Why is 0 < -0x80000000?

This is quite subtle.

Every integer literal in your program has a type. Which type it has is regulated by a table in 6.4.4.1:

Suffix      Decimal Constant    Octal or Hexadecimal Constant

none        int                 int
            long int            unsigned int
            long long int       long int
                                unsigned long int
                                long long int
                                unsigned long long int

If a literal number can't fit inside the default int type, it will attempt the next larger type as indicated in the above table. So for regular decimal integer literals it goes like:

• Try int
• If it can't fit, try long
• If it can't fit, try long long.

Hex literals behave differently though! If the literal can't fit inside a signed type like int, it will first try unsigned int before moving on to trying larger types. See the difference in the above table.

So on a 32 bit system, your literal 0x80000000 is of type unsigned int.

This means that you can apply the unary - operator on the literal without invoking implementation-defined behavior, as you otherwise would when overflowing a signed integer. Instead, you will get the value 0x80000000, a positive value.

bal < INT32_MIN invokes the usual arithmetic conversions and the result of the expression 0x80000000 is promoted from unsigned int to long long. The value 0x80000000 is preserved and 0 is less than 0x80000000, hence the result.

When you replace the literal with 2147483648L you use decimal notation and therefore the compiler doesn't pick unsigned int, but rather tries to fit it inside a long. Also the L suffix says that you want a long if possible. The L suffix actually has similar rules if you continue to read the mentioned table in 6.4.4.1: if the number doesn't fit inside the requested long, which it doesn't in the 32 bit case, the compiler will give you a long long where it will fit just fine.

0x80000000 is an unsigned literal with value 2147483648.

Applying the unary minus on this still gives you an unsigned type with a non-zero value. (In fact, for a non-zero value x, the value you end up with is UINT_MAX - x + 1.)