Fraction*[] is an array of Fraction* (an array of pointers). Fraction(*)[] is a pointer to Fraction[] (pointer to an array). The difference is that parentheses isolate the "pointer" from the Fraction, because otherwise the two would bind to each other and give you a different type than intended.
Mechanically, a * or a & would much rather bind to a type name than be isolated and represent the entire thing, so you have to use parentheses to isolate it from the element type. This is also true when declaring function pointers: int*(int, int) is a function that takes two ints and returns an int*, while int(*)(int, int) is a pointer to a function that takes two ints and returns an int.
Consider this simple program:
#include <iostream>
#include <typeinfo>
struct Type {};
// 1: Array of Type*.
void func(Type *arr [3]) {
std::cout << "Type* array.\n"
<< typeid(arr).name() << "\n\n";
}
// 2: Array of Type&.
// Illegal.
// void func(Type &arr [3]) {
// std::cout << "Type& array.\n"
// << typeid(arr).name() << "\n\n";
// }
// 3: Pointer to array of Type.
void func(Type (*arr) [3]) {
std::cout << "Pointer to Type array.\n"
<< typeid(arr).name() << "\n\n";
}
// 4: Reference to array of Type.
void func(Type (&arr) [3]) {
std::cout << "Reference to Type array.\n"
<< typeid(arr).name() << "\n\n";
}
int main() {
// Array of Type.
Type t_arr[3] = {};
// Array of Type*.
Type* tp_arr[3] = { &t_arr[0], &t_arr[1], &t_arr[2] };
// Array of Type&.
// Illegal.
// Type& tr_arr[3] = { t_arr[0], t_arr[1], t_arr[2] };
std::cout << "Type[3]: " << typeid(t_arr).name() << "\n\n";
func(t_arr); // Calls #4.
func(&t_arr); // Calls #3.
func(tp_arr); // Calls #1.
}
Depending on the compiler used, it'll output either mangled or unmangled types for arr, and the output shows that all three are different types:
// MSVC:
Type[3]: struct Type [3]
Reference to Type array.
struct Type [3]
Pointer to Type array.
struct Type (*)[3]
Type* array.
struct Type * *
// GCC:
Type[3]: A3_4Type
Reference to Type array.
A3_4Type
Pointer to Type array.
PA3_4Type
Type* array.
PP4Type
This syntax is a bit wonky if you're not used to it, and can be somewhat easy to mistype, so it may be a good idea to make a type alias if you need to use it.
// Array.
typedef Type Type_arr_t[3];
// Pointer.
typedef Type (*Type_arr_ptr_t)[3];
// Reference.
typedef Type (&Type_arr_ref_t)[3];
// ...
// Without typedefs.
Type arr [3];
Type (*arr_p)[3] = &arr;
Type (&arr_r)[3] = arr;
// With typedefs.
Type_arr_t arr2;
Type_arr_ptr_t arr2_p = &arr2;
Type_arr_ref_t arr2_r = arr2;
This is extremely useful when declaring functions that return pointers or references to arrays, because they look silly without typedefs, and are really easy to get wrong and/or forget the syntax for.
typedef Type (*Type_arr_ptr_t)[3];
typedef Type (&Type_arr_ref_t)[3];
// Without typedefs.
Type (*return_ptr())[3];
Type (&return_ref())[3];
// With typedefs.
Type_arr_ptr_t return_ptr_2();
Type_arr_ref_t return_ref_2();
For more information regarding how to parse something like this, see the clockwise spiral rule.
Note: When an array is passed by value as a function parameter, and in many other situations (specifically, in any situation where an array isn't expected, but a pointer is), type and dimension information is lost, and it is implicitly converted to a pointer to the first element of the array; this is known as the array decaying into a pointer. This is demonstrated in func(Type*[3]) above, where the compiler takes a parameter type of Type*[3], an array of Type*, and replaces it with Type**, a pointer to Type*; the [3] is lost, and replaced with a simple *, because functions can take pointers but not arrays. When func() is called, the array will decay due to this. Due to this, the following signatures are treated as identical, with the parameter being Type** in all three.
void func(Type*[3]);
void func(Type*[] ); // Dimension isn't needed, since it'll be replaced anyways.
void func(Type** );
This is done because it's more efficient than trying to pass the entire array by value (it only needs to pass a pointer, which easily fits inside a single register, instead of trying to load the entire thing into memory), and because encoding the array type into the function's parameter list would remove any flexibility from the function regarding the size of the array it can take (if a function were to take Type[3], then you couldn't pass it a Type[4] or a Type[2]). Due to this, the compiler will silently replace a Type[N] or Type[] with a Type*, causing the array to decay when passed. This can be avoided by specifically taking a pointer or reference to the array; while this is as efficient as letting the array decay (the former because it still just passes a pointer, the latter because most compilers implement references with pointers), it loses out on flexibility (which is why it's usually paired with templates, which restore the flexibility, without removing any of the strictness).
// Will take any pointer to a Type array, and replace N with the number of elements.
// Compiler will generate a distinct version of `func()` for each unique N.
template<size_t N>
void func(Type (*)[N]);
// Will take any reference to a Type array, and replace N with the number of elements.
// Compiler will generate a distinct version of `func()` for each unique N.
template<size_t N>
void func(Type (&)[N]);
Note, however, that C doesn't have the luxury of templates, and thus any code that is intended to work with both languages should either use the C idiom of passing a "size" parameter along with the array, or be written specifically for a certain size of array; the former is more flexible, while the latter is useful if you will never need to take an array of any other size.
void func1(Type *arr, size_t sz);
void func2(Type (*arr)[3]);
Also note that there are situations where an array won't decay into a pointer.
// Example array.
Type arr[3];
// Function parameter.
void func(Type arr[3]);
void func(Type (*arr)[3]);
void func(Type (&arr)[3]);
// Function template parameter.
template<typename T>
void temp(T t);
// Class template parameter.
template<typename T>
struct S { typedef T type; };
// Specialised class template parameter.
template<typename T> struct S2;
template<typename T, size_t Sz>
struct S2<T[Sz]> { typedef T type[Sz]; };
func(arr); // C: arr decays into Type*.
// C++: arr either binds to a Type(&)[3], or decays into Type*.
// If both are available, causes error due to ambiguous function call.
func(&arr); // C/C++: No decay, &arr is Type(*)[3].
sizeof(arr); // C/C++: No decay, evaluates to (sizeof(Type) * 3).
alignof(arr); // C/C++: No decay, evaluates to alignof(Type).
decltype(arr); // C++: No decay, evaluates to Type[3].
typeid(arr); // C++: No decay, evaluates to a std::type_info for Type[3].
for (Type& t : arr); // C++: No decay, ranged-based for accepts arrays.
temp(arr); // C++: arr decays to Type* during function template deduction.
temp<Type[3]>(arr); // C++: No decay, deduction isn't required.
// For class templates, deduction isn't performed, so array types used as template parameters
// don't decay.
S<Type[3]>::type; // C++: No decay, type is Type[3].
S2<Type[3]>::type; // C++: No decay, type is Type[3].
// String literals are arrays, too.
decltype("Hello."); // C++: No decay, evaluates to const char[7].
char c_arr[] = "Hello."; // C/C++: No decay, c_arr is a local array, of type char[7],
// containing copy of "Hello."
const char* c_ptr = "Hello."; // C/C++: const char[7] "Hello." is stored in read-only
// memory, and ptr points to it.
// There may be other cases in which arrays don't decay, which I'm currently not aware of.
So, in short, while, say, Type[3] is an array type, and Fraction*[5] is an array type, there are cases where a declaration of the two will be silently replaced with a Type* or Fraction**, respectively, by the compiler, and where type and dimension information will be lost due to this; this loss is known as array decay or array-to-pointer decay.
Thanks go to juanchopanza for reminding me to mention array-to-pointer decay.
