Implicit conversions

When an expression is used in the context where a value of a different type is expected, conversion may occur:

int n = 1L; // expression 1L has type long, int is expected
n = 2.1; // expression 2.1 has type double, int is expected
char *p = malloc(10); // expression malloc(10) has type void*, char* is expected

Conversions take place in the following situations:

Conversion as if by assignment

In the assignment operator, the value of the right-hand operand is converted to the unqualified type of the left-hand operand.
In scalar initialization, the value of the initializer expression is converted to the unqualified type of the object being initialized
In a function-call expression, to a function that has a prototype, the value of each argument expression is converted to the type of the unqualified declared types of the corresponding parameter
In a return statement, the value of the operand of return is converted to an object having the return type of the function

Note that actual assignment, in addition to the conversion, also removes extra range and precision from floating-point types and prohibits overlaps; those characteristics do not apply to conversion as if by assignment.

Default argument promotions

In a function call expression when the call is made to

1) a function without a prototype

2) a variadic function, where the argument expression is one of the trailing arguments that are matched against the ellipsis parameter

Each argument of integer type undergoes integer promotion (see below), and each argument of type float is implicitly converted to the type double

int add_nums(int count, ...);
int sum = add_nums(2, 'c', true); // add_nums is called with three ints: (2, 99, 1)

Note that float complex and float imaginary are not promoted to double complex and double imaginary in this context.

Usual arithmetic conversions

The arguments of the following arithmetic operators undergo implicit conversions for the purpose of obtaining the common real type, which is the type in which the calculation is performed:

binary arithmetic *, /, %, +, -
relational operators <, >, <=, >=, ==, !=
binary bitwise arithmetic &, ^, |,
the conditional operator ?:

1) If one operand is long double, long double complex, or long double imaginary, the other operand is implicitly converted as follows:

integer or real floating type to long double
complex type to long double complex
imaginary type to long double imaginary

2) Otherwise, if one operand is double, double complex, or double imaginary, the other operand is implicitly converted as follows:

integer or real floating type to double
complex type to double complex
imaginary type to double imaginary

3) Otherwise, if one operand is float, float complex, or float imaginary, the other operand is implicitly converted as follows:

integer type to float (the only real type possible is float, which remains as-is)
complex type remains float complex
imaginary type remains float imaginary

4) Otherwise, both operands are integers. Both operands undergo integer promotions (see below); then, after integer promotion, one of the following cases applies:

If the types are the same, that type is the common type.
Else, the types are different:
- If the types have the same signedness (both signed or both unsigned), the operand whose type has the lesser conversion rank¹ is implicitly converted² to the other type.
- Else, the operands have different signedness:
  - If the unsigned type has conversion rank greater than or equal to the rank of the signed type, then the operand with the signed type is implicitly converted to the unsigned type.
  - Else, the unsigned type has conversion rank less than the signed type:
    - If the signed type can represent all values of the unsigned type, then the operand with the unsigned type is implicitly converted to the signed type.
    - Else, both operands undergo implicit conversion to the unsigned type counterpart of the signed operand's type.

1. Refer to "integer promotions" below for the rules on ranking.

2. Refer to "integer conversions" under "implicit conversion semantics" below.

1.f + 20000001; // int is converted to float, giving 20000000.00
                // addition and then rounding to float gives 20000000.00
 
(char)'a' + 1L; // first, char 'a', which is 97, is promoted to int
                // different types: int and long
                // same signedness: both signed
                // different rank: long is of greater rank than int
                // therefore, int 97 is converted to long 97
                // the result is 97 + 1 = 98 of type signed long
 
2u - 10; // different types: unsigned int and signed int
         // different signedness
         // same rank
         // therefore, signed int 10 is converted to unsigned int 10
         // since the arithmetic operation is performed for unsigned integers (see "Arithmetic operators" topic),
         // the calculation performed is (2 - 10) modulo (2 raised to n), where n is the number of bits of unsigned int
         // if unsigned int is 32-bit long, then 
         // the result is (-8) modulo (2 raised to 32) = 4294967288 of type unsigned int
 
5UL - 2ULL; // different types: unsigned long and unsigned long long
            // same signedness
            // different rank: rank of unsigned long long is greater
            // therefore, unsigned long 5 is converted to unsigned long long 5
            // since the arithmetic operation is performed for unsigned integers (see "Arithmetic operators" topic),
            // if unsigned long long is 64-bit long, then
            // the result is (5 - 2) modulo (2 raised to 64) = 3 of type unsigned long long
 
0UL - 1LL; // different types: unsigned long and signed long long
           // different signedness
           // different rank: rank of signed long long is greater.
           // if ULONG_MAX > LLONG_MAX, then signed long long cannot represent all unsigned long
           // therefore, this is the last case: both operands are converted to unsigned long long
           // unsigned long 0 is converted to unsigned long long 0
           // long long 1 is converted to unsigned long long 1
           // since the arithmetic operation is performed for unsigned integers (see "Arithmetic operators" topic),
           // if unsigned long long is 64-bit long, then  
           // the calculation is (0 - 1) modulo (2 raised to 64)
           // thus, the result is 18446744073709551615 (ULLONG_MAX) of type unsigned long long

The result type is determined as follows:

if both operands are complex, the result type is complex
if both operands are imaginary, the result type is imaginary
if both operands are real, the result type is real
if the two floating-point operands have different type domains (complex vs. real, complex vs imaginary, or imaginary vs. real), the result type is complex

double complex z = 1 + 2*I;
double f = 3.0;
z + f; // z remains as-is, f is converted to double, the result is double complex

As always, the result of a floating-point operator may have greater range and precision than is indicated by its type (see FLT_EVAL_METHOD).

Note: real and imaginary operands are not implicitly converted to complex because doing so would require extra computation, while producing undesirable results in certain cases involving infinities, NaNs and signed zeros. For example, if reals were converted to complex, 2.0×(3.0+i∞) would evaluate as (2.0+i0.0)×(3.0+i∞) ⇒ (2.0×3.0–0.0×∞) + i(2.0×∞+0.0×3.0) ⇒ NaN+i∞ rather than the correct 6.0+i∞. If imaginaries were converted to complex, i2.0×(∞+i3.0) would evaluate as (0.0+i2.0) × (∞+i3.0) ⇒ (0.0×∞ – 2.0×3.0) + i(0.0×3.0 + 2.0×∞) ⇒ NaN + i∞ instead of –6.0 + i∞.

Note: regardless of usual arithmetic conversions, the calculation may always be performed in a narrower type than specified by these rules under the as-if rule

Value transformations

Lvalue conversion

Any lvalue expression of any non-array type, when used in any context other than

as the operand of the address-of operator (if allowed)
as the operand of the pre/post increment and decrement operators.
as the left-hand operand of the member access (dot) operator.
as the left-hand operand of the assignment and compound assignment operators.
as the operand of sizeof

undergoes lvalue conversion: the type remains the same, but loses const/volatile/restrict-qualifiers and atomic properties, if any. The value remains the same, but loses its lvalue properties (the address may no longer be taken).

If the lvalue has incomplete type, the behavior is undefined.

If the lvalue designates an object of automatic storage duration whose address was never taken and if that object was uninitialized (not declared with an initializer and no assignment to it has been performed prior to use), the behavior is undefined.

This conversion models the memory load of the value of the object from its location.

volatile int n = 1;
int x = n;            // lvalue conversion on n reads the value of n
volatile int* p = &n; // no lvalue conversion: does not read the value of n

Array to pointer conversion

Any lvalue expression of array type, when used in any context other than

as the operand of the address-of operator
as the operand of sizeof
as the string literal used for array initialization

undergoes a conversion to the non-lvalue pointer to its first element.

If the array was declared register, the behavior is undefined.

int a[3], b[3][4];
int* p = a;      // conversion to &a[0]
int (*q)[4] = b; // conversion to &b[0]

Function to pointer conversion

Any function designator expression, when used in any context other than

as the operand of the address-of operator
as the operand of sizeof

undergoes a conversion to the non-lvalue pointer to the function designated by the expression.

int f(int);
int (*p)(int) = f; // conversion to &f
(***p)(1); // repeated dereference to f and conversion back to &f

Implicit conversion semantics

Implicit conversion, whether as if by assignment or a usual arithmetic conversion, consists of two stages:

1) value transformation (if applicable)

2) one of the conversions listed below (if it can produce the target type)

Compatible types

Conversion of a value of any type to any compatible type is always a no-op and does not change the representation.

uint8_t (*a)[10];         // if uint8_t is a typedef to unsigned char
unsigned char (*b)[] = a; // then these pointer types are compatible

Integer promotions

Integer promotion is the implicit conversion of a value of any integer type with rank less or equal to rank of int or of a bit field of type _Bool, int, signed int, unsigned int, to the value of type int or unsigned int

If int can represent the entire range of values of the original type (or the range of values of the original bit field), the value is converted to type int. Otherwise the value is converted to unsigned int.

Integer promotions preserve the value, including the sign:

int main(void) {
   void f(); // old-style function declaration
   char x = 'a'; // integer conversion from int to char
   f(x); // integer promotion from char back to int
}
void f(x) int x; {} // the function expects int

rank above is a property of every integer type and is defined as follows:

1) the ranks of all signed integer types are different and increase with their precision: rank of signed char < rank of short < rank of int < rank of long int < rank of long long int

2) the ranks of all signed integer types equal the ranks of the corresponding unsigned integer types

3) the rank of any standard integer type is greater than the rank of any extended integer type of the same size (that is, rank of __int64 < rank of long long int, but rank of long long < rank of __int128 due to the rule (1))

4) rank of char equals rank of signed char and rank of unsigned char

5) the rank of _Bool is less than the rank of any other standard integer type

6) the rank of any enumerated type equals the rank of its compatible integer type

7) ranking is transitive: if rank of T1 < rank of T2 and rank of T2 < rank of T3 then rank of T1 < rank of T3

8) any aspects of relative ranking of extended integer types not covered above are implementation defined

Note: integer promotions are applied only

as part of usual arithmetic conversions (see above)
as part of default argument promotions (see above)
to the operand of the unary arithmetic operators + and -
to the operand of the unary bitwise operator ~
to both operands of the shift operators << and >>

Boolean conversion

A value of any scalar type can be implicitly converted to _Bool. The values that compare equal to zero are converted to 0, all other values are converted to 1

bool b1 = 0.5;              // b1 == 1 (0.5 converted to int would be zero)
bool b2 = 2.0*_Imaginary_I; // b2 == 1 (but converted to int would be zero)
bool b3 = 0.0 + 3.0*I;      // b3 == 1 (but converted to int would be zero)
bool b4 = 0.0/0.0;          // b4 == 1 (NaN does not compare equal to zero)

Integer conversions

A value of any integer type can be implicitly converted to any other integer type. Except where covered by promotions and boolean conversions above, the rules are:

if the target type can represent the value, the value is unchanged
otherwise, if the target type is unsigned, the value $2 b$ , where $b$ is the number of bits in the target type, is repeatedly subtracted or added to the source value until the result fits in the target type. In other words, unsigned integers implement modulo arithmetic.
otherwise, if the target type is signed, the behavior is implementation-defined (which may include raising a signal)

char x = 'a'; // int -> char, result unchanged
unsigned char n = -123456; // target is unsigned, result is 192 (that is, -123456+483*256)
signed char m = 123456;    // target is signed, result is implementation-defined
assert(sizeof(int) > -1);  // assert fails:
                           // operator > requests conversion of -1 to size_t,
                           // target is unsigned, result is SIZE_MAX

Real floating-integer conversions

A finite value of any real floating type can be implicitly converted to any integer type. Except where covered by boolean conversion above, the rules are:

The fractional part is discarded (truncated towards zero).

If the resulting value can be represented by the target type, that value is used
otherwise, the behavior is undefined

int n = 3.14; // n == 3
int x = 1e10; // undefined behavior for 32-bit int

A value of any integer type can be implicitly converted to any real floating type.

if the value can be represented exactly by the target type, it is unchanged
if the value can be represented, but cannot be represented exactly, the result is the nearest higher or the nearest lower value (in other words, rounding direction is implementation-defined), although if IEEE arithmetic is supported, rounding is to nearest. It is unspecified whether FE_INEXACT is raised in this case.
if the value cannot be represented, the behavior is undefined, although if IEEE arithmetic is supported, FE_INVALID is raised and the result value is unspecified.

The result of this conversion may have greater range and precision than its target type indicates (see FLT_EVAL_METHOD.

If control over FE_INEXACT is needed in floating-to-integer conversions, rint and nearbyint may be used.

double d = 10; // d = 10.00
float f = 20000001; // f = 20000000.00 (FE_INEXACT)
float x = 1+(long long)FLT_MAX; // undefined behavior

Real floating point conversions

A value of any real floating type can be implicitly converted to any other real floating type.

If the value can be represented by the target type exactly, it is unchanged
if the value can be represented, but cannot be represented exactly, the result is the nearest higher or the nearest lower value (in other words, rounding direction is implementation-defined), although if IEEE arithmetic is supported, rounding is to nearest
if the value cannot be represented, the behavior is undefined

The result of this conversion may have greater range and precision than its target type indicates (see FLT_EVAL_METHOD.

double d = 0.1; // d = 0.1000000000000000055511151231257827021181583404541015625
float f = d;    // f = 0.100000001490116119384765625
float x = 2*(double)FLT_MAX; // undefined

Complex type conversions

A value of any complex type can be implicitly converted to any other complex type. The real part and the imaginary part individually follow the conversion rules for the real floating types.

double complex d = 0.1 + 0.1*I;
float complex f = d; // f is (0.100000001490116119384765625, 0.100000001490116119384765625)

Imaginary type conversions

A value of any imaginary type can be implicitly converted to any other imaginary type. The imaginary part follows the conversion rules for the real floating types.

double imaginary d = 0.1*_Imaginary_I;
float imaginary f = d; // f is 0.100000001490116119384765625*I

Real-complex conversions

A value of any real floating type can be implicitly converted to any complex type.

The real part of the result is determined by the conversion rules for the real floating types
The imaginary part of the result is positive zero (or unsigned zero on non-IEEE systems)

A value of any complex type can be implicitly converted to any real floating type

The real part is converted following the rules for the real floating types
The imaginary part is discarded

Note: in complex-to-real conversion, a NaN in the imaginary part will not propagate to the real result.

double complex z = 0.5 + 3*I;
float f = z;  // the imaginary part is discarded, f is set to 0.5
z = f;        // sets z to 0.5 + 0*I

Real-imaginary conversions

A value of any imaginary type can be implicitly converted to any real type (integer or floating-point). The result is always a positive (or unsigned) zero, except when the target type is _Bool, in which case boolean conversion rules apply.

A value of any real type can be implicitly converted to any imaginary type. The result is always a positive imaginary zero.

double imaginary z = 3*I;
bool b = z;  // Boolean conversion: sets b to true 
float f = z; // Real-imaginary conversion: sets f to 0.0 
z = 3.14;    // Imaginary-real conversion: sets z to 0*_Imaginary_I

Complex-imaginary conversions

A value of any imaginary type can be implicitly converted to any complex type.

The real part of the result is the positive zero
The imaginary part of the result follows the conversion rules for the corresponding real types

A value of any complex type can be implicitly converted to any imaginary type

The real part is discarded
The imaginary part of the result follows the conversion rules for the corresponding real types

double imaginary z = I * (3*I); // the complex result -3.0+0i loses real part
                                // sets z to 0*_Imaginary_I

Pointer conversions

A pointer to void can be implicitly converted to and from any pointer to object type with the following semantics:

If a pointer to object is converted to a pointer to void and back, its value compares equal to the original pointer.
No other guarantees are offered

int* p = malloc(10 * sizeof(int)); // malloc returns void*

A pointer to an unqualified type may be implicitly converted to the pointer to qualified version of that type (in other words, const, volatile, and restrict qualifiers can be added. The original pointer and the result compare equal.

int n;
const int* p = &n; // &n has type int*

Any integer constant expression with value 0 as well as integer pointer expression with value zero cast to the type void* can be implicitly converted to any pointer type (both pointer to object and pointer to function). The result is the null pointer value of its type, guaranteed to compare unequal to any non-null pointer value of that type. This integer or void* expression is known as null pointer constant and the standard library provides one definition of this constant as the macro NULL .

int* p = 0;
double* q = NULL;

Notes

Although signed integer overflow in any arithmetic operator is undefined behavior, overflowing a signed integer type in an integer conversion is merely unspecified behavior.

On the other hand, although unsigned integer overflow in any arithmetic operator (and in integer conversion) is a well-defined operation and follows the rules of modulo arithmetic, overflowing an unsigned integer in a floating-to-integer conversion is undefined behavior: the values of real floating type that can be converted to unsigned integer are the values from the open interval $(-1; Unnn_MAX+1)$ .

unsigned int n = -1.0; // undefined behavior

Conversions between pointers and integers (except from pointer to _Bool and from integer constant expression with the value zero to pointer), between pointers to objects (except where either to or from is a pointer to void) and conversions between pointers to functions (except when the functions have compatible types) are never implicit and require a cast operator.

There are no conversions (implicit or explicit) between pointers to functions and pointers to objects (including void*) or integers.

References

C11 standard (ISO/IEC 9899:2011):

6.3 Conversions (p: 50-56)

C99 standard (ISO/IEC 9899:1999):

6.3 Conversions (p: 42-48)

C89/C90 standard (ISO/IEC 9899:1990):

3.2 Conversions

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