# Memory Allocation for High-Dimensional Data Structures

Environment: Windows NT SP5, Windows 95b/98, Visual C++ 6

### 1. General Methods

For a very large application, dynamic memory allocation is common in C/C++ programming.
For example, I ported Basin Modeling application from SUN workstation to PC 486
in 1992, cutting memory usage up to 90%. Generally two types of dynamic memory
allocation methods are wildly used to deal with high dimensional data structures.

One is to use 1D to represent nD as shown in the follow:

```// 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);
```

The other is directly to use nD as shown in the follow:

```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);

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

MemDemo.cpp demonstrates how to use memory allocation functions in the above files.
It tests both float, double, and data structure types.