Arithmetic types

(See also type for type system overview and the list of type-related utilities that are provided by the C library).

Character types

• signed char - type for signed character representation.
• unsigned char - type for unsigned character representation. Also used to inspect object representations (raw memory).
• char - type for character representation. Equivalent to either signed char or unsigned char (which one is implementation-defined and may be controlled by a compiler commandline switch), but char is a distinct type, different from both signed char and unsigned char

Note that the standard library also defines typedef names wchar_t , char16_t, and char32_t (since C11) to represent wide characters.

Integer types

• short int (also accessible as short, may use the keyword signed)
• unsigned short int (also accessible as unsigned short)
• int (also accessible as signed int)
• unsigned int (also accessible as unsigned), the unsigned counterpart of int, implementing modulo arithmetic. Suitable for bit manipulations.
• long int (also accessible as long)
• unsigned long int (also accessible as unsigned long)

Note: as with all type specifiers, any order is permitted: unsigned long long int and long int unsigned long name the same type.

The following table summarizes all available integer types and their properties:

Besides the minimal bit counts, the C Standard guarantees that 1 == sizeof(char) <= sizeof(short) <= sizeof(int) <= sizeof(long) <= sizeof(long long).

Note: this allows the extreme case in which bytes are sized 64 bits, all types (including char) are 64 bits wide, and sizeof returns 1 for every type.

Note: integer arithmetic is defined differently for the signed and unsigned integer types. See arithmetic operators, in particular integer overflows.

Data models

The choices made by each implementation about the sizes of the fundamental types are collectively known as data model. Four data models found wide acceptance:

32 bit systems:

• LP32 or 2/4/4 (int is 16-bit, long and pointer are 32-bit)
• Win16 API
• ILP32 or 4/4/4 (int, long, and pointer are 32-bit);
• Win32 API
• Unix and Unix-like systems (Linux, Mac OS X)

64 bit systems:

• LLP64 or 4/4/8 (int and long are 32-bit, pointer is 64-bit)
• Win64 API
• LP64 or 4/8/8 (int is 32-bit, long and pointer are 64-bit)
• Unix and Unix-like systems (Linux, Mac OS X)

Other models are very rare. For example, ILP64 (8/8/8: int, long, and pointer are 64-bit) only appeared in some early 64-bit Unix systems (e.g. Unicos on Cray).

Note that exact-width integer types are available in <stdint.h> since C99.

Real floating types

C has three or six (since C23) types for representing real floating-point values:

• float - single precision floating point type. Matches IEEE-754 binary32 format if supported.
• double - double precision floating point type. Matches IEEE-754 binary64 format if supported.
• long double - extended precision floating point type. Matches IEEE-754 binary128 format if supported, otherwise matches IEEE-754 binary64-extended format if supported, otherwise matches some non-IEEE-754 extended floating-point format as long as its precision is better than binary64 and range is at least as good as binary64, otherwise matches IEEE-754 binary64 format.
  • binary128 format is used by some HP-UX, SPARC, MIPS, ARM64, and z/OS implementations.
  • The most well known IEEE-754 binary64-extended format is 80-bit x87 extended precision format. It is used by many x86 and x86-64 implementations (a notable exception is MSVC, which implements long double in the same format as double, i.e. binary64).

Floating-point types may support special values:

• infinity (positive and negative), see INFINITY
• the negative zero, -0.0. It compares equal to the positive zero, but is meaningful in some arithmetic operations, e.g. 1.0/0.0 == INFINITY, but 1.0/-0.0 == -INFINITY)
• not-a-number (NaN), which does not compare equal with anything (including itself). Multiple bit patterns represent NaNs, see nan, NAN. Note that C takes no special notice of signaling NaNs (specified by IEEE-754), and treats all NaNs as quiet.

Real floating-point numbers may be used with arithmetic operators + - / * and various mathematical functions from <math.h>. Both built-in operators and library functions may raise floating-point exceptions and set errno as described in math_errhandling.

Floating-point expressions may have greater range and precision than indicated by their types, see FLT_EVAL_METHOD. Assignment, return, and cast force the range and precision to the one associated with the declared type.

Floating-point expressions may also be contracted, that is, calculated as if all intermediate values have infinite range and precision, see #pragma STDC FP_CONTRACT.

Some operations on floating-point numbers are affected by and modify the state of the floating-point environment (most notably, the rounding direction).

Implicit conversions are defined between real floating types and integer, complex, and imaginary types.

See Limits of floating point types and the math.h library for additional details, limits, and properties of the floating-point types.

#include <complex.h>
#include <stdio.h>
int main(void)
{
    double complex z = 1 + 2*I;
    z = 1/z;
    printf("1/(1.0+2.0i) = %.1f%+.1fi\n", creal(z), cimag(z));
}

1/(1.0+2.0i) = 0.2-0.4i

float a[4] = {1, 2, 3, 4};
float complex z1, z2;
memcpy(&z1, a, sizeof z1); // z1 becomes 1.0 + 2.0i
memcpy(&z2, a+2, sizeof z2); // z2 becomes 3.0 + 4.0i

#include <stdio.h>
#include <complex.h>
#include <math.h>
int main(void)
{
   double complex z = (1 + 0*I) * (INFINITY + I*INFINITY);
// textbook formula would give
// (1+i0)(∞+i∞) ⇒ (1×∞ – 0×∞) + i(0×∞+1×∞) ⇒ NaN + I*NaN
// but C gives a complex infinity
   printf("%f + i*%f\n", creal(z), cimag(z));
 
// textbook formula would give
// cexp(∞+iNaN) ⇒ exp(∞)×(cis(NaN)) ⇒ NaN + I*NaN
// but C gives  ±∞+i*nan
   double complex y = cexp(INFINITY + I*NAN);
   printf("%f + i*%f\n", creal(y), cimag(y));
 
}

inf + i*inf 
inf + i*nan

#include <complex.h>
#include <stdio.h>
int main(void)
{
    double imaginary z = 3*I;
    z = 1/z;
    printf("1/(3.0i) = %+.1fi\n", cimag(z));
}

1/(3.0i) = -0.3i

Keywords

char, int, short, long, signed, unsigned, float, double. _Bool, _Complex, _Imaginary, _Decimal32, _Decimal64, _Decimal128.

Range of values

The following table provides a reference for the limits of common numeric representations.

Prior to C23, the C Standard allowed any signed integer representation, and the minimum guaranteed range of N-bit signed integers was from \(\scriptsize -(2^{N-1}-1)\)-(2N-1
-1) to \(\scriptsize +2^{N-1}-1\)+2N-1
-1 (e.g. -127 to 127 for a signed 8-bit type), which corresponds to the limits of one's complement or sign-and-magnitude.

However, all popular data models (including all of ILP32, LP32, LP64, LLP64) and almost all C compilers use two's complement representation (the only known exceptions are some compliers for UNISYS), and as of C23, it is the only representation allowed by the standard, with the guaranteed range from \(\scriptsize -2^{N-1}\)-2N-1
to \(\scriptsize +2^{N-1}-1\)+2N-1
-1 (e.g. -128 to 127 for a signed 8-bit type).

1. The object representation usually occupies 96/128 bits on 32/64-bit platforms respectively.

Note: actual (as opposed to guaranteed minimal) ranges are available in the library headers <limits.h> and <float.h>.

See also