Intro

Simple things are always the hardest to explain.

In C++, arithmetic types include integral types and floating-point types.

The Integer

Let’s begin with the most popular integer type, int:

int i = 0;

In C++, int is fixed in width. This means that its size cannot change, and there’s a limited range of values it can hold.

  • Typically, an int is 32 bits or 4 bytes, and the range is -2,147,483,648 to +2,147,483,647

Length Modifiers

Often, a different size of integer is desired:

  • A bigger integer to hold a larger range of values
  • A smaller integer to be more space efficient

Thankfully, we have the modifiers long and short:

  • long int: an integer type whose rank is higher than int
  • short int: an integer type whose rank is lower than int
  • A plain long is the same as long int. Similarly, a plain short is the same as short int

So, is long int bigger than int and short int smaller than int?

This is where things start to get interesting.

Take long int. The C++ standard only guarantees that it is at least as big as int. It does not have to be bigger.

In fact:

  • On most versions of Windows, sizeof(long) is 4, same as sizeof(int)
  • On 64-bit Linux distros, sizeof(long) is 8

Note that even when they have the same width, int and long int are two different types. Likewise, int and short int are always two different types.

  • Typically (on both Windows and Linux), a short int is 16 bit

What if you want even bigger or smaller integer types? Well, if you want to go bigger, just slap another long:

  • long long int: an integer type whose rank is higher than long int
  • Typically, long long int is 64 bit

How about going smaller?

Now, if a C++ novice is asked this question right after being told about long long int, their response is likely:

short short int

Alas, there is no such thing as short short int in C++ (or C). It is spelled

signed char

Huh? What does signed come from and what is char doing here? Are we still talking about integers??

I cannot provide a better answer than

Well, for historical reasons, it is what it is

Signedness Modifiers

All C++ integers are either signed or unsigned.

  • signed types can hold negative values
  • unsigned types can only hold non-negative values

Further, integer arithmetic is different between signed and unsigned:

  • signed integer overflow is undefined behavior (read: very bad)
  • unsigned integer overflow is well-defined - it wraps around
  • That does not mean unsigned types are safer!
    • In fact, I’ve encountered bugs that could have been avoided were signed type used
    • Both signed and unsigned are useful in different use cases

If we don’t specify the signedness, it defaults to signed. That is:

  • int is the same as signed int
  • long is the same as signed long
  • short is the same as signed short

and so on.

Except for char.

signed char is not the same as char. In fact, the following are three distinct types:

  • signed char
  • char
  • unsigned char

All three are character types. However, only signed char and unsigned char are considered standard integer types.

The unfortunate fact is, char is overloaded to mean at least three different things.

  1. char can mean character, the basic unit of a string
  2. char can mean byte, the basic unit of raw memory
  3. char can mean integer, as we’ve seen with signed char and unsigned char

The direction of C++ seems to be that char should only mean character.

  • Use std::byte if you mean a byte
  • Use std::int8_t if you mean an integer

Although, there is a lot of existing code out there, and char is ubiquitous.

Looking back, really:

  • signed char should have been short short
  • unsigned char should have been unsigned short short

Fixed width integer types

In summary, we have 10 standard integer types: there are 5 ranks, each with signed and unsigned variants.

The C++ standard only guarantees minimal bit counts and that the each rank is at least as wide as the last:

// char:      at least 8 bit
// short:     at least 16 bit
// int:       at least 16 bit
// long:      at least 32 bit
// long long: at least 64 bit

sizeof(char) <= sizeof(short) <= sizeof(int) <= sizeof(long) <= sizeof(long long)
  • For complete info, refer to here

If precise width is demanded, there are fixed width integer types at our disposal:

  • int8_t: exactly 8-bit signed integer
  • uint8_t: exactly 8-bit unsigned integer
  • … and so on, up to int64_t and uint64_t

Aside from width precision, these types are more coherant when it comes to naming/spelling. You don’t need to worry about long or short or char or the order thereof.

  • long signed long is legal

With fixed width integers, the only pattern is [u]intN_t and that’s it!

The inconvenience is that you have to #include <cstdint>. That, and technically they are defined in namespace std, so the more tedious but correct way to spell them is e.g. std::int32_t.

  • This matters, because in the future if there’s only import std; for pulling in the standard library, you need to std:: prefix to find these types

In reality, the [u]intN_t may be (but not required to be) typedefs of the standard integer types. For example:

  • int32_t may be defined as using int32_t = int;
  • uint8_t may be defined as using uint8_t = unsigned char;
  • int64_t may be long on one system, but long long on another

That’s the whole point of these integer types: platform-independent access to fixed width integers.

Floating-point types

Aside from integral types, floating-point types are other category of arithmetic types.

There are three standard floating-point types:

  • float is single precision floating-point type
  • double is double precision floating-point type
  • long double is extended precision floating-point type

Alas, the spelling of these types is, again, less than perfect.

  • If double is double precision, why is single precision not single?
  • If long is used to denote “higher precision”, why is double not long float?

The short answer is again “for historical reasons, it is what it is”. We just have to get used to it.

Since C++23, there are fixed width floating-point types, similar to their fixed width integer cousins:

  • float16_t
  • float32_t
  • float64_t
  • …

However, these are never the standard floating-point types (float, double, long double). They are (aliases to) extended floating-point types.

Finally, floating-point types are inherently signed. There is no unsigned float. Nor is there signed float.

Arithmetic Operations

Now comes the hard part.

Seriously; the previous parts are easy

Consider a binary arithmetic operation, T @ U, where T and U denote two arithmetic types. @ can be +, -, *, and so on.

C++ requires converting T and U to a common type before carrying out the operation. The main 3 rules are:

  1. If at least one of them is floating-point, then the common type is the largest floating-point.
    • int @ float => float @ float
    • float @ double => double @ double
  2. All char and short variants are first converted to int; this is known as integer promotion.
    • char @ char => int @ int
    • unsigned short @ unsigned short => int @ int
  3. For two integer types with the same signedness, the one with higher rank is the common type
    • int @ long => long @ long
    • unsigned int @ unsigned long => unsigned long @ unsigned long

Now, when it comes to mixed signedness operation, such as unsigned int @ long, the recommendation is:

  • Don’t.

No, really. The rules for this area are complex and the results can be surprising. Most compilers warn about this sort of operation, for good reasons.

  • If you want to challenge yourself, you may take look at this infographic from hackingcpp.com

Since C++20, we even introduce integer comparison functions:

  • cmp_less(T, U)
  • cmp_greater(T, U)
  • …

Precisely because the builtin mixed-signedness operations are error-prone.

Afterword

When it comes to basic stuff like integers and floating-points, pretty much everything was inherited from C, which has been for a long while. Some design probably made sense “back then”, but there is definitely better design today. Unfortunately, we don’t get to do-over; backward compatibility is pivotal to C, and in turn C compatibility is pivotal to C++.