Memory Sequence of Multi-Dimensional Arrays

1.5.7 Memory Sequence of Multi-Dimensional Arrays

Multi-dimensional arrays (of up to 7-D) can be defined in FORTRAN77. However, the actual memory system does not have a multi-dimensional structure, and it is managed one-dimensionally. The order for unfolding a multi-dimensional array into a 1-D array is defined in the FORTRAN77 standard, and so it is possible to combine multi-dimensional arrays to 1-D arrays (to give a 1-D name to multi-dimensional arrays.) For example, in the case of

      REAL         X(6), Y(2,3)

      COMPLEX      Z(3)

      EQUIVALENCE (X,Y,Z)

the variables X, Y, Z all are arrays with 6 words (48 bytes), and they occupy the same memory area according to the EQUIVALENCE statement. The variables are aligned in the following order.

`X(1)`	`X(2)`	`X(3)`	`X(4)`	`X(5)`	`X(6)`
`Y(1,1)`	`Y(2,1)`	`Y(1,2)`	`Y(2,2)`	`Y(1,3)`	`Y(2,3)`
`Re(Z(1))`	`Im(Z(1))`	`Re(Z(2))`	`Im(Z(2))`	`Re(Z(3))`	`Im(Z(3))`

The 2-D array Y is unfolded into a 1-D array in a way so that the left subscript changes first. Complex number data Z is unfolded as a sequence of 2 floating-point numbers. Therefore, the value of X(3) will be exactly the same as Y(1,2), Re(Z(2)).

This rule is actively used in many programs to treat multi-dimensional arrays as 1-D arrays or to treat complex-number data as floating-point-number data. This rule is close to the hardware of computers, so it may appear machine-dependent, but this is "standard language" defined in FORTRAN77 standard.