OpenMP with matrices and vectors - optimization

What is the best way to utilize OpenMP with a matrix-vector product? Would the for directive suffice (if so, where should I place it? I assume outer loop would be more efficient) or would I need schedule, etc..?
Also, how would I take advantage different algorithms to attempt this m-v product most efficiently?
Thanks

The first step you should take is the obvious one, wrap the outermost loop in a parallel for directive. As you assume. It's always worth experimenting a bit to get some evidence to support your (and my) assumptions, but if you were only allowed to make 1 change that would be the one to make.
I don't know much about cache-oblivious algorithms but I understand that they, generally, work by recursive division of a problem into sub-problems. This doesn't seem to fit with the application of parallel for directives. I suspect you could implement such an algorithm with OpenMP's tasks, but I suspect that the overhead of doing this would outweigh any execution improvements on any m-v product of reasonable dimensions.
(If you demonstrate the falsity of this argument on m-v products of size N I will retort 'N's not a reasonable dimension'. As ever with these performance questions, evidence trumps argument every time.)
Finally, depending on your compiler and the availability of libraries, you may not need to use OpenMP for m-v calculations, you might find auto-parallelisation works efficiently, or already have a library implementation which multi-threads this sort of computation.

Related

To what extent shall we optimize time complexity?

Theory vs practice here.
Regarding time complexity, and I have a conceptual question that we didn't get to go deeper into in class.
Here it is:
There's a barbaric BROOT force algorithm, O(n^3)... and we got it down o O(n) and it was considered good enough. If we dive in deeper, it is actually O(n)+O(n), two separate iterations of the input. I came up with another way which was actually O(n/2). But those two algorithms are considered to be the same since both are O(n) and as n reaches infinity, it makes no difference, so not necessary at all once we reach O(n).
My question is:
In reality, in practice, we always have a finite number of inputs (admittedly occasionally in the trillions). So following the time complexity logic, O(n/2) is four times as fast as O(2n). So if we can make it faster, why not?
Time complexity is not everything. As you already noticed, the Big-Oh can hide a lot and also assumes that all operations cost the same.
In Practice you should always try to find a fast/the fastest solution for your problem. Sometimes this means that you use a algorithm with a bad complexity but good constants if you know that your problem is always small. Depending on your use case, you also want to implement optimizations that utilize hardware properties like cache optimizations.

Dynamic number of test cases in genetic programming?

When looking at Genetic programming papers, it seems to me that the number of test cases is always fixed. However, most mutations should (?) at every stage of the execution be very deleterious, i. e. make it obvious after one test case that the mutated program performs much worse than the previous one. What happens if you, at first, only try very few (one?) test case and look whether the mutation makes any sense?
Is it maybe so that different test cases test for different features of the solutions, and one mutation will probably improve only one of those features?
I don't know if I agree with your assumption that most mutations should be very deleterious, but you shouldn't care even if they were. Your goal is not to optimize the individuals, but to optimize the population. So trying to determine if a "mutation makes any sense" is exactly what genetic programming is supposed to do: i.e. eliminate mutations that "don't make sense." Your only "guidance" for the algorithm should come through the fitness function.
I'm also not sure what you mean with "test case", but for me it sounds like you are looking for something related to multi-objective-optimization (MOO). That means you try to optimize a solution regarding different aspects of the problem - therefore you do not need to mutate/evaluate a population for a specific test-case, but to find a multi objective fitness function.
"The main idea in MOO is the notion of Pareto dominance" (http://www.gp-field-guide.org.uk)
I think this is a good idea in theory but tricky to put into practice. I can't remember seeing this approach actually used before but I wouldn't be surprised if it has.
I presume your motivation for doing this is to improve the efficiency of the applying the fitness function - you can stop evaluation early and discard the individual (or set fitness to 0) if the tests look like they're going to be terrible.
One challenge is to decide how many test cases to apply; discarding an individual after one random test case is surely not a good idea as the test case could be a real outlier. Perhaps terminating evaluation after 50% of test cases if the fitness of the individual was <10% of the best would probably not discard any very good individuals; on the other hand it might not be worth it given a lot of individuals will be of middle-of-the road fitness and might well only save a small proportion of the computation. You could adjust the numbers so you save more effort, but the more effort you try to save the more chances you have of genuinely good individuals being discarded by accident.
Factor in the extra time to taken to code this and possible bugs etc. and I shouldn't think the benefit would be worthwhile (unless this is a research project in which case it might be interesting to try it and see).
I think it's a good idea. Fitness evaluation is the most computational intense process in GP, so estimating the fitness value of individuals in order to reduce the computational expense of actually calculating the fitness could be an important optimization.
Your idea is a form of fitness approximation, sometimes it's called lazy evaluation (try searching these words, there are some research papers).
There are also distinct but somewhat overlapping schemes, for instance:
Dynamic Subset Selection (Chris Gathercole, Peter Ross) is a method to select a small subset of the training data set on which to actually carry out the GP algorithm;
Segment-Based Genetic Programming (Nailah Al-Madi, Simone Ludwig) is a technique that reduces the execution time of GP by partitioning the dataset into segments and using the segments in the fitness evaluation process.
PS also in the Brood Recombination Crossover (Tackett) child programs are usually evaluated on a restricted number of test cases to speed up the crossover.

basic operations cpu time cost

I was wondering, how to optimize loops for systems with very limited resources. Let's say, if we have a basic for loop, like ( written in javascript):
for(var i = someArr.length - 1; i > -1; i--)
{
someArr[i]
}
I honestly don't know, isn't != cheaper than > ?
I would be grateful for any resources covering computing cost in context of basic operators, like the aforementioned, >>, ~, !, and so on.
Performance on a modern CPU is far from trivial. Here are a couple of things that complicate it:
Computers are fast. Your CPU can execute upwards of 6 billion instructions per second. So even the slowest instruction can be executed millions of times per second, meaning that it only really matters if you use it very often
Modern CPU's have hundreds of instructions in flight simultaneously. They are pipelined, meaning that while one instruction is being read, another is reading from registers, a third one is executing, and a fourth one is writing back to a register. Modern CPU's have 15-20 of such stages. On top of this, they can execute 3-4 instructions at the same time on each of these stages. And they can reorder these instructions. If the multiplication unit is being used by another instruction, perhaps we can find an addition instruction to execute instead, for example. So even if you have some slow instructions mixed in, their cost can be hidden very well most of the time, by executing other instructions while waiting for the slow one to finish.
Memory is hundreds of times slower than the CPU. The instructions being executed don't really matter if their cost is dwarfed by retrieval of data from memory. And even this isn't reliable, because the CPU has its own onboard caches to attempt to hide this cost.
So the short answer is "don't try to outsmart the compiler". If you are able to choose between two equivalent expressions, the compiler is probably able to do the same, and will pick the most efficient one. The cost of an instruction varies, depending on all the above factors. Which other instructions are executing, what data is in the CPU's cache, which precise CPU model is the code running on, and so on. Code that is super efficient in one case may be very inefficient in other cases. The compiler will try to pick the most generally efficient instructions, and schedule them as well as possible. Unless you know more than the compiler about this, you're unlikely to be able to do a better job of it.
Don't try such microoptimizations unless you really know what you're doing. As the above shows, low-level performance is a ridiculously complex subject, and it's very easy to write "optimizations" that result in far slower code. Or which just sacrifice readability on something that makes no difference at all.
Further, most of your code simply doesn't have a measurable impact on performance.
People generally love quoting (or misquoting) Knuth on this subject:
We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil
People often interpret this as "don't bother trying to optimize your code". If you actually read the full quote, some much more interesting consequences should become clear:
Most of the time, we should forget about microoptimizations. Most code is executed so rarely that optimizations won't matter. Keeping in mind the number of instructions a CPU can execute per second, it is obvious that a block of code has to be executed very often for optimizations in it to have any effect. So about 97% of the time, your optimizations will be a waste of time. But he also says that sometimes (3% of the time), your optimizations will matter. And obviously, looking for those 3% is a bit like looking for a needle in a haystack. If you just decide to "optimize your code" in general, you're going to waste your time on the first 97%. Instead, you need to first locate the 3% that actually need optimizing. In other words, run your code through a profiler, and let it tell you which code takes up the most CPU time. Then you know where to optimize. And then your optimizations are no longer premature.
It is extraordinarily unlikely that such micro-optimizations will make a noticeable difference to your code in any but the most extreme (real time embedded systems?) circumstances. Your time would probably be better served worrying about making your code readable and maintainable.
When in doubt, always begin by asking Donald Knuth:
http://shreevatsa.wordpress.com/2008/05/16/premature-optimization-is-the-root-of-all-evil/
Or, for a slightly less high-brow take on micro-optimization:
http://www.codinghorror.com/blog/archives/000185.html
Most comparations have same coast, because the processor simply compares it in all aspects, then after that it takes a decision based on flags generated by this previous comparation so the comparation signal doesn't matter at all. But some architectures try to accelerate this process based on the value you are comparing with, like comparations against 0.
As far as I know, bitwise operations are the cheapest operations, slightly faster than addition and subtraction. Multiplication and division operations are a little more expensive, and comparation is the highest coast operation.
That's like asking for a fish, when I would rather teach you to fish.
There are simple ways to see for yourself how long things take. My favorite is to just copy the code 10 times, and then wrap it in a loop of 10^8 times. If I run it and look at my watch, the number of seconds it takes translates to nanoseconds.
Saying don't do premature optimization is a "don't be". If you want a "do be" you could try a proactive performance tuning technique like this.
BTW my favorite way of coding your loop is:
for (i = N; --i >= 0;){...}
Premature Optimization can be dangerous the best approach would be to write your application without worrying about that and then find the slow points and optimize those. If you are really worried about this use a lower level language. An interpreted language like javascript will cost you some processing power when compared to a lower level language like C.
In this particular case, > vs = is probably not a perfomance issue. HOWEVER > is generally safer choice because prevents cases where you modified the code from running off into the weeds and stuck in a infinite loop.

When is optimisation premature?

As Knuth said,
We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil.
This is something which often comes up in Stack Overflow answers to questions like "which is the most efficient loop mechanism", "SQL optimisation techniques?" (and so on). The standard answer to these optimisation-tips questions is to profile your code and see if it's a problem first, and if it's not, then therefore your new technique is unneeded.
My question is, if a particular technique is different but not particularly obscure or obfuscated, can that really be considered a premature optimisation?
Here's a related article by Randall Hyde called The Fallacy of Premature Optimization.
Don Knuth started the literate programming movement because he believed that the most important function of computer code is to communicate the programmer's intent to a human reader. Any coding practice that makes your code harder to understand in the name of performance is a premature optimization.
Certain idioms that were introduced in the name of optimization have become so popular that everyone understands them and they have become expected, not premature. Examples include
Using pointer arithmetic instead of array notation in C, including the use of such idioms as
for (p = q; p < lim; p++)
Rebinding global variables to local variables in Lua, as in
local table, io, string, math
= table, io, string, math
Beyond such idioms, take shortcuts at your peril.
All optimization is premature unless
A program is too slow (many people forget this part).
You have a measurement (profile or similar) showing that the optimization could improve things.
(It's also permissible to optimize for memory.)
Direct answer to question:
If your "different" technique makes the program harder to understand, then it's a premature optimization.
EDIT: In response to comments, using quicksort instead of a simpler algorithm like insertion sort is another example of an idiom that everyone understands and expects. (Although if you write your own sort routine instead of using the library sort routine, one hopes you have a very good reason.)
IMHO, 90% of your optimization should occur at design stage, based on percieved current, and more importantly, future requirements. If you have to take out a profiler because your application doesn't scale to the required load you have left it too late, and IMO will waste a lot of time and effort while failing to correct the problem.
Typically the only optimizations that are worthwhile are those that gain you an order of magnitude performance improvement in terms of speed, or a multiplier in terms of storage or bandwidth. These types of optimizations typically relate to algorithm selection and storage strategy, and are extremely difficult to reverse into existing code. They may go as deep as influencing the decision on the language in which you implement your system.
So my advice, optimize early, based on your requirements, not your code, and look to the possible extended life of your app.
If you haven't profiled, it's premature.
My question is, if a particular
technique is different but not
particularly obscure or obfuscated,
can that really be considered a
premature optimisation?
Um... So you have two techniques ready at hand, identical in cost (same effort to use, read, modify) and one is more efficient. No, using the more efficient one would not, in that case, be premature.
Interrupting your code-writing to look for alternatives to common programming constructs / library routines on the off-chance that there's a more efficient version hanging around somewhere even though for all you know the relative speed of what you're writing will never actually matter... That's premature.
Here's the problem I see with the whole concept of avoiding premature optimization.
There's a disconnect between saying it and doing it.
I've done lots of performance tuning, squeezing large factors out of otherwise well-designed code, seemingly done without premature optimization.
Here's an example.
In almost every case, the reason for the suboptimal performance is what I call galloping generality, which is the use of abstract multi-layer classes and thorough object-oriented design, where simple concepts would be less elegant but entirely sufficient.
And in the teaching material where these abstract design concepts are taught, such as notification-driven architecture, and information-hiding where simply setting a boolean property of an object can have an unbounded ripple effect of activities, what is the reason given? Efficiency.
So, was that premature optimization or not?
First, get the code working. Second, verify that the code is correct. Third, make it fast.
Any code change that is done before stage #3 is definitely premature. I am not entirely sure how to classify design choices made before that (like using well-suited data structures), but I prefer to veer towards using abstractions taht are easy to program with rather than those who are well-performing, until I am at a stage where I can start using profiling and having a correct (though frequently slow) reference implementation to compare results with.
From a database perspective, not to consider optimal design at the design stage is foolhardy at best. Databases do not refactor easily. Once they are poorly designed (this is what a design that doesn't consider optimization is no matter how you might try to hide behind the nonsense of premature optimization), is almost never able to recover from that becasue the database is too basic to the operation of the whole system. It is far less costly to design correctly considering the optimal code for the situation you expect than to wait until the there are a million users and people are screaming becasue you used cursors throughout the application. Other optimizations such as using sargeable code, selecting what look to be the best possible indexes, etc. only make sense to do at design time. There is a reason why quick and dirty is called that. Because it can't work well ever, so don't use quickness as a substitute for good code. Also frankly when you understand performance tuning in databases, you can write code that is more likely to perform well in the same time or less than it takes to write code which doesn't perform well. Not taking the time to learn what is good performing database design is developer laziness, not best practice.
What you seem to be talking about is optimization like using a hash-based lookup container vs an indexed one like an array when a lot of key lookups will be done. This is not premature optimization, but something you should decide in the design phase.
The kind of optimization the Knuth rule is about is minimizing the length the most common codepaths, optimizing the code that is run most by for example rewriting in assembly or simplifying the code, making it less general. But doing this has no use until you are certain which parts of code need this kind of optimization and optimizing will (could?) make the code harder to understand or maintain, hence "premature optimization is the root of all evil".
Knuth also says it is always better to, instead of optimizing, change the algorithms your program uses, the approach it takes to a problem. For example whereas a little tweaking might give you a 10% increase of speed with optimization, changing fundamentally the way your program works might make it 10x faster.
In reaction to a lot of the other comments posted on this question: algorithm selection != optimization
The point of the maxim is that, typically, optimization is convoluted and complex. And typically, you the architect/designer/programmer/maintainer need clear and concise code in order to understand what is going on.
If a particular optimization is clear and concise, feel free to experiment with it (but do go back and check whether that optimization is effective). The point is to keep the code clear and concise throughout the development process, until the benefits of performance outweigh the induced costs of writing and maintaining the optimizations.
Optimization can happen at different levels of granularity, from very high-level to very low-level:
Start with a good architecture, loose coupling, modularity, etc.
Choose the right data structures and algorithms for the problem.
Optimize for memory, trying to fit more code/data in the cache. The memory subsystem is 10 to 100 times slower than the CPU, and if your data gets paged to disk, it's 1000 to 10,000 times slower. Being cautious about memory consumption is more likely to provide major gains than optimizing individual instructions.
Within each function, make appropriate use of flow-control statements. (Move immutable expressions outside of the loop body. Put the most common value first in a switch/case, etc.)
Within each statement, use the most efficient expressions yielding the correct result. (Multiply vs. shift, etc)
Nit-picking about whether to use a divide expression or a shift expression isn't necessarily premature optimization. It's only premature if you do so without first optimizing the architecture, data structures, algorithms, memory footprint, and flow-control.
And of course, any optimization is premature if you don't define a goal performance threshold.
In most cases, either:
A) You can reach the goal performance threshold by performing high-level optimizations, so it's not necessary to fiddle with the expressions.
or
B) Even after performing all possible optimizations, you won't meet your goal performance threshold, and the low-level optimizations don't make enough difference in performance to justify the loss of readability.
In my experience, most optimization problems can be solved at either the architecture/design or data-structure/algorithm level. Optimizing for memory footprint is often (though not always) called for. But it's rarely necessary to optimize the flow control & expression logic. And in those cases where it actually is necessary, it's rarely sufficient.
I try to only optimise when a performance issue is confirmed.
My definition of premature optimisation is 'effort wasted on code that is not known to be a performance problem.' There is most definitely a time and place for optimisation. However, the trick is to spend the extra cost only where it counts to the performance of the application and where the additional cost outweighs the performance hit.
When writing code (or a DB query) I strive to write 'efficient' code (i.e. code that performs its intended function, quickly and completely with simplest logic reasonable.) Note that 'efficient' code is not necessarily the same as 'optimised' code. Optimisations often introduce additional complexity into code which increases both the development and maintenance cost of that code.
My advice: Try to only pay the cost of optimisation when you can quantify the benefit.
When programming, a number of parameters are vital. Among these are:
Readability
Maintainability
Complexity
Robustness
Correctness
Performance
Development time
Optimisation (going for performance) often comes at the expense of other parameters, and must be balanced against the "loss" in these areas.
When you have the option of choosing well-known algorithms that perform well, the cost of "optimising" up-front is often acceptable.
Norman's answer is excellent. Somehow, you routinely do some "premature optimization" which are, actually, best practices, because doing otherwise is known to be totally inefficient.
For example, to add to Norman's list:
Using StringBuilder concatenation in Java (or C#, etc.) instead of String + String (in a loop);
Avoiding to loop in C like: for (i = 0; i < strlen(str); i++) (because strlen here is a function call walking the string each time, called on each loop);
It seems in most JavaScript implementations, it is faster to do too for (i = 0 l = str.length; i < l; i++) and it is still readable, so OK.
And so on. But such micro-optimizations should never come at the cost of readability of code.
The need to use a profiler should be left for extreme cases. The engineers of the project should be aware of where performance bottlenecks are.
I think "premature optimisation" is incredibly subjective.
If I am writing some code and I know that I should be using a Hashtable then I will do that. I won't implement it in some flawed way and then wait for the bug report to arrive a month or a year later when somebody is having a problem with it.
Redesign is more costly than optimising a design in obvious ways from the start.
Obviously some small things will be missed the first time around but these are rarely key design decisions.
Therefore: NOT optimising a design is IMO a code smell in and of itself.
It's worth noting that Knuth's original quote came from a paper he wrote promoting the use of goto in carefully selected and measured areas as a way to eliminate hotspots. His quote was a caveat he added to justify his rationale for using goto in order to speed up those critical loops.
[...] again, this is a noticeable saving in the overall running speed,
if, say, the average value of n is about 20, and if the search routine
is performed about a million or so times in the program. Such loop
optimizations [using gotos] are not difficult to learn and, as I have
said, they are appropriate in just a small part of a program, yet they
often yield substantial savings. [...]
And continues:
The conventional wisdom shared by many of today's software engineers
calls for ignoring efficiency in the small; but I believe this is
simply an overreaction to the abuses they see being practiced by
pennywise-and-pound-foolish programmers, who can't debug or maintain
their "optimized" programs. In established engineering disciplines a
12% improvement, easily obtained, is never considered marginal; and I
believe the same viewpoint should prevail in software engineering. Of
course I wouldn't bother making such optimizations on a oneshot job,
but when it's a question of preparing quality programs, I don't want
to restrict myself to tools that deny me such efficiencies [i.e., goto
statements in this context].
Keep in mind how he used "optimized" in quotes (the software probably isn't actually efficient). Also note how he isn't just criticizing these "pennywise-and-pound-foolish" programmers, but also the people who react by suggesting you should always ignore small inefficiencies. Finally, to the frequently-quoted part:
There is no doubt that the grail of efficiency leads to abuse.
Programmers waste enormous amounts of time thinking about, or worrying
about, the speed of noncritical parts of their programs, and these
attempts at efficiency actually have a strong negative impact when
debugging and maintenance are considered. We should forgot about small
efficiencies, say 97% of the time; premature optimization is the root
of all evil.
... and then some more about the importance of profiling tools:
It is often a mistake to make a priori judgments about what parts of a
program are really critical, since the universal experience of
programmers who have been using measurement tools has been that their
intuitive guesses fail. After working with such tools for seven years,
I've become convinced that all compilers written from now on should be
designed to provide all programmers with feedback indicating what
parts of their programs are costing the most; indeed, this feedback
should be supplied automatically unless it has been specifically
turned off.
People have misused his quote all over the place, often suggesting that micro-optimizations are premature when his entire paper was advocating micro-optimizations! One of the groups of people he was criticizing who echo this "conventional wisdom" as he put of always ignoring efficiencies in the small are often misusing his quote which was originally directed, in part, against such types who discourage all forms of micro-optimization.
Yet it was a quote in favor of appropriately applied micro-optimizations when used by an experienced hand holding a profiler. Today's analogical equivalent might be like, "People shouldn't be taking blind stabs at optimizing their software, but custom memory allocators can make a huge difference when applied in key areas to improve locality of reference," or, "Handwritten SIMD code using an SoA rep is really hard to maintain and you shouldn't be using it all over the place, but it can consume memory much faster when applied appropriately by an experienced and guided hand."
Any time you're trying to promote carefully-applied micro-optimizations as Knuth promoted above, it's good to throw in a disclaimer to discourage novices from getting too excited and blindly taking stabs at optimization, like rewriting their entire software to use goto. That's in part what he was doing. His quote was effectively a part of a big disclaimer, just like someone doing a motorcycle jump over a flaming fire pit might add a disclaimer that amateurs shouldn't try this at home while simultaneously criticizing those who try without proper knowledge and equipment and get hurt.
What he deemed "premature optimizations" were optimizations applied by people who effectively didn't know what they were doing: didn't know if the optimization was really needed, didn't measure with proper tools, maybe didn't understand the nature of their compiler or computer architecture, and most of all, were "pennywise-and-pound-foolish", meaning they overlooked the big opportunities to optimize (save millions of dollars) by trying to pinch pennies, and all while creating code they can no longer effectively debug and maintain.
If you don't fit in the "pennywise-and-pound-foolish" category, then you aren't prematurely optimizing by Knuth's standards, even if you're using a goto in order to speed up a critical loop (something which is unlikely to help much against today's optimizers, but if it did, and in a genuinely critical area, then you wouldn't be prematurely optimizing). If you're actually applying whatever you're doing in areas that are genuinely needed and they genuinely benefit from it, then you're doing just great in the eyes of Knuth.
Premature optimization to me means trying to improve the efficiency of your code before you have a working system, and before you have actually profiled it and know where the bottleneck is. Even after that, readability and maintainability should come before optimization in many cases.
I don't think that recognized best practices are premature optimizations. It's more about burning time on the what ifs that are potential performance problems depending on the usage scenarios. A good example: If you burn a week trying to optimize reflecting over an object before you have proof that it is a bottleneck you are prematurely optimizing.
Unless you find that you need more performance out of your application, due to either a user or business need, there's little reason to worry about optimizing. Even then, don't do anything until you've profiled your code. Then attack the parts which take the most time.
The way I see it is, if you optimize something without knowing how much performance you can gain in different scenario IS a premature optimization. The goal of code should really making it easiest for human to read.
As I posted on a similar question, the rules of optimisation are:
1) Don't optimise
2) (for experts only) Optimise later
When is optimisation premature? Usually.
The exception is perhaps in your design, or in well encapsulated code that is heavily used. In the past I've worked on some time critical code (an RSA implementation) where looking at the assembler that the compiler produced and removing a single unnecessary instruction in an inner loop gave a 30% speedup. But, the speedup from using more sophisticated algorithms was orders of magnitude more than that.
Another question to ask yourself when optimising is "am I doing the equivalent of optimising for a 300 baud modem here?". In other words, will Moore's law make your optimisation irrelevant before too long. Many problems of scaling can be solved just by throwing more hardware at the problem.
Last but not least it's premature to optimise before the program is going too slowly. If it's web application you're talking about, you can run it under load to see where the bottlenecks are - but the likelihood is that you will have the same scaling problems as most other sites, and the same solutions will apply.
edit: Incidentally, regarding the linked article, I would question many of the assumptions made. Firstly it's not true that Moore's law stopped working in the 90s. Secondly, it's not obvious that user's time is more valuable than programmer's time. Most users are (to say the least) not frantically using every CPU cycle available anyhow, they are probably waiting for the network to do something. Plus there is an opportunity cost when programmer's time is diverted from implementing something else, to shaving a few milliseconds off something that the program does while the user is on the phone. Anything longer than that isn't usually optimisation, it's bug fixing.

Compiler optimizations: Where/how can I get a feel for what the payoff is for different optimizations?

In my independent study of various compiler books and web sites, I am learning about many different ways that a compiler can optimize the code that is being compiled, but I am having trouble figuring out how much of a benefit each optimization will tend to give.
How do most compiler writers go about deciding which optimizations to implement first? Or which optimizations are worth the effort or not worth the effort? I realize that this will vary between types of code and even individual programs, but I'm hoping that there is enough similarity between most programs to say, for instance, that one given technique will usually give you a better performance gain than another technique.
I found when implementing textbook compiler optimizations that some of them tended to reverse the improvements made by other optimizations. This entailed a lot of work trying to find the right balance between them.
So there really isn't a good answer to your question. Everything is a tradeoff. Many optimizations work well on one type of code, but are pessimizations for other types. It's like designing a house - if you make the kitchen bigger, the pantry gets smaller.
The real work in building an optimizer is trying out the various combinations, benchmarking the results, and, like a master chef, picking the right mix of ingredients.
Tongue in cheek:
Hubris
Benchmarks
Embarrassment
More seriously, it depends on your compiler's architecture and goals. Here's one person's experience...
Go for the "big payoffs":
native code generation
register allocation
instruction scheduling
Go for the remaining "low hanging fruit":
strength reduction
constant propagation
copy propagation
Keep bennchmarking.
Look at the output; fix anything that looks stupid.
It is usually the case that combining optimizations, or even repeating optimization passes, is more effective than you might expect. The benefit is more than the sum of the parts.
You may find that introduction of one optimization may necessitate another. For example, SSA with Briggs-Chaitin register allocation really benefits from copy propagation.
Historically, there are "algorithmical" optimizations from which the code should benefit in most of the cases, like loop unrolling (and compiler writers should implement those "documented" and "tested" optimizations first).
Then there are types of optimizations that could benefit from the type of processor used (like using SIMD instructions on modern CPUs).
See Compiler Optimizations on Wikipedia for a reference.
Finally, various type of optimizations could be tested profiling the code or doing accurate timing of repeated executions.
I'm not a compiler writer, but why not just incrementally optimize portions of your code, profiling all the while?
My optimization scheme usually goes:
1) make sure the program is working
2) find something to optimize
3) optimize it
4) compare the test results with what came out from 1; if they are different, then the optimization is actually a breaking change.
5) compare the timing difference
Incrementally, I'll get it faster.
I choose which portions to focus on by using a profiler. I'm not sure what extra information you'll garner by asking the compiler writers.
This really depends on what you are compiling. There is was a reasonably good discussion about this on the LLVM mailing list recently, it is of course somewhat specific to the optimizers they have available. They use abbreviations for a lot of their optimization passes, if you not familiar with any of acronyms they are tossing around you can look at their passes page for documentation. Ultimately you can spend years reading academic papers on this subject.
This is one of those topics where academic papers (ACM perhaps?) may be one of the better sources of up-to-date information. The best thing to do if you really want to know could be to create some code in unoptimized form and some in the form that the optimization would take (loops unrolled, etc) and actually figure out where the gains are likely to be using a compiler with optimizations turned off.
It is worth noting that in many cases, compiler writers will NOT spend much time, if any, on ensuring that their libraries are optimized. Benchmarks tend to de-emphasize or even ignore library differences, presumably because you can just use different libraries. For example, the permutation algorithms in GCC are asymptotically* less efficient than they could be when trying to permute complex data. This relates to incorrectly making deep copies during calls to swap functions. This will likely be corrected in most compilers with the introduction of rvalue references (part of the C++0x standard). Rewriting the STL to be much faster is surprisingly easy.
*This assumes the size of the class being permuted is variable. E.g. permutting a vector of vectors of ints would slow down if the vectors of ints were larger.
One that can give big speedups but is rarely done is to insert memory prefetch instructions. The trick is to figure out what memory the program will be wanting far enough in advance, never ask for the wrong memory and never overflow the D-cache.