Array references in arithmetic expressions

Elements of arrays can be accessed quickly if the elements are stored in a block of consecutive location. Array can be one dimensional or two dimensional.

For one dimensional array:

1. A: array[low..high] of the ith elements is at:  
2. base + (i-low)*width → i*width + (base - low*width)  

Multi-dimensional arrays:

Row major or column major forms

• Row major: a[1,1], a[1,2], a[1,3], a[2,1], a[2,2], a[2,3]
• Column major: a[1,1], a[2,1], a[1, 2], a[2, 2],a[1, 3],a[2,3]
• In raw major form, the address of a[i1, i2] is
• Base+((i1-low1)*(high2-low2+1)+i2-low2)*width

Translation scheme for array elements

Limit(array, j) returns nj=highj-lowj+1

place: the temporaryor variables

offset: offset from the base, null if not an array reference

The production:

1. S  →  L := E  
2.    E  →  E+E  
3.    E  →  (E)  
4.    E  →  L  
5.    L  →  Elist ]  
6.    L  →  id  
7.    Elist →   Elist, E  
8.    Elist  →   id[E  

A suitable transition scheme for array elements would be:

Production Rule	Semantic Action
S → L := E	{if L.offset = null then emit(L.place ':=' E.place)  else EMIT (L.place'['L.offset ']' ':=' E.place); }
E → E+E	{E.place := newtemp;  EMIT (E.place ':=' E1.place '+' E2.place); }
E → (E)	{E.place := E1.place;}
E → L	{if L.offset = null then E.place = L.place   else {E.place = newtemp;   EMIT (E.place ':=' L.place '[' L.offset ']');    } }
L → Elist ]	{L.place = newtemp; L.offset = newtemp;   EMIT (L.place ':=' c(Elist.array));   EMIT (L.offset ':=' Elist.place '*' width(Elist.array); }
L → id	{L.place = lookup(id.name);   L.offset = null; }
Elist → Elist, E	{t := newtemp;   m := Elist1.ndim + 1;   EMIT (t ':=' Elist1.place '*' limit(Elist1.array, m));   EMIT (t, ':=' t '+' E.place);   Elist.array = Elist1.array;   Elist.place := t;   Elist.ndim := m; }
Elist → id[E	{Elist.array := lookup(id.name);   Elist.place := E.place   Elist.ndim := 1; }

Where:

ndim denotes the number of dimensions.

limit(array, i) function returns the upper limit along with the dimension of array

width(array) returns the number of byte for one element of array.