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Does C division truncate?

Published in C Division 3 mins read

Yes, integer division in C truncates toward zero.

Understanding Truncation in C Division

When dividing two integers in C, the result is also an integer. If the division results in a non-integer value, the fractional part is discarded. This process is called truncation. The key characteristic of C's integer division is that it always truncates towards zero. This means:

  • If the result is positive, the fractional part is simply dropped (e.g., 7 / 3 results in 2).
  • If the result is negative, the fractional part is dropped, moving the result closer to zero (e.g., -7 / 3 results in -2).

Examples of Integer Division in C

Here are some examples to illustrate how truncation works in C:

Expression Result Explanation
5 / 2 2 The actual result is 2.5, but the fractional part (.5) is dropped, leaving 2.
-5 / 2 -2 The actual result is -2.5, but the fractional part (.5) is dropped, and we move towards zero, resulting in -2.
10 / 3 3 The actual result is 3.333..., but the fractional part is dropped, resulting in 3.
-10 / 3 -3 The actual result is -3.333..., but the fractional part is dropped, and we move towards zero, resulting in -3.
0 / 5 0 Any integer divided by a larger integer will result in zero, as the result is less than 1, and the fractional part is truncated to zero.

Why Truncation Matters

Understanding truncation is crucial for several reasons:

  • Accurate Calculations: Truncation can lead to unexpected results if you're not aware of it. If you need a more accurate result (including the fractional part), you should use floating-point numbers (float or double).

  • Conditional Statements: Truncation affects the outcome of conditional statements that rely on division.

  • Avoiding Errors: Being mindful of truncation can prevent logic errors in your code.

Alternatives to Truncation

As the reference mentions, sometimes rounding is more appropriate than truncation. C doesn't automatically round during integer division, but you can implement rounding manually if needed. However, rounding isn't trivial. One common approach is to add 0.5 (or -0.5 for negative numbers) before the division to achieve rounding towards the nearest integer.

#include <stdio.h>
#include <math.h>

int main() {
  int a = 7;
  int b = 3;

  // Truncation (default behavior)
  int truncated_result = a / b;
  printf("Truncated: %d / %d = %d\n", a, b, truncated_result);

  // Rounding to nearest integer (positive example)
  int rounded_result_positive = (int)floor((double)a / b + 0.5); // Using floor to round down.  Casting to int truncates.
  printf("Rounded (positive): %d / %d = %d\n", a, b, rounded_result_positive);

  int c = -7;

   // Rounding to nearest integer (negative example)
  int rounded_result_negative = (int)ceil((double)c / b - 0.5); // Using ceil to round up. Casting to int truncates.
  printf("Rounded (negative): %d / %d = %d\n", c, b, rounded_result_negative);


  return 0;
}

This example shows how floor() and ceil() from math.h can be used to achieve rounding to the nearest integer. However, this approach is not always preferred because it requires including the math.h header, converting to floating point and casting back to integer, and thus has a performance overhead.

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