Can compiler optimization introduce bugs? - optimization

Today I had a discussion with a friend of mine and we debated for a couple of hours about "compiler optimization".
I defended the point that sometimes, a compiler optimization might introduce bugs or at least, undesired behavior.
My friend totally disagreed, saying that "compilers are built by smart people and do smart things" and thus, can never go wrong.
He didn't convince me at all, but I have to admit I lack of real-life examples to strengthen my point.
Who is right here? If I am, do you have any real-life example where a compiler optimization produced a bug in the resulting software? If I'm mistaking, should I stop programming and learn fishing instead?

Compiler optimizations can introduce bugs or undesirable behaviour. That's why you can turn them off.
One example: a compiler can optimize the read/write access to a memory location, doing things like eliminating duplicate reads or duplicate writes, or re-ordering certain operations. If the memory location in question is only used by a single thread and is actually memory, that may be ok. But if the memory location is a hardware device IO register, then re-ordering or eliminating writes may be completely wrong. In this situation you normally have to write code knowing that the compiler might "optimize" it, and thus knowing that the naive approach doesn't work.
Update: As Adam Robinson pointed out in a comment, the scenario I describe above is more of a programming error than an optimizer error. But the point I was trying to illustrate is that some programs, which are otherwise correct, combined with some optimizations, which otherwise work properly, can introduce bugs in the program when they are combined together. In some cases the language specification says "You must do things this way because these kinds of optimizations may occur and your program will fail", in which case it's a bug in the code. But sometimes a compiler has a (usually optional) optimization feature that can generate incorrect code because the compiler is trying too hard to optimize the code or can't detect that the optimization is inappropriate. In this case the programmer must know when it is safe to turn on the optimization in question.
Another example:
The linux kernel had a bug where a potentially NULL pointer was being dereferenced before a test for that pointer being null. However, in some cases it was possible to map memory to address zero, thus allowing the dereferencing to succeed. The compiler, upon noticing that the pointer was dereferenced, assumed that it couldn't be NULL, then removed the NULL test later and all the code in that branch. This introduced a security vulnerability into the code, as the function would proceed to use an invalid pointer containing attacker-supplied data. For cases where the pointer was legitimately null and the memory wasn't mapped to address zero, the kernel would still OOPS as before. So prior to optimization the code contained one bug; after it contained two, and one of them allowed a local root exploit.
CERT has a presentation called "Dangerous Optimizations and the Loss of Causality" by Robert C. Seacord which lists a lot of optimizations that introduce (or expose) bugs in programs. It discusses the various kinds of optimizations that are possible, from "doing what the hardware does" to "trap all possible undefined behaviour" to "do anything that's not disallowed".
Some examples of code that's perfectly fine until an aggressively-optimizing compiler gets its hands on it:
Checking for overflow
// fails because the overflow test gets removed
if (ptr + len < ptr || ptr + len > max) return EINVAL;
Using overflow artithmetic at all:
// The compiler optimizes this to an infinite loop
for (i = 1; i > 0; i += i) ++j;
Clearing memory of sensitive information:
// the compiler can remove these "useless writes"
memset(password_buffer, 0, sizeof(password_buffer));
The problem here is that compilers have, for decades, been less aggressive in optimization, and so generations of C programmers learn and understand things like fixed-size twos complement addition and how it overflows. Then the C language standard is amended by compiler developers, and the subtle rules change, despite the hardware not changing. The C language spec is a contract between the developers and compilers, but the terms of the agreement are subject to change over time and not everyone understands every detail, or agrees that the details are even sensible.
This is why most compilers offer flags to turn off (or turn on) optimizations. Is your program written with the understanding that integers might overflow? Then you should turn off overflow optimizations, because they can introduce bugs. Does your program strictly avoid aliasing pointers? Then you can turn on the optimizations that assume pointers are never aliased. Does your program try to clear memory to avoid leaking information? Oh, in that case you're out of luck: you either need to turn off dead-code-removal or you need to know, ahead of time, that your compiler is going to eliminate your "dead" code, and use some work-around for it.

When a bug goes away by disabling optimizations, most of the time it's still your fault
I am responsible for a commercial app, written mostly in C++ - started with VC5, ported to VC6 early, now successfully ported to VC2008. It grew to over 1 Million lines in the last 10 years.
In that time I could confirm a single code generation bug thast occured when agressive optimizations where enabled.
So why am I complaining? Because in the same time, there were dozens of bugs that made me doubt the compiler - but it turned out to be my insufficient understanding of the C++ standard. The standard makes room for optimizations the compiler may or may not make use of.
Over the years on different forums, I've seen many posts blaming the compiler, ultimately turning out to be bugs in the original code. No doubt many of them obscure bugs that need a detailed understanding of concepts used in the standard, but source code bugs nonetheless.
Why I reply so late: stop blaming the compiler before you have confirmed it's actually the compiler's fault.

Compiler (and runtime) optimization can certainly introduce undesired behaviour - but it at least should only happen if you're relying on unspecified behaviour (or indeed making incorrect assumptions about well-specified behaviour).
Now beyond that, of course compilers can have bugs in them. Some of those may be around optimisations, and the implications could be very subtle - indeed they're likely to be, as obvious bugs are more likely to be fixed.
Assuming you include JITs as compilers, I've seen bugs in released versions of both the .NET JIT and the Hotspot JVM (I don't have details at the moment, unfortunately) which were reproducible in particularly odd situations. Whether they were due to particular optimisations or not, I don't know.

To combine the other posts:
Compilers do occasionally have bugs in their code, like most software. The "smart people" argument is completely irrelevant to this, as NASA satellites and other apps built by smart people also have bugs. The coding that does optimization is different coding from that which doesn't, so if the bug happens to be in the optimizer then indeed your optimized code may contain errors while your non-optimized code will not.
As Mr. Shiny and New pointed out, it's possible for code that is naive with regard to concurrency and/or timing issues to run satisfactorily without optimization yet fail with optimization as this may change the timing of execution. You could blame such a problem on the source code, but if it will only manifest when optimized, some people might blame optimization.

Just one example: a few days ago, someone discovered that gcc 4.5 with the option -foptimize-sibling-calls (which is implied by -O2) produces an Emacs executable that segfaults on startup.
This has apparently been fixed since.

I've never heard of or used a compiler whose directives could not alter the behaviour of a program. Generally this is a good thing, but it does require you to read the manual.
AND I had a recent situation where a compiler directive 'removed' a bug. Of course, the bug is really still there but I have a temporary workaround until I fix the program properly.

Yes. A good example is the double-checked locking pattern. In C++ there is no way to safely implement double-checked locking because the compiler can re-order instructions in ways that make sense in a single-threaded system but not in a multi-threaded one. A full discussion can be found at http://www.aristeia.com/Papers/DDJ_Jul_Aug_2004_revised.pdf

Is it likely? Not in a major product, but it's certainly possible. Compiler optimizations are generated code; no matter where code comes from (you write it or something generates it), it can contain errors.

I encountered this a few times with a newer compiler building old code. The old code would work but relied on undefined behavior in some cases, like improperly defined / cast operator overload. It would work in VS2003 or VS2005 debug build, but in release it would crash.
Opening up the assembly generated it was clear that the compiler had just removed 80% of the functionality of the function in question. Rewriting the code to not use undefined behavior cleared it up.
More obvious example: VS2008 vs GCC
Declared:
Function foo( const type & tp );
Called:
foo( foo2() );
where foo2() returns an object of class type;
Tends to crash in GCC because the object isn't allocated on the stack in this case, but VS does some optimization to get around this and it will probably work.

Aliasing can cause problems with certain optimizations, which is why compilers have an option to disable those optimizations. From Wikipedia:
To enable such optimizations in a predictable manner, the ISO standard for the C programming language (including its newer C99 edition) specifies that it is illegal (with some exceptions) for pointers of different types to reference the same memory location. This rule, known as "strict aliasing", allows impressive increases in performance[citation needed], but has been known to break some otherwise valid code. Several software projects intentionally violate this portion of the C99 standard. For example, Python 2.x did so to implement reference counting,[1] and required changes to the basic object structs in Python 3 to enable this optimisation. The Linux kernel does this because strict aliasing causes problems with optimization of inlined code.[2] In such cases, when compiled with gcc, the option -fno-strict-aliasing is invoked to prevent unwanted or invalid optimizations that could produce incorrect code.

Yes, compiler optimizations can be dangerous. Usually hard real-time software projects forbids optimizations for this very reason. Anyway, do you know of any software with no bugs?
Aggressive optimizations may cache or even do strange assumptions with your variables. The problem is not only with the stability of your code, but also they can fool your debugger. I have seen several times a debugger failing to represent the memory contents because some optimizations retained a variable value within the registers of the micro
The very same thing can happen to your code. The optimization puts a variable into a register and do not write to the variable until it has finished. Now imagine how different things can be if your code has pointers to variables in your stack and it has several threads

It's theoretically possible, sure. But if you don't trust the tools to do what they are supposed to do, why use them? But right away, anyone arguing from the position of
"compilers are built by smart people
and do smart things" and thus, can
never go wrong.
is making a foolish argument.
So, until you have reason to believe that a compiler is doing so, why posture about it?

I certainly agree that it's silly to say the because compilers are written by "smart people" that they are therefore infallible. Smart people designed the Hindenberg and the Tacoma Narrows Bridge, too. Even if it's true that compiler-writers are among the smartest programmers out there, it's also true that compilers are among the most complex programs out there. Of course they have bugs.
On the other hand, experience tells us that the reliability of commercial compilers is very high. I've had many many times that someone told me that the reason why is program doesn't work MUST be because of a bug in the compiler because he has checked it very carefully and he is sure that it is 100% correct ... and then we find that in fact the program has an error and not the compiler. I'm trying to think of times that I've personally run across something that I was truly sure was an error in the compiler, and I can only recall one example.
So in general: Trust your compiler. But are they ever wrong? Sure.

It can happen. It has even affected Linux.

As I recall, early Delphi 1 had a bug where the results of Min and Max were reversed. There was also an obscure bug with some floating point values only when the floating point value was used within a dll. Admittedly, it has been more than a decade, so my memory may be a bit fuzzy.

I have had a problem in .NET 3.5 if you build with optimization, add another variable to a method which is named similarly to an existing variable of the same type in the same scope then one of the two (new or old variable) will not be valid at runtime and all references to the invalid variable are replaced with references to the other.
So, for example, if I have abcd of MyCustomClass type and I have abdc of MyCustomClass type and I set abcd.a=5 and abdc.a=7 then both variables will have property a=7. To fix the issue both variables should be removed, the program compiled (hopefully without errors) then they should be re-added.
I think I have run into this problem a few times with .NET 4.0 and C# when doing Silverlight applications also. At my last job we ran into the problem quite often in C++. It might have been because the compilations took 15 minutes so we would only build the libraries we needed, but sometimes the optimized code was exactly the same as the previous build even though new code had been added and no build errors had been reported.
Yes, code optimizers are built by smart people. They are also very complicated so having bugs is common. I suggest fully testing any optimized release of a large product. Usually limited use products are not worth a full release, but they should still be generally tested to make sure they perform their common tasks correctly.

Compiler optimization can reveal (or activate) dormant (or hidden) bugs in your code. There may be a bug in your C++ code that you don't know of, that you just don't see it. In that case, it is a hidden or dormant bug, because that branch of the code is not executed [enough number of times].
The likelihood of a bug in your code is much bigger (thousands of times more) than a bug in the compiler's code: Because the compilers are tested extensively. By TDD plus practically by all people who have use them since their release!). So it is virtually unlikely that a bug is discovered by you and not discovered by literally hundreds of thousands of times it is used by other people.
A dormant bug or hidden bug is just a bug that is not revealed itself to the programmer yet. People who can claim that their C++ code does not have (hidden) bugs are very rare. It requires C++ knowledge (very few can claim for that) and extensive testing of the code. It is not just about the programmer, but about the code itself (the style of development). Being bug-prone is in the character of the code (how rigorously it is tested) or/and the programmer (how disciplined is in test and how well knows C++ and programming).
Security+Concurrency bugs: This is even worse if we include concurrency and security as bugs. But after all, these 'are' bugs. Writing a code that is in the first place bug-free in terms of concurrency and security is almost impossible. That's why there is always already a bug in the code, which can be revealed (or forgotten) in compiler optimization.

More, and more aggressive optimizations could be enabled if the program you compile has a good testing suite. Then it is possible to run that suite and be somewhat more sure the program operates correctly. Also, you can prepare your own tests that match closely that do you plan to do in production.
It is also true that any large program may have (and probably indeed has) some bugs independently on which switches do you use to compile it.

I work on a large engineering application, and every now and then we see release only crashes and other problems reported by clients. Our code has 37 files (out of around
6000) where we have this at the top of the file, to turn off optimization to fix such crashes:
#pragma optimize( "", off)
(We use Microsoft Visual C++ native, 2015, but it is true for just about any compiler, except maybe Intel Fortran 2016 update 2 where we have not yet turned of any optimizations.)
If you search through the Microsoft Visual Studio feedback site you can find some optimization bugs there as well. We occasionally log some of ours (if you can reproduce it easily enough with a small section of code and you are willing to take the time) and they do get fixed, but sadly others get introduced again. smiles
Compilers are programs written by people, and any big program has bugs, trust me on that. The compiler optimization options most certainly has bugs and turning on optimization can certainly introduce bugs in your program.

Everything that you can possibly imagine doing with or to a program will introduce bugs.

Because of exhaustive testing and the relative simplicity of actual C++ code (C++ has under 100 keywords / operators) compiler bugs are relatively rare. Bad programming style often is the only thing encounters them. And usually the compiler will crash or produce an internal compiler error instead. The only exception to this rule is GCC. GCC, especially older versions, had a lot of experimental optimizations enabled in O3 and sometimes even the other O levels. GCC also targets so many backends that this leaves more room for bugs in their intermediate representation.

I had a problem with .net 4 yesterday with something that looks like...
double x=0.4;
if(x<0.5) { below5(); } else { above5(); }
And it would call above5(); But if I actually use x somewhere, it would call below5();
double x=0.4;
if(x<0.5) { below5(); } else { System.Console.Write(x); above5(); }
Not the exact same code but similar.

Related

Are there any reasons to compile without optimizations?

In most projects I don't see any -Ox flags, which you think would be standard for every project, since it could dramatically increase the speed of the program.
Are there any specific reasons to not compile with -Ox or it's non-gcc counterparts?
It's much easier to debug an unoptimised program, because the object code tends to be a more direct translation of the source code. With optimisation enabled the compiler might re-order statements or eliminate them entirely by coalescing several operations into one. That means when debugging a program (or a core dump) there isn't such a direct mapping from a position in the program image to a line of source code.
GCC 4.8 adds a new optimisation level that is a great compromise between performance and debuggability:
A new general optimization level, -Og, has been introduced. It addresses the need for fast compilation and a superior debugging experience while providing a reasonable level of runtime performance. Overall experience for development should be better than the default optimization level -O0.
With -Og the compiler does simple optimisations that don't make it harder to debug and don't take too long to compile, so the code performs better than completely unoptimised code but can still be debugged.
One reason is if you want to step through the code with a debugger. If optimizations are enabled statements can be reordered or missed out and the execution of the program will not have to follow what is in the source code step-by-step. Values of variables may not be available because they have been optimized out. Thus it is hard to reason about what the program is doing as you run it in the debugger.
Another reason for avoiding optimization is that you have used undefined behaviour in your program, and optimization could cause your program to break. (In fact, that is a reason for using optimization - to find such bugs.)
This makes Debug more accurate without optimization.
Unused variables, redundant statements will not be skipped.
On a somewhat older project, all our tests were done with debug build, including a lot of print statements. For the final build, delivered to the customer, it was decided not to use a less-tested retail build (using gcc's full optimization options), since that could introduce timing related issues (actually, the finding of defects now masked due to the specific timing of the debug builds), and since the customer was happy enough with the current speed of operation.
On my current project, a lot of code is to be placed in ROM (initially: all), and then we obviously don't want to remove dead code, as future updates - to be placed in ram - can then still make use of the rom code, reducing space requirements in ram.
Also, what would be the default? Optimize for space, or for execution time? Not choosing is the only right choice to make.

Is optimization necessary when code generation is targeting a runtime with JIT?

I'm planning on writing a programming language targeting the .NET platform which led me to start thinking about the code generation aspect of targeting such a platform. I'm new at writing compilers but I know there is optimization done as one of the phases in compiling (or there can be). I started to wonder about the any benefit to spending time optimizing the output (in this case CIL but this would apply to the JVM too) because the JIT compiler and things like the JVM's HotSpot could optimize at run time. Is there any benefit from optimizing the generated code (CIL or the JVM equivalent) when targeting .NET or JVM since the JIT will already optimize?
It depends. There are countless optimizations. Any given compiler (your compiler, the JIT compiler, or any other compiler) necessarily implements only a subset of those. This choice depends on available time, typical/expected input code, priorities, etc. and therefore the engineers who built the JIT compiler may have selected optimizations which work well for the programs they were expecting, but not so well for the kind of program you care about.
You will have to determine what optimizations the JIT compiler misses. The way to do this is, of course, empirical: Actually write programs, letting the JIT compiler optimize them (be sure to do this part properly - disable debugging, compile for release, choose realistic benchmarks, etc.), and then inspect the final machine code. Look for unexpected code (you will, of course, need assembly knowledge for this) and determine if it's a missed optimization or if the JIT was smarter than you thought.
If it is a missed optimization, you have another problem: You can't output the machine code you want, you have to generate different IL instead.
A missed optimization is probably due to a language feature the VM doesn't know (e.g. multi methods on the JVM). You lowered it into the VM's terms during compilation but the translation you chose doesn't sit well with the JIT's order of passes, heuristics, etc.
As you can't just output machine code yourself, you must now find an alternative IL fragment for the same input language code. Ideally, one which the JIT compiler does handle well. Finding that may be an exercise in imagination, but it's not technically hard, just guesswork interleaved with benchmarking.
As another answer points out, JIT compilers work under time constraints. This may lead to optimizations that could happen being missed (e.g. constant propagation running out of time), but as the creators of the JIT compiler faced the same problem, this probably isn't too severe if you don't create much larger/more complicated code.
If you create such bad code that the JIT compiler can't fix it all, then you have to duplicate its optimizations in your AOT compiler. I'm not convinced that this is a likely scenario though, and even if it happens even very simple optimizations should mostly fix the problem.
So, in summary: Start with a straightforward translation, then seek out missed optimizations and either make it easier to optimize for the JIT compiler, or do it yourself (if possible - adaptive optimization is much harder in an AOT setting).
I think this question is hard to answer in general.
For example, the F# compiler performs a tail call optimization, because having tail-recursive functions is common in that language, the F# compiler can do a better job at optimizing them in some cases than the JIT compiler and some versions of the JIT compiler don't perform the optimization at all.
So, your language might have some common operation whose straightforward implementation wouldn't perform well. In that case, it makes sense emitting IL code that's optimized.
What I think you should do is the same as when you're writing a normal program: first write your code in a way that is simple and readable. Only if something doesn't perform well, attempt to optimize that. It might be worth considering that you might need some optimizations in the future and make your code modular enough, so that you don't have to rewrite half of it because of some optimization. But for now, that should be enough.
Writing a compiler is hard enough job already (even if you're targeting an IL). Finish it first and think about optimizations later.
Generally, JIT compilers have some thresholds governing how much optimization they will attempt to perform. These may be based on the size of a method's IL and/or the amount of time already spent JIT compiling the method. So yes, IL which has already been optimized may benefit from further JIT optimization. As always, there is a trade-off: how much time do you want to spend adding AOT optimizations to your compiler (and testing/maintaining them) versus how quickly your code can be JIT compiled, and with what level of optimization.
The magnitude of the improvement depends largely on how much simpler (and smaller) the AOT-optimized IL is relative to the unoptimized IL, as well as the thresholds governing the JIT compiler (which, at least for the Microsoft CLR, are not widely known). The only way to find out is to do some testing yourself.

static and dynamic code analysis

I found several questions about this topic, and all of them with lot of references, but still I don't have a clear idea about that, because most of the references speak about concrete tools and not about the concept in general of the analysis. Thus I have some questions:
About Static analysis:
1. I would like to have a reference, or a summary of which techniques are successful and have more relevance nowadays.
2. What really can they do about discovering bugs, can we make a summary or it is depending of the tool?
About symbolic execution:
1. Where could be enclose symbolic execution? I guess depending of the approach,
I would like to know if they are dynamic analysis, or mix of static and dynamic analysis if it is possible to determine.
I found problems to differentiated the two different techniques in the tools, even I think I know the theoretical difference.
I'm actually working with C
Thanks in advance
I'm trying to give a short answer:
Static analysis looks at the syntactical structure of code and draws conclusions about the program behavior. These conclusions must not always be correct.
A typical example of static analysis is data flow analysis, where you compute sets like used, read, write for every statement. This will help to find e.g. uninitialized values.
You can also analyze the code regarding code-patterns. This way, these tools can be used to check if you are complying to a specific coding standard. A prominent coding standard example is MISRA. This coding standard is used for safety critical systems and avoids problematic constructs in C. This way you can already say a lot about the robustness of your applications against memory leaks, dangling pointers, etc.
Dynamic analysis is not looking at the syntax only, but takes state information into account. In symbolic execution, you are adding assumptions about the possible values of all variables to the statements.
The most expensive and powerful method of dynamic analysis is model checking, where you really look at all possible execution states of the system. You can think of a model checked system as a system that is tested with 100% coverage - but there are of course a lot of practical problems that prevent real systems to be checked that way.
These methods are very powerful, and you can gain a lot from the static code analysis tools especially when combined with a good coding standard.
A feature my software team found really impressive is e.g. that it will tell you in C++ when a class with virtual methods does not have a virtual destructor. Easy to check in fact, but really helpful.
The commercial tools are very expensive, but worth the money, once you learned how to use them. A typical problem in the beginning is that you will get a lot of false alarms, and don't know where to look for the real problem.
Note that nowadays g++ has some of this stuff already built-in, and that you can use something like pclint which is free.
Sorry - this is already getting quite long...hope it's interesting.
The term "static analysis" means that the analysis does not actually run a code. On the other hand, "dynamic analysis" runs a code and also requires some kinds of real test inputs. That is the definition. Nothing more.
Static analysis employs various formal methods such as abstract interpretation, model checking, and symbolic execution. In general, abstract interpretation or model checking is suitable for software verification. Symbolic execution is more appropriate for the purpose of bug finding.
Symbolic execution is categorized into static analysis. However, there is a hybrid method called concolic execution which uses both symbolic execution and dynamic testing.
Added for Zane's comment:
Maybe my explanation was little confusing.
The difference between software verification and bug finding is whether the analysis is sound or not. For example, when we say the buffer overrun analyzer is sound, it means that the analyzer must report all possible buffer overruns. If the analyzer reports nothing, it proves the absence of buffer overruns in the target program. Because model checking is the method that guarantees soundness, it is mostly used for software verification.
On the other hands, symbolic execution which is actively used by today's most commercial static analyzers does not guarantee soundness since sound analysis inherently issues lots, lots of false positives. For the purpose of bug finding, it is more important to reduce false positives even if some true positives are also lost.
In summary,
soundness: there are no false negatives
completeness: there are no false positives
software verification: soundness is more important than completeness
bug finding: completeness is more important than soundness

Does "DO-178B level A" prohibits optimizing compilers?

There is an "DO-178B" level A and level B certification for airborne systems. Does it prohibit using of optimizating compilers?
E.g. Some compilers will reorder instructions to get more performance. Does DO-178B lev.A or lev.B prohibits this reordering?
Most modern CPU have such reordering builtin in the hardware. Are they allowed to be used within DO-178B lev.A softare/hardware systems?
First, and critically: For this type of question, if the answer matters, you need to get a formal professional opinion from someone who is competent to provide it, or discuss this with your certification authority. Any reply you will get here should not be relied on.
With that said, I will assume you are asking from a point of curiousity and will not be relying on the answer in any meaningful way, and I will attempt to answer in that vein. I am not a professional, and this is not professional advice.
The most on-point documentation I could find online with a quick search was this FAA guideline paper about a related topic: http://www.faa.gov/aircraft/air_cert/design_approvals/air_software/cast/cast_papers/media/cast-12.pdf. This paper describes the conditions under which one must do verification of the generated object code rather than the source code. In particular, it gives a number of examples that will occur even in non-optimized code -- automatic variable initialization and exception handling are a couple of examples. On compiler optimization, it notes:
Compiler optimization is another area addressed under section 4.4.2a of DO-178B/ED-12B. This involves the analytical determination that the optimization features do not compromise the ability of the test cases to demonstrate requirements-based testing and structural coverage consistent with the software level. This is a separate issue from the traceability and additional verifications issues addressed by Section 4.4.2b. This is outside the scope of this paper.
I do not have a copy of DO-178B handy to read section 4.4.2a, but I would note that (a) there are procedures for handling other cases where the object code does not correspond to the source code in a one-to-one manner, and (b) this pretty strongly implies that compiler optimization is discussed rather than outright prohibited.
It's also pretty clear from a number of the discussions in that paper that the answer to "we can't trace things between the source code and the object code" is to validate the object code in some manner -- in other words, there is a solution other than prohibiting such things.
Thus, I would conclude that at least some compiler optimizations must be permitted.
In particular, the sort of reordering that you describe is quite traceable, and it seems almost certain to me that it would be permitted.
DO-178B is not absolute and is open to interpretation. If you switch off optimisation there is no questions and nothing to explain. By sticking to the most obvious interpretation you avoid having to sell your interpretation to certification authorities later on and opening your self up to questions about how you did things.
When you optimise your code it is hard to do the source to instruction traceability that is required for level A. In addition if you are using Do-178B getting that extra 5% out of your software is not your greatest concern. The ease of completing all the required certification steps should be your primary concern since that is what is going to be sucking up all your time.
The hardware part of your question is interesting. For software optimisation code is not just reordered it is changed as well. But for hardware the code is not changed to get higher speed only the execution order. I have to ask around to get more info on what the thinking is on this.
I have only superficial knowledge of DO-178B (I do not work day-to-day with it, but I build tools for people who do).
The standard takes traceability very seriously. High-level requirements are declined into low-level requirements, which are implemented by the source code, which is compiled by the compiler. At each of these steps, one must be able to justify what was done in terms of the specifications produced by the previous step.
For the compiler, this means that one must be able to read the assembly and trace one particular instruction to the source code statement that caused this instruction to be generated.
So, in short, yes, I think this prohibits most optimizations.
Concerning the hardware this software is run on, it is verified differently (but I guess just as stringently). The relevant standard is then DO-254, and I do not know anything about it.
With optimization, you need to verify the generated code at the object assembly language level. There are compiler suites and libraries for embedded real-time multitasking that have been previously verified in other projects, giving you a comfort level that they can be verified again - but you still need to verify the code used in your application.
To avoid delays and having to explain things just turn off optimizations and cache. This makes the code deterministic. Also try not to use GCC if possible and go for a qualified compiler such as IAR or DDCI or Irvine Compilers or something. Instead of trying bang the screw with a fancy hammer get a screw driver that works for the screw. Because when that plane crashes with 200 people on board, with mothers, fathers and children and they find out that the compiler reordered code and that caused the failure you will wish that you only had the right screw driver.

Can I control register allocation in g++?

I have highly optimized piece of C++ and making even small changes in places far from hot spots can hit performance as much as 20%. After deeper investigation it turned out to be (probably) slightly different registers used in hot spots.
I can control inlineing with always_inline attribute, but can I control register allocation?
If you really want to mess with the register alloation then you can force GCC to allocate local and global variables in certain registers.
You do this with a special variable declaration like this:
register int test_integer asm ("EBX");
Works for other architectures as well, just replace EBX with a target specific register name.
For more info on this I suggest you take a look at the gcc documentation:
http://gcc.gnu.org/onlinedocs/gcc-4.3.3/gcc/Local-Reg-Vars.html
My suggestion however is not to mess with the register allocation unless you have very good reasons for it. If you allocate some registers yourself the allocator has less registers to work with and you may end up with a code that is worse than the code you started with.
If your function is that performance critical that you get 20% performance differences between compiles it may be a good idea to write that thing in inline-assembler.
EDIT: As strager pointed out the compiler is not forced to use the register for the variable. It's only forced to use the register if the variable is used at all. E.g. if the variable it does not survive an optimization pass it won't be used. Also the register can be used for other variables as well.
In general the register keyword is simply ignored by all modern compilers. The only exception is the (relatively) recent addition of an error if you attempt to take the address of a variable you've marked with the register keyword.
I've experienced this sort of pain as well, and eventually found the only real way around it was to look at output assembly to try and determine what is causing gcc to go off the deepend. There are other things you can do but it depends on exactly what your code is trying to do. I was working in a very very large function with a large amount of computed goto mayhem in which minor (seemingly innocuous) changes could cause catastrophic performance hits. If you're doing similar there are a few things you can do to try and mitigate the problem, but the details are somewhat icky so i'll forgo discussing them here unless it's actually relevant.
It depends on the processor you are using. Or should I say, yes you can with the register keyword, but this is frowned upon unless you are using a simple processor with no pipe-lining and a single core. These days GCC can do a way better job than you can with register allocation. Trust it.