Pointer Arithmetic & Multi-Dimensional Array Subscripts

A pointer variable stores a memory address. In C, adding an integer k to a pointer p of type T^* does NOT add k bytes! It adds: k × sizeof(T) bytes.

Pointer Scaling Rule:

$Address(p + k) = Address(p) + k × sizeof(*p)$

Subscript Equivalence:

The array subscript expression A[i] is syntactically translated by the compiler as * (A + i). Because addition is commutative:

$A[i] \equiv (A + i) \equiv (i + A) \equiv i[A]$

Array Decay Rule:

In almost all C expressions, an array name of type T[N] automatically decays into a pointer of type T^* pointing to its first element (&A[0]).

The Two Exceptions to Array Decay:

1. When used as operand to sizeof: sizeof(A) yields total array capacity N × sizeof(T).

2. When used as operand to address-of &: &A yields a pointer to the entire array of type T(*)[N].