Lesson 4 - Learning Goals

... -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 l023)

• 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 -l0⁷⁷ to +10⁷⁷. 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:

         +       add

         -       subtract

         *       multiply

          /       integer divide : 17./5. = 3.4

          **    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 Types

DATA TYPE	MAIN FRAME	MICRO
CHARACTER	8 BITS = 1 BYTE	8 BITS
INTEGER	32 BITS	16 BITS
REAL	32 BITS	32 BITS
LOGICAL	1 BIT	1 BIT

FORTRAN Also Allows

DATA TYPE	SIZE
INTEGER (LEN=2)	2 BYTES
REAL (LEN=4)	4 BYTES
REAL (LEN=8)	8 BYTES
DOUBLE PRECISION	8 BYTES
COMPLEX	8 BYTES

.

.

.

MORE

FORTRAN Variables

  1- A quantity that can vary.

  2- A location in memory.

  3- A name used to refer to.

Rules for Choosing a 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

Declaration Statements

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

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.

Implicit Declaration in FORTRAN

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):

are INTEGER variable otherwise, they are implicitly declared as REAL VARIABLE.

EXAMPLE :

1) INTEGER :

          INUM

          INDEX

          LSUM

          MONTH

2) REAL :

          TOTAL

          SUM

          VALUE

          TITLE

Common FORTRAN ''Gotcha's''

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
Highest	( )
	**	Right to left
	* /	Left to right
Lowest	+ -	Left to right

    2**2**3 = 2²³ = 2⁸ = 256

    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

Assignment Statement

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