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The compiler problem here was in explicit scheduling, not counting outgoing registers. Modern C compilers for x86 architectures already do the latter.

I recall learning that the important part of the optimization phase for Itanium was based on runtime performance analysis, not just static optimizations.

That's true, but figuring out the maximum number of arguments passed to another function is trivial; I would think it isn't harder than determining how much space one needs for local variables in an Algol-like language.

That's definitely true, but counting function parameters was only a small part of the difficulty. Weren't most of the problems related to optimization being harder and less effective than predicted?

Because they had to deal with all the issues in Itanium Architecture Parts 1, 2, 3,..., n where the sum is a lot harder than this issue. ;)