Math operations with long long in c

问题

Given long long x, long long y, and int z, how can trunc((x+y+z)/3) be calculated using fully defined operations in C but excluding unsigned long long and wider arithmetic?

(trunc(x) is “rounding toward zero”: It is x if x is an integer and otherwise is the next integer toward zero.)

回答1:

You can calculate the average of two integers x and y without the risk of overflow as follows (pseudocode):

int average = (x and y have the same sign)
    ? x + (y - x) / 2
    : (x + y) / 2;

This is not symmetric due to integer truncation. If you want to always round towards 0, you need to do something slightly more complicated:

int average = (x and y have the same sign)
    ? (x and y are both even or both odd)
          ? x + (y - x) / 2
          : x + (y - x - sgn(x)) / 2
    : (x + y) / 2;

where sgn is the signum function (-1, 0, or +1 depending on whether the argument is negative, zero, or positive). There are lots of implementations of sgn(x), but one nice one is: (x > 0) - (x < 0).

If you want to always round down...that's left as an exercise. :)

回答2:

To average two unsigned numbers in C, you can use the fact that (L + R)/2 = L + (R-L)/2. Using the form on the right hand side guarantees the arithmetic will not overflow.

来源：https://stackoverflow.com/questions/64546414/math-operations-with-long-long-in-c