Math operations with long long in c

Question

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.)

@deniskalistrat: You need to specify the entire problem in the problem statement. — Eric Postpischil, Oct 26 '20 at 23:53
@EricPostpischil Imagine that i need to find the avg of three numbers (two of them will be long long and one will be just normal int), how can I calculate it properly in c, assuming that i cannot use anything bigger than long long type? — deniskalistrat, Oct 27 '20 at 00:15
@deniskalistrat: Is the updated problem statement I wrote correct and complete? It says fractions are rounded toward zero. Does it matter in which directions fractions are rounded? Could they be to-nearest or always down (toward −∞, same as floor(x)), or does it matter? — Eric Postpischil, Oct 27 '20 at 00:20
duplicate: [Average of 3 long integers](https://stackoverflow.com/q/23949785/995714) — phuclv, Oct 27 '20 at 00:24
For 2 `long long`, perhaps [Take the average of two signed numbers](https://stackoverflow.com/a/29834136/2410359) — chux - Reinstate Monica, Oct 27 '20 at 00:51
Vote to reopen is premature until OP confirms the edit is correct and complete. — Eric Postpischil, Oct 27 '20 at 02:28

Ted Hopp · Answer 1 · 2020-10-27T12:42:43.807

3

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. :)

edited Oct 27 '20 at 12:42

answered Oct 26 '20 at 23:48

Ted Hopp

232,168
48
399
521

1

Hmmm, consider (6,3) and (3,6) give different answers, so not commutative. – chux - Reinstate Monica Oct 27 '20 at 00:45
For me, `printf("%d\n", 6 + (3 - 6) / 2);` --> 4 and `printf("%d\n", 3 + (6 - 3) / 2);` --> 5. Are you using C99 or later? Early C is looser defined – chux - Reinstate Monica Oct 27 '20 at 02:24
`6+(3-6)/2` → `6+(-3)/2` → `6+-1` → `5`. `3+(6-3)/2` → `3+3/2` → `3+1` → `4`. – Eric Postpischil Oct 27 '20 at 02:25
@chux-ReinstateMonica - I stand corrected (and so does my answer) .Thanks for pointing out this issue. :) – Ted Hopp Oct 27 '20 at 04:51
@EricPostpischil - Right you are. I updated my answer to deal with that. – Ted Hopp Oct 27 '20 at 04:51
1

For me with new update, `printf("%d\n", average(1,3));` --> 1. Expect 2. Overflows with `average(INT_MIN, -1)` – chux - Reinstate Monica Oct 27 '20 at 05:34
@chux-ReinstateMonica - *sigh*. Thanks again. As delusional programmers often say, "There! I've fixed the last bug!" – Ted Hopp Oct 27 '20 at 12:35

score 0 · Answer 2 · answered Oct 26 '20 at 23:45

0

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.

answered Oct 26 '20 at 23:45

steeps

65
6

1

*"Using the form on the right hand side guarantees the arithmetic will not overflow"* - not really, it can overflow if R is positive and L negative. – Marco Bonelli Oct 27 '20 at 01:51
The question is for signed numbers, not unsigned. – Eric Postpischil Oct 27 '20 at 02:27

Math operations with long long in c

2 Answers2

Linked