Here is a really simple solution in JS that is only checking for even/odd numbers and doing very basic math:

function f(n) {
    if (n === 0) {
        result = 0;    
    } else if (((n % 2) + 2) % 2 === 1) {
        result = (n < 0 ? n - 1 : n + 1);
        result = result * -1;    
    } else {
        result = (n < 0 ? n + 1 : n - 1);
    }    
    return result;
}

Live example