difficulty is handling the case when a load spans two cache lines or even pages, which can't happen with bytes or aligned half-words). More and more ISAs are adding guaranteed support for unaligned load/store in recent versions, though. (e.g. MIPS32/64 Release 6 in 2014, and I think AArch64 and recent 32-bit ARM).
The 4th edition of Stroustrup's book was published in 2013 when Alpha had been dead for years. The first edition was published in 1985, when RISC was the new big idea (e.g. Stanford MIPS in 1983, according to Wikipedia's timeline of computing HW, but "modern" CPUs at that time were byte-addressable with byte stores. Cyber CDC 6600 was word-addressable and probably still around, but couldn't be called modern.
Even very word-oriented RISC machines like MIPS and SPARC have byte store and byte load (with sign or zero extension) instructions. They don't support unaligned word loads, simplifying the cache (or memory access if there is no cache) and load ports, but you can load any single byte with one instruction, and more importantly store a byte without any architecturally-visible non-atomic rewrite of the surrounding bytes. (Although cached stores can
I suppose C++11 (which introduces a thread-aware memory model to the language) on Alpha would need to use 32-bit char if targeting a version of the Alpha ISA without byte stores. Or it would have to use software atomic-RMW with LL/SC when it couldn't prove that no other threads could have a pointer that would let them write neighbouring bytes.
IDK how slow byte load/store instructions are in any CPUs where they're implemented in hardware but not as cheap as word loads/stores. Byte loads are cheap on x86 as long as you use movzx/movsx to avoid partial-register false dependencies or merging stalls. On AMD pre-Ryzen, movsx/movzx needs an extra ALU uop, but otherwise zero/sign extension is handled right in the load port on Intel and AMD CPUs.) The main x86 downside is that you need a separate load instruction instead of using a memory operand as a source for an ALU instruction (if you're adding a zero-extended byte to a 32-bit integer), saving front-end uop throughput bandwidth and code-size. Or if you're just adding a byte to a byte register, there's basically no downside on x86. RISC load-store ISAs always need separate load and store instructions anyway. x86 byte stores are no more expensive that 32-bit stores.
As a performance issue, a good C++ implementation for hardware with slow byte stores might put each char in its own word and use word loads/stores whenever possible (e.g. for globals outside structs, and for locals on the stack). IDK if any real implementations of MIPS / ARM / whatever have slow byte load/store, but if so maybe gcc has -mtune= options to control it.
That doesn't help for char[], or dereferencing a char * when you don't know where it might be pointing. (This includes volatile char* which you'd use for MMIO.) So having the compiler+linker put char variables in separate words isn't a complete solution, just a performance hack if true byte stores are slow.
PS: More about Alpha:
Alpha is interesting for a lot of reasons: one of the few clean-slate 64-bit ISAs, not an extension to an existing 32-bit ISA. And one of the more recent clean-slate ISAs, Itanium being another from several years later which attempted some neat CPU-architecture ideas.
From the Linux Alpha HOWTO.
When the Alpha architecture was introduced, it was unique amongst RISC architectures for eschewing 8-bit and 16-bit loads and stores. It supported 32-bit and 64-bit loads and stores (longword and quadword, in Digital's nomenclature). The co-architects (Dick Sites, Rich Witek) justified this decision by citing the advantages:
Byte support in the cache and memory sub-system tends to slow down accesses for 32-bit and 64-bit quantities.
Byte support makes it hard to build high-speed error-correction circuitry into the cache/memory sub-system.
Alpha compensates by providing powerful instructions for manipulating bytes and byte groups within 64-bit registers. Standard benchmarks for string operations (e.g., some of the Byte benchmarks) show that Alpha performs very well on byte manipulation.
Not only are x86 CPUs capable of reading and writing a single byte, all modern general purpose CPUs are capable of it. More importantly most modern CPUs (including x86, ARM, MIPS, PowerPC, and SPARC) are capable of atomically reading and writing single bytes.
I'm not sure what Stroustrup was referring to. There used to be a few word addressable machines that weren't capable of 8-bit byte addressing, like the Cray, and as Peter Cordes mentioned early Alpha CPUs didn't support byte loads and stores, but today the only CPUs incapable of byte loads and stores are certain DSPs used in niche applications. Even if we assume he means most modern CPUs don't have atomic byte load and stores this isn't true of most CPUs.
However, simple atomic loads and stores aren't of much use in multithreaded programming. You also typically need ordering guarantees and a way to make read-modify-write operations atomic. Another consideration is that while CPU a may have byte load and store instructions, compiler isn't required to use them. A compiler, for example, could still generate the code Stroustrup describes, loading both b and c using a single word load instruction as an optimization.
So while you do need a well defined memory model, if only so the compiler is forced to generate the code you expect, the problem isn't that modern CPUs aren't capable of loading or storing anything smaller than a word.
The author seems to be concerned about thread 1 and thread 2 getting into a situation where the read-modify-writes (not in software, the software does two separate instructions of a byte size, somewhere down the line logic has to do a read-modify-write) instead of the ideal read modify write read modify write, becomes a read read modify modify write write or some other timing such that both read the pre-modified version and the last one to write wins. read read modify modify write write, or read modify read modify write write or read modify read write modify write.
The concern is to start with 0x1122 and one thread wants to make it 0x33XX the other wants to make it 0xXX44, but with for example a read read modify modify write write you end up with 0x1144 or 0x3322, but not 0x3344
A sane (system/logic) design just doesn't have that problem certainly not for a general purpose processor like this, I have worked on designs with timing issues like this but that is not what we are talking about here, completely different system designs for different purposes. The read-modify-write does not span a long enough distance in a sane design, and x86s are sane designs.
The read-modify-write would happen very near the first SRAM involved (ideally L1 when running an x86 in a typical fashion with an operating system capable of running C++ compiled multi-threaded programs) and happen within a few clock cycles as the ram is at the speed of the bus ideally. And as Peter pointed out this is considered to be the whole cache line that experiences this, within the cache, not a read-modify-write between the processor core and the cache.
The notion of "at the same time" even with multi-core systems isn't necessarily at the same time, eventually you get serialized because performance isn't based on them being parallel from beginning to end, it is based on keeping the busses loaded.
The quote is saying variables allocated to the same word in memory, so that is the same program. Two separate programs are not going to share an address space like that. so
You are welcome to try this, make a multithreaded program that one writes to say address 0xnnn00000 the other writes to address 0xnnnn00001, each does a write, then a read or better several writes of the same value than one read, check the read was the byte they wrote, then repeats with a different value. Let that run for a while, hours/days/weeks/months. See if you trip up the system...use assembly for the actual write instructions to make sure it is doing what you asked (not C++ or any compiler that does or claims it will not put these items in the same word). Can add delays to allow for more cache evictions, but that reduces your odds of "at the same time" collisions.
Your example so long as you insure you are not sitting on two sides of a boundary (cache, or other) like 0xNNNNFFFFF and 0xNNNN00000, isolate the two byte writes to addresses like 0xNNNN00000 and 0xNNNN00001 have the instructions back to back and see if you get a read read modify modify write write. Wrap a test around it, that the two values are different each loop, you read back the word as a whole at whatever delay later as you desire and check the two values. Repeat for days/weeks/months/years to see if it fails. Read up on your processors execution and microcode features to see what it does with this instruction sequence and as needed create a different instruction sequence that tries to get the transactions initiated within a handful or so clock cycles on the far side of the processor core.
EDIT
the problem with the quotes is that this is all about language and the use of. "like most modern hardware" puts the whole of the topic/text in a touchy position, it is too vague, one side can argue all I have to do is find one case that is true to make all the rest true, likewise one side could argue if I find one case the all of the rest is not true. Using the word like kind of messes with that as a possible get out of jail free card.
The reality is that a significant percentage of our data is stored in DRAM in 8 bit wide memories, just that we don't access them as 8 bit wide normally we access 8 of them at a time, 64 bits wide. In some number of weeks/months/years/decades this statement will be incorrect.
The larger quote says "at the same time" and then says read ... first, write ... last, well first and last and at the same time don't make sense together, is it parallel or serial? The context as a whole is concerned about the above read read modify modify write write variations where you have one writing last and depending on when that one read determines if both modifications happened or not. Not about at the same time which "like most modern hardware" doesn't make sense things that start off actually parallel in separate cores/modules eventually get serialized if they are aiming at the same flip-flop/transistor in a memory, one eventually has to wait for the other to go first. Being physics based I don't see this being incorrect in the coming weeks/months/years.
This is correct. An x86_64 CPU, just like an original x86 CPU, is not able to read or write anything smaller than an (in this case 64-bit) word from rsp. to memory. And it will not typically read or write less than a whole cache line, though there are ways to bypass the cache, especially in writing (see below).
In this context, though, Stroustrup refers to potential data races (lack of atomicity on an observable level). This correctness issue is irrelevant on x86_64, because of the cache coherency protocol, which you mentioned. In other words, yes, the CPU is limited to whole word transfers, but this is transparently handled, and you as a programmer generally do not have to worry about it. In fact, the C++ language, starting from C++11, guarantees that concurrent operations on distinct memory locations have well-defined behavior, i.e. the one you'd expect. Even if the hardware did not guarantee this, the implementation would have to find a way by generating possibly more complex code.
That said, it can still be a good idea to keep the fact that whole words or even cache lines are always involved at the machine level in the back of your head, for two reasons.
First, and this is only relevant for people who write device drivers, or design devices, memory-mapped I/O may be sensitive to the way it is accessed. As an example, think of a device that exposes a 64-bit write-only command register in the physical address space. It may then be necessary to:
Disable caching. It is not valid to read a cache line, change a single word, and write back the cache line. Also, even if it were valid, there would still be a great risk that commands might be lost because the CPU cache is not written back soon enough. At the very least, the page needs to be configured as "write-through", which means writes take immediate effect. Therefore, an x86_64 page table entry contains flags that control the CPU's caching behavior for this page.
Ensure that the whole word is always written, on the assembly level. E.g. consider a case where you write the value 1 into the register, followed by a 2. A compiler, especially when optimizing for space, might decide to overwrite only the least significant byte because the others are already supposed to be zero (that is, for ordinary RAM), or it might instead remove the first write because this value appears to be immediately overwritten anyway. However, neither is supposed to happen here. In C/C++, the volatile keyword is vital to prevent such unsuitable optimizations.
Second, and this is relevant for almost any developer writing multi-threaded programs, the cache coherency protocol, while neatly averting disaster, can have a huge performance cost if it is "abused".
Here's a – somewhat contrived – example of a very bad data structure. Assume you have 16 threads parsing some text from a file. Each thread has an id from 0 to 15.
// shared state
char c[16];
FILE *file[16];
void threadFunc(int id)
{
while ((c[id] = getc(file[id])) != EOF)
{
// ...
}
}
This is safe because each thread operates on a different memory location. However, these memory locations would typically reside on the same cache line, or at most are split over two cache lines. The cache coherency protocol is then used to properly synchronize the accesses to c[id]. And herein lies the problem, because this forces every other thread to wait until the cache line becomes exclusively available before doing anything with c[id], unless it is already running on the core that "owns" the cache line. Assuming several, e.g. 16, cores, cache coherency will typically transfer the cache line from one core to another all the time. For obvious reasons, this effect is known as "cache line ping-pong". It creates a horrible performance bottleneck. It is the result of a very bad case of false sharing, i.e. threads sharing a physical cache line without actually accessing the same logical memory locations.
In contrast to this, especially if one took the extra step of ensuring that the file array resides on its own cache line, using it would be completely harmless (on x86_64) from a performance perspective because the pointers are only read from, most the time. In this case, multiple cores can "share" the cache line as read-only. Only when any core tries to write to the cache line, it has to tell the other cores that it is going to "seize" the cache line for exclusive access.
(This is greatly simplified, as there are different levels of CPU caches, and several cores might share the same L2 or L3 cache, but it should give you a basic idea of the problem.)
Not sure what Stroustrup meant by "WORD".
Maybe it is the minimum size of memory storage of the machine?
Anyway not all machines were created with 8bit (BYTE) resolution.
In fact I recommend this awesome article by Eric S. Raymond describing some of the history of computers:
http://www.catb.org/esr/faqs/things-every-hacker-once-knew/
"... It used also to be generally known that 36-bit architectures
explained some unfortunate features of the C language. The original
Unix machine, the PDP-7, featured 18-bit words corresponding to
half-words on larger 36-bit computers. These were more naturally
represented as six octal (3-bit) digits."
Stroustrup is not saying that no machine can perform loads and stores smaller than their native word size, he is saying that a machine couldn't.
While this seems surprising at first, it's nothing esoteric.
For starter, we will ignore the cache hierarchy, we will take that into account later.
Assume there are no caches between the CPU and the memory.
The big problem with memory is density, trying to put more bits possible into the smallest area.
In order to achieve that it is convenient, from an electrical design point of view, to expose a bus as wider as possible (this favours the reuse of some electrical signals, I haven't looked at the specific details though).
So, in architecture where big memories are needed (like the x86) or a simple low-cost design is favourable (for example where RISC machines are involved), the memory bus is larger than the smallest addressable unit (typically the byte).
Depending on the budget and legacy of the project the memory can expose a wider bus alone or along with some sideband signals to select a particular unit into it.
What does this mean practically?
If you take a look at the datasheet of a DDR3 DIMM you'll see that there are 64 DQ0–DQ63 pins to read/write the data.
This is the data bus, 64-bit wide, 8 bytes at a time.
This 8 bytes thing is very well founded in the x86 architecture to the point that Intel refers to it in the WC section of its optimisation manual where it says that data are transferred from the 64 bytes fill buffer (remember: we are ignoring the caches for now, but this is similar to how a cache line gets written back) in bursts of 8 bytes (hopefully, continuously).
Does this mean that the x86 can only write QWORDS (64-bit)?
No, the same datasheet shows that each DIMM has the DM0–DM7 ,DQ0–DQ7 and DQS0–DQS7 signals to mask, direct and strobe each of the 8 bytes in the 64-bit data bus.
So x86 can read and write bytes natively and atomically.
However, now it's easy to see that this could not be the case for every architecture.
For instance, the VGA video memory was DWORD (32-bit) addressable and making it fit in the byte addressable world of the 8086 led to the messy bit-planes.
In general specific purpose architecture, like DSPs, could not have a byte addressable memory at the hardware level.
There is a twist: we have just talked about the memory data bus, this is the lowest layer possible.
Some CPUs can have instructions that build a byte addressable memory on top of a word addressable memory.
What does that mean?
It's easy to load a smaller part of a word: just discard the rest of the bytes!
Unfortunately, I can't recall the name of the architecture (if it even existed at all!) where the processor simulated a load of an unaligned byte by reading the aligned word containing it and rotating the result before saving it in a register.
With stores, the matter is more complex: if we can't simply write the part of the word that we just updated we need to write the unchanged remaining part too.
The CPU, or the programmer, must read the old content, update it and write it back.
This is a Read-Modify-Write operation and it is a core concept when discussing atomicity.
Consider:
/* Assume unsigned char is 1 byte and a word is 4 bytes */
unsigned char foo[4] = {};
/* Thread 0 Thread 1 */
foo[0] = 1; foo[1] = 2;
Is there a data race?
This is safe on x86 because they can write bytes, but what if the architecture cannot?
Both threads would have to read the whole foo array, modify it and write it back.
In pseudo-C this would be
/* Assume unsigned char is 1 byte and a word is 4 bytes */
unsigned char foo[4] = {};
/* Thread 0 Thread 1 */
/* What a CPU would do (IS) What a CPU would do (IS) */
int tmp0 = *((int*)foo) int tmp1 = *((int*)foo)
/* Assume little endian Assume little endian */
tmp0 = (tmp0 & ~0xff) | 1; tmp1 = (tmp1 & ~0xff00) | 0x200;
/* Store it back Store it back */
*((int*)foo) = tmp0; *((int*)foo) = tmp1;
We can now see what Stroustrup was talking about: the two stores *((int*)foo) = tmpX obstruct each other, to see this consider this possible execution sequence:
int tmp0 = *((int*)foo) /* T0 */
tmp0 = (tmp0 & ~0xff) | 1; /* T1 */
int tmp1 = *((int*)foo) /* T1 */
tmp1 = (tmp1 & ~0xff00) | 0x200; /* T1 */
*((int*)foo) = tmp1; /* T0 */
*((int*)foo) = tmp0; /* T0, Whooopsy */
If the C++ didn't have a memory model these kinds of nuisances would have been implementation specific details, leaving the C++ a useless programming language in a multithreading environment.
Considering how common is the situation depicted in the toy example, Stroustrup stressed out the importance of a well-defined memory model.
Formalizing a memory model is hard work, it's an exhausting, error-prone and abstract process so I also see a bit of pride in the words of Stroustrup.
I have not brushed up on the C++ memory model but updating different array elements is fine.
That's a very strong guarantee.
We have left out the caches but that doesn't really change anything, at least for the x86 case.
The x86 writes to memory through the caches, the caches are evicted in lines of 64 bytes.
Internally each core can update a line at any position atomically unless a load/store crosses a line boundary (e.g. by writing near the end of it).
This can be avoided by naturally aligning data (can you prove that?).
In a multi-code/socket environment, the cache coherency protocol ensures that only a CPU at a time is allowed to freely write to a cached line of memory (the CPU that has it in the Exclusive or Modified state).
Basically, the MESI family of protocol use a concept similar to locking found the DBMSs.
This has the effect, for the writing purpose, of "assigning" different memory regions to different CPUs.
So it doesn't really affect the discussion of above.

How to measure read/cycle or instructions/cycle?

I want to thoroughly measure and tune my C/C++ code to perform better with caches on a x86_64 system. I know how to measure time with a counter (QueryPerformanceCounter on my Windows machine) but I'm wondering how would one measure the instructions per cycle or reads/write per cycle with respect to the working set.
How should I proceed to measure these values?
Modern processors (i.e., those not very constrained that are less than some 20 years old) are superscalar, i.e., they execute more than one instruction at a time (given correct instruction ordering). Latest x86 processors translate the CISC instructions into internal RISC instructions, reorder them and execute the result, have even several regster banks so instructions using "the same registers" can be done in parallel. There isn't any reasonable way to define the "time the instruction execution takes" today.
The current CPUs are much faster than memory (a few hundred instructions is the typical cost of accessing memory), they are all heavily dependent on cache for performance. And then you have all kinds of funny effects of cores sharing (or not) parts of cache, ...
Tuning code for maximal performance starts with the software architecture, goes on to program organization, algorithm and data structure selection (here a modicum of cache/virtual memory awareness is useful too), careful programming and (as te most extreme measures to squeeze out the last 2% of performance) considerations like the ones you mention (and the other favorite, "rewrite in assembly"). And the ordering is that one because the first levels give more performance for the same cost. Measure before digging in, programmers are notoriously unreliable in finding bottlenecks. And consider the cost of reorganizing code for performance, both in the work itself, in convincing yourself this complex code is correct, and maintenance. Given the relative costs of computers and people, extreme performance tuning rarely makes any sense (perhaps for heavily travelled code paths in popular operating systems, in common code paths generated by a compiler, but almost nowhere else).
If you are really interested in where your code is hitting cache and where it is hitting memory, and the processor is less than about 10-15 years old in its design, then there are performance counters in the processor. You need driver level software to access these registers, so you probably don't want to write your own tools for this. Fortunately, you don't have to.
There is tools like VTune from Intel, CodeAnalyst from AMD and oprofile for Linux (works with both AMD and Intel processors).
There are a whole range of different registers that count the number of instructions actually completed, the number of cycles the processor is waiting for . You can also get a count of things like "number of memory reads", "number of cache misses", "number of TLB misses", "number of FPU instructions".
The next, more tricky part, is of course to try to fix any of these sort of issues, and as mentioned in another answer, programmers aren't always good at tweaking these sort of things - and it's certainly time consuming, not to mention that what works well on processor model X will not necessarily run fast on model Y (there were some tuning tricks for early Pentium 4 that works VERY badly on AMD processors - if on the other hand, you tune that code for AMD processors of that age, you get code that runs well on the same generation Intel processor too!)
You might be interested in the rdtsc x86 instruction, which reads a relative number of cycles.
See http://www.fftw.org/cycle.h for an implementation to read the counter in many compilers.
However, I'd suggest simply measuring using QueryPerformanceCounter. It is rare that the actual number of cycles is important, to tune code you typically only need to be able to compare relative time measurements, and rdtsc has many pitfalls (though probably not applicable to the situation you described):
On multiprocessor systems, there is not a single coherent cycle counter value.
Modern processors often adjust the frequency, changing the rate of change in time with respect to the rate of change in cycles.

Determine Values AND/OR Address of Values in CPU Cache

Is there a way to determine exactly what values, memory addresses, and/or other information currently resides in the CPU cache (L1, L2, etc.) - for current or all processes?
I've been doing quite a bit a reading which shows how to optimize programs to utilize the CPU cache more effectively. However, I'm looking for a way to truly determine if certain approaches are effective.
Bottom line: is it possible to be 100% certain what does and does not make it into the CPU cache.
Searching for this topic returns several results on how to determine the cache size, but not contents.
Edit: To clarify some of the comments below: Since software would undoubtedly alter the cache, do CPU manufactures have a tool / hardware diagnostic system (built-in) which provides this functionality?
Without using specialized hardware, you cannot directly inspect what is in the CPU cache. The act of running any software to inspect the CPU cache would alter the state of the cache.
The best approach I have found is simply to identify real hot spots in your application and benchmark alternative algorithms on hardware the code will run on in production (or on a range of likely hardware if you do not have control over the production environment).
In addition to Eric J.'s answer, I'll add that while I'm sure the big chip manufacturers do have such tools it's unlikely that such a "debug" facility would be made available to regular mortals like you and I, but even if it were, it wouldn't really be of much help.
Why? It's unlikely that you are having performance issues that you've traced to cache and which cannot be solved using the well-known and "common sense" techniques for maintaining high cache-hit ratios.
Have you really optimized all other hotspots in the code and poor cache behavior by the CPU is the problem? I very much doubt that.
Additionally, as food for thought: do you really want to optimize your program's behavior to only one or two particular CPUs? After all, caching algorithms change all the time, as do the parameters of the caches, sometimes dramatically.
If you have a relatively modern processor running Windows then take a look at
http://software.intel.com/en-us/articles/intel-performance-counter-monitor-a-better-way-to-measure-cpu-utilization
and see if that might provide some of what you are looking for.
To optimize for one specific CPU cache size is usually in vain since this optimization will break when your assumptions about the CPU cache sizes are wrong when you execute on a different CPU.
But there is a way out there. You should optimize for certain access patterns to allow the CPU to easily predict what memory locations should be read next (the most obvious one is a linear increasing read). To be able to fully utilize a CPU you should read about cache oblivious algorithms where most of them follow a divide and conquer strategy where a problem is divided into sub parts to a certain extent until all memory accesses fit completly into the CPU cache.
It is also noteworthy to mention that you have a code and data cache which are separate. Herb Sutter has a nice video online where he talks about the CPU internals in depth.
The Visual Studio Profiler can collect CPU counters dealing with memory and L2 counters. These options are available when you select instrumentation profiling.
Intel has also a paper online which talks in greater detail about these CPU counters and what the task manager of Windows and Linux do show you and how wrong it is for todays CPUs which do work internally asynchronous and parallel at many diffent levels. Unfortunatley there is no tool from intel to display this stuff directly. The only tool I do know is the VS profiler. Perhaps VTune has similar capabilities.
If you have gone this far to optimize your code you might look as well into GPU programming. You need at least a PHD to get your head around SIMD instructions, cache locality, ... to get perhaps a factor 5 over your original design. But by porting your algorithm to a GPU you get a factor 100 with much less effort ony a decent graphics card. NVidia GPUs which do support CUDA (all today sold cards do support it) can be very nicely programmed in a C dialect. There are even wrapper for managed code (.NET) to take advantage of the full power of GPUs.
You can stay platform agnostic by using OpenCL but NVidia OpenCL support is very bad. The OpenCL drivers are at least 8 times slower than its CUDA counterpart.
Almost everything you do will be in the cache at the moment when you use it, unless you are reading memory that has been configured as "uncacheable" - typically, that's frame buffer memory of your graphics card. The other way to "not hit the cache" is to use specific load and store instructions that are "non-temporal". Everything else is read into the L1 cache before it reaches the target registers inside the CPU itself.
For nearly all cases, CPU's do have a fairly good system of knowing what to keep and what to throw away in the cache, and the cache is nearly always "full" - not necessarily of useful stuff, if, for example you are working your way through an enormous array, it will just contain a lot of "old array" [this is where the "non-temporal" memory operations come in handy, as they allow you to read and/or write data that won't be stored in the cache, since next time you get back to the same point, it won't be in the cache ANYWAYS].
And yes, processors usually have special registers [that can be accessed in kernel drivers] that can inspect the contents of the cache. But they are quite tricky to use without at the same time losing the content of the cache(s). And they are definitely not useful as "how much of array A is in the cache" type checking. They are specifically for "Hmm, it looks like cache-line 1234 is broken, I'd better read the cached data to see if it's really the value it should be" when processors aren't working as they should.
As DanS says, there are performance counters that you can read from suitable software [need to be in the kernel to use those registers too, so you need some sort of "driver" software for that]. In Linux, there's "perf". And AMD has a similar set of performance counters that can be used to find out, for example "how many cache misses have we had over this period of time" or "how many cache hits in L" have we had, etc.

C++ cache aware programming

is there a way in C++ to determine the CPU's cache size? i have an algorithm that processes a lot of data and i'd like to break this data down into chunks such that they fit into the cache. Is this possible?
Can you give me any other hints on programming with cache-size in mind (especially in regard to multithreaded/multicore data processing)?
Thanks!
According to "What every programmer should know about memory", by Ulrich Drepper you can do the following on Linux:
Once we have a formula for the memory
requirement we can compare it with the
cache size. As mentioned before, the
cache might be shared with multiple
other cores. Currently {There
definitely will sometime soon be a
better way!} the only way to get
correct information without hardcoding
knowledge is through the /sys
filesystem. In Table 5.2 we have seen
the what the kernel publishes about
the hardware. A program has to find
the directory:
/sys/devices/system/cpu/cpu*/cache
This is listed in Section 6: What Programmers Can Do.
He also describes a short test right under Figure 6.5 which can be used to determine L1D cache size if you can't get it from the OS.
There is one more thing I ran across in his paper: sysconf(_SC_LEVEL2_CACHE_SIZE) is a system call on Linux which is supposed to return the L2 cache size although it doesn't seem to be well documented.
C++ itself doesn't "care" about CPU caches, so there's no support for querying cache-sizes built into the language. If you are developing for Windows, then there's the GetLogicalProcessorInformation()-function, which can be used to query information about the CPU caches.
Preallocate a large array. Then access each element sequentially and record the time for each access. Ideally there will be a jump in access time when cache miss occurs. Then you can calculate your L1 Cache. It might not work but worth trying.
read the cpuid of the cpu (x86) and then determine the cache-size by a look-up-table. The table has to be filled with the cache sizes the manufacturer of the cpu publishes in its programming manuals.
Depending on what you're trying to do, you might also leave it to some library. Since you mention multicore processing, you might want to have a look at Intel Threading Building Blocks.
TBB includes cache aware memory allocators. More specifically, check cache_aligned_allocator (in the reference documentation, I couldn't find any direct link).
Interestingly enough, I wrote a program to do this awhile ago (in C though, but I'm sure it will be easy to incorporate in C++ code).
http://github.com/wowus/CacheLineDetection/blob/master/Cache%20Line%20Detection/cache.c
The get_cache_line function is the interesting one, which returns the location of right before the biggest spike in timing data of array accesses. It correctly guessed on my machine! If anything else, it can help you make your own.
It's based off of this article, which originally piqued my interest: http://igoro.com/archive/gallery-of-processor-cache-effects/
You can see this thread: http://software.intel.com/en-us/forums/topic/296674
The short answer is in this other thread:
On modern IA-32 hardware, the cache line size is 64. The value 128 is
a legacy of the Intel Netburst Microarchitecture (e.g. Intel Pentium
D) where 64-byte lines are paired into 128-byte sectors. When a line
in a sector is fetched, the hardware automatically fetches the other
line in the sector too. So from a false sharing perspective, the
effective line size is 128 bytes on the Netburst processors. (http://software.intel.com/en-us/forums/topic/292721)
IIRC, GCC has a __builtin_prefetch hint.
http://gcc.gnu.org/onlinedocs/gcc-3.3.6/gcc/Other-Builtins.html
has an excellent section on this. Basically, it suggests:
__builtin_prefetch (&array[i + LookAhead], rw, locality);
where rw is a 0 (prepare for read) or 1 (prepare for a write) value, and locality uses the number 0-3, where zero is no locality, and 3 is very strong locality.
Both are optional. LookAhead would be the number of elements to look ahead to. If memory access were 100 cycles, and the unrolled loops are two cycles apart, LookAhead could be set to 50 or 51.
There are two cases that need to be distinguished. Do you need to know the cache sizes at compile time or at runtime?
Determining the cache-size at compile-time
For some applications, you know the exact architecture that your code will run on, for example, if you can compile the code directly on the host machine. In that case, simplify looking up the size and hard-coding it is an option (could be automated in the build system). On most machines today, the L1 cache line should be 64 bytes.
If you want to avoid that complexity or if you need to support compilation on unknown architectures, you can use the C++17 feature std::hardware_constructive_interference_size as a good fallback. It will provide a compile-time estimation for the cache line, but be aware of its limitations. Note that the compiler cannot guess perfectly when it creates the binary, as the size of the cache-line is, in general, architecture dependent.
Determining the cache-size at runtime
At runtime, you have the advantage that you know the exact machine, but you will need platform specific code to read the information from the OS. A good starting point is the code snippet from this answer, which supports the major platforms (Windows, Linux, MacOS). In a similar fashion, you can also read the L2 cache size at runtime.
I would advise against trying to guess the cache line by running benchmarks at startup and measuring which one performed best. It might well work, but it is also error-prone if the CPU is used by other processes.
Combining both approaches
If you have to ship one binary and the machines that it will later run on features a range of different architectures with varying cache sizes, you could create specialized code parts for each cache size, and then dynamically (at application startup) choose the best fitting one.
The cache will usually do the right thing. The only real worry for normal programmer is false sharing, and you can't take care of that at runtime because it requires compiler directives.

Overhead of casting double to float?

So I have megabytes of data stored as doubles that need to be sent over a network... now I don't need the precision that a double offers, so I want to convert these to a float before sending them over the network. What is the overhead of simply doing:
float myFloat = (float)myDouble;
I'll be doing this operation several million times every few seconds and don't want to slow anything down. Thanks
EDIT: My platform is x64 with Visual Studio 2008.
EDIT 2: I have no control over how they are stored.
As Michael Burr said, while the overhead strongly depends on your platform, the overhead is definitely less than the time needed to send them over the wire.
a rough estimate:
800MBit/s payload on a excellent Gigabit wire, 25M-floats/second.
On a 2GHz single core, that gives you a whopping 80 clock cycles for each value converted to break even - anythign less, and you will save time. That should be more than enough on all architectures :)
A simple load-store cycle (barring all caching delays) should be below 5 cycles per value. With instruction interleaving, SIMD extensions and/or parallelizing on multiple cores, you are likely to do multiple conversions in a single cycle.
Also, the receiver will be happy having to handle only half the data. Remember that memory access time is nonlinear.
The only thing arguing against the conversion would be is if the transfer should have minimal CPU load: a modern architecture could transfer the data from disk/memory to bus without CPU intervention. However, with above numbers I'd say that doesn't matter in practice.
[edit]
I checked some numbers, the 387 coprocessor would indeed have taken around 70 cycles for a load-store cycle. On the initial pentium, you are down to 3 cycles without any parallelization.
So, unless you run a gigabit network on a 386...
It's going to depend on your implementation of C++ libraries. Test it and see.
Even if it does take time this will not be the slow point in your application.
Your FPU can do the conversion a lot quicker than it can send network traffic (so the bottleneck here will more than likely be the write to the socket).
But as with al things like this measure it and see.
Personally I don't think any time spent here will affect the real time spent sending the data.
Assuming that you're talking about a significant number of packets to ship the data (a reasonable assumption if you're sending millions of values) casting the doubles to float will likely reduce the number of network packets by about half (assuming sizeof(double)==8 and sizeof(float)==4).
Almost certainly the savings in network traffic will dominate whatever time is spent performing the conversion. But as everyone says, measuring some tests will be the proof of the pudding.
Bearing in mind that most compilers deal with doubles a lot more efficiently than floats -- many promote float to double before performing operations on them -- I'd consider taking the block of data, ZIPping/compressing it, then sending the compressed block across. Depending on what your data looks like, you could get 60-90% compression, vs. the 50% you'd get converting 8-byte values to four bytes.
You don't have any choice but to measure them yourself and see. You could use timers to measure them. Looks like some has already implemented a neat C++ timer class
I think this cast is a lot cheaper than you think since it doesn't really involve any kind of calculation. In fact, it's just bitshifting to get rid of some of the digits of exponent and mantissa.
It will also depend on the CPU and what floating point support it has. In the bad old days (1980s), processors supported integer operations only. Floating point math had to be emulated in software. A separate chip for floating point (a coprocessor) could be bought separately.
Modern CPUs now have SIMD instructions, so large amounts of floating point data can be processed at once. These instructions include MMX, SSE, 3DNow! and the like. Your compiler may know how to make use of these instructions, but you may need to write your code in a particular way, and turn on the right options.
Finally, the fastest way to process floating point data is in a video card. A fairly new language called OpenCL lets you send tasks to the video card to be processed there.
It all depends on how much performance you need.