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C - Integer Promotions

A C compiler promotes certain data types to a higher rank for consistency in arithmetic operations of integers. In addition to the standard int data type, C language lets you work with its subtypes such as char, short int, long int etc. Each of these data types occupy different number of memory locations. For example, the size of standard int is 4 bytes, whereas char type is 2 bytes of length. When an arithmetic operation involves integer data types of unequal length, the compiler employs the policy of promotion as explained in this chapter.

Integer Promotions

As a general principle, the integer types smaller than int are promoted when an operation is performed on them. If all values of the original type can be represented as an int, the value of the smaller type is converted to an int; otherwise, it is converted to an unsigned int.

One must understand the concept of integer promotion to write reliable C code, and avoid unexpected problems related to the size of data types and arithmetic operations on smaller integer types.

In the example below, the two variables a and b seem to be storing the same value, but are not equal.

Example

#include <stdio.h>

int main()
{
   char a = 251;
   unsigned char b = a;

   printf("a = %c", a);
   printf("\nb = %c", b);

   if (a == b)
      printf("\nSame");
   else
      printf("\nNot Same");
   return 0;
}

Output

a = √
b = √
Not Same

This happens because 'a' and 'b' are treated as integers during comparison. 'a' is a signed char converted to int as -5, while 'b' is an unsigned char converted to int as 251.

Mechanism of Integer Promotions with Example

Consider the following C code −

Example

#include <stdio.h>
int main()
{
   char a = 'e', b = '2', c = 'M';

   char d = (a * b) / c;
   printf ("d as int: %d as char: %c", d, d);
   return 0;
}

Output

d as int: 65 as char: A

Let us try to understand the mechanism of integer promotions with this example. In the arithmetic expression (a*b)/c, the bracket is solved first. All the variables are of signed char type, which is of 2 byte length and can store integers between -128 to 127. Hence the multiplication goes beyond the range of char but the compiler doesn't report any error.

When Integer Promotion is Applied?

The C compiler applies "integer promotion" when it deals with arithmetic operations involving small types like char. Before the multiplication of these char types, the compiler changes them to int type. So, in this case, (a * b) gets converted to int, which can accommodate the result of multiplication, i.e., 1200.

Integer promotions are applied as part of the usual arithmetic conversions to certain argument expressions; operands of the unary +, -, and ~ operators; and operands of the shift operators.

Example

#include <stdio.h>
int main()
{
   char a = 10;

   int b = a >> 3;
   printf ("b as int: %d as char: %c", b, b);
   return 0;
}

Output

b as int: 1 as char: 

In the above example, shifting the bit structure of a to the left by three bits still results in its value within the range of char (a<<3 results in 80). However, the example below, the rank of the char variable is prompted to int so that its left shift operation goes beyond the range of char type.

Example

#include <stdio.h>
int main()
{
   char a = 50;

   int b = a << 2;
   printf ("b as int: %d as char: %c", b, b);
   return 0;
}

Output

b as int: 200 as char: ╚

Integer Promotion Rules

Promotion rules help the C compiler in maintaining consistency and avoiding unexpected results. The fundamental principle behind the rules of promotion is to ensure that the expression's type is adjusted to accommodate the widest data type involved, preventing data loss or truncation. The following is the summary of promotion rules as per C11 specifications −

  • The integer types in C are char, short, int, long, long long and enum. The booleans also treated as an integer type when it comes to type promotions.

  • No two signed integer types shall have the same rank, even if they have the same representation.

  • The rank of a signed integer type shall be greater than the rank of any signed integer type with less precision.

  • The rank of long int > the rank of int > the rank of short int > the rank of signed char.

  • The rank of char is equal to the rank of signed char and unsigned char.

  • Whenever a small integer type is used in an expression, it is implicitly converted to int which is always signed.

  • All small integer types, irrespective of sign, are implicitly converted to (signed) int when used in most expressions.

In short −

  • Byte and short values − They are promoted to int.

  • If one operand is a long − The entire expression is promoted to long.

  • If one operand is a float − The entire expression is promoted to float.

  • If any of the operands is double − The result is promoted to double.

Example

Here, the variables x and y are of char data type. When the division operation is performed on them, they automatically get promoted to int and the resultant value is stored in z.

#include <stdio.h> 

int main() { 
   char x = 68;
   char y = 34;
    
   printf("The value of x is: %d", x);
   printf("\nThe value of y is: %d", y);
    
   char z = x/y;
   printf("\nThe value of z : %d", z);
    
   return 0; 
}

Output

The value of x is: 68
The value of y is: 34
The value of z : 2
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