C++ integer types a tutorial !

 

The integer types in C++ are fundamental types . A fundamental type , has a mapping to hardware , so the operations performed on a fundamental type , are hardware performed .

Boolean , Characters , and integer types , are called the integral types . The integral types and the floating point types are called the arithmetic types .

What are the C++ integer types

An integer type is a whole number , as in -1 or 1 . A whole number does not contain a fractional part , such as .2 .

Integer types can either be unsigned or signed . An unsigned integer , can only be non negative , for example 0 , or 1 , whereas a signed integer , can be negative , positive , or zero , as in -1 , or 3 .

C++ standards , prior to C++20 , do not specify the algorithm for representing the signed , or unsigned integer types . A signed integer , can be represented , using one’s complements , two’s complement , or sign and magnitude . C++20 , specifies that signed integers , must be represented using two’s complement .

The C++ standards dictates that unsigned arithmetic , such as addition , or subtraction , must obey arithmetic modulo two , to the power n , this is related to overflow . Overflow happens , when the result is too large to fit in the allocated width , for an integer type .

An integer type , can have multiple type specifiers , for example : int , signed int , and signed , represent the same integer type int , which is signed . This being said , an integer type can be declared in multiple ways , or using multiple keywords.

short int , short 
unsigned short int , unsigned short 
int , signed , signed int 
unsigned int  , unsigned 
long int , signed long int , signed long 
unsigned long int , unsigned long , 
long long int , signed long long int, signed long long , long long
unsigned long long int , unsigned long long 

It is clear , from the preceding list , that for signed integer types , it is not necessary to use the keyword signed .

A signed integer type , and its unsigned version , such as int , and unsigned int , have the same storage size and alignment . Alignment is where in memory , an object can be placed .

An implementation can define other integer types , called the extended integer types . For each extended integer type , a signed , and an unsigned version , must be defined .

What are the C++ integer types ranges

The C++ standard specifies the minimum ranges , that a signed or an unsigned integer type , might have , an implementation , can define larger ranges .

Before C++ 20 , and because signed integer types could have , a sign and magnitude representation , the minimum ranges were :

TypeNegative or zero valuePositive value
short-3276732767
unsigned short065535
int-3276732767
unsigned int065535
long-21474836472147483647
unsigned long04294967295
long long-92233720368547758079223372036854775807
unsigned long long018446744073709551615

Starting C++20 , the minimum ranges are :

TypeNegative or zero valuePositive value
short-3276832767
unsigned short065535
int-3276832767
unsigned int065535
long-21474836482147483647
unsigned long04294967295
long long-92233720368547758089223372036854775807
unsigned long long018446744073709551615

The minimum ranges of the integral types , as implemented on a given machine , are defined by the C++ header climits .

#include<iostream>
#include<climits>

int main(void ){
  using std::cout;
  using std::endl;

  cout << "CHAR_BIT : "  << CHAR_BIT << endl;
  /*Print the number of bits in a char .*/

  cout << "SCHAR_MIN : " << SCHAR_MIN << endl;
  /*Print the minimum value of signed char .*/

  cout << "SCHAR_MAX : " << SCHAR_MAX << endl;
  /*Print the maximum value of signed char .*/

  cout << "UCHAR_MAX : " << UCHAR_MAX << endl;
  /*Print the maximum value of unsigned char .*/

  cout << "CHAR_MIN : " << CHAR_MIN << endl;
  /*Print the minimum value of char .*/

  cout << "CHAR_MAX : " << CHAR_MAX  << endl;
  /*Print the maximum value of char .*/

  cout << "MB_LEN_MAX : " << MB_LEN_MAX << endl;
  /*Print maximum number of bytes available in
    a multibyte character .*/

  cout << "SHRT_MIN : " << SHRT_MIN << endl;
  /*Print the minimum value of short .*/

  cout << "SHRT_MAX : " <<  SHRT_MAX  << endl;
  /*Print the maximum value of short .*/

  cout << "USHRT_MAX : " <<  USHRT_MAX << endl;
  /*Print the minimum value of unsigned short .*/

  cout << "INT_MIN : " << INT_MIN << endl;
  /*Print the minimum value of int .*/

  cout << "INT_MAX : " <<  INT_MAX << endl;
  /*Print the maximum value of int .*/

  cout << "UINT_MAX : " << UINT_MAX << endl;
  /*Print the maximum value of unsigned int .*/

  cout << "LONG_MIN : " << LONG_MIN  << endl;
  /*Print the minimum value of long .*/

  cout << "LONG_MAX : " << LONG_MAX  << endl;
  /*Print the maximum value of long .*/

  cout << "ULONG_MAX : " <<  ULONG_MAX << endl;
  /*Print the maximum value of unsigned long .*/

  cout << "LLONG_MIN : " <<  LLONG_MIN << endl;
  /*Print the minimum value of long long .*/

  cout << "LLONG_MAX : " << LLONG_MAX  << endl;
  /*Print the maximum value of long long .*/

  cout << "ULLONG_MAX : " << ULLONG_MAX  << endl; 
  /*Print the maximum value of unsigned long long .*/ }

/*Output 
CHAR_BIT : 8
SCHAR_MIN : -128
SCHAR_MAX : 127
UCHAR_MAX : 255
CHAR_MIN : -128
CHAR_MAX : 127
MB_LEN_MAX : 6
SHRT_MIN : -32768
SHRT_MAX : 32767
USHRT_MAX : 65535
INT_MIN : -2147483648
INT_MAX : 2147483647
UINT_MAX : 4294967295
LONG_MIN : -9223372036854775808
LONG_MAX : 9223372036854775807
ULONG_MAX : 18446744073709551615
LLONG_MIN : -9223372036854775808
LLONG_MAX : 9223372036854775807
ULLONG_MAX : 18446744073709551615 */

The sizeof operator , returns the number of bytes , which are reserved for a given type , hence it can be used to get the number of bytes , reserved for integer types .

#include<iostream>

int main(void ){
  using std::cout;
  using std::endl;

  cout << sizeof(short ) << endl;
  //Output on this machine : 2

  cout << sizeof(int ) << endl;
  //Output on this machine : 4

  cout << sizeof(long ) << endl ;
  //Output on this machine : 8

  cout << sizeof(long long ) << endl;
  /*Output on this machine : 8 */ }

C++ integer literals types

An integer literal such as 17 , can be written in base 2 , 8 , 10 , or 16 , as follows :

#include<iostream>

int main(void ){
  using std::cout;
  using std::endl;

  cout << "17 in binary is : " << 0b1'00'01 << endl;
  /*Binary literals start by 0B , case insensitive ,
    a single quote can be use in any integer
    literal for readability .*/

  cout << "17 in octal is : " << 021 << endl;
  /*Octal literals start by 0 .*/

  cout << "17 in hexadecimal is : " << 0x11 << endl;
  /*Hexadecimal literals start by
   0X , case insensitive .*/

  cout << "17 in decimal is : " << 17 << endl;
  /*Decimal literals must not start by
    0 .*/

/*Output :
17 in binary is : 17
17 in octal is : 17
17 in hexadecimal is : 17
17 in decimal is : 17 */ }

Since C++ is a typed language , an integer literal has a type . An integer literal is always non negative , the negation operator - , is applied on the gotten integer literal type .

Decimal integer literals , have a default type of int , if too large to fit in an int , they will have a long type , if too large to fit in a long , they will have the long long type . If still too large to fit , and the implementation defines extended integer types , they are tried , as described , if still too large , the behavior is implementation defined .

Binary , octal , and hexadecimal integer literals , have a default type of int , if too large to fit in an int , they will have a type of unsigned int , if too large to fit in an unsigned int , they will have a type of long , next unsigned long , next long long , next unsigned long long , next if the implementation defines extended integer types , they are tried as stated , if still too large , the behavior is implementation defined .

#include<iostream>

int main(void ){
  using std::cout;
  using std::endl;

  unsigned int var_i = -2147483648;
  /*int on this machine has a range of
    [-2147483648 , 2147483647 ] .
    2147483648 is larger than INT_MAX ,
    2147483648 is a decimal integer literal ,
    hence long int is tried .
    long int on this machine has a range of
    [-9223372036854775808 , 9223372036854775807 ]
    , hence 2147483648 is of type long int .
    The negation operator is applied on
    2147483648 , as such -2147483648 , is gotten .
    var_i is an unsigned int , and the gotten
    value is a long . Hence the gotten value
    is converted first to unsigned long , bits
    are kept as is , just reinterpreted , so
    the converted value is 2147483648 in
    unsigned long , next the converted value
    is truncated to an unsigned int , the value 
    is preserved in truncation . */

  cout << var_i << endl ;
  /*Output :
    2147483648 .*/

  var_i = -0x80000000;
  /*0x80000000 in hexadecimal is equal to
    2147483648 in decimal . 
    First int is tried .
    On this machine it has a range of
    [-2147483648 , 2147483647 ] , next
    unsigned int is tried . 
    On this machine  , unsigned int has 
    a range of [0 , 4294967295 ]  ,
    hence 0x80000000 is of type unsigned 
    int .
    The negation operator is applied , 
    modulo 4294967296 is applied , and the 
    result is 2147483648 .*/

    cout << var_i << endl ;
    /*Output :
      2147483648 .*/ }

The suffixes l , and ll , case insensitive , can be used with an integer literal , to state that it is of type long , or long long . In such cases , and to determine the type of the integer literal , the compiler starts from long , or long long , depending on the suffix , and try the next types , as described earlier .

The suffix u , case insensitive , can be applied to an integer literal , to state that it is unsigned . In such case , unsigned int is first tried , followed by unsigned long , followed by unsigned long long . If still too large , and the implementation defines extended integer types , the extended integer types are tried , as stated , if still too large , the behavior is implementation defined .

The suffix u can be used with the suffixes l , and ll to state that an integer literal is unsigned long , or unsigned long long . In such a case , the compiler tries , the next larger unsigned type , if the literal is too large to fit ,and if no unsigned integer type can fit the literal , then the behavior is implementation defined .

#include<iostream>

int main(void ){
  using	std::cout;
  using	std::endl;

  int var_i = 2147483648u;
  /*The suffix u is used , as such
    the integer literal 2147483648
    is of an unsigned integer type .
    unsigned int , on this machine
    has a range of [0 , 4294967295 ]
    , 2147483648 can fit in this range ,
    so 2147483648 is of type unsigned int .
    var_i is a signed int , as such the
    gotten unsigned value , is reinterpreted 
    as being signed .*/

  cout << var_i << endl ;
  /*Output
    -2147483648 */

  var_i = 9223372036854775807L ;
  /*9223372036854775807 is suffixed with
    L , as such long is first tried .
    Long on this machine , has a range
    [-9223372036854775808 , 9223372036854775807 ] .
    It can hold 9223372036854775807 , so the
    integer literal is of type long .
    var_i is of type int , as such ,
    the gotten long value is truncated ,
    and the result is -1 .*/

  cout << var_i << endl ;
  /*Output :
    -1 */ 

  auto var_ul = 1lu;
  /*The integer literal 1 , is suffixed 
    with lu , so it is of the unsigned long 
    type . 
    auto is used , as not to write the
    type of var_ul , since the integer
    literal is of type unsigned long , hence
    var_ul , is of type unsigned long . 
    ul could have been used instead of lu .*/ }

C++ Standard library integer types

The integer types defined by the C++ standard , are defined to have a least width , as such a least range , so the range of a standard integer type , is not uniform across all implementations .

For example , on a 16 bit architecture , int have typically a width of 16 bits , whereas on a 32 bits architecture , int has typically a width of 32 bits .

The question to ask is as such , what if what was needed , is to have a fixed length width , for an integer type , across all implementations ?

The standard library header cstdint , defines fixed width integer types , they are :

int8_t 
uint8_t
/*Fixed width 8 bits signed and 
  unsigned integers .*/

int16_t 
uint16_t 
/*Fixed width 16 bits signed and 
  unsigned integers .*/

int32_t
uint32_t
/*Fixed width 32 bits signed and 
  unsigned integers .*/

int64_t
uint64_t
/*Fixed width 64 bits signed and 
  unsigned integers .*/

The fixed width integer types , are optional , so it is not necessary for an implementation to provide them .

What about , if what was needed , is an integer type , for which a processor in an execution environment , so where the program is being executed , is faster to perform operations , and this integer type , is to be of a minimum length ? The standard library cstdint header , defines the following integer types , that fit these requirements :

int_fast8_t
uint_fast8_t
/*Fastest , signed , unsigned integer 
  types , that have at least 8 bits .*/

int_fast16_t
uint_fast6_t
/*Fastest , signed , unsigned integer 
  types , that have at least 16 bits .*/

int_fast32_t
uint_fast32_t
/*Fastest , signed , unsigned integer 
  types , that have at least 32 bits .*/

int_fast64_t
uint_fast64_t
/*Fastest , signed , unsigned integer 
  types , that have at least 64 bits .*/

Finally what if what was needed , is to have the largest integer type , available on an implementation . To fulfill , this requirement , the cstdint header defines :

intmax_t
uintmax_t
/*widest signed , unsigned , integer types 
  available on an implementation .*/