Data Types simple and compound abstraction and implementation
Data Types
simple and compoundabstraction and implementation
A brief history simple types arrays - compounds of same type strings records – compounds of different types pointers and references user defined types abstract data types objects
Simple types
integer floating point binary-coded decimal
character boolean user-defined types
usually in hardware
usually in software
not composed of other types hardware or software implemented
Integer
2’s complement unsigned operations exact within range range depends on size of virtual cell- typical size: 1, 2, 4, 8 bytes
Floating Point
based on scientific notation representations and operations are
approximate range and precision depend on size of
virtual cell (usually 4 or 8 bytes)
1 11 52 bits
Binary Coded Decimal
‘exact’ decimal arithmetic decimal digits in 4 bit code range and precision depend on size of
virtual cell – 2 digits per byte
4 4
5 9 0 5 1 8 7 8
defined decimal point
Character
ASCII – 128 character set – 1 byte Unicode – 2 byte extension usually coded as unsigned integer
Boolean
1 bit is sufficient but... no bit-wise addressability in hardware store in a byte – space inefficient store 8 per byte – execution
inefficient c: 0=false, non-zero=true
User-defined types
implemented (like character and boolean usually are) as a coding of unsigned integer
enumerated type: (Pascal example)type suit = (club, diamond, heart, spade);
var lead: suit;
lead := heart;
internally represented as { 0, 1, 2, 3 }
operations:
User-defined types
implemented as a restricted range of integer
subrange type: (Ada example)subtype CENTURY20 is INTEGER range 1900..1999;
BIRTHYEAR: CENTURY20;
BIRTHYEAR := 1981;
User-defined types
Type compatibility issues:-can two enumerated types contain
same constant?-can defined types be coerced with
integer, with each other?
Memory management intro
The parser creates a symbol table of identifiers including variables: Some information, name plus more, is
bound at this time and as the program is compiled by storage in symbol table:e.g. int x;
--> x type: intaddr: offset
namenametypetype addressaddress
Strings
First use: output formatting only Quasi-primitive type in most
languages (not just arrays of character)
- operations: initialization, substring, catenation, comparison
The length problem: fixed or varying? No standard string model
c
char *s = “abc”;
int len = strlen(s);
array of char with terminal:
extended syntax
library of methods
Strings - examples
JAVA
String s = “abc”+x;
s = s.substring(0,2);
fixed length array
extended syntax
class with 70 methods
a b c 0
Strings - representations fixed length and content
(static) fixed length and varying
content (FORTRAN) varying length and content by
reallocation (java String) varying length and content by
extension (java StringBuffer) Varying length and content(c)
Static strLengthAddress
Dynamic strMaxLengthCurrLengthAddress
char*Address
In symbol table
Compound (1) Arrays
collection of elements of one type access to individual elements is
computed at execution time by position, O(1), or O(dim)
Arrays – design decisions
indexing:dimensions – limit? recursive?types – int, other, user defined?first index: 0, 1, variablerange checking – no(c),
yes(java)lexemes – ‘subscripts’ = (),[]?
Arrays – design decisions binding times
type, index typeindex range(ie array size), space
staticfixed stack-dynamicstack-dynamicheap-dynamic
initial values of elementsat storage allocation? e.g. int[] x =
{1,2,3};
Arrays – operations
on elements – based on type on entire array as variables -
- vector and matrix operations e.g.,APL- sub array (~ substring)
subarray dimensions(slices)
Arrays – storage
<array>element type, size
index typeindex lower boundindex upper bound
address
address
lower bound upper bound
Arrays – element access
<array>element type, size
index typeindex lower boundindex upper bound
address
address
lower bound i
address of a[i] =
address + (i-lower bound)*size
Arrays - multidimensional
contiguous or not row major, column major order computed location of element
Jagged arrays
Implemented as arrays of arrays<array>
<array>, 4index type
index lower boundindex upper bound
address
address
<array><array>
<array>, 3<array>, 3index type
index type
index lower boundindex lower bound
index upper boundindex upper bound
addressaddress
<array><array>
<array>, 7<array>, 7index type
index type
index lower boundindex lower bound
index upper boundindex upper bound
addressaddress
<array><array>
<array>, 4<array>, 4index type
index type
index lower boundindex lower bound
index upper boundindex upper bound
addressaddress
<array><array>
<array>, 5<array>, 5index type
index type
index lower boundindex lower bound
index upper boundindex upper bound
addressaddress
(2) Associative Arrays - maps
values accessed by keys,not indices no order of elements automatic growth of capacity operations: add/set, get, remove fast search for individual data slower for batch processing than
array Java classes; Perl data structure
Associative Arrays - implementation
hash tables based on key value most operations ‘near O(1)’ expanding capacity may be O(n)
For a java class that combines features of array and associative array, see LinkedHashMap
(3) Records
multiple elements of any type elements accessed by field name design issues:
- hierarchical definition(records within records)
- syntax of naming- scopes for elliptical (incomplete) reference to fields
Records - implementation<array> a
element type, size
index type
index lower bound
index upper bound
address
address
lower bound upper bound
<record>dept
array [1..4] of char 0 (offset)
code
address
Caddress O S C 3127
dept course
integer4
type course =
record dept : array[1..4] of char; code : integer;
end
(4) Pascal variant records (unions)
type coord = (polar, cart);
point =
record
case rep : coord of
polar: ( radians : boolean;
radius : real;
angle : real);
cart: ( x : real;
y : real);
end;
Note:
•varying space requirements
•discriminant field is optional (rep)
•type checking loopholes: Ada has similar variant record but closed these loopholes
Other unions
Fortran EQUIVALENCE c union not inside records no type checking
* unions do not cause type coercion - data is reinterpreted
Sebesta’s c example
union flextype {
int intE1;
float floatE1;
}
union flexType ell;
float x;
ell.intE1 = 27;
x = ell.floatE1;
Sebesta’s c example
union flextype {
int intE1;
float floatE1;
}
union flexType ell;
float x;
ell.intE1 = 27;
x = ell.floatE1;
(5) Sets (Pascal)
defined on one (discrete) base type implementation imposes maximum
size (set of integer;-not possible)
type day = (M, Tu, W, Th, F, Sa, Su); dayset = set of day;var work, wknd : dayset; today : day;today = F;work = [M, Tu, W, Th, F];wknd = [Sa, Su, F];if (today in work and wknd) ...
1 1 0111 0
0 0 1100 1
0 0 0100 0
(6) Pointers and references
references are dereferenced pointers (whatever that means)
primary purpose: dynamic memory access
secondary purpose: indirect addressing as in machine instructions
Pointers (and references)
data type that stores an address in the format of the machine (usually 4 bytes) or a “null”
a pointer must be dereferenced to get the data at the address it contains
a reference is a pointer data type that is automatically dereferenced
Dereferencing example
In c++:
double x,y;
Point p(0.0,0.0);
Point *pref;
pref = &p;
x = p.X;
y = (*pref).Y;
In Java:
Point2D.Double p;
p = new Point2D.Double(0.0,0.0);
double xCoord = p.x;
Dereferencing and field access combined
Dereferencing Field access
Pointers hold addresses
Indirect addressingIn c: pointer to statically allocated memory
int a,b;
int *iptr, *jptr;
a = 100;
iptr = &a;
jptr = iptr;
b = *jptr;
int x, y, arr[4];
int *iptr;
iptr = arr;
arr[2] = 33;
x = iptr[2];
y = *(iptr + 2);
Security loophole…
Pointer arithmetic
Arithmetic operations on addresses
int x;
int *iptr;
iptr = &x;
for (;;){
<< process loc (*iptr)>>
iptr++;
}
Scan through memory starting at x
Basic dynamic memory management model:
Heap manager keeps list of available memory cells
“Allocate” operation transfers cell from list in heap to program
“Deallocate” transfers cell from program back to list in heap
Tradeoffs of fixed or variable sized cells
Problems with pointers and dynamic memory:1
Dangling reference: pointer points to de-allocated memory
Point *q;
Point *p = new Point(0,0);
q = p;
delete p;
// q is dangling - reference to q should cause
// an error - ‘tombstones’ will do error check
Problems with pointers and dynamic memory: 2
Memory leakage: memory cell with no reference to it
Point *p = new Point(0,0);
p = new Point(3,4);
// memory containing Point(0,0) object
// is inaccessible - counting references will help
Cause of reference problems
Multiple references to a memory cell Deallocation of memory cells
Where is responsibility?-automatic deallocation (garbage collection)
OR -user responsibility (explicit ‘delete’)
User management of memory
Dangling references can be detected as errors but not prevented- tombstones
- lock and key Memory leakage is a continuing
problem
int *p =*q = 6;
p = null;
int *p =*q = 6;
p = null;
p 6
q
p 6
q
Garbage Collection
1. Reference counting: ongoing “eager”-memory cells returned to heap as soon as all references removed.
2. Garbage collection: occasional “lazy”-let unreferenced memory cells ‘leak’ till heap is nearly empty then collect them
Reference counting:
2p = null;
1
0q = null;
Reference count in cell
Count 0 -> return cell to heap
Classic problem:
circular linked lists
int *p = *q = 6;
Garbage Collection: (mark-sweep)
1. All cells in memory marked inaccessible(f)
2. Follow all references in program and mark cells accessible(t);
f
t
t
‘Accessible’ marker in cell
3. Return inaccessible cells to heap
f
t
t
Classic problem:
effect on program performance
A sloppy java example from Main (Data Structures)public class ObjectStack{ private Object[] data; private int manyItems; .... public Object pop() { if (manyItems==0) throw new EmptyStackException(); return data[--manyItems]; //leaves reference in data }}
Managing heap ofvariable-sized cells
Necessary for objects with different space requirements
Problem: tracking cell size Problem: heap defragmentation
- keep blocks list in size order?- keep blocks list in sequence order?