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  2. Exactly how “fast” are modern CPUs?

Exactly how “fast” are modern CPUs?

由 南笙酒味 提交于 2019-11-29 21:48:41

Modern processors such as Core 2 Duo that you mention are both superscalar and pipelined. They have multiple execution units per core and are actually working on more than one instruction at a time per core; this is the superscalar part. The pipelined part means that there is a latency from when an instruction is read in and "issued" to when it completes execution and this time varies depending on the dependencies between that instruction and the others moving through the other execution units at the same time. So, in effect, the timing of any given instruction varies depending on what is around it and what it is depending on. This means that a given instruction has sort of a best case and worst case execution time based on a number of factors. Because of the multiple execution units you can actually have more than one instruction completing execution per core clock, but sometimes there is several clocks between completions if the pipeline has to stall waiting for memory or dependencies in the pipelines.

All of the above is just from the view of the CPU core itself. Then you have interactions with the caches and contention for bandwidth with the other cores. The Bus Interface Unit of the CPU deals with getting instructions and data fed into the core and putting results back out of the core through the caches to memory.

Rough order of magnitude rules of thumb to be taken with a grain of salt:

  • Register to Register operations take 1 core clock to execute. This should generally be conservative especially as more of these appear in sequence.
  • Memory related load and store operations take 1 memory bus clock to execute. This should be very conservative. With a high cache hit rate it will be more like 2 CPU bus clocks which is the clock rate of the bus between the CPU core and the cache, but not necessarily the core's clock.
HUAGHAGUAH

It is nearly impossible to provide accurate timing information that you are expecting in a way that will be USEFUL to you.

The following concepts affect instruction timing; some can vary from moment to moment:

  • Micro-op decomposition
  • Operation pipelining
  • Super-scalar execution
  • Out of order execution
  • SMT / SMP execution
  • Floating point mode
  • Branch prediction / pre-fetch
  • Cache latency
  • Memory latency
  • Clock speed throttling
  • etc

Consult a book on modern computer architecture if you need any further explanation on the above concepts.

The best way to measure the speed of your code is (surprise!) to measure the speed of your code running the same workload and under the same conditions as you expect it to when "in the real world".

Using a description largely based on Intel Pentium architecture, to cut a very very long story short:

  • the processor has a number of "execution units" that can perform different types of 'micro-ops'; instructions may be split into several micro-ops
  • the different execution units essentially run in parallel
  • each micro-op ties up the corresponding execution unit for a certain number of clock cycles so meanwhile no other instruction can use that execution unit: e.g. "floating point add" may tie up the "FP execute" unit for 2 clock cycles
  • execution units are grouped by "port", and each clock cycle, a new micro-op can be sent to each port (assuming the relevant execution unit is free at that moment); some units can also be sent an "extra op" halfway through the cycle; so each clock cycle, a certain number of ops can start executing;
  • the processor can re-order micro-ops where this doesn't break dependencies (or where the result can still be reconstructed) to take advantage of which execution units are free at a given moment
  • so instructions can be executing in parallel, but which parts of which instructions are executing at any one time is quite a complex situation
  • the overall time for a given instruction thus depends on how long it had to "wait" for the necessary execution units to become available, the actual time that those ops spent running on the given units, plus any extra time required to "tie up the result"

Since the timing of an instruction depends on the surrounding instructions, in practice, it's usually best to time a representative piece of code than try and worry about individual instructions. However:

  • Intel (and presumably other manufacturers) publish a list of instruction throughput and latency timings
  • the throughput is the number of clock cycles actually needed on the relevant execution unit(s)
  • the latency is a "worst case" number of clock cycles required, once an instruction starts executing, before the result of that execution is available as input to another instruction

So for example, if, say, floating point add and multiply instructions each have a throughput of 2 and a latency of 5 (actually, for multiply it's a bit greater I think), that means that adding a register to itself or multiplying it by itself will likely take two clock cycles (since there are no other dependent values), whereas adding it the result of a previous multiplication will take something like or a bit less than 2+5 clock cycles, depending where you start/finish timing, and on all sorts of other things. (During some of those clock cycles, another add/multiply operation could be taking place, so it's arguable how many cycles you actually attribute to the individual add/mutliply instructions anyway...)

Oh, and just as a concrete example. For following Java code

public void runTest(double[] data, double randomVal) {
  for (int i = data.length-1; i >= 0; i--) {
    data[i] = data[i] + randomVal;
  }
}

Hotspot 1.6.12 JIT-compiles the inner loop sequence to the following Intel code, consisting of a load-add-store for each position in the array (with 'randomVal' being held in XMM0a in this case):

  0b3     MOVSD  XMM1a,[EBP + #16]
  0b8     ADDSD  XMM1a,XMM0a
  0bc     MOVSD  [EBP + #16],XMM1a
  0c1     MOVSD  XMM1a,[EBP + #8]
  0c6     ADDSD  XMM1a,XMM0a
  0ca     MOVSD  [EBP + #8],XMM1a
  ...

each group of load-add-store appears to take 5 clock cycles.

It's not that simple. The timing for your two instructions won't help you gauge performance of a larger set of instructions much. That's because modern processors can execute many operations in parallel, and have large caches so "moving a value to memory" happens at a time quite removed from the instruction's execution.

So, best case is zero (when executed in parallel with other instructions). But how does that help you?

This web page shows some benchmarks, including some %MIPS/MHz results. As you can see, on many benchmarks there are multiple instructions executed per clock cycle. The charts also show the effects of cache size and memory speed.

Modern processors do even more tricky things.

Out-of-order execution. If it is possible to do so without affecting correct behavior, the processors may execute instructions in a different order than they are listed in your program. This can hide the latency of long-running instructions.

Register renaming. Processors often have more physical registers than addressable registers in their instruction set (so-called "architectural" registers). This can be either for backward compatibility, or simply to enable efficient instruction encodings. As a program runs, the processor will "rename" the architectural registers it uses to whatever physical registers are free. This allows the processor to realize more parallelism than existed in the original program.

For instance, if you have a long sequence of operations on EAX and ECX, followed by instructions that re-initialize EAX and ECX to new values and perform another long sequence of operations, the processor can use different physical registers for both tasks, and execute them in parallel.

The Intel P6 microarchitecture does both out-of-order execution and register renaming. The Core 2 architecture is the latest derivative of the P6.

To actually answer your question - it is basically impossible for you to determine performance by hand in the face of all these architectural optimizations.

The kind of prediction you're asking for is hopeless.

If you want a rule of thumb, here are some rules of thumb:

  • In the time it takes to get a word from level 2 cache, a processor can execute at least 10 instructions. So worry about memory access, not instruction counts---computation in registers is almost free.

  • In the time it takes to get a word from RAM, a processor can execute thousands of instructions (this number varies by a couple of order of magnitude depending on the details of your hardware). Make sure this happens only on a cold cache; otherwise nothing else matters.

  • If you're running on x86 CPUs, there aren't enough registers. Try not to have more than 5 live variables in your code at any moment. Or better yet, move to AMD64 (x86_64) and double the number of registers. With 16 registers, and parameters passed in registers, you can quit worrying about registers.

There was a time when every year I would ask an architect what rules of thumb I should use to predict the cost of the code my compilers generate. I've stopped, because the last time I received a useful answer was in 1999. (The answer was "make sure your loops fit in the reorder buffer". All those who know what a reorder buffer is may now raise your hands. Bonus points if you can discover the size of the reorder buffer on any computer you are currently using.)

This only answers part of your question, but I found this table from Wikipedia on locality of reference helpful. It describes the speed of access to and amount of memory in different levels of the memory hierarchy, using approximate 2006 times:

  • CPU registers (8-32 registers) – immediate access (0-1 clock cycles)
  • L1 CPU caches (32 KiB to 128 KiB) – fast access (3 clock cycles)
  • L2 CPU caches (128 KiB to 12 MiB) – slightly slower access (10 clock cycles)
  • Main physical memory (RAM) (256 MiB to 4 GiB) – slow access (100 clock cycles)
  • Disk (file system) (1 GiB to 1 TiB) – very slow (10,000,000 clock cycles)
  • Remote Memory (such as other computers or the Internet) (Practically unlimited) – speed varies

You can download the Intel 64 and IA-32 manuals here.

But what you really need is the stuff from Agner Fog.

He has a lot of additional infos, for example his manual "Instruction tables: Lists of instruction latencies, throughputs and micro-operation breakdowns for Intel and AMD CPUs".

Or test programs for counting clock cycles (he uses the time stamp counter).

A lot of good answers on this thread already, but one topic is so far unmentioned: branch misprediction.

Because all modern processors are pipelined, when the instruction decoder runs into an instruction like "jump if equal", it has no idea which way the instruction will jump, and so it just guesses. It then continues feeding instructions into the pipeline based on that guess. If it made the correct prediction, the thruput and latency of the jump instruction is essentially zero. If it makes the wrong guess, the thruput and latency of the same jump instruction could be 50 or a 100 cycles.

Note that the same instruction can have the "zero cost" the first time it's executed in a loop and the really huge cost the next time the same instruction is executed!

All you need is in the appropriate CPU manuals. Both AMD and Intel have PDF's available on their website describing the latencies of every instruction.

Just keep in mind the complexity of modern CPU's. They don't execute one instruction at a time, they can load 3-4 instructions per cycle, and almost all instructions are pipelined so when the next instructions are loaded, the current ones are nowhere near finished. It also reorders instructions to allow for a more efficient scheduling. A modern CPU can easily have 50 instructions in progress at a time.

So you're asking the wrong question. The time taken for a single instruction varies wildly depending on how and when you measure. It depends on how busy the instruction decoder is, on branch predictor, on scheduling and on which other instructions are being scheduled, in addition to the simple issues like caching.

An interesting quote from Alan Kay in 2004:

Just as an aside, to give you an interesting benchmark—on roughly the same system, roughly optimized the same way, a benchmark from 1979 at Xerox PARC runs only 50 times faster today. Moore’s law has given us somewhere between 40,000 and 60,000 times improvement in that time. So there’s approximately a factor of 1,000 in efficiency that has been lost by bad CPU architectures.

The implication seems to be that CPU performance enhancements seems to focus on areas where they have relatively little impact on the software we really write.

As Doug already noted, the best case is zero (superscalar processor, multiple execution units, data already in L1 cache).

The worst case is up to several miliseconds (when the OS handles a pagefault and has to fetch the data/instruction from the disk). Excluding disk/swapping it still depends on whether you have a NUMA machine, which kind of topology it has, in which memory node the data lies, whether there is concurrent access from another CPU (bus locking and cache synchronization protocols), etc.

I recommend downloading the AMD software optimization guide.

I don't think the worst case is bounded on some platforms. When you have multiple cores and processors vying for the same locations or adjacent memory locations you can see all kinds of degradation in performance. Cache lines have to get moved around from processor to processor. I've haven't seen a good worst case number for memory operations on modern platforms.

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