1. Memory representation of variables

1.1. Abstract

In this page, we present how Scilab v5 stores the variables. More precisely, we present the internal storage of doubles, booleans, strings, polynomials, sparse matrices and lists.

1.2. How does Scilab store variables in memory ?

In the stack, Scilab mixes integers ( 32 bits ) and doubles ( 64 bits ) so we need to use specific commands to convert addresses.

Commands to access stack values :

• istk( iAddr ) with iAddr is a Scilab format address, returns a pointer to a value ( integer )
• sadr( iAddr + xxx ) with iAddr is a Scilab format address, returns a new Scilab format address with offset xxx. This command take case of mix integer/double
• stk( iAddr ) with iAddr is a Scilab format address returned by sadr command, returns a pointer to a array of double values

1.2.1. Matrix of double

iAddrBase is the address ( scilab format ) of Type :

Type = *istk( iAddBase ); // Returns variable type
Lines = *istk( iAddrBase + 1 ); // Returns number of lines in the matrix
Columns = *istk( iAddrBase + 2 ); // Returns number of columns in the matrix
Complex = *istk( iAddrBase + 3 ); // Returns 0 if real, 1 if complex
Real_Part = stk( sadr( iAddrBase + 4 ) ); // Returns a pointer on a real array of double values, size = Lines * Columns
Img_Part = stk( sadr( iAddrBase + 4 + Lines * Columns ) ); // Returns a pointer on a imaginary array of double values, size = Lines * Columns

1.2.1.1. Sample for a real matrix [2, 3] :

A = [ 1 , 2 , 3 ]
    [ 4 , 5 , 6 ]  

1.2.1.2. Sample for a complex matrix [2,3] :

B = [ -i      , 2 - 3i , -4 + 5i  ]
    [ -6 - 7i , -9     , 10 + 11i ]  

1.2.2. Matrix of boolean

iAddrBase is the address ( scilab format ) of Type :

Type = *istk( iAddBase ); // Returns variable type
Lines = *istk( iAddrBase + 1 ); // Returns number of lines in the matrix
Columns = *istk( iAddrBase + 2 ); // Returns number of columns in the matrix
Values = *istk( iAddrBase + 3 ); // Returns a pointer to integer array of boolean values (0 for false, 1 for true),size = Lines * Columns

1.2.2.1. Sample for a boolean matrix [2, 3] :

A = [ %T , %T , %F ]
    [ %F , %T , %F ]  

1.2.3. Matrix of strings

Type = *istk( iAddrBase ); // Returns variable type
Lines = *istk( iAddrBase + 1 ); // Returns number of lines in the matrix
Columns = *istk( iAddrBase + 2 ); // Returns number of columns in the matrix
Complex = *istk( iAddrBase + 3 ); // Returns 0
Offset = istk(iAddrBase + 4 ); // Returns an array of offset, size = Lines * Columns + 1
Data = stk( iAddrBase + 4 + 1 + Lines * Columns ); // Returns a pointer on the first charater of the first string, size = Offset[MAX-1] - 1

A = [ "Scilab"   , "is"
      "a"        , "beautiful"
      "software" , ":)"]  

1.2.4. Matrix of polynomials

Type = *istk( iAddBase ); // Returns variable type
Lines = *istk( iAddrBase + 1 ); // Returns number of lines in the matrix
Columns = *istk( iAddrBase + 2 ); // Returns number of columns in the matrix
Complex = *istk( iAddrBase + 3 ); // Returns 0 if real, 1 if complex
Variable Name = *istk( iAddrBase + 4 ); // Returns a pointer on an array of interger, size = 4
Offset = istk(iAddrBase + 8 ); // Returns an array of offset, size = Lines * Columns + 1
Real_Part = stk( sadr( iAddrBase + 8 + 1 + Lines * Columns ) ); // Returns a pointer on a real array of double values, size = Offset[MAX-1] - 1
Img_Part = stk( sadr( iAddrBase + 8 + Lines * Columns + Offset[MAX-1]) ); // Returns a pointer on a imaginary array of double values, size = Offset[MAX-1] - 1

1.2.4.1. Sample for a matrix of real polynomials :

A = [ x + 2,
      3 * x^2 -4x + 5,
     -6 * x^3 + 7x - 8]  

1.2.4.2. Sample for a matrix of complex polynomials :

A = [ (i-2) * x + (-3i + 4),
    (5 - 6i) * x^2 + (8i) * x + (9 - 10i),
    (-11 + 12i) * x^3 + (-13)* x + (15 - 16i)]  

1.2.5. Sparse matrix

Type = *istk( iAddBase ); // Returns variable type
Lines = *istk( iAddrBase + 1 ); // Returns number of lines in the matrix
Columns = *istk( iAddrBase + 2 ); // Returns number of columns in the matrix
Complex = *istk( iAddrBase + 3 ); // Returns 0 if real, 1 if complex
Total Items = *istk( iAddrBase + 4 ); // Returns number of items in the sparse
Line Items = istk(iAddrBase + 5 ); // Number of items in each Line, size = Lines
Column position = istk(iAddrBase + 5 + Lines ); // Column positions for each item, size = Total Items
Real_Part = stk( sadr( iAddrBase + 5 + Lines + Total Items) ); // Returns a pointer on a real array of double values, size = Total Items
Img_Part = stk( sadr( iAddrBase + 5 + Lines + Total Items + Total Items ); // Returns a pointer on a imaginary array of double values, size = Total Items

1.2.5.1. Sample for real sparse :

A =

A = (4, 10)
    (1,2)  = 1
    (1,7)  = 4
    (3,10) = 2
    (4,3)  = 5
    (4,5)  = 3
    (4,8)  = 6   

1.2.5.2. Sample for complex sparse :

A =

A = (4, 10)
    (1,2)  = -i
    (1,7)  = 6+7i
    (3,10) = -2+3i
    (4,3)  = 8-9i
    (4,5)  = 4-5i
    (4,8)  = -10   

1.2.6. List

Type = *istk(iAddrBase); // Returns variable type
Items = *istk(iAddrBase + 1); // Returns the numbers of items in the list
Offset = istk(iAddrBase + 1); // Returns array of offset between each item

In the list all items are store like standard variables.

Sample : List with 3 items

1. Matrix of double ( 2 x 2 )
   

2. List with 2 items
   

   21. Matrix of double complex ( 2 x 2 )
       

   22. Matrix of string ( 2 x 2 )
       

3. Matrix of double ( 2 x 2 )
   

A = { 
      Item 1 : [ 1, 2
                 3, 4],
      Item 2 : { 
          Item 2.1 : [ 5 + 6i    , 7 - 8i
                       -9 - 10i   , -11 + 12i ],
          Item 2.2 : [ "Scilab"  , "5.0.1"
                       "is"      , "released" ] },
      Item 3 : [ 13, 14
                 15, 16 ] }