10.3 — Numeric conversions

In the previous lesson (10.2 -- Floating-point and integral promotion), we covered numeric promotions, which are conversions of specific narrower numeric types to wider numeric types (typically int or double) that can be processed efficiently.

C++ supports another category of numeric type conversions, called numeric conversions. These numeric conversions cover additional type conversions between fundamental types.

There are five basic types of numeric conversions.

1. Converting an integral type to any other integral type (excluding integral promotions):

short s = 3; // convert int to short
long l = 3; // convert int to long
char ch = s; // convert short to char
unsigned int u = 3; // convert int to unsigned int

2. Converting a floating point type to any other floating point type (excluding floating point promotions):

float f = 3.0; // convert double to float
long double ld = 3.0; // convert double to long double

3. Converting a floating point type to any integral type:

int i = 3.5; // convert double to int

4. Converting an integral type to any floating point type:

double d = 3; // convert int to double

5. Converting an integral type or a floating point type to a bool:

bool b1 = 3; // convert int to bool
bool b2 = 3.0; // convert double to bool

Safe and unsafe conversions

Unlike numeric promotions (which are always value-preserving and thus “safe”), many numeric conversions are unsafe. An unsafe conversion is one where at least one value of the source type cannot be converted into an equal value of the destination type.

Numeric conversions fall into three general safety categories:

1. Value-preserving conversions are safe numeric conversions where the destination type can exactly represent all possible values in the source type.

For example, int to long and short to double are safe conversions, as the source value can always be converted to an equal value of the destination type.

int main()
{
    int n { 5 };
    long l = n; // okay, produces long value 5

    short s { 5 };
    double d = s; // okay, produces double value 5.0

    return 0;
}

Compilers will typically not issue warnings for implicit value-preserving conversions.

A value converted using a value-preserving conversion can always be converted back to the source type, resulting in a value that is equivalent to the original value:

#include <iostream>

int main()
{
    int n = static_cast<int>(static_cast<long>(3)); // convert int 3 to long and back
    std::cout << n << '\n';                         // prints 3

    char c = static_cast<char>(static_cast<double>('c')); // convert 'c' to double and back
    std::cout << c << '\n';                               // prints 'c'

    return 0;
}

2. Reinterpretive conversions are unsafe numeric conversions where the converted value may be different than the source value, but no data is lost. Signed/unsigned conversions fall into this category.

For example, when converting a signed int to an unsigned int:

int main()
{
    int n1 { 5 };
    unsigned int u1 { n1 }; // okay: will be converted to unsigned int 5 (value preserved)

    int n2 { -5 };
    unsigned int u2 { n2 }; // bad: will result in large integer outside range of signed int

    return 0;
}

In the case of u1, the signed int value 5 is converted to unsigned int value 5. Thus, the value is preserved in this case.

In the case of u2, the signed int value -5 is converted to an unsigned int. Since an unsigned int can’t represent negative numbers, the result will be modulo wrapped to a large integral value that is outside the range of a signed int. The value is not preserved in this case.

Such value changes are typically undesirable, and will often cause the program to exhibit unexpected or implementation-defined behavior.

Values converted using a reinterpretive conversion can be converted back to the source type, resulting in a value equivalent to the original value (even if the initial conversion produced a value out of range of the source type). As such, reinterpretive conversions do not lose data during the conversion process.

#include <iostream>

int main()
{
    int u = static_cast<int>(static_cast<unsigned int>(-5)); // convert '-5' to unsigned and back
    std::cout << u << '\n'; // prints -5
    
    return 0;
}

3. Lossy conversions are unsafe numeric conversions where data may be lost during the conversion.

For example, double to int is a conversion that may result in data loss:

int i = 3.0; // okay: will be converted to int value 3 (value preserved)
int j = 3.5; // data lost: will be converted to int value 3 (fractional value 0.5 lost)

Conversion from double to float can also result in data loss:

float f = 1.2;        // okay: will be converted to float value 1.2 (value preserved)
float g = 1.23456789; // data lost: will be converted to float 1.23457 (precision lost)

Converting a value that has lost data back to the source type will result in a value that is different than the original value:

#include <iostream>

int main()
{
    double d { static_cast<double>(static_cast<int>(3.5)) }; // convert double 3.5 to int and back
    std::cout << d << '\n'; // prints 3

    double d2 { static_cast<double>(static_cast<float>(1.23456789)) }; // convert double 1.23456789 to float and back
    std::cout << d2 << '\n'; // prints 1.23457

    return 0;
}

For example, if double value 3.5 is converted to int value 3, the fractional component 0.5 is lost. When 3 is converted back to a double, the result is 3.0, not 3.5.

Compilers will generally issue a warning (or in some cases, an error) when an implicit lossy conversion would be performed at runtime.

#include <iostream>

int main()
{
    std::cout << static_cast<long long>(static_cast<double>(10000000000000001LL));

    return 0;
}

10000000000000000

Unsafe conversions should be avoided as much as possible. However, this is not always possible. When unsafe conversions are used, it is most often when:

• We can constrain the values to be converted to just those that can be converted to equal values. For example, an int can be safely converted to an unsigned int when we can guarantee that the int is non-negative.
• We don’t mind that some data is lost because it is not relevant. For example, converting an int to a bool results in the loss of data, but we’re typically okay with this because we’re just checking if the int has value 0 or not.

More on numeric conversions

The specific rules for numeric conversions are complicated and numerous, so here are the most important things to remember.

• In all cases, converting a value into a type whose range doesn’t support that value will lead to results that are probably unexpected. For example:

int main()
{
    int i{ 30000 };
    char c = i; // chars have range -128 to 127

    std::cout << static_cast<int>(c) << '\n';

    return 0;
}

In this example, we’ve assigned a large integer to a variable with type char (that has range -128 to 127). This causes the char to overflow, and produces an unexpected result:

48

• Remember that overflow is well-defined for unsigned values and produces undefined behavior for signed values.
• Converting from a larger integral or floating point type to a smaller type from the same family will generally work so long as the value fits in the range of the smaller type. For example:

    int i{ 2 };
    short s = i; // convert from int to short
    std::cout << s << '\n';

    double d{ 0.1234 };
    float f = d;
    std::cout << f << '\n';

This produces the expected result:

2
0.1234

• In the case of floating point values, some rounding may occur due to a loss of precision in the smaller type. For example:

    float f = 0.123456789; // double value 0.123456789 has 9 significant digits, but float can only support about 7
    std::cout << std::setprecision(9) << f << '\n'; // std::setprecision defined in iomanip header

In this case, we see a loss of precision because the float can’t hold as much precision as a double:

0.123456791

• Converting from an integer to a floating point number generally works as long as the value fits within the range of the floating point type. For example:

    int i{ 10 };
    float f = i;
    std::cout << f << '\n';

This produces the expected result:

10

• Converting from a floating point to an integer works as long as the value fits within the range of the integer, but any fractional values are lost. For example:

    int i = 3.5;
    std::cout << i << '\n';

In this example, the fractional value (.5) is lost, leaving the following result:

3

While the numeric conversion rules might seem scary, in reality the compiler will generally warn you if you try to do something dangerous (excluding some signed/unsigned conversions).