Lesson 4 - Learning
Goals

4.1 More on data types

4.2 Arithmetic operations

4.3 Concept of a computer variable

4.4 Declaration statements

4.5 Implicit declarations in FORTRAN

4.6 Integer division

4.7 Mixed Mode aritmetic

4.8 FORTRAN 90 - PRINT statement

4.9 Design and setup of a complete program

**1. INTEGERS
**

- Represent discrete, exact numbers :

... 3 2 1 0 1 2 3 ...

- Written as a string of digits with optional sign.
- Can take all integer values within a certain range which depends on the machine, typically 32,768 to 32,767 (16 bits) or 2,147,483,648 to 2,147,483,647 (32 bits).
- Used in arithmetic expressions, and as subscripts.
- Basic operations:

+ add

- subtract

* multiply

/ integer divide : 17/5 = 3 (remainder of 2 thrown away)

** raise
to power = exponentiation

**2. REALS
**

- Represent measured quantities, corresponding to real numbers.

.16 0 00014 -0.3 6.02E23 (means 6.02 x l0exp23)

- Written as a string of digits with optional sign and mandatory decimal point, plus optional exponent (E followed by integer).
- Can represent broader range of values, typically around -l0exp77 to +10exp77. Again, this depends on the machine.
- Most quantities represented only « approximately .»
- Used in arithmetic expressions only.
- Real number with no fraction
(3.0 or 3.)
*not*the same as an integer (3)!!!

- Basic operations:

&nbs\ p; + add

&nbs\ p; - subtract

&nbs\ p; * multiply

/ integer divide : 17/5 = 3.4

** &bsp; raise
to power = exponentiation

**3. CHARACTER
DATA
**

- Represent strings of one or more characters

'HELLO, WORLD' 'PROF. G. RATZER' '398-7082'

- Used for textual information, and for communication with user.
- Use two single-quotes to represent quote in string :

'
"HOW"S IT GOIN", EH?" '

**4. LOGICAL DATA
**

- Can only represent one of two states:

.TRUE.
.FALSE.

- Used to represent truth values and in decision-making.

- Basic operations:

.AND. logical AND -- result true if both are true

.OR. logical OR -- result true if at least one is true

.NOT. changes .TRUE. to .FALSE. and vice versa

DATA TYPE | MAIN FRAME | MICRO |

**FORTRAN ALSO ALLOWS
**

INTEGER (LEN=2) => 2 BYTES

REAL (LEN=4) => 4 BYTES

REAL (LEN=8) => 8 BYTES

DOUBLE PRECISION 8 BYTES

COMPLEX 8 BYTES

.

.

.

MORE

1- A quantity that can vary.

2- A location in memory.

3- A name used to refer to.

**RULES FOR CHOOSING NAME
**

A) 1 to 6 characters ( FORTRAN 77 )

or
1 to 31 characters ( FORTRAN 90 )

B) First character must be A
... Z, rest A...Z plus 0...9

__EXAMPLES :
__

TODAY

SINGLE

MAX

MIN

X

ZMAT

APOLLO13 -> NOT VALID IN FORTRAN 77

THISISTOOLONGTOBEAGOODVARIABLENAME -> NOT VALID

7UP -> NOT VALID

!ALLO -> NOT VALID

22CATCH -> NOT VALID

For each data type and corresponding
constant there are what are called declaration statements, which
are used to define the type of** **data to be associated with
a chosen FORTRAN variable. Thus

INTEGER
:: K, PTR

REAL
:: SUM, COST, VALUE

CHARACTER
(LEN=20) :: NAME, ADDRSS

LOGICAL
:: SINGLE

The declaration statements should
be placed at the beginning of a program, before any executable
statements like a PRINT statement. The above declarations define
K and PTR to be INTEGER variables and any data assigned to these
variables will be stored as a whole number, without any fractional
part.

Likewise the variables SUM, COST
and VALUE should be used in calculations which may require a numeric
value with a fractional part.

The CHARACTER statement usually
has a length attribute - namely 20. This specifies that both the
variables NAME and ADDRSS may be used to store a string of up
to 20 alphanumeric characters.

The LOGICAL variable SINGLE may only be assigned the value .TRUE. or .FALSE.

You should ALWAYS declare all
the variables you will use in your program.

If you forget, FORTRAN will assume
that ...

variable names starting with
one of these letters (FIRST letter of variable name):

**I J K L M N
**

ARE **INTEGER** VARIABLE

otherwise, they are implicitely
declared as **REAL** VARIABLE.

__EXAMPLE :
__

1) **INTEGER** :

__ I__NUM

__ I__NDEX

__ L__SUM

__ M__ONTH

2) **REAL** :

__ T__OTAL

__ S__UM

__ V__ALUE

__ T__ITLE

1) Integer conversions

- Truncation ( I=2.89 I gets 2 )
- Integer division ( X = 2/3 X gets 0.0 )

2) Undeclared variables

- Wrong type
- Spelling mistakes

3) Priority of operators

Priority | Operations | Order |

2**2**3 = 2^(2^3) = 2^8 = 256 4^3

B/C*D = (B*D)/C

4) Watch your punctuation !

DO J=1.10

PRINT *,J

END DO

**The rules governing Mixed
Mode expressions are as follows.
**1. Apply the priority
rules for the selection of the arithmetic operations to be performed
first.

( ) High priority

** Medium priority

* / Same priority

+
Low priority

Operators with the same priority
in an assignment are processed from **left to right**.

2. If both of the selected variables
or constants are INTEGER, do the operation in INTEGER.

3. IF both of the selected variables
or constants are REAL, do the operation in REAL.

4. If one is INTEGER and one
is REAL, convert the INTEGER data to REAL and do the operation
in REAL.

Repeat the process until the expression is reduced to a single value. Note that internally, the computer must do arithmetic between data of the same type, both INTEGER or both REAL. Apart from these rules which apply to the evaluation of expressions on the right of the equal sign in an Assignment statement, there may still be conversion to a different type on the left of the equal sign.

! **Arithmetic
in print statements**

!

PROGRAM ARITHMETIC

!

IMPLICIT NONE

PRINT *, '2+2 = ', 2+2

PRINT *, '2 ** 3 = ', 2**3

PRINT *, 'WITH REALS : ', 2.**3.

PRINT *, 'PARENTHESES : (-2+3)*(4+5) = ', (-2+3)*(4+5)

PRINT *, 'WITHOUT : ', -2+3*4+5

PRINT *, 'LOGIC : ', .TRUE., .FALSE.

PRINT *, 'CONTRADICT : (NOT TRUE) = ', .NOT. .TRUE.

PRINT *, 'AND : (TRUE AND FALSE) = ', .TRUE. .AND. .FALSE.

STOP

END PROGRAM ARITHMETIC

__PROGRAM OUTPUT :
__

2+2 = 4

2 ** 3 = 8

WITH REALS : 8.00000

PARENTHESES : (-2+3)*(4+5) = 9

WITHOUT : 15

LOGIC : T F

CONTRADICT : (NOT TRUE) = F

AND : (TRUE AND FALSE) = F

__General form :__

** Variable
= Expression
**

__Expression can be :
__

1)
Constant

2)
Variable

3) Combination of constants and variables

( combined with operators, ref.
to data type operators )

__EXAMPLE :
__

PROGRAM EXAMPLE

IMPLICIT NONE

INTEGER :: AGE,PDS

REAL :: TOTAL, COST

CHARACTER (LEN=20) :: NAME

LOGICAL :: LOVED

AGE = 20

AGE = 20 + AGE

PDS = 10

TOTAL = (PDS*30.)/3

COST = TOTAL*1.13955

NAME = 'LUCIE'

LOVED = .TRUE.

STOP

END PROGRAM EXAMPLE

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