Memory Allocation for High-Dimensional Data Structures

1. General Methods

// ignore pointer validation and use malloc and free for instance
Type* p = (Type *)malloc(s1*s2* ... *sn*sizeof(Type));
for(i1 = 0; i1 < s1; i1 ++) 
 for(i2 = 0; i2 < s2; i2 ++)
  //... 
  for(in = 0; in < sn; in ++)
   p[(...((i1*s2+i2)*s3+i3)...)*sn+in] = ...; 
   //do something using p 
free(A);

Type *p1, **p2, ..., **...*pn;
  
p1 = (Type *)malloc(sizeof(Type)*s1*s2*...*sn*sizeof(Type));
p2 = (Type **)malloc(sizeof(Type*)*s1*s2*...*sn-1);
//...
pn = (Type **...*)calloc(sizeof(Type**...*)s1, size);

// need assign address properly
for(i = 0; i < s1*s2*...*sn-1; i ++)
 *(p2+i) = &p1[sn*i*sizeof(Type)];

for(i = 0; i < s1; i ++)
 *(p3+i) = &p2[sn-1*i];
//...

for(i = 0; i < s1*s2*...*sn-2; i ++)
 *(pn+i) = &pn-1[s2*i];

for(i1 = 0; i1 < s1; i1 ++) 
 for(i2 = 0; i2 < s2; i2 ++)
  //...
  for(in = 0; in < sn; in ++)
   pn[i1][i2]...[in] = ...; 
   //do something using pn

free(**...*p);  //(n-1)-dimensional pointer

//...

free(*p);
free(p);

2. Source Code

1. MemA.h uses C++ template and operator overloading to implement 1D, 2D, and 3D based on method 1. It is easy to extend to high dimension, such as 4D and 5D. It is especially useful to port applications from Fortran to C++.
   Member functions

   • bool CDynArray<Type>::SetSize(int i);

   • bool CDynArray<Type>::SetSize(int i, int j);

   • bool CDynArray<Type>::SetSize(int i, int j, int k);

   • Type& CDynArray<Type>::operator ()(int i);

   • Type& CDynArray<Type>::operator ()(int i, int j);

   • Type& CDynArray<Type>::operator ()(int i, int j, int k);

   • void CDynArray<Type>::Remove();

2. MemB.h uses C++ template to implement 1D, 2D, and 3D based on method 2.
   Member functions

   • // One dimension

   • Type* CMalloc<Type>::Malloc(int I);

   • void CMalloc<Type>::Free(T*& X);

   • // Two dimension

   • Type** CMalloc<Type>::Malloc(int I, int J);

   • void CMalloc<Type>::Free(T**& X);

   • // Three dimension

   • Type** CMalloc<Type>::Malloc(int I, int J, int K);
     			
     void CMalloc<Type>::Free(T***& X);
     		

3. MemC.h and MemC.c only use C to implement 2D and 3D based on method 2.
   Member functions

   • void** Malloc2(int, int, size_t);

   • void*** Malloc3(int, int, int, size_t);

   • void Free2(void**);

   • void Free3(void***);

3. Demo Project

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