# Floating Point Operations & Associativity in C, C++ and Java

Do Floating point operations follow property of associativity? In other words, do we always get the same results for expressions “(A + B) + C” and “A + (B + C)”

One may expect that floating numbers to follow the rule of associativity in programming languages as they are associative mathematically. However, this is not true in all cases.

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Consider below C/C++ program.

`// C/C++ program to demonstrate that floating point` `// addition may not be associative.` `#include<stdio.h>` `int` `main()` `{` ` ` `// A and B have sane values but apposite signs` ` ` `float` `A = -500000000;` ` ` `float` `B = 500000000;` ` ` ` ` `float` `C = 1;` ` ` ` ` `printf` `(` `"A + (B + C) is equal to %f \n"` `, A + (B + C));` ` ` `printf` `(` `"(A + B) + C is equal to %f"` `, (A + B) + C);` ` ` ` ` `return` `0;` `}` |

Output:

A + (B + C) is equal to 0.000000 (A + B) + C is equal to 1.000000

It is evident from the above-given output that the floating-point arithmetic may not follow the law of associativity in every case. This is due to the format in which the floating-point numbers are stored and represented, it rounds off the numbers during calculations, hence, the associative laws of algebra do not necessarily hold for floating-point numbers. In this case,

Explanation for above output:A + (B + C):(B + C) = 500000000.0 + 1.0 = 500000000.0 (rounded off during floating point arithmetic) A + (B + C) = -500000000.0 + 500000000.0 = 0.000000(A + B) + C:(A + B) = -500000000.0 + 500000000.0 = 0.000000 (A + B) + C = 0.000000 + 1 = 1.000000

**How about Java?**

We get the same results in Java as Java also uses similar representation for floating-point numbers.

`// Java program to demonstrate that floating-point` `// addition may not be associative` `import` `java.io.*;` ` ` `class` `Main` `{` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `// A and B have sane values but apposite signs` ` ` `float` `A = -` `500000000` `;` ` ` `float` `B = ` `500000000` `;` ` ` ` ` `float` `C = ` `1` `;` ` ` ` ` `System.out.println(` `"A + (B + C) is equal to "` `+ ` ` ` `(A + (B + C)));` ` ` `System.out.println(` `"(A + B) + C is equal to "` `+ ` ` ` `((A + B) + C));` ` ` `}` `}` |

Output:

A + (B + C) is equal to 0.000000 (A + B) + C is equal to 1.000000

**How about integers?**

Now let’s try the same calculations when the data type is integer. Here is a piece of code for your observation:

`#include<stdio.h>` `#include<stdio.h>` `int` `main()` `{` ` ` `// A and B have sane values but apposite signs` ` ` `int` `A = -500000000;` ` ` `int` `B = 500000000;` ` ` ` ` `int` `C = 1;` ` ` ` ` `printf` `(` `" A + (B + C) is equal to %d \n"` `, A + (B + C));` ` ` `printf` `(` `"(A + B) + C is equal to %d"` `, (A + B) + C);` ` ` ` ` `return` `0;` `}` |

Output:

A + (B + C) is equal to 1 (A + B) + C is equal to 1

This article is contributed by **Pranjal Mathur**. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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