If int n = INT_MIN, why (-n)/2 is positive?-CodePudding

I've been experimenting with the lowest signed 32-bit integer. I wrote the following program:

#include <iostream>
#include <climits>

int main() {
  int n = 1<<31; //-2³¹
  std::cout<<"a) n            = "<< (n)            <<"\n";
  std::cout<<"b) -n           = "<< (-n)           <<"\n";
  std::cout<<"c) -INT_MIN     = "<< (-INT_MIN)     <<"\n"; //-Woverflow printed
  std::cout<<"d) n/2          = "<< (n/2)          <<"\n";
  std::cout<<"e) n/-2         = "<< (n/-2)         <<"\n";
  std::cout<<"f) -n/2         = "<< (-n/2)         <<"\n";
  std::cout<<"g) (-n)/2       = "<< ((-n)/2)       <<"\n";
  std::cout<<"h) (-INT_MIN)/2 = "<< ((-INT_MIN)/2) <<"\n"; //-Woverflow printed
}

I compiled it with g and got the following output:

a) n            = -2147483648
b) -n           = -2147483648
c) -INT_MIN     = -2147483648
d) n/2          = -1073741824
e) n/-2         = 1073741824
f) -n/2         = 1073741824
g) (-n)/2       = 1073741824
h) (-INT_MIN)/2 = -1073741824

The first surprise are examples b) and c), showing that -n equals n, but I understood this: -n = 2³² - n = 2³¹, which converted to int becomes -(2³¹).

However, I fail to understand example f). I found that unary minus operator has precedence over division (https://en.cppreference.com/w/cpp/language/operator_precedence). I expected that first -n is calculated as n, and then n/2 should be negative, as in example d) – but it is not the case.

I thought that I misunderstood the operator precedence, so I added brackets in example g), but this changed nothing.

And finally, in example h) I changed n to INT_MIN, which has the same value, but the result of the operation became negative!

What do I miss in understanding examples f) and g)? What is the difference between n and INT_MIN in this case? Is what I observe specific to the language, or may it depend on the compiler?

CodePudding user response：

The absolute value of INT_MIN is more than the (absolute) value of INT_MAX. The operation -n produces a result that is outside of representable values when n == INT_MIN. When an arithmetic operation on signed integer produces an unrepresentable value, the behaviour of the program is undefined.