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CS253 Fixed Width Integers

The Rules

Unlike languages such as Java, C++ integer sizes aren’t fixed:

• sizeof(char) ≤ sizeof(short) ≤ sizeof(int) ≤ sizeof(long) ≤ sizeof(long long)
• char: at least 8 bits, maybe signed, maybe unsigned
• short, int: at least 16 bits
• long: at least 32 bits
• long long: at least 64 bits

This Computer

char c = -1;
cout << "char is " << (c<0 ? "signed\n" : "unsigned\n")
     << "char signed: " << boolalpha
     << numeric_limits<char>::is_signed    << '\n'
     << "char: "      << sizeof(char)      << '\n'
     << "short: "     << sizeof(short)     << '\n'
     << "int: "       << sizeof(int)       << '\n'
     << "long: "      << sizeof(long)      << '\n'
     << "long long: " << sizeof(long long) << '\n';

char is signed
char signed: true
char: 1
short: 2
int: 4
long: 8
long long: 8

Rationale

The intention is that int is the natural size for integer values on this computer. The C/C++ languages are quite concerned about efficiency, and int operations must be quick. It would be silly to have a 64-bit computer doing extra work to fake overflow in a 16-bit int.

On 16-bit computers, int was 16 bits. int has been stuck at 32 bits for too long, maybe due to bad code that assumes 32-bit ints.

Indeed, occasionally, I want an integer type that is exactly 32 bits. Perhaps I’m simulating hardware that has 32-bit registers. Perhaps I want reproducible overflow characteristics for a random number generator.

Poor Solution

• So, how do I reliably get a 32-bit integer?
• The old solution was to use conditional compilation:

#ifdef STUPID_16_BIT_COMPUTER
    typedef long int32;
#elif MAC_COMPUTER
    typedef int int32;
#elif HP_COMPUTER
    typedef long long int32;
#else
    #error Cannot figure out 32-bit int size.
#endif

Fragile!

Better Solution

Rather than guessing sizes, based on compiler version and machine type, it would be great if we could convince the compiler implementors (who actually know) to tell us how to get integers of various sizes.

That’s what the <cstdint> header file is for.

<cstdint>

<cstdint> (alias <stdint.h> in C) provides aliases (typedefs):

• Exact sizes: int8_t int16_t int32_t int64_t
• Fastest at least this big: int_fast8_t int_fast16_t int_fast32_t int_fast64_t
• Smallest at least this big: int_least8_t int_least16_t int_least32_t int_least64_t
• Biggest signed integer: intmax_t
• Holds a pointer: intptr_t

and all of those with a leading u for unsigned: uint8_t, …

Explanation

Exact sizes (int8_t, …)

These are the exact size—no smaller, no bigger.

Fastest at least this big (int_fast8_t, …)

The fastest type that can hold at least this many bits. Speed matters; space doesn’t. On a 64-bit computer that has to do extra work to simulate 16-bit overflow, it would be faster to use all 64 bits.

Smallest at least this big (int_least8_t, …)

Space matters; speed doesn’t.

Biggest signed integer (intmax_t)

I just want the biggest range this computer can offer.

Holds a pointer (intptr_t)

I want to hold a pointer, or perhaps the difference between two pointers.

Exact Types are Optional

• The following types are optional. If the computer can’t do exactly this size, then the symbol isn’t defined. Compilation fails; the programmer deals with it.
  • int8_t
  • int16_t
  • int32_t
  • int64_t
  • intptr_t
• On an old 32-bit computer, no int64_t.
• On a computer with only 64-bit types, no int8_t, int16_t, and int32_t.
• On a computer with only 80-bit types, no int8_t, int16_t, int32_t, and int64_t.
• On a computer with 32-bit integers, but a 64-bit address space, no intptr_t.

Everything Else is Mandatory

• This implies that all the other types are mandatory:
  • Fastest at least this big: int_fast8_t int_fast16_t int_fast32_t int_fast64_t
  • Smallest at least this big: int_least8_t int_least16_t int_least32_t int_least64_t
• But, what if we’re on a pure 32-bit machine? We can’t do int_fast64_t or int_least64_t!
  • Sure, we can. Fake them in software. Add the lower 32 bits, propagate the carry into the upper 32 bits, add them. This is machine language, after all.

This Computer

cout << sizeof(int8_t)        << '\n'
     << sizeof(int16_t)       << '\n'
     << sizeof(int32_t)       << '\n'
     << sizeof(int64_t)       << '\n'
                              << '\n'
     << sizeof(int_fast8_t)   << '\n'
     << sizeof(int_fast16_t)  << '\n'
     << sizeof(int_fast32_t)  << '\n'
     << sizeof(int_fast64_t)  << '\n'
                              << '\n'
     << sizeof(int_least8_t)  << '\n'
     << sizeof(int_least16_t) << '\n'
     << sizeof(int_least32_t) << '\n'
     << sizeof(int_least64_t) << '\n'
                              << '\n'
     << sizeof(intmax_t)      << '\n'
     << sizeof(intptr_t)      << '\n';

1
2
4
8

1
8
8
8

1
2
4
8

8
8

Data Models

One speaks of a Data Model, e.g., LP64, which means that Longs and Pointers are 64 bits wide.

Type	LP32	ILP32	LLP64	LP64	ILP64	SILP64
short	16	16	16	16	16	64
int	16	32	32	32	64	64
long	32	32	32	64	64	64
long long	?	?	64	64	64	64
pointer, size_t	32	32	64	64	64	64

#ifdef __LP64__  // non-standard
    cout << "LP64\n";
#endif

LP64