How does a compiler deal with inlined exported functions? - c++

If a header file contains a function definition it can be inlined by the compiler. If the function is exported, the function's name and implementation must also be made available to clients during linkage. How does a compiler achieve this? Does it both inline the function and provide an implementation for external callers?
Consider Foo.h:
class Foo
{
int bar() { return 1; }
};
Foo::bar may be inlined or not in library foo.so. If another piece of code includes Foo.h does it always create its own copy of Foo::bar, whether inlined or not?

Header files are just copy-pasted into the source file — that's all #include does. A function is only inline if declared using that keyword or if defined inside the class definition, and inline is only a hint; it doesn't force the compiler to produce different code or prohibit you from doing anything you could otherwise do.
You can still take the address of an inline function, or equivalently, as you mention, export it. For those uses, the compiler simply treats it as non-inline and uses a One Definition Rule (the rule which says the user can't apply two definitions to the same function, class, etc) to "ensure" the function is defined once and only one copy is exported. Normally you are only allowed to have one definition among all sources; an inline function must have one definition which is repeated exactly in each source it is used.
Here is what the standard has to say about inline extern functions (7.1.2/4):
An inline function shall be defined in
every translation unit in which it is
used and shall have exactly the same
definition in every case (3.2). [Note:
a call to the inline function may be
encountered before its defi- nition
appears in the translation unit. ] If
a function with external linkage is
declared inline in one transla- tion
unit, it shall be declared inline in
all translation units in which it
appears; no diagnostic is required. An
inline function with external linkage
shall have the same address in all
translation units. A static local
variable in an extern inline function
always refers to the same object. A
string literal in an extern inline
function is the same object in
different translation units.

It usually means that it ends up creating a separate inlined method for every obj file that uses it at link time. It can also fail or refuse to inline many things, so this can cause a problem because you can wind up with bloated objs without getting the performance benefitting of inlining. The same thing can happen with virtual method inlining so it can be worth forcing inining and setting warning for inline failure (about the only useful warning message compilers give).

By export, I'm guessing you mean something such as getting a pointer to the function and later calling the function through the pointer.
Yes, in that case, the compiler will generate a regular function so that it can be invoked from a pointer.
One way to do this is with a link-once section. The idea is that in translation unit gets the code in a special type of section that has a name based on the function name. During linking, the linker will only keep one instance of identically named link-once sections.

inlined functions do not exist in the compiled binary: that is because they are taken and placed directly at the call site (so called IN-LINE). Each usage of the inlined function results in the complete code to be pulled in at that place.
So inlined functions cannot be exported because they do not exist. But you can still use them if you have a definition in one header. And yes, you MUST provide a definition for an inlined function, otherwise you cannot use it.
If you managed to export an inlined function then it is sure that it is not inline anymore: inline is not a strict semantic element. Depending on the compiler and compiler settings, one compiler might choose to inline, another not, sometimes provide a warning, sometimes even an error (which personnally I would prefer being the default behaviour, because it shows up the places where unintended things occur)

Related

Can a very short function become inlined even if it was not explicitly defined as inline?

I know in advance that, when writing a program in C or C++, even if I declare a function as "inline" the compiler is free to ignore this and decide not to expand it at each (or any) call.
Is the opposite true as well? That is, can a compiler automatically inline a very short function that wasn't defined as inline if the compiler believes doing so will lead to a performance gain?
Two other subquestions: is this behaviour defined somewhere in the ANSI standards? Is C different from C++ in this regard, or do they behave the same?
inline is non-binding with regards to whether or not a function will be inlined by the compiler. This was originally what it was intended to do. But since then, it's been realized that whether or not a function is worth inlining depends as much on the call site as the function itself and is best left to the compiler to decide.
From https://en.cppreference.com/w/cpp/language/inline :
Since this meaning of the keyword inline is non-binding, compilers are free to use inline substitution for any function that's not marked inline, and are free to generate function calls to any function marked inline. Those optimization choices do not change the rules regarding multiple definitions and shared statics listed above.
Edit : Since you asked for C as well, from https://en.cppreference.com/w/c/language/inline :
The intent of the inline specifier is to serve as a hint for the compiler to perform optimizations, such as function inlining, which require the definition of a function to be visible at the call site. The compilers can (and usually do) ignore presence or absence of the inline specifier for the purpose of optimization.
Regarding the relation between C and C++, the inline specifier is treated differently in each language.
In C++: inline functions (and function like entities, and variables (since C++17) ) that have not been previously declared with internal linkage will have external linkage and be visible from other compilation units. Since inline functions (usually) reside in header files, this means that the same function will have repeated definitions across different compilation units (this is would be a violation of the One definition rule but the inline makes it legal). At the end of the build process (when linking an executable or a shared lib), inline definitions of the same entity are merged together. Informally, C++ inline means: "there may be multiple identical definitions of some function across multiple source files, but I want them to end up as a unique definition".
In C: If extern is not explicitly specified, then an inline function definition is not visible from other translation units, different translation units may have different definitions with inline specifier for the same function name. Also, there may exist (at most) one definition for a function name that is both inline and extern and this qualifies that function as the one that is externally visible (ie gets selected when one applies the address of & operator to the function name). The One definition rule from C and its relation with extern and inline is somehow different from C++.
can a compiler automatically inline a very short function that wasn't defined as inline if the compiler believes doing so will lead to a performance gain?
Limitation:
When code uses a pointer to the function, then the function needs to exist non-inlined.
Limitation:
When the function is visible outside the local .c file (not static), this prevents simplistic inlined code.
Not a limitation:
The length of the function is not an absolute limitation, albeit a practical one.
I've worked with embedded processor that commonly inline static functions. (Given code does not use a pointer to them.)
The usefulness of the inline keyword does not affect the ability for a compiler to inline function.
When it comes to the standard, the keyword inline has nothing to do with inlining.
The rules (in c++) are basically:
A function which is not declared inline can by only defined in one translation union. It still needs to be delared in each translation unit where it is used.
A function which is declared inline has to be defined in each translation unit where it is odr-used (ord-use means to call the function or to take the pointer,...).
So, in a standard project setting it is almost always correct to follow the following two rules. Functions that are defined in a header file, are always to be declared inline. Functions defined in a *.cpp-file are never declared inline.
This said, I think the compiler cannot really draw any conclusions about the programmer wanted inlining from using or not using keyword inline. The name of the keyword is an unfortunate legacy from a bad naming.

Is inline forced when method body is in header file?

I know that the inline keyword is only a hint for the compiler, and not forced (unless using __forceinline e.g. in MSVC).
Is it also the case when declaring the inlined function in header? In which compilation unit will the compiler put the code?
inline is not just a hint to the compiler.
An inline function may be defined in multiple translation units, and all of these definitions will have the same type, address, and definition.
If a function is defined in a header, then it must be declared inline, or it will violate the One Definition Rule when it is included in multiple translation units.
An inline function is either:
A function at global scope can be declared inline using the keyword inline.
A function defined entirely inside a class/struct/union definition, whether it's a member function or a non-member friend function, is always inline.
A function declared constexpr is always inline.
(source)
Is it also the case [that inline is a hint] when declaring the inlined function in header?
Yes. The inline keyword is always a hint to the compiler to perform "inlining".
However, please note that this is only a hint. The compiler is free to ignore it (and many do).
The real reason compilers are able to perform inlining on inline functions is that the whole definition is available. You will notice the same inlining with static functions and instantiated function templates.
In which compilation unit will the compiler put the code?
Before linkage, the inline function will be fully defined in any compilation unit that defines it. It will be compiled in its entirety into each object file.
During linkage, the linker will determine which definition to use, and discard all the others.
See also this question and its answers.
The code will be present in all compillation units that include this header. The main point of inline is saying to the linker that this function can be found in multiple object files and any of these copies can be chosen by linker.
Inline is not forced, ever. If you define a method inside the class definition, it is implicitly inlined. It's like defining it outside the class definition except with inline implied. This has nothing to do with what file the definition is in.
When a function you requested to inline is not actually inlined, it's up to the compiler to decide where to put it. In early days, you could get a non-exported copy in each file that header file was included in. Now, some strategy is applied like putting it in the same place as the first constructor, the first method, or where the virtual function table is. It's compiler-dependent.

Inline keyword vs header definition

What's the difference between using the inline keyword before a function and just declaring the whole function in the header?
so...
int whatever() { return 4; }
vs
.h:
inline int whatever();
.cpp:
inline int myClass::whatever()
{
return 4;
}
for that matter, what does this do:
inline int whatever() { return 4; }
There are several facets:
Language
When a function is marked with the inline keyword, then its definition should be available in the TU or the program is ill-formed.
Any function defined right in the class definition is implicitly marked inline.
A function marked inline (implicitly or explicitly) may be defined in several TUs (respecting the ODR), whereas it is not the case for regular functions.
Template functions (not fully specialized) get the same treatment as inline ones.
Compiler behavior
A function marked inline will be emitted as a weak symbol in each object file where it is necessary, this may increase their size (look up template bloat).
Whereas the compiler actually inlines the call (ie, copy/paste the code at the point of use instead of performing a regular function call) is entirely at the compiler's discretion. The presence of the keyword may, or not, influence the decision but it is, at best, a hint.
Linker behavior
Weak symbols are merged together to have a single occurrence in the final library. A good linker could check that the multiple definitions concur but this is not required.
without inline, you will likely end up with multiple exported symbols, if the function is declared at the namespace or global scope (results in linker errors).
however, for a class (as seen in your example), most compilers implicitly declare the method as inline (-fno-default-inline will disable that default on GCC).
if you declare a function as inline, the compiler may expect to see its definition in the translation. therefore, you should reserve it for the times the definition is visible.
at a higher level: a definition in the class declaration is frequently visible to more translations. this can result in better optimization, and it can result in increased compile times.
unless hand optimization and fast compiles are both important, it's unusual to use the keyword in a class declaration these days.
The purpose of inline is to allow a function to be defined in more than one translation unit, which is necessary for some compilers to be able to inline it wherever it's used. It should be used whenever you define a function in a header file, although you can omit it when defining a template, or a function inside a class definition.
Defining it in a header without inline is a very bad idea; if you include the header from more than one translation unit, then you break the One Definition Rule; your code probably won't link, and may exhibit undefined behaviour if it does.
Declaring it in a header with inline but defining it in a source file is also a very bad idea; the definition must be available in any translation unit that uses it, but by defining it in a source file it is only available in one translation unit. If another source file includes the header and tries to call the function, then your program is invalid.
This question explains a lot about inline functions What does __inline__ mean ? (even though it was about inline keyword.)
Basically, it has nothing to do with the header. Declaring the whole function in the header just changes which source file has that the source of the function is in. Inline keyword modifies where the resulting compiled function will be put - in it's own place, so that every call will go there, or in place of every call (better for performance). However compilers sometimes choose which functions or methods to make inline for themselves, and keywords are simply suggestions for the compiler. Even functions which were not specified inline can be chosen by the compiler to become inline, if that gives better performance.
If you are linking multiple objects into an executable, there should normally only be one object that contains the definition of the function. For int whatever() { return 4; } - any translation unit that is used to produce an object will contain a definition (i.e. executable code) for the whatever function. The linker won't know which one to direct callers to. If inline is provided, then the executable code may or may not be inlined at the call sites, but if it's not the linker is allowed to assume that all the definitions are the same, and pick one arbitrarily to direct callers to. If somehow the definitions were not the same, then it's considered YOUR fault and you get undefined behaviour. To use inline, the definition must be known when compiler the call, so your idea of putting an inline declaration in a header and the inline definition in a .cpp file will only work if all the callers happen to be later in that same .cpp file - in general it's broken, and you'd expect the (nominally) inline function's definition to appear in the header that declares it (or for there to be a single definition without prior declaration).

Inline functions in C++

If we define a member function inside the class definition itself, is it necessarily treated inline or is it just a request to the compiler which it can ignore.
Yes, functions that are defined inside a class body are implicitly inline.
(As with other functions declared inline it doesn't mean that the complier has to perform inline expansion in places where the function is called, it just enables the permitted relaxations of the "one definition rule", combined with the requirement that a definition must be included in all translation units where the function is used.)
As stated by others, a method defined within a class is automatically requested inline.
It's useful to understand why.
Suppose it weren't. You'd have to generate code for such a function, and everywhere it is called, a jump to subroutine instruction would have to reference the location, via the linker.
class A {
public:
void f() { ... your code ... }
};
Every time this code is seen, if it's not inline, the compiler can only assume it must be generated, so it would generate a symbol. Suppose it was like this:
A__f_v:
If that symbol were global, then if you happened to include this class code multiple times in different modules, you would have a multiply defined symbol error at link time. So it can't be global. Instead, it's file local.
Imagine you include the above header file in a number of modules. In each one, it's going to generate a local copy of that code. Which is better than not compiling at all, but you're getting multiple copies of the code when you really need only one.
This leads the the following conclusion: if your compiler is not going to inline a function, you are significantly better off declaring it somewhere once, and not requesting it to be inlined.
Unfortunately, what is and is not inline is not portable. It's defined by the compiler writer. A good rule of thumb is to always make every one liner, particularly all functions which themselves just call a function, inline, as you remove overhead. Anything below three lines of linear code is almost certainly ok. But if you have a loop in the code, the question is whether the compiler will allow it inline, and more to the point, how much benefit you would see even if it did what you want.
consider this inline code:
inline int add(int a, int b) { return a + b; }
It's not only almost as small as the prototype would be in source code, but the assembly language generated by the inline code is smaller than the call to a routine would be. So this code is smaller, and faster.
And, if you happen to be passing in constants:
int c= add(5,4);
It's resolved at compile time and there is no code.
In gcc, I recently noticed that even if I don't inline code, if it's local to a file, they will sneakily inline it anyway. It's only if I declare the function in a separate source module that they do not optimize away the call.
On the other end of the spectrum, suppose you request inline on a 1000 line piece of code. Even if your compiler is silly enough to go along with it, the only thing you save is the call itself, and the cost is that every time you call it, the compiler must paste all that code in. If you call that code n times, your code grows by the size of the routine * n. So anything bigger than 10 lines is pretty much not worth inlining, except for the special case where it is only called a very small number of times. An example of that might be in a private method called by only 2 others.
If you request to inline a method containing a loop, it only makes sense if it often executes a small number of times. But consider a loop which iterates one million times. Even if the code is inlined, the percentage of time spent in the call is tiny. So if you have methods with loops in it, which tend to be bigger anyway, those are worth removing from the header file because they a) will tend to be rejected as inline by the compiler and b) even if they were inlined, are generally not going to provide any benefit
It is necessarily treated by the compiler as a request for inline -- which it can ignore. There are some idioms for defining some functions in the header (e.g. empty virtual destructors) and some necessary header definitions (template functions), but other than that see GotW #33 for more information.
Some have noted that the compiler may even inline functions you never asked it to, but I'm not sure whether that would defeat the purpose of requesting to inline a function.
It is indeed inlined - but any inline request can be ignored by the compiler.
It is a request to the compiler that it can ignore.
The 2003 ISO C++ standard says
7.1.2/2 A function declaration (8.3.5, 9.3, 11.4) with an inline
specifier declares an inline
function. The inline specifier
indicates to the implementation that
inline substitution of the function
body at the point of call is to be
preferred to the usual function call
mechanism. An implementation is not
required to perform this inline
substitution at the point of call;
however, even if this inline
substitution is omitted, the other
rules for inline functions defined
by 7.1.2 shall still be respected.
7.1.2/3 A function defined within a class definition is an inline
function. The inline specifier shall
not appear on a block scope function
declaration.
7.1.2/4 An inline function shall be defined in every translation unit in
which it is used and shall have
exactly the same definition in every
case (3.2). [Note: a call to the
inline function may be encountered
before its defi-nition appears in the
translation unit. ] If a function
with external linkage is declared
inline in one transla-tion unit, it
shall be declared inline in all
translation units in which it
appears; no diagnostic is required. An
inline function with external
linkage shall have the same address in
all translation units. A static
local variable in an extern inline
function always refers to the same
object. A string literal in an
extern inline function is the same
object in different translation
units.
There are two things that shouldn't be lumped together:
How you mark a function as being inline: define it with inline in front of the signature or define it at declaration point;
What the compiler will treat such inline marking: regardless of how you marked the function as inline it will be treated as a request by the compiler.

Inline member functions in C++

ISO C++ says that the inline definition of member function in C++ is the same as declaring it with inline. This means that the function will be defined in every compilation unit the member function is used. However, if the function call cannot be inlined for whatever reason, the function is to be instantiated "as usual". (http://msdn.microsoft.com/en-us/library/z8y1yy88%28VS.71%29.aspx) The problem I have with this definition is that it does not tell in which translation unit it would be instantiated.
The problem I encountered is that when facing two object files in a single static library, both of which have the reference to some inline member function which cannot be inlined, the linker might "pick" an arbitrary object file as a source for the definition. This particular choice might introduce unneeded dependencies. (among other things)
For instance:
In a static library
A.h:
class A{
public:
virtual bool foo() { return true; }
};
U1.cpp:
A a1;
U2.cpp:
A a2;
and lots of dependencies
In another project
main.cpp:
#include "A.h"
int main(){
A a;
a.foo();
return 0;
}
The second project refers the first. How do I know which definition the compiler will use, and, consequently which object files with their dependencies will be linked in? Is there anything the standard says on that matter? (Tried, but failed to find that)
Thanks
Edit: since I've seen some people misunderstand what the question is, I'd like to emphasize: If the compiler decided to create a symbol for that function (and in this case, it will, because of 'virtualness', there will be several (externally-seen) instantiations in different object file, which definition (from which object file?) will the linker choose?)
Just my two cents. This is not about virtual function in particular, but about inline and member-functions generally. Maybe it is useful.
C++
As far as Standard C++ is concerned, a inline function must be defined in every translation unit in which it is used. And an non-static inline function will have the same static variables in every translation unit and the same address. The compiler/linker will have to merge the multiple definitions into one function to achieve this. So, always place the definition of an inline function into the header - or place no declaration of it into the header if you define it only in the implementation file (".cpp") (for a non-member function), because if you would, and someone used it, you would get a linker error about an undefined function or something similar.
This is different from non-inline functions which must be defined only once in an entire program (one-definition-rule). For inline functions, multiple definitions as outlined above are rather the normal case. And this is independent on whether the call is atually inlined or not. The rules about inline functions still matter. Whether the Microsoft compiler adheres to those rules or not - i can't tell you. If it adheres to the Standard in that regard, then it will. However, i could imagine some combination using virtual, dlls and different TUs could be problematic. I've never tested it but i believe there are no problems.
For member-functions, if you define your function in the class, it is implicitly inline. And because it appears in the header, the rule that it has to be defined in every translation unit in which it is used is automatically satisfied. However, if you define the function out-of-class and in a header file (for example because there is a circular dependency with code in between), then that definition has to be inline if you include the corresponding file more than once, to avoid multiple-definition errors thrown by the linker. Example of a file f.h:
struct f {
// inline required here or before the definition below
inline void g();
};
void f::g() { ... }
This would have the same effect as placing the definition straight into the class definition.
C99
Note that the rules about inline functions are more complicated for C99 than for C++. Here, an inline function can be defined as an inline definition, of which can exist more than one in the entire program. But if such a (inline-) definition is used (e.g if it is called), then there must be also exactly one external definition in the entire program contained in another translation unit. Rationale for this (quoting from a PDF explaining the rationale behind several C99 features):
Inlining in C99 does extend the C++ specification in two ways. First, if a function is declared inline in one translation unit, it need not be declared inline in every other translation unit. This allows, for example, a library function that is to be inlined within the library but available only through an external definition elsewhere. The alternative of using a wrapper function for the external function requires an additional name; and it may also adversely impact performance if a translator does not actually do inline substitution.
Second, the requirement that all definitions of an inline function be "exactly the same" is replaced by the requirement that the behavior of the program should not depend on whether a call is implemented with a visible inline definition, or the external definition, of a function. This allows an inline definition to be specialized for its use within a particular translation unit. For example, the external definition of a library function might include some argument validation that is not needed for calls made from other functions in the same library. These extensions do offer some advantages; and programmers who are concerned about compatibility can simply abide by the stricter C++ rules.
Why do i include C99 into here? Because i know that the Microsoft compiler supports some stuff of C99. So in those MSDN pages, some stuff may come from C99 too - haven't figured anything in particular though. One should be careful when reading it and when applying those techniques to ones own C++ code intended to be portable C++. Probably informing which parts are C99 specific, and which not.
A good place to test small C++ snippets for Standard conformance is the comeau online compiler. If it gets rejected, one can be pretty sure it is not strictly Standard conforming.
When you have an inline method that is forced to be non-inlined by the compiler, it will really instantiate the method in every compiled unit that uses it. Today most compilers are smart enough to instantiate a method only if needed (if used) so merely including the header file will not force instantiation. The linker, as you said, will pick one of the instantiations to include in the executable file - but keep in mind that the record inside the object module is of a special kind (for instance, a COMDEF) in order to give the linker enough information to know how to discard duplicated instances. These records will not, therefore, result in unwanted dependencies between modules, because the linker will use them with less priority than "regular" records to resolve dependencies.
In the example you gave, you really don't know, but it doesn't matter. The linker won't resolve dependencies based on non-inlined instances alone ever. The result (in terms of modules included by the linker) will be as good as if the inline method didn't exist.
AFAIK, there is no standard definition of how and when a C++ compiler will inline a function call. These are usually "recommendations" that the compiler is in no way required to follow. In fact, different users may want different behaviors. One user may care about speed, while another may care about small generated object file size. In addition, compilers and platforms are different. Some compilers may apply smarter analysis, some may not. Some compilers may generate longer code from the inline, or work on a platform where calls are too expensive, etc.
When you have an inline function, the compiler should still generate a symbol for it and eventually resolve a single version of it. So that if it is in a static library, people can still call the function not in inline. In other words, it still acts as a normal function,.
The only effect of the inline is that some cases, the compiler will see the call, see the inline, and skip the call completely, but the function should still be there, it's just not getting called in this case.
If the compiler decided to create a symbol for that function (and in this case, it will, because of 'virtualness', there will be several (externally-seen) instantiations in different object file, which definition (from which object file?) will the linker choose?)
The definition that is present in the corresponding translation unit. And a translation unit cannot, and I repeat, cannot have but exactly one such definition. The standard is clear about that.
[...]the linker might "pick" an arbitrary object file as a source for the definition.
EDIT: To avoid any further misunderstanding, let me make my point clear: As per my reading of the standard, the ability to have multiple definition across different TUs does not give us any practical leverage. By practical, I mean having even slightly varying implementations. Now, if all your TUs have the exact same definition, why bother which TU the definition is being picked up from?
If you browse through the standard you will find the One Definition Rule is applied everywhere. Even though it is allowed to have multiple definitions of an inline function:
3.2 One Definition Rule:
5 There can be more than one definition of a class type (Clause 9), concept (14.9), concept map (14.9.2), enumeration type (7.2), inline function with external linkage (7.1.2), [...]
Read it in conjunction with
3 [...] An inline function shall be defined in every translation unit in which it is used.
This means that the function will be defined in every compilation unit [...]
and
7.1.2 Function Specifiers
2 A function declaration (8.3.5, 9.3, 11.4) with an inline specifier declares an inline function. The inline specifier indicates to the implementation that inline substitution of the function body at the point of call is to be preferred to the usual function call mechanism. An implementation is not required to perform this inline substitution at the point of call; however, even if this inline substitution is omitted, the other rules
for inline functions defined by 7.1.2 shall still be respected.
3 A function defined within a class definition is an inline function. The inline specifier shall not appear on a block scope function declaration.[footnote: 82] If the inline specifier is used in a friend declaration, that declaration shall be a definition or the function shall have previously been declared inline.
and the footnote:
82) The inline keyword has no effect on the linkage of a function.
§ 7.1.2 138
as well as:
4 An inline function shall be defined in every translation unit in which it is used and shall have exactly the same definition in every case (3.2). [ Note: a call to the inline function may be encountered before its definition appears in the translation unit. —end note ] If the definition of a function appears in a translation unit before its first declaration as inline, the program is ill-formed. If a function with external linkage is
declared inline in one translation unit, it shall be declared inline in all translation units in which it appears; no diagnostic is required. An inline function with external linkage shall have the same address in all translation units. A static local variable in an extern inline function always refers to the same object. A string literal in the body of an extern inline function is the same object in different translation units. [ Note: A string literal appearing in a default argument expression is not in the body of an inline function merely because the expression is used in a function call from that inline function. —end note ]
Distilled: Its ok to have multiple definitions, but they must have the same look and feel in every translation unit and address -- but that doesn't really give you much to cheer about. Having multiple deinition across translation units is therefore not defined (note: I am not saying you are invoking UB, yet).
As for the virtual thingy -- there won't be any inlining. Period.
The standard says:
The same declaration must be available
There must be one definition
From MSDN:
A given inline member function must be declared the same way in every compilation unit. This constraint causes inline functions to behave as if they were instantiated functions. Additionally, there must be exactly one definition of an inline function.
Your A.h contains the class definition and the member foo()'s definition.
U1.cpp and U2.cpp both define two different objects of class A.
You create another A object in main(). This is just fine.
So far, I have seen only one definition of A::foo() which is inline. (Remember that a function defined within the class declaration is always inlined whether or not it is preceded by the inline keyword.)
Don't inline your functions if you want to ensure they get compiled into a specific library.