“Multiple definition” when using (mock) header files for templates

I am aware that definitions of C++ templated functions have to be placed in header files. However, for reasons of improved readability and structure of a (potentially) big library I am making, I separated the declarations from the implementations, into "mock" headers (which #include the implementation files, quite like this structure of files). Note that am I am aware that the implementation of templated functions must be included at compile time, and I am doing that.

In short, I have a "multiple definition" error when I add a non-templated function declaration into the implementation file. Long explanation with examples follows.

When the pair of "mock" header + implementation files only contain the declaration/implementation pair of the templated function, everything works fine. It also works fine when I add an implementation of a new templated function only in the implementation file.

Working example (I would #include "algo.h" in my main.cpp when I wanted to use this functionality):

"Mock" header file algo.h:

#ifndef ALGO_H
#define ALGO_H

namespace fl{
    template <typename Compare>
    void algo(.. non-templated args .., Compare order = std::less<int>());
}

#include "tpp/algo.cpp"

#endif // ALGO_H

Implementation file tpp/algo.cpp: (currently just algo.tpp)
Note: Using the tpp/.cpp file was in the initial version, now I am using a .tpp file per @πάντα ῥεῖ's suggestion, explanation in the end.

#ifndef TPP_ALGO
#define TPP_ALGO

#include "../algo.h"

namespace fl{

    template <typename Compare>
    void subFunctionality(Compare order, .. args ..){ /* impl */ }

    template <typename Compare>
    void algo(.. non-templated args .., Compare order){
         subFunctionality(order, .. args ..);
        // implementation
    }
}

#endif // TPP_ALGO

The problem arises when I add a non-templated function implementation in the implementation file. (Non-working) example of the tpp/algo.cpp _{^{(currently just algo.tpp)}} (using the same algo.h):

#ifndef TPP_ALGO
#define TPP_ALGO

#include "../algo.h"

namespace fl{

    template <typename Compare>
    void subFunctionality(Compare order, .. args ..){ /* impl */ }

    void moreSubFun(.. args ..) { /* impl */ }

    template <typename Compare>
    void algo( .. non-templated args ..., Compare order){
         subFunctionality(order, .. args ..);
         moreSubFun(.. args ..);
         // more stuff
    }
}

#endif // TPP_ALGO

I get the "multiple definition" error (from where I included it in main.cpp), like so:

obj/Release/main.o                 In function `fl::moreSubFun(...)':
main.cpp                           multiple definitions of `fl::moreSubFun(..)'
obj/Release/../tpp/algo.o:algo.cpp first defined here

Why does this happen only to non-templated functions, while it works fine for the templated, and more importantly, how do I solve this problem?

I looked all around SO, and I can't find anything useful :( Ideally, I am looking for something as close to my own file-structure as possible (but I'll take anything that works while still using some separation into "mock" .h + tpp/.cpp). Do I have to take out the additional sub-functionalities into a separate, non-templated pair of .h/.cpp files, or is there other solutions? (The sub-functionalities should ideally not be visible to the end-user).

I am reluctant to use inline when defining fl::moreSubFunc(..) as the function is pretty big (and I was taught inline should ideally only be used with small functions). This does solve the problem, but I'm looking to see if there is a different solution.

I am working in Code::Blocks, using gcc version 4.7.2. This is the initial reason my implementation file is tpp/.cpp (.cpp extension), since Code::Blocks does not support it by default. This is changed in the current implementation following @πάντα ῥεῖ's suggestion (look below).

Late edit (After I taught the solution was found) I taught @πάντα ῥεῖ's answer solves the problem. I tweaked Code::Blocks to accept .tpp files (either treating it as header or source files). Initially, this solution worked.

However, this solution worked only when the algo.h file was included in only one other file: when I included it only in main.cpp. However, as soon as I tried including it in another source file (e.g. algo2.cpp) that would use those algorithms (in addition to main.cpp), the multiple definition problem came back.

Bottom line, the problem still persists as soon as I include the algo.h in more than one file, and I am still looking for a solution.

Your problem occurs because function templates are treated differently at link time from "plain" free functions. Functions must obey the One Definition Rule (ODR); that is, they must be defined in no more than one translation unit. Otherwise, when you get to link time, you end up with multiple definition errors like the one you cited. This same rule also applies to classes, types, and objects in general.

This would seem to preclude the use of templates at all; they must be fully included in every translation unit in which they are used. However, the ODR makes an exception for a few cases. Quoting from Wikipedia:

Some things, like types, templates, and extern inline functions, can be defined in more than one translation unit. For a given entity, each definition must be the same. Non-extern objects and functions in different translation units are different entities, even if their names and types are the same.

This is why you don't run into multiple definition errors with the template functions. At link time, the linker finds the duplicate symbol definitions and removes all duplicates (as long as they are all equivalent; otherwise, this would be an error). Therefore, your program links successfully with exactly one definition of each required symbol.

For your case, your problem occurs because you are including non-template functions in more than one translation unit (everywhere that the .cpp file is included). There would be a few ways of fixing this:

If the template functions are part of a class, you could move the non-template functions to lie in that class as well. This would bring it under the symbol-deduplicating umbrella of the owning template class.
Mark the functions as inline.
Break the non-template functions out into another .cpp file that you then compile separately. That will be the only translation unit that houses them.

In general you should compile .cpp file separately and link it later. But if you want (or must) do it this way, mark all non-template functions as inline. This should help.

As a good rule of thumb:

"Never ever include a .cpp file."

You shouldn't give these template implementation files a .cpp extension. Your build system might include them automatically then.

The conventionally used extensions for such files are e.g. .tcc or .icc. Add these to your project, as you would add other header files.
Don't include them in the project as separately build and linked translation units, if they are used with an #include statement from another header file.

UPDATE:
As you were asking for Code Blocks specifically, you'll just need to tweak your file extension settings a bit, to get these files included in your project correctly, and have them syntax colored as usual:

1. Add the new file type to the file extension settings