Review of lecture 3

1
Review of lecture 3

• Data type and declaration
• INTEGER
• E.g., a, b, c
• REAL
• E.g., x, y, z, w
• LOGICAL
• COMPLEX
• CHARACTER
• Examples
• INTEGERa1,b-5,c5
• REALx2.0

2
Review of lecture 3 (cont.)

• Arithmetic expressions
• E.g., 5 2 3
• E.g., b2 4ac
• It has a value by itself
• E.g. expression 5 23 has a value of 11

3
Review of lecture 3 (cont.)

• Evaluating Complex Expressions
• Precedence
• Associativity (For expressions having operators
  with the same precedence).

4
Review of lecture 3 (cont.)

• Mixed Mode Expressions
• If one operand of an arithmetic operator is
  INTEGER and the other is REAL
• the INTEGER value is converted to REAL
• the operation is performed
• the result is REAL
• 1 2.5 ? 3.5
• 1/2.0 ? 0.5
• 2.0/8 ? 0.25
• -32.0 ? -9.0
• 4.0(1/2) ? 1.0 (since 1/2 ? 0)
• 3/5 5.0 ? 0.0 (since 3/5 ?0)

5
Review of lecture 3 (cont.)

• Statements
• Assignment statement
• Variable expression
• e.g., b -5
• (never the other way around, 5b is not valid!)
• General statement
• INTEGER a, b, c
• write (,) Hello world!

6
Selection in FORTRAN

• Lecture 4
• By Nathan Friedman and Yi Lin
• Jan 16, 2007

7
Roots of a Quadratic (again)

• ! ------------------------------------------------
  --
• ! Solve Ax2 Bx C 0 given BB-4AC gt 0
• ! ------------------------------------------------
  --
• PROGRAM QuadraticEquation
• IMPLICIT NONE
• REAL a, b, c, d, root1, root2
• ! read in the coefficients a, b and c
• WRITE(,) "A, B, C Please "
• READ(,) a, b, c
• ! compute the square root of discriminant d
• d SQRT(bb - 4.0ac)
• ! solve the equation
• root1 (-b d)/(2.0a) ! first root
• root2 (-b - d)/(2.0a) ! second root
• ! display the results

8
Run Time Error

• We assumed that the discriminant was positive
• What if it wasnt?
• We would get an error when we run the program and
  attempt to compute the square root and the
  program would abort
• What should we do?
• Avoid trying to perform an illegal operation by
  branching around it -- use a selection control
  structure

9
Quadratics example
dbb 4.0ac
Dgt0.0
.TRUE.
.FALSE.
Calc root1, root2
Ouput no real roots!
end
10
IF-THEN-ELSE-END IF

• Used to select between two alternative sequences
  of statements.
• They keywords delineate the statement blocks.
• Syntax
• IF (logical-expression) THEN
• first statement block, s_1
• ELSE
• second statement block, s_2
• END IF

11
IF-THEN-ELSE-END IF

• Semantics
• Evaluate the logical expression. It can have
  value .TRUE. or value .FALSE.
• If the value is .TRUE., evaluate s_1, the first
  block of statements
• If the value is .FALSE., evlaluate s_2, the
  second block of statements
• After finishing either s_1 or s_2, execute the
  statement following the END IF

12
Roots of Quadratic v.2

• ! ------------------------------------------------
  ----------------
• ! Solve Ax2 Bx C 0 given BB-4AC gt 0
  
• ! ------------------------------------------------
  ----------------
• PROGRAM QuadraticEquation
• IMPLICIT NONE
• REAL a, b, c, d, root, root2
• ! read in the coefficients a, b and c
• WRITE(,) "A, B, C Please "
• READ(,) a, b, c
• !compute the square root of discriminant d
• d bb - 4.0ac
• IF (d gt 0.0) THEN ! is it
  solvable?
• d SQRT(d)
• root1 (-b d)/(2.0a) ! first root
• root2 (-b - d)/(2.0a) ! second root
• WRITE(,) "Roots are ", root1, " and ",
  root2
• ELSE ! complex roots

13
Logical Expressions

• Relational operators return result of .TRUE. or
  .FALSE
• lt, lt, gt, gt, , /
• Relational operators are of lower precedence than
  all arithmetic operators
• 2 7 gt 3 3 ? .TRUE.
• There is no associativity
• a lt b lt c ? illegal
• Note that means is equal to but means
  assign the value on the right

14
Data Type Logical

• Where do .TRUE. and .FALSE. come from?
• FORTRAN has a LOGICAL data type, just like it has
  INTEGER and REAL types
• We can declare variables to be of this type and
  assign values to them
• LOGICAL positive_x, condition
• condition .TRUE.
• positive_x x gt 0

15
Is Number Even or Odd?

• IF (MOD(number, 2) 0) THEN
• WRITE(,) number, " is even"
• ELSE
• WRITE(,) number, " is odd"
• END IF

MOD(a, b) Intrinsic function, returning the
remainder of a/b
16
Find Absolute Value

• REAL x, absolute_x
• x .....
• IF (x gt 0.0) THEN
• absolute_x x
• ELSE
• absolute_x -x
• END IF
• WRITE(,) The absolute value of ,
• x, is , absolute_x
• Note the use of to indicate continue on next
  line

17
Which value is smaller?

• INTEGER a, b, min
• READ(,) a, b
• IF (a lt b) THEN
• min a
• ELSE
• min b
• END IF
• Write(,) The smaller of , a,
• and , b, is , min

18
IF-THEN-END IF

• The IF-THEN-ELSE-END IF form allows us to choose
  between two alternatives
• There is another simpler selection mechanism that
  allows us to choose whether or not to perform a
  single block of actions
• We either perform the actions and go on, or skip
  them and go on

19
IF-THEN-END IF

• Syntax
• IF (logical expression) THEN
• block of statements
• END IF
• Semantics
• Evaluate the logical expression
• If it evaluates to .TRUE. execute the block of
  statements and then continue with the statement
  following the END IF
• If the result is .FALSE. skip the block and
  continue with the statement following the END IF

20
Examples of IF-THEN-END IF

• absolute_x x
• IF (x lt 0.0) THEN
• absolute_x -x
• END IF
• WRITE(,) "The absolute value of ", x, " is ",
  absolute_x
• -------------------------------------------------
• INTEGER a, b, min
• READ(,) a, b
• min a
• IF (a gt b) THEN
• min b
• END IF
• Write(,) "The smaller of ", a, " and ", b, " is
  ", min

21
Logical IF

• An even simpler form is sometimes useful
• Syntax
• IF (logical expression) single-statement
• Semantics equivalent to
• IF (logical expression) THEN
• single-statement
• END IF

22
Examples of Logical IF

• absolute_x x
• IF (x lt 0.0) absolute_x -x
• WRITE(,) "The absolute value of ", x,
• " is" ,"absolute_x
• -------------------------------------------------
• INTEGER a, b, min
• READ(,) a, b
• min a
• IF (a gt b) min b
• Write(,) "The smaller of ", a, " and ", b,
• " is ", min

23
IF-THEN-ELSE IF-END IF

• IF-THEN-ELSE-ENDIF can only handle processes
  which have two options.
• Sometimes we have more than 2 options for one
  process.
• For example, in the quadratic equation problem,
  there may be two equivalent roots. We want to
  detect this and complex roots at the same time.
• Solution put another IF-THEN-ELSE-ENDIF in the
  ELSE block

24
IF-THEN-ELSE IF-END IF

• Syntax
• IF (logical-expression1) THEN
• first statement block, s_1
• ELSE
• IF (logical-expression2) THEN
• second statement block, s_2
• ELSE
• third statement block, s_3
• END IF
• END IF

25
IF-THEN-ELSE IF-END IF

• Semantics
• Evaluate the logical expression 1. It can have
  value .TRUE. or value .FALSE.
• If the value is .TRUE., evaluate s_1, the first
  block of statements
• If the value is .FALSE.,
• evaluate the logical expression 2. It can have
  value .TRUE. Or value .FALSE.
• If the value is .TRUE., evaluate s_2, the second
  block of statements
• If the value is .FALSE., evaluate s_3, the third
  block of statements
• After finishing either s_2 or s_3, execute the
  statement following ENDIF
• After finishing either s_1 or s_2 or s_3, execute
  the statement following the END IF

26
Roots of Quadratic v.3

• ! ------------------------------------------------
  ---
• ! Solve Ax2 Bx C 0 given BB-4AC gt 0
  
• ! Detect complex roots and repeated roots.
• ! ------------------------------------------------
  ---
• PROGRAM QuadraticEquation
• IMPLICIT NONE
• REAL a, b, c, d, root1, root2
• ! read in the coefficients a, b and c
• READ(,) a, b, c
• ! comute the discriminant d
• d bb - 4.0ac
• IF (d gt 0.0) THEN ! distinct
  roots?
• d SQRT(d)
• root1 (-b d)/(2.0a) ! first root
• root2 (-b - d)/(2.0a) ! second root
• WRITE(,) 'Roots are ', root1, ' and ',
  root2
• ELSE

27
IF-THEN-ELSE IF-END IF

• You can put IF-THEN-ELSE IF-ENDIF within ELSE
  block repeatedly.
• IF (logical-expression1) THEN
• first statement block, s_1
• ELSE
• IF (logical-expression2) THEN
• second statement block, s_2
• ELSE
• IF-THEN-ELSE IF-ENDIF
• END IF
• END IF
• There is a concise way to do this.

28
IF-ELSEIF-ELSE-ENDIF

• syntax
• IF (logical expression 1) THEN
• block 1
• ELSEIF (logical expression 2) THEN
• block 2
• ...
• ELSEIF (logical expression N-1) THEN
• block N-1
• ELSE
• block N
• ENDIF

29
IF-ELSEIF-ELSE-ENDIF

• Semantics
• First evaluate the logical expression 1. It can
  have value .TRUE. or value .FALSE.
• If the value is .TRUE., evaluate the first block
  of statements.
• If the value is .FALSE., evaluate the logical
  expression 2. It can have value .TRUE. or value
  .FALSE.
• If the value is .TRUE., evaluate the second block
  of statements.
• Repeat this until all logical expressions have
  been evaluated.
• If none of them are .TRUE., evaluate block N
  within ELSE and ENDIF. After that, execute the
  statement following the ENDIF

30
Roots of Quadratic v.4

• --------------------------------------------------
  -
• ! Solve Ax2 Bx C 0 given BB-4AC gt 0
  
• ! Detect complex roots and repeated roots.
• ! ------------------------------------------------
  ---
• PROGRAM QuadraticEquation
• IMPLICIT NONE
• REAL a, b, c, d, root1,root2
• ! read in the coefficients a, b and c
• READ(,) a, b, c
• ! compute the discriminant d
• d bb - 4.0ac
• IF (d gt 0.0) THEN ! distinct
  roots?
• d SQRT(d)
• root1 (-b d)/(2.0a) ! first root
• root2 (-b - d)/(2.0a) ! second root
• WRITE(,) 'Roots are ', root1, ' and ',
  root2
• ELSEIF (d 0.0) THEN ! repeated
  roots?
• WRITE(,) 'The repeated root is ',
  -b/(2.0a)

31
Example in previous midterms

• PROGRAM X
• IMPLICIT NONE
• LOGICAL A,B,C
• INTEGER I,J,K
• I 5/22.5
• J 13.0/3.0 0.66
• K 5
• A (IJ)
• B (K gt J)
• C (KI)
• WRITE (,) A, B, C
• END PROGRAM

• 1- T T T
• 2- T F T
• 3- T F F
• 4- F T F
• 5- None of the above

32
Complex Logical Expressions

• In addition to relational operators, more complex
  logical expressions can be formed using logical
  operators
• The Logical Operators listed in order of
  decreasing precedence are
• .NOT.
• .AND.
• .OR.
• .EQV., .NEQV.
• The precedence of all logical operators is lower
  than all relational operators
• They all associate from left to right except .NOT.

High
Low
33
Logical operator .AND. ()
ltexp1gt ltexp2gt

• Examples
• (2gt1) .and. (3lt4) .TRUE.
• (2gt1) .and. (3gt4) .FALSE.
• (2lt1) .and. (3lt4) .FALSE.
• (2lt1) .and. (3gt4) .FALSE.

ltexp1gt .AND. ltexp2gt
exp2
exp1
.TRUE.
.FALSE.
.FALSE.
.FALSE.
34
Logical operator .OR. ()
ltexp1gt ltexp2gt

• Examples
• (2gt1) .OR. (3lt4) .TRUE.
• (2gt1) .OR. (3gt4) .TRUE.
• (2lt1) .OR. (3lt4) .TRUE.
• (2lt1) .OR. (3gt4) .FALSE.

ltexp1gt .OR. ltexp2gt
exp2
exp1
35
Logical operator .EQV.

• Examples
• (2gt1) .EQV. (3lt4) .TRUE.
• (2gt1) .EQV. (3gt4) .FALSE.
• (2lt1) .EQV. (3lt4) .FALSE.
• (2lt1) .EQV. (3gt4) .TRUE.

ltexp1gt .EQV. ltexp2gt
exp2
exp1
36
Logical operator .NEQV.

• Examples
• (2gt1) .NEQV. (3lt4) .FALSE.
• (2gt1) . NEQV. (3gt4) . TRUE.
• (2lt1) . NEQV. (3lt4) .TRUE.
• (2lt1) . NEQV. (3gt4) .FALSE.

ltexp1gt .NEQV. ltexp2gt
exp2
exp1
37
Logical operator .NOT.

• Examples
• .NOT. (2lt1) .TRUE.
• .NOT. (2gt1) .FALSE.

.NOT. ltexpgt
exp
38
Examples

• Suppose we have the declaration
• INTEGER age34, old92, young16
• What is the value of the following expressions?
• age / old
• age gt young
• age 62
• age56 .and. old/92
• age56 .or. old/92
• age56 .or. .not.(old/92)
• .not. (age56 .or. old/92)

39
Another Example

• Suppose the integer variable, n has value 4.
• n2 1 gt 10 .AND. .NOT. n lt 3
• ? 42 1 gt 10 .AND. .NOT. 4 lt 3
• 42 1 gt 10 .AND. .NOT. 4 lt 3
• 16 1 gt 10 .AND. .NOT. 4 lt 3
• 16 1 gt 10 .AND. .NOT. 4 lt 3
• 17 gt 10 .AND. .NOT. 4 lt 3
• 17 gt 10 .AND. .NOT. 4 lt 3
• .TRUE. .AND. .NOT. 4 lt 3
• .TRUE. .AND. .NOT. 4 lt 3
• .TRUE. .AND. .NOT. .FALSE.
• .TRUE. .AND. .NOT. .FALSE.
• .TRUE. .AND. .TRUE.
• .TRUE.

40
Example in the final of Fall 2006

• What is the output of the following Fortran
  program?
• PROGRAM exam
• IMPLICIT NONE
• LOGICAL X,Y
• INTEGER I2, J3
• REAL A5.0,B9.0
• X (A/I) lt (B/J)
• Y (J/I) (B/A)
• X X .AND. Y
• Y X .OR. Y
• WRITE (,) X, Y
• END PROGRAM exam

• a). T F
• b). T T
• c). F T
• d). F F
• e). The program does not compile