Basic Programming Concepts

Variables and Constants

Program Structure

• every program contains two parts

• declarative part

– contains definition of the data items used

• executable part

– contains definition of operations to be performed on the data

• declarative part occurs before the executable

Declarations

• contains several declarative statements

• declarative statement defines data items

• data items are named and called variables

• variable name represents locations which will hold the value of the data item

• variable name also used to denote the value

• every variable is also given a type

• the type of a variable defines its possible values and operations

Intrinsic Types

• every programming language has some built in types called intrinsic types

• in Fortran, some of these are integer, real, logical, and character

• integer and real are numeric types

• possible values are ‘integers’ and ‘reals’

• arithmetic operations can be performed on numeric types

Declarations in Fortran

integer :: i, j, k

• declares 3 variables i, j, k of type integer

real :: x, y

• declares 2 variables x and y of type real

• any number of such declarative statements may be present in a program

• all of them occur before executable statements

Declarative Statement

• general form of declarative statement

type, [attributes] :: list_of_variables

• type defines the type of the variables

• attributes is a list of optional attributes which define additional properties of the variables

• list_of variables is a list of variable names which have the type and attributes specified

Variables

• every variable name represents a sequence of consecutive memory locations which will hold its value

• the number of locations assigned to a variable depend on its type

• typically, integers and reals use one location

Variable Names in Fortran

• can contain 1 to 31 characters

• allowed characters are ‘a…z, A…Z, 0…9’ and the special symbol _

• variable names must start with a letter

• blanks are not allowed

• no distinction between upper and lower case

• meaningful names should be used

• reserved words (real,..) should not be used

Variable Names

• valid variable names

– i, mass, angular_momentum, H_2O

• invalid variable names

– today's-date, 2m,

• equivalent variable names

– force, Force, FORCE, FoRcE, fOrCe

– all of these denote the same variable

• same form should be used throughout

Integer Variables

• the possible values of an integer variable depend on the computer/ compiler

• typically, one location containing 32 bits is used for representing an integer

• thus possible values range between

-2147483647 to 2147483647 ( 2³¹-1)

• a possible representation of -100

Real Variables

• are represented using exponents

• also called floating point representation

• 102.356 would be represented as

^• 1.02356*10²

• base is usually a power of 2

• typically, base = 16, 26 bits for mantissa and 6 bits for the exponent ( including sign bits)

Approximations in Real Values

• 0.2 cannot be represented exactly

• 0.001100110011001100110011…

• possible representation

• this value is 0.2*(1-2^-24)

• normalized representation

• binary point before first bit of mantissa

• exponent is smallest possible

Real Variables

• largest real value

= 2¹²⁸ ~ 3.4*10³⁸

• smallest positive real value

= 2^-149 ~ 1.4*10^-45

• can vary with compilers

• some compilers ensure symmetric range

• overflow or underflow may occur

Errors in Real Values

• round-off errors occur in real values due to finite precision

• absolute value of error can be large

• error in 0.2*2¹⁰⁰ is 2⁷⁶

• however, relative error is always small

• error/absolute value <= 2^-22 (except for very small values)

• only 7 decimal digits are significant

• possible to increase precision/range if required

Constants

• a constant of a particular type is a specific value of that type

• 12, -102, 3456843 are integer constants

• integer constants are written in decimal

• -2.04, 1.03e+2, -2.3e-3 are real constants

• real constants are written in decimal using fixed or floating point

• real constants must include a decimal point with a digit before and after it

Parameter Attribute

• a name can be declared to be a constant by giving it the parameter attribute

integer, parameter :: base = 10

• defines base to be an integer constant whose value is 10

• value of base is fixed throughout the program

• naming of a constant explains its meaning

• to change its value, only one change needed

Initializing Variables

• variables can be given an initial value when they are declared

integer, parameter :: base = 10

integer :: digit = 5, number = base

real, parameter :: pi = 3.1415926

real :: radius = 1.0

• base, pi are constants whose value is fixed

• digit, number, radius are variables which have been assigned an initial value

Summary

• variables are used to store data

• every variable is given a name and type

• variables declared to be integer or real are used to store numerical values

• upper bound on value of an integer variable

• real variables can represent larger numbers

• loss of accuracy in using real type variables

• absolute error may be large but relative error is small

Summary

• constants are values of a specific type

• real and integer constants written in decimal

• reals may be written using fixed or floating point representation

• constants can be given a name using the parameter attribute

• naming constants makes their meaning clear and simplifies modification of programs