Fortran 95 2003 for scientists and engineers

to Computers and the Fortran LanguageComputer Languages Each computer has its own machine language Assembly used to execute very basic operations.. to Computers and the Fortran Language

Fortran 95-2003 for Scientists and

Engineers

Transparencies prepared by Anthony

T Chronopoulos

Chapter 1 Intro to Computers and the Fortran Language

Input Devices (e.g keyboard, tapes etc)

Output Devices (e.g display, monitor, tapes etc).

The CPU

The Central Processing Unit is "heart“ (or better “brain”) of a computer

The CPU consists of three main parts:

The Control Unit - coordinates activities of the computer

The Arithmetic Logic Unit (ALU) - performs the calculations

Registers - store a small amount of data and instructions

Chapter 1 Intro to Computers and the Fortran Language

• Main Memory (RAM)

It is larger than the Registers and smaller than the hard drive.

It temporarily stores the program currently being run by the computer and also the data required by the programs.

RAM is volatile, i.e when power is interrupted, then what was stored in RAM is lost.

Secondary Memory

It is a permanent (non-volatile) storage.

The hard drive is the best example, but also USB, CDs, tapes, etc The size of hard drives is larger than that of RAM However, accessing data stored on a hard drive (or other secondary memory) takes much longer (5-10 times) than from RAM.

Chapter 1 Intro to Computers and the Fortran Language

Computer Languages

Each computer has its own machine language (Assembly) used to execute very basic

operations Operations are: load and store (data, to and from memory), and add, subtract, multiply, or divide

The problem with a machine language is that it is very difficult to program and use, and also

it can be unique for a computer.

Thus, computer scientists design high-level language

that are easy to program and use The programs must

be converted to a machine-language (by compilers and

linkers) for the computer to run them Examples are

Fortran, C, C++, Java etc

The benefit of a high-level language (e.g Fortran) is that a program and can be compiled on any machine that has a Fortran compiler

Chapter 1 Intro to Computers and the Fortran Language

Data Representation in a Computer

Data is represented by millions of switches, each of which can be either ON (1) or OFF (0) 0 and 1 are the two binary digits (bits).

We use a combination of 0's and 1's to represent the other numbers (and characters as

well).The smallest common combination of bits (0's and 1's) is called a byte A byte is a group of 8 bits A word is a group of 2, 4, or 8 bytes Our PCs have 4-byte words

• The Binary Number System

The number system used by humans is the decimal system The decimal system is a base=10 system.

There are 10 digits (0-9) Each digit in a number represents a power of 10.

The number 221 is:

2 * 10^2+ 2 * 10^1 + 1 * 10^0

(where 10^i is 10 raised to exponent i =0,1,2, )

Chapter 1 Intro to Computers and the Fortran Language

Similarly, converting a number from binary (base 2) to decimal (base 10).

The number 101:

1 * 2^2+ 0 * 2^1 + 1 * 2^0 = 4 +0+ 1 = 5

If n bits are available, then those bits can represent 2^n possible values.

e.g One byte (n=8 bits) can represent 256 possible values Two bytes (n=16 bits) can represent 65,536 possible values.

Which of the following ranges would best describe the possible values of a byte?

(1) 0 , , 255 (2) 1 , , 256 (3) -127 , , 128

(4) -128 , , 127 The answer is (4)

The reason is that the computer must store both

positive and negative integers The following

example illustrates how this can be achieved

Chapter 1 Intro to Computers and the Fortran Language

Example from the car odometer/milometer (Note: content not in Book

will not be used in Exams)

Milometer readings during travel.

e.g Storage of 8-digit integers, in base=10 system:

Chapter 1 Intro to Computers and the Fortran Language

e.g Storage of (4-bit) integers:

When using the binary system, the effect is that

if the first binary digit (or bit) is a one then the number is negative,

while if it is zero the number is positive.

• Two other number systems that are also useful are octal (base 8) and hexadecimal (base 16).

• Table 1-1 shows the conversion between these systems for the decimals: 0,1, …,15

Chapter 1 Intro to Computers and the Fortran Language

Types of Data

Three common types of data are stored in a computer's memory: character, integer, real Each type has unique characteristics and takes up a different amount of memory.

Character Data

A typical system for representing character data may include the following:

Letters: A through Z and a through z

Digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Miscellaneous symbols, e.g (", ', ?, , <, >, =, %, &)

Chapter 1 Intro to Computers and the Fortran Language

• In the past, it has been common to use just one byte of memory to represent a maximum of

256 characters (ASCII)

• To represent characters found in many languages, one can use use 2 bytes of memory which allows 65,536 possible characters (Unicode)

Integer Data

Integer data ( e.g -1, -355, 0, 1993) are represented exactly on computers However, only a finite number can be stored Most machines will use 4 bytes of memory to represent integers

Smallest n-bit integer: -2^(n-1)

Largest n-bit integer: 2^(n-1) - 1

e.g n=32 for 4-byte numbers.

Chapter 1 Intro to Computers and the Fortran Language

With 4 bytes of memory we can represent numbers in the approx range [-2.15*billion, 2.15*billion].

Outside this range we get arithmetic overflow.

Integer data limitations: (1) No fractional parts.

(2) It is not possible to represent very large positive integers or very small negative integers.

Real Data

The real data type stores numbers in a format similar to scientific notation.

For example, the speed of light in a vacuum is about 299,800,000 meters per second The

number in scientific notation would be 2.998 * 10^8 (m/s) meters per second.

Chapter 1 Intro to Computers and the Fortran Language

A format similar to scientific notation will be used to represent real numbers in FORTRAN Real numbers occupy 4 bytes of memory These 4 bytes will be divided as follows:

3 byte for the fraction (or mantissa)

1 byte exponent

The mantissa will be a number between -1 and 1.

The exponent will contain the power of 2 required to scale the number to its actual value.

The real numbers are converted Consider any non-zero real number as

a fraction lying between 0.1 and 1.0, called the mantissa, which is multiplied

or divided by 10 a certain number of times, where this number is called the

exponent e.g 17877.0 (in fraction, base=10 form): 0.17877x10^5

10b

exponent mantissa

The same technique as was used for integers to distinguish positive and

negative numbers will be used for both the mantissa and the exponent.

Chapter 1 Intro to Computers and the Fortran Language

Precision and Range

Precision refers to the number of significant digits that can be preserved in a number (on a computer).

Based on the number of bits (or bytes) in the mantissa,

3 byte mantissa gives about 7 significant digits (between 1.0 and -1.0) e.g 12345678.4 is stored

as

12345678.0 The difference (i.e 0.4) is called the round-off error

Range is the difference between the largest and smallest numbers that can be represented The number of bits in the exponent e.g

1-byte exponent (with the 3-byte mantissa) allows a range of approximately 10^-38 to 10^38 (i.e [10^-38 , 10^38] )

Chapter 1 Intro to Computers and the Fortran Language

Evolution of Fortran:

Fortran I: Fig 1-5

Fortran 77: Fig 1-6

Fortran 90/2003: Fig 1-7

• Recommended Problems (not to be handed in)

• Page 12 , Quiz 1 (answers are on the back):

1(a),2(a),6,7

CHAPTER 2

CS1073

2.2 The Fortran Character Set (Table 2-1)

The following are valid in a Fortran 90/95 program:

alpha-numeric: a-z, A-Z, 0-9, and _ (the underscore);

Chapter 2: Basic Elements of Fortran

2.3 Structure of a FORTRAN Statement

A program consists of a series of statements designed to accomplish the goal to be

accomplished.

There are two basic types of statements:

Executable statements describe the actions taken by the program (additions, subtractions,

multiplications, divisions).

Non-executable statements provide information necessary for proper operation of the

program.

Rules on Fortran statements:

Each line may be up to 132 characters long.

A statement too long to fit in a single line may be continued on the next line by ending the

current line with an & (ampersand) e g

output = input1 + input2 ! sum the inputs

output = input1 & ! Also, sum the inputs + input2

Chapter 2: Basic Elements of Fortran

The above two statements are equivalent.

Commenting your code is very important To comment in FORTRAN, one uses the

exclamation point (!).

All comments after the ! are ignored by the compiler

One can use labels in some statements A label can be any number between 1 and 99999 Statement labels are less common in modern FORTRAN

Chapter 2: Basic Elements of Fortran

2.4 Structure of a FORTRAN Program

A FORTRAN program can be divided into three sections:

Declarations - This section consists of a group of non-executable statements at the start of the

program.

Execution - This section consists of one or more statements describing the actions to be

performed by the program.

Termination - This section consists of a statement (or statements) telling the computer to

stop/end running the program.

The program (in Fig 2-1) reads two numbers as input, multiplies them, and prints out the result PROGRAM my_first_program

! Purpose:

! To illustrate some of the basic features of a Fortran program.

!

! Declare the variables used in this program.

INTEGER :: i, j, k ! All variables are integers

! Get two values to store in variables i and j

WRITE (*,*) 'Enter the numbers to multiply: '

READ (*,*) i, j

Chapter 2: Basic Elements of Fortran

! Multiply the numbers together

Discussion of Program Above

The first statement of this program begins with the word PROGRAM This is a

non-executable statement that specifies the name of the program to the FORTRAN

compiler.

The name may be up to 31 characters long and be any combination of alphabetic characters,

digits, and the underscore.

The first character must be a letter.

The PROGRAM statement must be the first line of the program.

Chapter 2: Basic Elements of Fortran

The Declaration Section

This section begins with a comment stating that variable declarations are to follow.

The declaration begins with the data type (INTEGER) followed by two colons and then the

The Execution Section

The first statement in this section is the WRITE statement that tells the user to enter the input The second statement will read the input and assign the values to the corresponding variables The third statement multiplies the two variables and the product is assigned to a third

variable

The last executable statement prints the product to the screen.

Chapter 2: Basic Elements of Fortran

The Termination Section

The STOP statement tells the computer to stop running the program

The use of the STOP command is optional here

The END PROGRAM statement informs the compiler that no more statements exist

Compiling and Executing the FORTRAN Program

Before a program can be run (executed) it must be compiled into an executable program.

In this process the code may also be linked to various system libraries.

Chapter 2: Basic Elements of Fortran

2.5 Constants and Variables

A constant is a data object that is defined before a program is executed and it does/can not

change during the execution of the program.

Constants are used in developing a good/correct programs in solving math problems (e.g the circle constant PI ).

A variable is a data object that can change value during the execution of a program Referring to the sample program above:

The data objects i,j,k are variables.

Each variable (or constant) must have a unique name inside the program.

Chapter 2: Basic Elements of Fortran

The names may contain up to 31 characters and any combination of alphabetic characters,

digits, and the underscore

The first character must always be alphabetic.

• The name we assign a variable (or constant) should be meaningful in terms of the

purpose that it is used to solve the problem (e.g.

• time, distance, grade etc).

Chapter 2: Basic Elements of Fortran

Integers

Integers are numbers without a decimal point

e.g -999 , +17, 1234 (not allowed: 1,234 , +17 )

No commas may be embedded within an integer constant.

If the number is positive, the sign + is optional, but the - is required to for negative.

Integer variables contain the value of an integer data type.

There is a maximum and a minimum value that an integer can take The range is determined

by how much memory is (in terms of no of bytes) given to a variable of the integer type.

Real Numbers

Real (or floating-point) numbers represent values with a fraction

Real constants can be written with or without an exponent e.g 10 , -999.9, 1.0E-3 (i.e 0.001

or 001 )

Not allowed: 1,000 , 111E3, -12.0E1.5, 1.0x

10^-3

Chapter 2: Basic Elements of Fortran

The mantissa should contain a decimal point A real variable is a variable that contains the

value of a real data type

There is a maximum and a minimum value that a real var/constant can take The range is

determined by how much memory is (in terms of no of bytes) given to a variable of the real type.

A character constant is a string of characters enclosed in a single or double quotes.

Any characters representable on a computer (not just the Fortran characters) are legal in a

character context (i.e if enclosed in quotes).

e.g ‘this is’, ‘ ‘, ‘[^]’, “3.1345”

Chapter 2: Basic Elements of Fortran

Mismatching or using an odd number of quotes are common mistakes in programming e.g not correct character: ‘this is , ‘this is”

A character variable is a variable containing a value of character data type e.g c = ‘this is’ Character variables/constants with more than one character are often referred to as strings The character constant '8' is different from the integer constant 8.

2.5.4, 2.10 Variables and the IMPLICIT NONE

Checking a constant (e.g.7, 3.14156, 'John'), it is easy to determine which type it may be

However, for a variable, we must assign a type to that variable Assigning a type reserves the memory needed to store the data expected (e.g.4 bytes for: 7 , 3.14156 and

2 bytes/letter for: 'John')

Chapter 2: Basic Elements of Fortran

There is a default type given to all variables for which a type is not explicitly given This is

used in Fortran versions before Fortran 90 In this case, the first letter of the names of variables or constants determines the type

Prior to Fortran 90: Var/const names with letters i,j,k,l,m,n as first letter imply INTEGER ,

where as the rest of the letters imply REAL

Note: Fortran upper/lower case is the same We use lower case for var’s names e.g i, x, c and upper case for key-words (e.g READ(*,*), STOP).

In Fortran 90/95, 2003 we declare the type of

The REAL, INTEGER for all var/constants e.g.

INTEGER :: height

REAL :: second

The IMPLICIT NONE used after the keyword PROGRAM means that we must specify a

type for each variable you declare