Why Do C and C Require Integer Conversion Before Arithmetic Operations?

Unveiling the Rationales Behind Integer Conversion in Arithmetic Operations

The necessity for converting short data type to int in C and C before performing arithmetic operations has puzzled many. This requirement finds its origins in the history of these languages.

Rationale for Integer Conversion

According to the Rationale for International Standard—Programming Languages—C, Section 6.3.1.8, the decision to perform calculations with wider types was made for several reasons:

• Performance: Wider types can often generate more efficient code.
• Precision: Wider types provide higher precision, reducing the likelihood of incorrect answers.

The Usual Arithmetic Conversions

Section 6.3.1.8 of the C99 standard defines the "usual arithmetic conversions" applied to operands in arithmetic expressions. For short data type operands, these conversions proceed in two stages:

1. Integer Promotions

As outlined in Section 6.3.1.1 of the C99 standard, short integers are converted to int if int can represent all values of short; otherwise, they are converted to unsigned int. This promotes consistency in calculations without compromising representation accuracy.

2. Usual Arithmetic Conversions

The promoted short integers (either int or unsigned int) then undergo further conversions based on the specific arithmetic operation.

The "Unsigned Preserving" and "Value Preserving" Approaches

During the standardization process, there were debates between two approaches to integer promotions:

• Unsigned preserving: Promoting short and unsigned short to unsigned int.
• Value preserving: Promoting to signed int if it can represent all values of the original type; otherwise, promoting to unsigned int.

The value preserving approach was adopted, allowing for more consistent behavior and accurate representation, especially in environments where short is represented by a data type smaller than int.

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