Handling of Arrays, Strings and Other Data Structures

Up to this point, we have studied simple data types and basic arrays
built on those simple data types.

Some of the simple data types studied include.

a)  Integers: both halfword and fullword.

b)  Packed decimal

c)  Character data.

This lecture will cover the following:

1.  A generalized “self describing” array that includes limits on the
permitted index values.  Only 1–D and 2–D arrays will be considered.

2.  Options for a string data type and how that differs from a character array.

3.  Use of indirect addressing with pointer structures generalized to
include descriptions of the data item pointed to.

Structures of Arrays

We first consider the problem of converting an index in a one–dimensional
array into an byte displacement.

We then consider two ways of organizing a two–dimensional array, and
proceed to convert the index pair into a byte displacement.

The simple array type has two variants:

0–based:   The first element in the array is either AR[0] for a singly
dimensioned array or AR[0][0] for a 2–D array.

1–based:   The first element in the array is either AR[1] for a singly
dimensioned array or AR[1][1] for a 2–D array.

We shall follow the convention of using only 0–based arrays.

One reason is that it allows for efficient conversion from a set of indices
into a displacement from the base address.

By definition, the base address of an array will be the address of its first
element: either the address of AR[0] or AR[0][0].

Byte Displacement and Addressing Array Elements

The General Case

We first consider addressing issues for an array that contains either character
halfword, or fullword data.  It will be constrained to one of these types.

The addressing issue is well illustrated for a singly dimensioned array.

 Byte Offset 0 1 2 3 4 5 6 7 8 9 10 11 Characters C[0] C[1] C[2] C[3] C[4] C[5] C[6] C[7] C[8] C[9] C[10] C[11] Halfwords HW[0] HW[1] HW[2] HW[3] HW[4] HW[5] Fullwords FW[0] FW[1] FW[2]

For each of these examples, suppose that the array begins at address X.

In other words, the address declared for the array is that of its element 0.

The character entries would be: C[0] at X, C[1] at X + 1, C[2] at X + 2, etc.

The halfword entries would be: HW[0] at X, HW[1] at X + 2, etc.

The fullword entries would be: FW[0] at X, FW[1] at X + 4, etc.

Byte Displacement and Addressing Array Elements

Our Case

I have decided not to write macros that handle the general case, but to
concentrate on arrays that store 4–byte fullwords.

The goal is to focus on array handling and not macro writing.

The data structure for such an array will be designed under
the following considerations.

1.  It must have a descriptor specifying the maximum allowable index.
In this data structure, I store the size and derive the maximum index.

2.  It might store a descriptor specifying the minimum allowable index.
For a 0–based array, that index is 0.

3.  It should be created by a macro that allows the size to be specified
at assembly time.  Once specified, the array size will not change.

What Do We Need to Know About a 1–D Array?

Here, I assume the following:

1.  The array is statically allocated; once loaded, its size is set.

2.  The array is “zero based”; its first element has index 0.

I decide to include this “base value” in the array declaration, just
to show how to do it.

3.  The array is self–describing for its maximum size.

Here is an example of the proposed data structure as it would be written
in System 370 Assembler.  The array is named “
ARRAY”.

ARBASE   DC F‘0’       THE FIRST INDEX IS 0

ARSIZE   DC F‘100’     SIZE OF THE ARRAY

ARRAY    DC 100F‘0’    STORAGE FOR THE ARRAY

I want to generalize this to allow for a macro construction that will specify
both the array name and its size.

The Constructor for a One–Dimensional Array

Here is the macro I used to construct a one–dimensional array
while following the design considerations listed above.

33          MACRO

34 &L1      ARMAKE &NAME,&SIZE

35 &L1      B X&SYSNDX

36 &NAME.B  DC F'0'        ZERO BASED ARRAY

37 &NAME.S  DC F'&SIZE'

38 &NAME.V  DC &SIZE.F'0'

39 X&SYSNDX SLA R3,0

40          MEND

Line 34:    The macro is named “ARMAKE” for “Array Make”.
It takes two arguments: the array name and array size.
A typical invocation:
ARMAKE XX,20 creates an array called XX.

Note the “&L1” on line 34 and repeated on line 35.  This allows a macro
definition to be given a label that will persist into the generated code.

More on the 1–D Constructor

33          MACRO

34 &L1      ARMAKE &NAME,&SIZE

35 &L1      B X&SYSNDX

36 &NAME.B  DC F'0'        ZERO BASED ARRAY

37 &NAME.S  DC F'&SIZE'

38 &NAME.V  DC &SIZE.F'0'

39 X&SYSNDX SLA R3,0

40          MEND

Line 35:    A macro is used to generate a code sequence.  Since I am using it
to create a data structure, I must provide code to jump around the
data, so that the data will not be executed.

While it might be possible to place all invocations of this macro
in a program location that will not be executed, I do not assume that.

Line 36:    I put in the lower bound on the index just to show what such a
declaration might look like.

Line 37     This holds the size of the array.

Label Concatenations in the Constructor

33          MACRO

34 &L1      ARMAKE &NAME,&SIZE

35 &L1      B X&SYSNDX

36 &NAME.B  DC F'0'        ZERO BASED ARRAY

37 &NAME.S  DC F'&SIZE'

38 &NAME.V  DC &SIZE.F'0'

39 X&SYSNDX SLA R3,0

40          MEND

Recall that the system variable symbol &SYSNDX in a counter that contains
a four digit number unique to the macro expansion.

Line 39 uses one style of concatenation to produce a unique label.

Suppose that this is the third macro expansion; the label would be “X0003”.

Lines 36, 37, and 38 use another type of concatenation, based on the dot.

If &NAME is XX, then the labels are XXB, XXS, and XXV.

Sample Expansions of the 1–D Constructor Macro

90          ARMAKE XX,20

000014 47F0 C06A            00070    91+         B X0003

000018 00000000                      92+XXB      DC F'0'

00001C 00000014                      93+XXS      DC F'20'

000020 0000000000000000              94+XXV      DC 20F'0'

000070 8B30 0000            00000    95+X0003    SLA R3,0

96          ARMAKE YY,40

000074 47F0 C11A            00120    97+         B X0004

000078 00000000                      98+YYB      DC F'0'

00007C 00000028                      99+YYS      DC F'40'

000080 0000000000000000             100+YYV      DC 40F'0'

000120 8B30 0000            00000   101+X0004    SLA R3,0

Notice the labels generated.

Two More Macros for 1–D Arrays

I now define two macros to use the data structure defined above.

I call these ARPUT and ARGET.  Each will use R4 as a working register.

Macro ARPUT &NAME,&INDX stores the contents of register R4
into the indexed element of the named 1–D array.

Consider the high–level language statement A2[10] = Y.

This becomes      L  R4,Y

ARPUT A2,=F‘10’  GET ELEMENT 10

Consider the high–level language statement Y = A3[20].

This becomes      ARGET A3,=F‘20’  CHANGE ELEMENT 20

ST R4,Y

NOTE:  For some reason, I decided to implement the index as a fullword
when I wrote the code.  I just continue the practice in this slide.

Design of the Macros

The two macros, ARPUT and ARGET, share much of the same design.

Much is centered on proper handling of the index, which is passed as a
fullword.  It would probably make more sense to use a halfword for the index.

Here are the essential processing steps.

1.  The index value is examined.  If it is negative, the macro exits.

2.  If the value in the index is not less than the number of elements in the
array, the macro exits.  For N elements, valid indices are 0
Ł K < N.

3.  Using the SLA instruction, the index value is multiplied by 4
in order to get a byte offset from the base address.

4.  ARPUT stores the value in R4 into the indexed address.

The ARPUT Macro

Here is the macro definition.

44          MACRO

45 &L2      ARPUT &NAME,&INDX

46 &L2      ST    R3,S&SYSNDX

47          L     R3,&INDX

48          C     R3,&NAME.B

49          BL    Z&SYSNDX

50          C     R3,&NAME.S

51          BNL   Z&SYSNDX

52          SLA   R3,2

53          ST    R4,&NAME.V(R3)

54          B     Z&SYSNDX

55 S&SYSNDX DC    F'0'

56 Z&SYSNDX L     R3,S&SYSNDX

57          MEND

Note the two labels, S&SYSNDX and Z&SYSNDX, generated by concatenation
with the System Variable Symbol
&SYSNDX.

This allows the macro to use conditional branching.

ARPUT Expanded

Here is an invocation of ARPUT and its expansion.

107          ARPUT XX,=F'10'

000126 5030 C146            0014C   108+         ST    R3,S0005

00012A 5830 C46A            00470   109+         L     R3,=F'10'

00012E 5930 C012            00018   110+         C     R3,XXB

000132 4740 C14A            00150   111+         BL    Z0005

000136 5930 C016            0001C   112+         C     R3,XXS

00013A 47B0 C14A            00150   113+         BNL   Z0005

00013E 8B30 0002            00002   114+         SLA   R3,2

000142 5043 C01A            00020   115+         ST    R4,XXV(R3)

000146 47F0 C14A            00150   116+         B     Z0005

00014A 0000

00014C 00000000                     117+S0005    DC    F'0'

000150 5830 C146            0014C   118+Z0005    L     R3,S0005

Note the labels generated by use of the System Variable Symbol &SYSNDX.

Actions for This Macro Invocation

We now examine the actions of the macro ARPUT.

108+         ST    R3,S0005

Register R3 will be used to hold the index into the array.  This line saves
the value so that it can be restored at the end of the macro.

109+         L     R3,=F'10'

Register R3 is loaded with the index to be used for the macro.

As the index was specified as a literal in the invocation, this
is copied in the macro expansion.

ARPUT: Checking the Index Value

The value of the array index is now in register R3.

110+         C     R3,XXB

111+         BL    Z0005

112+         C     R3,XXS

113+         BNL   Z0005

This code checks that the index value is within permissible bounds.

The requirement is that XXB Ł Index < XXS.

If this is not met, the macro restores the value of R3 and exits.

If the requirement is met, the index is multiplied by 4
in order to convert it into a byte displacement from element 0.

114+         SLA   R3,2

ARPUT: Storing the Value

Here is the code to store the value into the array, called XXV.

115+         ST    R4,XXV(R3)

116+         B     Z0005

117+S0005    DC    F'0'

118+Z0005    L     R3,S0005

Line 115   This is the actual store command.

Line 116   Note the necessity of branching around the stored value,
so that the data will not be executed as if it were code.

Line 117   The save area for the macro.

Line 118   This restores the original value of R3, the register
used to hold the index value.

The ARGET Macro

Here is the macro definition.

61          MACRO

62 &L3      ARGET &NAME,&INDX

63 &L3      ST    R3,S&SYSNDX

64          L     R3,&INDX

65          C     R3,&NAME.B

66          BL    Z&SYSNDX

67          C     R3,&NAME.S

68          BNL   Z&SYSNDX

69          SLA   R3,2

70          L     R4,&NAME.V(R3)

71          B     Z&SYSNDX

72 S&SYSNDX DC    F'0'

73 Z&SYSNDX L     R3,S&SYSNDX

74          MEND

ARGET Expanded

Here is an invocation of the macro and its expansion.

119          ARGET YY,=F'20'

000154 5030 C172            00178   120+         ST    R3,S0006

000158 5830 C46E            00474   121+         L     R3,=F'20'

00015C 5930 C072            00078   122+         C     R3,YYB

000160 4740 C176            0017C   123+         BL    Z0006

000164 5930 C076            0007C   124+         C     R3,YYS

000168 47B0 C176            0017C   125+         BNL   Z0006

00016C 8B30 0002            00002   126+         SLA   R3,2

000170 5843 C07A            00080   127+         L     R4,YYV(R3)

000174 47F0 C176            0017C   128+         B     Z0006

000178 00000000                     129+S0006    DC    F'0'

00017C 5830 C172            00178   130+Z0006    L     R3,S0006

The only difference between this macro and ARPUT occurs in line 127
of the expansion.  Here the value is loaded into register R4.

Row–Major and Column–Major 2–D Arrays

The mapping of a one–dimensional array to linear address space is simple.

How do we map a two–dimensional array?  There are three standard options.
Two are called row–major and column–major order.

Consider the array declared as INT A[2][3], using 32–bit integers.

In this array the first index can have values 0 or 1 and the second 0, 1, or 2.

Suppose the first element is found at address A.  The following table shows
the allocation of these elements to the linear address space.

 Address Row Major Column Major A A[0][0] A[0][0] A + 4 A[0][1] A[1][0] A + 8 A[0][2] A[0][1] A + 12 A[1][0] A[1][1] A + 16 A[1][1] A[0][2] A + 20 A[1][2] A[1][2]

The mechanism for Java arrays is likely to be somewhat different.

Addressing Elements in Arrays of 32–Bit Fullwords

Consider first a singly dimensioned array that holds 4–byte fullwords.

Suppose that we have a two dimensional array declared as A[M][N],
where each of M and N has a fixed positive integer value.

Again, we assume 0–based arrays and ask for the address of an element
A[K][J], assuming that 0 Ł K < M and 0 Ł J < N.

At this point, I must specify either row–major or column–major ordering.

As FORTRAN is the only major language to use column–major ordering,
I shall assume row–major.  The formula is as follows.

Element offset = K·N + J, which leads to

Example: Declare A[2][3]

Suppose that element A[0][0] is at address A.

Element A[0][0] is at offset 4·(0·3 + 0) = 0, or address A + 0.

Element A[0][1] is at offset 4·(0·3 + 1) = 4, or address A + 4.

Element A[0][2] is at offset 4·(0·3 + 2) = 8, or address A + 8.

Element A[1][0] is at offset 4·(1·3 + 0) = 12, or address A + 12.

Element A[1][1] is at offset 4·(1·3 + 1) = 16, or address A + 16.

Element A[1][2] is at offset 4·(1·3 + 1) = 20, or address A + 20.

2–D Arrays: An Example Data Structure

Here is a first cut at what we might want the data structure to look like.

ARRB     DC F‘0’       ROW INDEX STARTS AT 0

ARRCNT   DC F‘30’      NUMBER OF ROWS

ARCB     DC F‘0’       COLUMN INDEX STARTS AT 0

ARCCNT   DC F‘20’      NUMBER OF COLUMNS

ARRAY    DC 600F‘0’    STORAGE FOR THE ARRAY

NOTE: The number 600 in the declaration of the storage for the array
is not independent of the row and column count.

It is the product of the row and column count.

We need a way to replace the number 600 by 30·20, indicating that the
size of the array is a computed value.

This leads us to the Macro feature called “SET Symbols”.

SET Symbols

The feature called “SET Symbols” allows for computing values in a macro,
based on the values or attributes of the symbolic parameters.

There are three basic types of SET symbols.

1.  Arithmetic  These are 32–bit numeric values, initialized to 0.

2.  Binary        These are 1–bit values, initialized to 0.

3.  Character    These are strings of characters, initialized to the null string.

Each of these comes in two varieties: Local and Global.

The local SET symbols have meaning only within the macro in which
they are defined.  Declarations in different macro expansions are independent.

The global SET symbols specify values that are to be known in other macro
expansions within the same assembly.

A proper use of a global SET symbol demands the use of conditional assembly
to insure that the symbol is defined once and only once.

Local and Global Set Declarations

Here are the instructions used to declare the SET symbols.

 Type Local Global Instruction Example Instruction Example Arithmetic LCLA LCLA &F1 GBLA GBLA &G1 Binary LCLB LCLB &F2 GBLB GBLB &G2 Character LCLC LCLC &F3 GBLC GBLC &G3

Each of these instructions declares a SET symbol that can have its value
assigned by one of the SET instructions.  There are three SET instructions.

SETA      SET Arithmetic           Use with LCLA or GBLA SET symbols.

SETB      SET Binary                 Use with LCLB or GBLB SET symbols.

SETC      SET Character String  Use with LCLC or GBLC SET symbols.

Placing the Conditional Assembly Instructions

The requirements for placement of these instructions depend on the Operating
System being run.  The following standards have two advantages:

1.  They are the preferred practice for clear programming, and

2.  They seem to be accepted by every version of the Operating System.

Here is the sequence of declarations.

1.  The macro prototype statement.

2.  The global declarations used: GBLA, GBLB, or GBLC

3.  The local declarations used:  LCLA, LCLB, or LCLC

4.  The appropriate SET instructions to give values to the SET symbols

5.  The macro body.

Example of the Preferred Sequence

The following silly macro is not even complete.  It illustrates the sequence
for declaration, but might be incorrect in some details.

MACRO

GBLC &DATES          HOLDS THE DATE

GBLB &DATEP          HAS DATES BEEN DEFINED

LCLA &LEN, &MID

AIF (&DATEP).N20     IS DATE DEFINED?

&DATES   DC C‘&SYSDATE’       SET THE DATE

&DATEP   SETB (1)             DECLARE IT SET

.N20     ANOP

&MID     SETA (120-&LEN)/2    MID POINT

&NAME    Start of macro body.

A Constructor Macro for the 2–D Array

This macro uses one arithmetic SET symbol to calculate the array size.
This has no line numbers because it has yet to be tested by assembling it.

MACRO

&L1      ARMAK2D &NAME,&ROWS,&COLS

LCLA &SIZE

&SIZE    SETA (&ROWS*&COLS)

&L1      B X&SYSNDX

&NAME.RB DC F'0'        ROW INDEX

&NAME.RS DC F'&ROWS'

&NAME.CB DC F'0'        COL INDEX

&NAME.CS DC F'&COLS'

&NAME.V  DC &SIZE.F'0'

X&SYSNDX SLA R3,0

MEND

Strings vs. Arrays of Characters

While a string may be considered an array of characters, this
is not the normal practice.

A string is a sequence of characters with a fixed length.

A string is stored in “string space”, which may be considered to be
a large dynamically allocated array that contains all of the strings used.

There are two ways to declare the length of a string.

1.  Allot a special “end of string” character, such as the character with
code
X‘00’, as done in C and C++.

2.  Store an explicit string length code, usually as a single byte that
prefixes the string.  A single byte can store an unsigned integer in
the range 0 through 255 inclusive.

In this method, the maximum string length is 255 characters.

There are variants on these two methods; some are worth consideration.

Example String

In this example, I used strings of digits that are encoded in EBCDIC.

The character sequence “12345” would be encoded as F1 F2 F3 F4 F5.

This is a sequence of five characters.  In either of the above methods, it
would require six bytes to be stored.

Here is the string, as would be stored by C++.

 Byte number 0 1 2 3 4 5 Contents F1 F2 F3 F4 F5 00

Here is the string, as would be stored by Visual Basic Version 6.

 Byte number 0 1 2 3 4 5 Contents 05 F1 F2 F3 F4 F5

Each method has its advantages.  The main difficulty with the first approach,
as it is implemented in C and C++, is that the programmer is responsible for
the terminating
X‘00’.  Failing to place it leads to strange run–time errors.

Sharing String Space

String variables usually are just pointers into string space.
Consider the following example in the style of Visual Basic.

Here, each of the symbols C1, C2, and C3
references a string of length 4.

C1 references the string “1301”

C2 references the string “1302”

C3 references the string “2108”

Using Indirect Pointers with Attributes

Another string storage method uses indirect pointers, as follows.

Here the intermediate node has the
following structure.

1.  A reference count
2.  The string length
3.
A pointer into string space.

There are two references to the first
string, of length 8: “CPSC 2105”.

There are three references to the second
string, also of length 8: “CPSC 2108”.

There are many advantages to this method of indirect reference, with attributes
stored in the intermediate node.  It is likely the method used by Java.