8.2 — Floating-point and integral promotion

In lesson 4.3 -- Object sizes and the sizeof operator, we noted that C++ has minimum size guarantees for each of the fundamental types. However, the actual size of these types can vary based on the compiler and architecture.

This variability was allowed so that the int and double data types could be set to the size that maximizes performance on a given architecture. For example, a 32-bit computer will typically be able to process 32-bits of data at a time. In such cases, an int would likely be set to a width of 32-bits, since this is the “natural” size of the data that the CPU operates on (and likely to be the most performant).

But what happens when we want our 32-bit CPU to modify an 8-bit value (such as a char) or a 16-bit value? Some 32-bit processors (such as the x86 series) can manipulate 8-bit or 16-bit values directly. However, doing so is often slower than manipulating 32-bit values! Other 32-bit CPUs (like the PowerPC), can only operate on 32-bit values, and additional tricks must be employed to manipulate narrower values.

Numeric promotion

Because C++ is designed to be portable and performant across a wide range of architectures, the language designers did not want to assume a given CPU would be able to efficiently manipulate values that were narrower than the natural data size for that CPU.

To help address this challenge, C++ defines a category of type conversions informally called the numeric promotions. A numeric promotion is the type conversion of a narrower numeric type (such as a char) to a wider numeric type (typically int or double) that can be processed efficiently and is less likely to have a result that overflows.

All numeric promotions are value-preserving, which means that all values in the original type are representable without loss of data or precision in the new type. Because such promotions are safe, the compiler will freely use numeric promotion as needed, and will not issue a warning when doing so.

Numeric promotion reduces redundancy

Numeric promotion solves another problem as well. Consider the case where you wanted to write a function to print a value of type int:

#include <iostream>

void printInt(int x)
{
    std::cout << x;
}

While this is straightforward, what happens if we want to also be able to print a value of type short, or type char? If type conversions did not exist, we’d have to write a different print function for short and another one for char. And don’t forget another version for unsigned char, signed char, unsigned short, wchar_t, char8_t, char16_t, and char32_t! You can see how this quickly becomes unmanageable.

Numeric promotion comes to the rescue here: we can write functions that have int and/or double parameters (such as the printInt() function above). That same code can then be called with arguments of types that can be numerically promoted to match the types of the function parameters.

Numeric promotion categories

The numeric promotion rules are divided into two subcategories: integral promotions and floating point promotions.

Floating point promotions

We’ll start with the easier one.

Using the floating point promotion rules, a value of type float can be converted to a value of type double.

This means we can write a function that takes a double and then call it with either a double or a float value:

#include <iostream>

void printDouble(double d)
{
    std::cout << d;
}

int main()
{
    printDouble(5.0); // no conversion necessary
    printDouble(4.0f); // numeric promotion of float to double

    return 0;
}

In the second call to printDouble(), the float literal 4.0f is promoted into a double, so that the type of argument matches the type of the function parameter.

Integral promotions

The integral promotion rules are more complicated.

Using the integral promotion rules, the following conversions can be made:

• signed char or signed short can be converted to int.
• unsigned char, char8_t, and unsigned short can be converted to int if int can hold the entire range of the type, or unsigned int otherwise.
• If char is signed by default, it follows the signed char conversion rules above. If it is unsigned by default, it follows the unsigned char conversion rules above.
• bool can be converted to int, with false becoming 0 and true becoming 1.

There are a few other integral promotion rules that are used less often. These can be found at https://en.cppreference.com/w/cpp/language/implicit_conversion#Integral_promotion.

In most cases, this lets us write a function taking an int parameter, and then use it with a wide variety of other integral types. For example:

#include <iostream>

void printInt(int x)
{
    std::cout << x;
}

int main()
{
    printInt(2);

    short s{ 3 }; // there is no short literal suffix, so we'll use a variable for this one
    printInt(s); // numeric promotion of short to int

    printInt('a'); // numeric promotion of char to int
    printInt(true); // numeric promotion of bool to int

    return 0;
}

There are two things worth noting here. First, on some systems, some of the integral types may be converted to unsigned int rather than int. Second, some narrower unsigned types (such as unsigned char) will be converted to larger signed types (such as int). So while integral promotion is value-preserving, it is not necessarily sign-preserving.

Not all value-preserving conversions are numeric promotions

Some value-preserving type conversions (such as char to short, int to long, or int to double) are not considered to be numeric promotions in C++ (they are numeric conversions, which we’ll cover shortly in lesson 8.3 -- Numeric conversions). This is because such conversions do not assist in the goal of converting smaller types to larger types that can be processed more efficiently.

The distinction is mostly academic. However, in certain cases, the compiler will favor numeric promotions over numeric conversions. We’ll see examples where this makes a difference when we cover function overload resolution (in upcoming lesson 8.11 -- Function overload resolution and ambiguous matches).