Casting int to bool in C/C++

I know that in C and C++, when casting bools to ints, (int)true == 1 and (int)false == 0. I'm wondering about casting in the reverse direction...

In the code below, all of the following assertions held true for me in .c files compiled with Visual Studio 2013 and Keil µVision 5. Notice (bool)2 == true.

What do the C and C++ standards say about casting non-zero, non-one integers to bools? Is this behavior specified? Please include citations.

#include <stdbool.h>
#include <assert.h>

void TestBoolCast(void)
{
    int i0 = 0, i1 = 1, i2 = 2;

    assert((bool)i0 == false);
    assert((bool)i1 == true);
    assert((bool)i2 == true);

    assert(!!i0 == false);
    assert(!!i1 == true);
    assert(!!i2 == true);
}

Not a duplicate of Can I assume (bool)true == (int)1 for any C++ compiler?:

1. Casting in the reverse direction (int --> bool).
2. No discussion there of non-zero, non-one values.

0 values of basic types ⁽¹⁾⁽²⁾map to false.

Other values map to true.

This convention was established in original C, via its flow control statements; C didn't have a boolean type at the time.

It's a common error to assume that as function return values, false indicates failure. But in particular from main it's false that indicates success. I've seen this done wrong many times, including in the Windows starter code for the D language (when you have folks like Walter Bright and Andrei Alexandrescu getting it wrong, then it's just dang easy to get wrong), hence this heads-up beware beware.

There's no need to cast to bool for built-in types because that conversion is implicit. However, Visual C++ (Microsoft's C++ compiler) has a tendency to issue a performance warning (!) for this, a pure silly-warning. A cast doesn't suffice to shut it up, but a conversion via double negation, i.e. return !!x, works nicely. One can read !! as a “convert to bool” operator, much as --> can be read as “goes to”. For those who are deeply into readability of operator notation. ;-)

^{1) C++14 §4.12/1 “A zero value, null pointer value, or null member pointer value is converted to false; any other value is converted to true. For direct-initialization (8.5), a prvalue of type std::nullptr_t can be converted to a prvalue of type bool; the resulting value is false.”
2) C99 and C11 §6.3.1.2/1 “When any scalar value is converted to _Bool, the result is 0 if the value compares equal to 0; otherwise, the result is 1.”}

The following cites the C11 standard (final draft).

6.3.1.2: When any scalar value is converted to _Bool, the result is 0 if the value compares equal to 0; otherwise, the result is 1.

bool (mapped by stdbool.h to the internal name _Bool for C) itself is an unsigned integer type:

... The type _Bool and the unsigned integer types that correspond to the standard signed integer types are the standard unsigned integer types.

According to 6.2.5p2:

An object declared as type _Bool is large enough to store the values 0 and 1.

AFAIK these definitions are semantically identical to C++ - with the minor difference of the built-in(!) names. bool for C++ and _Bool for C.

Note that C does not use the term rvalues as C++ does. However, in C pointers are scalars, so assigning a pointer to a _Bool behaves as in C++.