Why does autoboxing make some calls ambiguous in Java?

I noticed today that auto-boxing can sometimes cause ambiguity in method overload resolution. The simplest example appears to be this:

public class Test {
    static void f(Object a, boolean b) {}
    static void f(Object a, Object b) {}

    static void m(int a, boolean b) { f(a,b); }
}

When compiled, it causes the following error:

Test.java:5: reference to f is ambiguous, both method
    f(java.lang.Object,boolean) in Test and method
    f(java.lang.Object,java.lang.Object) in Test match

static void m(int a, boolean b) { f(a, b); }
                                  ^

The fix to this error is trivial: just use explicit auto-boxing:

static void m(int a, boolean b) { f((Object)a, b); }

Which correctly calls the first overload as expected.

So why did the overload resolution fail? Why didn't the compiler auto-box the first argument, and accept the second argument normally? Why did I have to request auto-boxing explicitly?

When you cast the first argument to Object yourself, the compiler will match the method without using autoboxing (JLS3 15.12.2):

The first phase (§15.12.2.2) performs overload resolution without permitting boxing or unboxing conversion, or the use of variable arity method invocation. If no applicable method is found during this phase then processing continues to the second phase.

If you don't cast it explicitly, it will go to the second phase of trying to find a matching method, allowing autoboxing, and then it is indeed ambiguous, because your second argument can be matched by boolean or Object.

The second phase (§15.12.2.3) performs overload resolution while allowing boxing and unboxing, but still precludes the use of variable arity method invocation.

Why, in the second phase, doesn't the compiler choose the second method because no autoboxing of the boolean argument is necessary? Because after it has found the two matching methods, only subtype conversion is used to determine the most specific method of the two, regardless of any boxing or unboxing that took place to match them in the first place (§15.12.2.5).

Also: the compiler can't always choose the most specific method based on the number of auto(un)boxing needed. It can still result in ambiguous cases. For example, this is still ambiguous:

public class Test {
    static void f(Object a, boolean b) {}
    static void f(int a, Object b) {}

    static void m(int a, boolean b) { f(a, b); } // ambiguous
}

Remember that the algorithm for choosing a matching method (compile-time step 2) is fixed and described in the JLS. Once in phase 2 there is no selective autoboxing or unboxing. The compiler will locate all the methods that are accessible (both methods in these cases) and applicable (again the two methods), and only then chooses the most specific one without looking at boxing/unboxing, which is ambiguous here.

The compiler did auto-box the first argument. Once that was done, it's the second argument that's ambiguous, as it could be seen as either boolean or Object.

This page explains the rules for autoboxing and selecting which method to invoke. The compiler first tries to select a method without using any autoboxing at all, because boxing and unboxing carry performance penalties. If no method can be selected without resorting to boxing, as in this case, then boxing is on the table for all arguments to that method.