constexpr error at compile-time, but no overhead at run-time

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Is there a way to cause a compile-time error with a constexpr function, but not do anything at run time?

You can use the exact same trick, but instead of using a throw-expression, use an expression that is not a constant expression but does what you want at runtime. For instance:

int runtime_fallback(int x) { return x; } // note, not constexpr
constexpr int f(int x) {
  return (x != 0) ? x : runtime_fallback(0);
}

constexpr int k1 = f(1); // ok
constexpr int k2 = f(0); // error, can't call 'runtime_fallback' in constant expression
int k3 = f(0);           // ok

Do relaxed constexpr rules in C++1y (C++14) change anything?

Not in this area, no. There are some forms of expression that are valid in constant expressions in C++14 but not in C++11, but neither throw-expressions nor calls to non-constexpr functions are on that list.

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