Basic Concepts of Programming

Syntax Rules

• Program specify operations to be performed by the CPU

• The specification has to be precise and unambiguous

• PL specifies elaborate syntactic rules for construction of programs

• Every PL comes up with a manual describing these rules

• Any violation is termed syntax error and flagged by the compiler

• So one main function of compiler is to detect errors in your programs

• When no error, it produces the executable or object code

• Object code executed to get results or outputs

Semantics

• The semantics of programs also specified by the language

• A precise specification of semantics also required

• Compiler writers take that as a basis for code generation

• It is essential the machine code is equivalent to the source code

• Programs should produce the same result independent of time and place (computers and compilers)

• Unfortunately, this is not true always!

• Standardization of Programming Languages

Program Structure

Every Fortran Program (true in most languages too)

– starts with the keyword Program and a name

• names are any identifiers starting with an alphabet

– ends with the keyword end

– has two parts

– A Declarative part followed by an Executable part

– Each part consists of a sequence of statements

Fortran Statements

• Every Statement optionally starts with a label

• A label is any number between 1 and 99999 used for identification

• Each line up to 132 (or 128) characters long

• For longer statements, use &

• Free source form (type anywhere!)

• Old Fortran programs input using punch cards and had a strict syntax

– The first 5 columns reserved for labels

– Continuation character at the 6^th column

– The total number of columns is 80

– etc.

• Beware: Your compiler may follow some of these restrictions, still

Declarations

• Each declarative statement defines one or more Data items, called variables

• Variables are identifiers with the first symbol, an alphabet

• Variables are abstractions of memory locations

• Machine programs operate on memory locations

• High level programs operate on variables

• Variables hold data values which can be accessed and changed during execution

• Variable declarations optionally indicate initial values

Types

• Variables have definite data types (like integer, real) specified in the declaration

• The type of a variable determine the values that can be stored

• The types also define the operations (eg. +,* for integer and real while // for string variable)

• Types further determine storage space

• Each language defines a number of intrinsic or built-in types

• Fortran 90 has

integer,real, character, complex, logical

• Fortran 90 allows users to define their own types too!

A General Declarative Statement

type_name [,attributes] :: variable_list

• type_name - name of the intrinsic type or defined type

• [..] - to denote optional strings

• attributes - define additional properties of variables

– More about attributes later

• variable_list - list of variables defined

• All the variables in the list declared to be of the specified type

• Eg. Integer :: abc, xyz, m01

Real :: x_coord,y_coord

Variables

• variable names in Fortran contain at most 31 characters

• Characters can be upper or lower case letters, numerals (0-9) or underscore `_‘

• name should start with a letter

• upper and lower case letters not distinguished:

e.g. Fort and fORT refer to the same variable

• no blanks allowed

• meaningful and indicative names be used

• words like real, program not to be used

Storage Allocation for Variables

• Compiler allocates an address in memory for variables

• The contiguous bits located at the address contain the binary representation of the value stored.

• The number of bits, dependent on type of the variables and the compiler used

• For each data type and compiler, a default value

• Default values changed using declarations

• Here are the typical default values:

– Integer: 32 bits

– Real: 32 bits

– Character: 8 bits

– Logical: 1 bit

Integer Representation

• How many integers are there?

• But memory is finite

• Only finitely many numbers can be stored!

• Fixed no. of bits are allocated for integers

• One of the bits represents the sign, called sign bit

• The usual size of integer is 32 bits

Integer Representation

Sign bit

Overflow & Underflow

• Largest representable value for 32 bits is (why?)

• ( 2³¹ - 1) = 214,74,83,647

• Overflow occurs when an integer exceeds this

^• Smallest value is: - 2³¹

• Underflow occurs when an integer is less than this value

KIND Parameter

• The compiler assigns a default size for

INTEGER :: ABCD

• The size can be changed by KIND parameter:

INTEGER(KIND=1) :: ABCD

• or equivalently

INTEGER(1) :: ABCD

• KIND parameter for integer may have values 1,2 or 3; 3 is the default

• Varying sizes for different kind values (machine dependent)

• 1 is of low precision (usually 8 bits); 3 high precision

Real Numbers

• What are real numbers?

5/8, 22/7, 0.001, 3.141, p, Ö2,1234567890.00023

• How many of them are there? infinite (uncountable)

• Only finitely many real numbers can be represented in a computer

• Fixed no. of bits allocated for real numbers

• For any n, there ia a real number requiring more than n bits

• There are numbers which require infinite number of digits!

• So, only finite approximations possible for many such numbers

Mantissa-Exponent Notation

• Many applications involving real numbers require representation of large range of numbers

– Astronomy, Physics calculations

• Common scientific representation found useful:

0.2 ´ 10³⁴, 0.09 ´ 10^-26

• 0.2, 0.09 are called Mantissa

• 34, -26 are exponents

• Base is 10

• This is a compact representation: small number of digits with large range of representable values

Floating Point Representation

• Mantissa-Exponent notations is used in computers

• Floating point representation, in computer parlance

• Fixed number of bits for mantissa and exponent

• The base is usually 2; sometimes it is 16

• Two kinds of representation

– Single Precision

– Double Precision

• No. of bits for double precision more

Real Representation

Sign bit

Approximations in Real Values

• 0.2 cannot be represented exactly

0.0011 0011 0011 0011 0011 0011 . . .

• possible representation in 25 bit mantissa

0.0011 0011 0011 0011 0011 0011 0

• this value is 0.2 ´ (1 - 2^-24) How?

Normalized Representation

• IEEE Standard

• Mantissa

– An implied 1 bit before the decimal point

– binary point before first bit in the mantissa

• Exponent

– Excess 127 (or 1023) representation

– All 0 and all 1 disallowed

– They are used for 0 and infinity

Real Variables

• largest real value (Single precision, IEEE Std)

~ 2¹²⁸ ~ 10³⁸

• smallest positive real value

2 ^-126 ~ 10^-38

• overflow or underflow occur when a number falls outside the range

• Round-off has to be done when exact representation require more bits

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 (in 25 bit representation)

• 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

Attributes

• One of the important attributes is PARAMETER

• Consider the statement:

REAL parameter :: pi = 3.141592

• This declares pi as a real variable with specified initial value

• The attribute PARAMETER indicates that the value of pi will remain unchanged in the program

• Any change is illegal

• The parameter attribute can be used for any variable declaration:

eg. integer PARAMETER :: min_value = 25

• Many more attributes are possible (look in the manual)