Arithmetic types
(See also type for type system overview and the list of type-related utilities that are provided by the C library.)
Boolean typeNote that conversion to _Bool(until C23)bool(since C23) does not work the same as conversion to other integer types: (bool)0.5 evaluates to true, whereas (int)0.5 evaluates to 0. |
(since C99) |
[edit] 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 and char8_t for UTF-8 characters(since C23).
[edit] 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)
- This is the most optimal integer type for the platform, and is guaranteed to be at least 16 bits. Most current systems use 32 bits (see Data models below).
- 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)
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(since C99) |
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(since C23) |
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:
Type specifier | Equivalent type | Width in bits by data model | ||||
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C standard | LP32 | ILP32 | LLP64 | LP64 | ||
char
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char | at least 8 |
8 | 8 | 8 | 8 |
signed char
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signed char | |||||
unsigned char
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unsigned char | |||||
short
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short int | at least 16 |
16 | 16 | 16 | 16 |
short int
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signed short
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signed short int
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unsigned short
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unsigned short int | |||||
unsigned short int
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int
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int | at least 16 |
16 | 32 | 32 | 32 |
signed
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signed int
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unsigned
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unsigned int | |||||
unsigned int
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long
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long int | at least 32 |
32 | 32 | 32 | 64 |
long int
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signed long
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signed long int
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unsigned long
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unsigned long int | |||||
unsigned long int
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long long
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long long int (C99) |
at least 64 |
64 | 64 | 64 | 64 |
long long int
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signed long long
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signed long long int
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unsigned long long
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unsigned long long int (C99) | |||||
unsigned long long int
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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 byte 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.
[edit] 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.
[edit] 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).
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(since C23) |
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.
Complex floating typesComplex floating types model the mathematical complex number, that is the numbers that can be written as a sum of a real number and a real number multiplied by the imaginary unit: a + bi The three complex types are
Note: as with all type specifiers, any order is permitted: long double complex, complex long double, and even double complex long name the same type. Run this code Output: 1/(1.0+2.0i) = 0.2-0.4i
Each complex type has the same object representation and alignment requirements as an array of two elements of the corresponding real type (float for float complex, double for double complex, long double for long double complex). The first element of the array holds the real part, and the second element of the array holds the imaginary component. Complex numbers may be used with arithmetic operators + - * and /, possibly mixed with imaginary and real numbers. There are many mathematical functions defined for complex numbers in <complex.h>. Both built-in operators and library functions may raise floating-point exceptions and set errno as described in math_errhandling. Increment and decrement are not defined for complex types. Relational operators are not defined for complex types (there is no notion of "less than").
In order to support the one-infinity model of complex number arithmetic, C regards any complex value with at least one infinite part as an infinity even if its other part is a NaN, guarantees that all operators and functions honor basic properties of infinities and provides cproj to map all infinities to the canonical one (see arithmetic operators for the exact rules). Run this code #include <complex.h> #include <math.h> #include <stdio.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%+f*i\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%+f*i\n", creal(y), cimag(y)); } Possible output: inf+inf*i inf+nan*i C also treats multiple infinities so as to preserve directional information where possible, despite the inherent limitations of the Cartesian representation: multiplying the imaginary unit by real infinity gives the correctly-signed imaginary infinity: i × ∞ = i∞. Also, i × (∞ – i∞) = ∞ + i∞ indicates the reasonable quadrant.
Imaginary floating typesImaginary floating types model the mathematical imaginary numbers, that is numbers that can be written as a real number multiplied by the imaginary unit: bi The three imaginary types are
Note: as with all type specifiers, any order is permitted: long double imaginary, imaginary long double, and even double imaginary long name the same type. Run this code Output: 1/(3.0i) = -0.3i
Each of the three imaginary types has the same object representation and alignment requirement as its corresponding real type (float for float imaginary, double for double imaginary, long double for long double imaginary). Note: despite that, imaginary types are distinct and not compatible with their corresponding real types, which prohibits aliasing. Imaginary numbers may be used with arithmetic operators + - * and /, possibly mixed with complex and real numbers. There are many mathematical functions defined for imaginary numbers in <complex.h>. Both built-in operators and library functions may raise floating-point exceptions and set errno as described in math_errhandling. Increment and decrement are not defined for imaginary types.
The imaginary numbers make it possible to express all complex numbers using the natural notation x + I*y (where I is defined as _Imaginary_I). Without imaginary types, certain special complex values cannot be created naturally. For example, if I is defined as _Complex_I, then writing 0.0 + I*INFINITY gives NaN as the real part, and CMPLX(0.0, INFINITY) must be used instead. Same goes for the numbers with the negative zero imaginary component, which are meaningful when working with the library functions with branch cuts, such as csqrt: 1.0 - 0.0*I results in the positive zero imaginary component if I is defined as _Complex_I and the negative zero imaginary part requires the use of CMPLX or conj. Imaginary types also simplify implementations; multiplication of an imaginary by a complex can be implemented straightforwardly with two multiplications if the imaginary types are supported, instead of four multiplications and two additions. |
(since C99) |
[edit] Keywords
- bool, true, false, char, int, short, long, signed, unsigned, float, double.
- _Bool, _BitInt, _Complex, _Imaginary, _Decimal32, _Decimal64, _Decimal128.
[edit] 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 -(2N-1
-1) to +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 -2N-1
to +2N-1
-1 (e.g. -128 to 127 for a signed 8-bit type).
Type | Size in bits | Format | Value range | |
---|---|---|---|---|
Approximate | Exact | |||
character | 8 | signed | −128 to 127 | |
unsigned | 0 to 255 | |||
16 | UTF-16 | 0 to 65535 | ||
32 | UTF-32 | 0 to 1114111 (0x10ffff) | ||
integer | 16 | signed | ± 3.27 · 104 | −32768 to 32767 |
unsigned | 0 to 6.55 · 104 | 0 to 65535 | ||
32 | signed | ± 2.14 · 109 | −2,147,483,648 to 2,147,483,647 | |
unsigned | 0 to 4.29 · 109 | 0 to 4,294,967,295 | ||
64 | signed | ± 9.22 · 1018 | −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 | |
unsigned | 0 to 1.84 · 1019 | 0 to 18,446,744,073,709,551,615 | ||
binary floating- point |
32 | IEEE-754 |
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64 | IEEE-754 |
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80[note 1] | x86 |
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128 | IEEE-754 |
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decimal floating point |
32 | IEEE-754 |
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64 | IEEE-754 |
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128 | IEEE-754 |
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- ↑ 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>.
[edit] See also
C++ documentation for Fundamental types
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