Your version only describes what happens if you do the operations serially, though. For example, a consumer SSD can do a million (or more) operations in a second not 50K, and you can send a lot more than 7 total packets between CA and the Netherlands in a second, but to do either of those you need to take advantage of parallelism.
If the reciprocal numbers are more intuitive for you you can still say an L1 cache reference takes 1/2,000,000,000 sec. It's "ops/sec" that makes it look like it's a throughput.
An interesting thing about the latency numbers is they mostly don't vary with scale, whereas something like the total throughput with your SSD or the Internet depends on the size of your storage or network setups, respectively. And aggregate CPU throughput varies with core count, for example.
I do think it's still interesting to think about throughputs (and other things like capacities) of a "reference deployment": that can affect architectural things like "can I do this in RAM?", "can I do this on one box?", "what optimizations do I need to fix potential bottlenecks in XYZ?", "is resource X or Y scarcer?" and so on. That was kind of done in "The Datacenter as a Computer" (https://pages.cs.wisc.edu/~shivaram/cs744-readings/dc-comput... and https://books.google.com/books?id=Td51DwAAQBAJ&pg=PA72#v=one... ) with a machine, rack, and cluster as the units. That diagram is about the storage hierarchy and doesn't mention compute, and a lot has improved since 2018, but an expanded table like that is still seems like an interesting tool for engineering a system.
The reason why that formatting is not used is because it’s not useful nor true. The table in the article is far more relevant to the person optimizing things. How many of those I can hypothetically execute per second is a data point for the marketing team. Everyone else is beholden to real world data sets and data reads and fetches that are widely distributed in terms of timing.
Both ops/sec and sec/op vary on clock rate, and clock rate varies across machines, and along the execution time of your program.
AFAIK, Cycles (a la _rdtsc) is as close as you can get to a stable performance measurement for an operation. You can compare it on chips with different clock rates and architectures, and derive meaningful insight. The same cannot be said for op/sec or sec/op.
Unfortunately, what you'll find if you dig into this is that cycles/op isn't as meaningful as you might imagine.
Most modern CPUs are out of order executors. That means that while a floating point operation might take 4 cycles to complete, if you put a bunch of other instructions around it like adds, divides, and multiplies, those will all finish at roughly the same time.
That makes it somewhat hard to reason about exactly how long any given set of operations will be. A FloatMul could take 4 cycles on it's own, and if you have
FloatMul
ADD
MUL
DIV
That can also take 4 cycles to finish. It's simply not as simple as saying "Let's add up the cycles for these 4 ops to get the total cycle count".
Realistically, what you'll actually be waiting on is cache and main memory. This fact is so reliable that it underpins SMT. It's why most modern CPUs will do that in some form.
Your critique applies to measuring one or a handful of instructions.
In practice you count the number of cycles over million or billion instructions. CPI is very meaningful and it is the main throughput performance metric for CPU core architects.
I agree that what you're saying is true, but in the context of my comment, I stand by the statement that cycles/op is still a more meaningful measurement of performance than seconds.
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Counter-nitpick .. your statement of "if you put a bunch of other instructions around it" assumes there are no data dependencies between instructions.
In the example you gave:
FloatMul
ADD
MUL
DIV
Sure .. if all of those are operating on independent data sources, they could conceivably retire on the same cycle, but in the context of the article (approximating the performance profile of a series of operations) we're assuming they have data dependencies on one another, and are going to be executed serially.
Your suggestion confuses latency and throughput. So it isn't correct.
For example, a modern CPU will be able to execute other instructions while waiting for a cache miss, and will also be able to have multiple cache loads in flight at once (especially for caches shared between cores).
Main memory is asynchronous too, so multiple loads might be in flight, per memory channel. Same goes for all the other layers here (multiple SSD transactions in flight at once, multiple network requests, etc)
Approximately everything in modern computers is async at the hardware level, often with multiple units handling the execution of the "thing". All the way from the network and SSD to the ALUs (arithmetic logic unit) in the CPU.
Modern CPUs are pipelined (and have been since the mid to late 90s), so they will be executing one instruction, decoding the next instruction and retiring (writing out the result of) the previous instruction all at once. But real pipelines have way more than the 3 basic stages I just listed. And they can reorder, do things in parallel, etc.
I'm aware of this to an extent. Do you know of any list of what degree of parallelization to expect out of various components? I know this whole napkin-math thing is mostly futile and the answer should mostly be "go test it", but just curious.
I was interviewing recently and was asked about implementing a web crawler and then were discussing bottlenecks (network fetching the pages, writing the content to disk, CPU usage for stuff like parsing the responses) and parallelism, and I wanted to just say "well, i'd test it to figure out what I was bottlenecked on and then iterate on my solution".
Some of this can be reduced to a trivial form, which is to say practiced in reality on a reasonable scale, by getting your hands on a microcontroller. Not RTOS or Linux or any of that, but just a microcontroller without an OS, and learning it and learning its internal fetching architecture and getting comfortable with timings, and seeing how the latency numbers go up when you introduce external memory such as SD Cards and the like. Knowing to read the assembly printout and see how the instruction cycles add up in the pipeline is also good, because at least you know what is happening. It will then make it much easier to apply the same careful mentality to this which is ultimately what this whole optimization game is about - optimizing where time is spent with what data. Otherwise, someone telling you so-and-so takes nanoseconds or microseconds will be alien to you because you wouldn’t normally be exposed to an environment where you regularly count in clock cycles. So consider this a learning opportunity.
Just be careful not to blindly apply the same techniques to a mobile or desktop class CPU or above.
A lot of code can be pessimized by golfing instruction counts, hurting instruction-level parallelism and microcode optimizations by introducing false data dependencies.
Compilers outperform humans here almost all the time.
Compilers massively outperform humans if the human has to write the entire program in assembly. Even if a human could write a sizable program in assembly, it would be subpar compared to what a compiler would write.
This is true.
However, that doesn't mean that looking at the generated asm / even writing some is useless! Just because you can't globally outperform the compiler, doesn't mean you can't do it locally! If you know where the bottleneck is, and make those few functions great, that's a force multiplier for you and your program.
It’s absolutely not useless, I do it often as a way to diagnose various kinds of problems. But it’s extremely rare that a handwritten version actually performs better.
It is not about outperforming the compiler - it’s about being comfortable with measuring where your clock cycles are spent, and for that you first need to be comfortable with clock cycle scale of timing. You’re not expected to rewrite the program in assembly. But you should have a general idea given an instruction what its execution entails, and where the data is actually coming from. A read from different busses means different timings.
Compilers make mistakes too and they can output very erroneous code. But that’s a different topic.
An old approach to micro-optimization is to look at the generated assembly, and trying to achieve the same thing with fewer instructions. However, modern CPUs are able to execute multiple instructions in parallel (out-of-order execution), and this mechanism relies on detecting data dependencies between instructions.
It means that the shorter sequence of instructions is not necessarily faster, and can in fact make the CPU stall unnecessarily.
The fastest sequence of instructions is the one that makes the best use of the CPU’s resources.
This formatting is more intuitive to me.
Your version only describes what happens if you do the operations serially, though. For example, a consumer SSD can do a million (or more) operations in a second not 50K, and you can send a lot more than 7 total packets between CA and the Netherlands in a second, but to do either of those you need to take advantage of parallelism.
If the reciprocal numbers are more intuitive for you you can still say an L1 cache reference takes 1/2,000,000,000 sec. It's "ops/sec" that makes it look like it's a throughput.
An interesting thing about the latency numbers is they mostly don't vary with scale, whereas something like the total throughput with your SSD or the Internet depends on the size of your storage or network setups, respectively. And aggregate CPU throughput varies with core count, for example.
I do think it's still interesting to think about throughputs (and other things like capacities) of a "reference deployment": that can affect architectural things like "can I do this in RAM?", "can I do this on one box?", "what optimizations do I need to fix potential bottlenecks in XYZ?", "is resource X or Y scarcer?" and so on. That was kind of done in "The Datacenter as a Computer" (https://pages.cs.wisc.edu/~shivaram/cs744-readings/dc-comput... and https://books.google.com/books?id=Td51DwAAQBAJ&pg=PA72#v=one... ) with a machine, rack, and cluster as the units. That diagram is about the storage hierarchy and doesn't mention compute, and a lot has improved since 2018, but an expanded table like that is still seems like an interesting tool for engineering a system.
The reason why that formatting is not used is because it’s not useful nor true. The table in the article is far more relevant to the person optimizing things. How many of those I can hypothetically execute per second is a data point for the marketing team. Everyone else is beholden to real world data sets and data reads and fetches that are widely distributed in terms of timing.
I prefer a different encoding: cycles/op
Both ops/sec and sec/op vary on clock rate, and clock rate varies across machines, and along the execution time of your program.
AFAIK, Cycles (a la _rdtsc) is as close as you can get to a stable performance measurement for an operation. You can compare it on chips with different clock rates and architectures, and derive meaningful insight. The same cannot be said for op/sec or sec/op.
Unfortunately, what you'll find if you dig into this is that cycles/op isn't as meaningful as you might imagine.
Most modern CPUs are out of order executors. That means that while a floating point operation might take 4 cycles to complete, if you put a bunch of other instructions around it like adds, divides, and multiplies, those will all finish at roughly the same time.
That makes it somewhat hard to reason about exactly how long any given set of operations will be. A FloatMul could take 4 cycles on it's own, and if you have
That can also take 4 cycles to finish. It's simply not as simple as saying "Let's add up the cycles for these 4 ops to get the total cycle count".Realistically, what you'll actually be waiting on is cache and main memory. This fact is so reliable that it underpins SMT. It's why most modern CPUs will do that in some form.
Your critique applies to measuring one or a handful of instructions. In practice you count the number of cycles over million or billion instructions. CPI is very meaningful and it is the main throughput performance metric for CPU core architects.
I agree that what you're saying is true, but in the context of my comment, I stand by the statement that cycles/op is still a more meaningful measurement of performance than seconds.
---
Counter-nitpick .. your statement of "if you put a bunch of other instructions around it" assumes there are no data dependencies between instructions.
In the example you gave:
Sure .. if all of those are operating on independent data sources, they could conceivably retire on the same cycle, but in the context of the article (approximating the performance profile of a series of operations) we're assuming they have data dependencies on one another, and are going to be executed serially.Your suggestion confuses latency and throughput. So it isn't correct.
For example, a modern CPU will be able to execute other instructions while waiting for a cache miss, and will also be able to have multiple cache loads in flight at once (especially for caches shared between cores).
Main memory is asynchronous too, so multiple loads might be in flight, per memory channel. Same goes for all the other layers here (multiple SSD transactions in flight at once, multiple network requests, etc)
Approximately everything in modern computers is async at the hardware level, often with multiple units handling the execution of the "thing". All the way from the network and SSD to the ALUs (arithmetic logic unit) in the CPU.
Modern CPUs are pipelined (and have been since the mid to late 90s), so they will be executing one instruction, decoding the next instruction and retiring (writing out the result of) the previous instruction all at once. But real pipelines have way more than the 3 basic stages I just listed. And they can reorder, do things in parallel, etc.
I'm aware of this to an extent. Do you know of any list of what degree of parallelization to expect out of various components? I know this whole napkin-math thing is mostly futile and the answer should mostly be "go test it", but just curious.
I was interviewing recently and was asked about implementing a web crawler and then were discussing bottlenecks (network fetching the pages, writing the content to disk, CPU usage for stuff like parsing the responses) and parallelism, and I wanted to just say "well, i'd test it to figure out what I was bottlenecked on and then iterate on my solution".
I’ve seen this list many many times and I’m always surprised it doesn’t include registers.
Register moves do not really play a factor in performance, unless its to move to/from vector registers.
H+P says register allocation is one of the most important—if not the most important—optimizations.
Some of this can be reduced to a trivial form, which is to say practiced in reality on a reasonable scale, by getting your hands on a microcontroller. Not RTOS or Linux or any of that, but just a microcontroller without an OS, and learning it and learning its internal fetching architecture and getting comfortable with timings, and seeing how the latency numbers go up when you introduce external memory such as SD Cards and the like. Knowing to read the assembly printout and see how the instruction cycles add up in the pipeline is also good, because at least you know what is happening. It will then make it much easier to apply the same careful mentality to this which is ultimately what this whole optimization game is about - optimizing where time is spent with what data. Otherwise, someone telling you so-and-so takes nanoseconds or microseconds will be alien to you because you wouldn’t normally be exposed to an environment where you regularly count in clock cycles. So consider this a learning opportunity.
Just be careful not to blindly apply the same techniques to a mobile or desktop class CPU or above.
A lot of code can be pessimized by golfing instruction counts, hurting instruction-level parallelism and microcode optimizations by introducing false data dependencies.
Compilers outperform humans here almost all the time.
Compilers massively outperform humans if the human has to write the entire program in assembly. Even if a human could write a sizable program in assembly, it would be subpar compared to what a compiler would write. This is true.
However, that doesn't mean that looking at the generated asm / even writing some is useless! Just because you can't globally outperform the compiler, doesn't mean you can't do it locally! If you know where the bottleneck is, and make those few functions great, that's a force multiplier for you and your program.
It’s absolutely not useless, I do it often as a way to diagnose various kinds of problems. But it’s extremely rare that a handwritten version actually performs better.
yo, completely off topic, but do you work on a voxel game/engine?
It is not about outperforming the compiler - it’s about being comfortable with measuring where your clock cycles are spent, and for that you first need to be comfortable with clock cycle scale of timing. You’re not expected to rewrite the program in assembly. But you should have a general idea given an instruction what its execution entails, and where the data is actually coming from. A read from different busses means different timings.
Compilers make mistakes too and they can output very erroneous code. But that’s a different topic.
Excellent corrective summary.
"Compilers can do all these great transformations, but they can also be incredibly dumb"
-Mike Acton, CPPCON 2014
"A lot of code can be pessimized by golfing instruction counts"
Can you explain what this phrase means?
An old approach to micro-optimization is to look at the generated assembly, and trying to achieve the same thing with fewer instructions. However, modern CPUs are able to execute multiple instructions in parallel (out-of-order execution), and this mechanism relies on detecting data dependencies between instructions.
It means that the shorter sequence of instructions is not necessarily faster, and can in fact make the CPU stall unnecessarily.
The fastest sequence of instructions is the one that makes the best use of the CPU’s resources.
> Compilers outperform humans here almost all the time.
I'm going to be annoying and nerd-snipe you here. It's, generally, really easy to beat the compiler.
https://scallywag.software/vim/blog/simd-perlin-noise-i
Wonderful article. I wish more people had this pragmatic approach when thinking about performance