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The Rationale for rule 8.10 says that inline functions with external linkage are not to be used, because it is not defined whether the function will in fact be inlined, or the external definition will be called.
However, this is also not defined for static functions: "Making a function an inline function suggests that calls to the function be as fast as possible. The extent to which such suggestions are effective is implementation-defined." (I'm using a draft of the C99 standard, http://www.open-std.org/JTC1/sc22/wg14/w.../n1256.pdf and this is 6.7.4.5. Footnote 121 spells it out more clearly: "For example, an implementation might never perform inline substitution...".)
So the behaviour of static inline functions is undefined in the same way as inline functions with external linkage.
It has been suggested that inline functions defined in header files should be defined with static linkage. Paragraph 6.7.4.3 of the above pdf says external linkage cannot reference indentifiers with internal linkage, but paragraph 6.7.4.6 says that any function with internal linkage can be inlined. So if an inline function is declared static, it can have local static variables. But there will be a different instance of the inline function for each .c file which includes the header with the function's definition, and each would have its own static variables! Effectively, you have a function definition with a static variable, the value of which differs depending on where it is called from. This will surely be unexpected behaviour to some programmers, and is therefore dangerous.
Was this considered when specifying that all inline functions should be static? Or is the draft wildly different from the final C99 spec?
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