Introduction to Fortran 90/95 by Stephen J. Chapman

Introduction to Fortran 90/95 by

Stephen J. Chapman

Grading system:

1. Attendance: 30%

2. Midterm: 30%

3. Final: 40%

Office hours: (PH224)

1. Tues. 11:10~12:00 14:40~15:30 2. Fri. 13:40~15:30

Ch. 1 Introduction To Computers And The Fortran Language

Sec. 1.1 The Computer

Main Memory

Secondary Memory

C P U

(Central processing unit) Input

devices

Output devices

Sec 1.2 Data Representation in a Computer

ON 1 OFF 0

byte : a group of 8 bits e.g.,

825 MB hard disk. ( 1MB = 10⁶ byte)

Sec 1.2.1 The Binary Number System

1 2 3 ₁₀ = 1 x 10² + 2 x 10¹ + 3 x 10⁰ = 123.

10² 10¹ 10⁰

The base 2 number system:

1 0 1 ₂ = 1 x 2² + 0 x 2¹ + 1 x 2⁰ = 5

1 1 1 ₂ = 1 x 2² + 1 x 2¹ + 1 x 2⁰ = 7 2² 2¹ 2⁰

3 bits can represent 8 possible values :

0 ~ 7 (or 000

~ 111

)

In general, n bits 2ⁿ possible values.

e.g.,

8 bits ( = 1 byte) 2⁸ = 256. (-128 ~ +127)

16 bits ( = 2 byte) 2¹⁶ = 65,536. (-32,768 ~ +32,767)

Sec 1.2.2 Types of Data Stored in Memory

• Character data : (western language, < 256, use 1 byte) A ~ Z (26)

a ~ z (26) 0 ~ 9 (10)

Miscellaneous symbols: ( ) { } ! … Special letters or symbols: à ë …

Coding systems: (see App. A, 8-bit codes)

• ASCII (American Standard Code for Information Interchange)

• EBCDIC (Extended Binary Coded Decimal Interchange Code)

*The unicode coding system uses 2 bytes for each character.

(for any language)

• Integer data: (negative, zero, positive) For an n-bit integer,

Smallest Integer value = - 2^n-1 Largest Integer value = 2^n-1 - 1 e.g., a 4-byte (= 32-bit) integer,

the smallest = -2,147,483,648 ( = - 2^32-1) the largest = 2,147,483,647 ( = 2^32-1-1)

*Overflow condition: An integer > the largest or < the smallest.

• Real data: (or floating-point data) The base 10 system:

299,800,000 = 2.998 x 10⁸ (scientific notation)

mantissa exponent

The base 2 system:

e.g.,

a 4-byte real number = 24-bit mantissa + 8-bit exponent value = mantissa x 2^exponent

Precision: The number of significant digits that can be preserved in a number.

e.g., 24-bit mantissa ± 2²³ (~ seven significant digits) Range: The diff. between the largest and the smallest numbers.

e.g., 8-bit exponent 2^-128 ~ 2¹²⁷ (range ~ 10^-38 to 10³⁸)

Sec 1.3 Computer Languages

• Machine language: The actual language that a computer recognizes and executes.

• High-level languages: Basic, C, Fortran, …

*The History of the Fortran Language Fortran = Formula translation

Fortran 66 Fortran 77 Fortran 90 Fortran 95 (1966) (1977) (1991) (1997)

Sec. 2.3 The Structure of a Fortran Statement

A Fortran program = a series of statements

• Executable statements: e.g., additions, subtractions, …

• Non-executable statements: providing information.

Free-source form: Fortran statements may be entered anywhere on a line, up to 132 characters long.

e.g.,

100 output = input1 + input2 ! Sum the inputs or

100 output = input1 & ! Sum the inputs + input2

Sec. 2.4 The Structure of a Fortran Program

Fig 2-1 (A simple Fortran program) PROGRAM my_first_program ! Purpose: …

! Declare the variables

INTEGER :: i, j, k !All variable are integers ! Get the variables

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

READ (*,*) i, j k = i * j

! Write out the result

WRITE (*,*) 'Result = ', k STOP

END PROGRAM

Declaration section

Execution section

Termination section

Sec. 2.4.4 Program Style

Text book :

• Capitalizing Fortran keywords ( e.g., READ, WRITE)

• Using lowercase for variables, parameters

Sec. 2.4.5 Compiling, Linking, and Executing the Fortran Program

Fig 2-2

Fortran

program Object

file

Executable program

(Compile) (Link)

Sec. 2.5 Constants and Variables

Valid variable names: time

distance

z123456789

I_want_to_go_home

(up to 31 chracters, and the 1st character in a name must always be alphabetic)

Invalid variable names: this_is _a_very_long_variable_name 3_days

A$ ($ is an illegal character)

my-help (“-” is an illegal character)

Five intrinsic types of Fortran constants and variables:

1. INTEGER 2. REAL

3. COMPLEX 4. LOGICAL

5. CHARACTER

(numeric) (logical)

(character)

Sec. 2.5.1 Integer Constant and Variables

Integer constants: (no decimal point) e.g.,

0 -999 +17

1,000,000 (X) -100. (X)

Integer variables:

16-bit integers 32-bit integers

(diff. kinds of integers, Ch. 7)

Sec. 2.5.2 Real Constants and Variables

e.g., 10.

-999.9

1.0E-3 (= 1.0 x 10^-3 or 0.001) 123.45E20

0.12E+1 1,000,000. (X) 111E3 (X)

-12.0E1.5 (X)

Real variables:

32-bit real numbers 64-bit real numbers

(diff. kinds of real numbers, Ch. 7)

Sec. 2.5.3 Character Constants and Variables

Character constants: [enclosed in single (‘) or double (“) quotes)]

e.g.,

‘This is a test!’

“This is a test!”

‘ ‘ (a single blank) ‘{^}’

‘3.141593’ (not a number) This is a test! (X)

‘This is a test!” (X)

A character variable contains a value of the character data type.

Sec. 2.5.4 Logical Constants and Variables

Character constants:

e.g., .TRUE.

.FALSE.

TRUE (X) .FALSE (X)

A logical variable contains a value of the logical data type.

Sec. 2.5.5 Default and Explicit Variable Typing

e.g., incr (integer data type) big (real data type)

Explicit typing: The type of a variable is explicitly defined in the declaration section.

e.g.,

PROGRAM example

INTEGER :: day, month, year REAL :: second

LOGICAL :: test1, test2 CHARACTER :: initial

(Executable statements)

*No default names for the character data type!

Sec. 2.5.6 Keeping Constants Consistent in a Program

Using the PARAMETER attribute :

type, PARAMETER :: name=value e.g.,

REAL, PARAMETER :: pi=3.14159

CHARACTER, PARAMETER :: error=‘unknown’

Sec. 2.6 Assignment Statements and Arithmetic Calculations

variable_name = expression e.g.,

I = I + 1 ( I + 1 I )

Arithmetic operators:

• binary operators:

a + b (a + b, addition) a – b (a – b, subtraction) a * b (a x b, multiplication) a / b (a/b, division)

a ** b (a^b, exponentiation)

• unary operators:

+ a - b Rules:

1. No two operators may occur side by side.

e.g.,

a*-b (X) a*(-b) a**-2 (X) a**(-2)

2. Implied multiplication is illegal.

e.g.,

x (y + z) (X) x*(y + z)

3. Parentheses may be used to group terms whenever desired e.g.,

2**((8+2) / 5)

Sec. 2.6.1 Integer Arithmetic

e.g.,

3/4 = 0, 6/4 = 1 7/4 = 1, 9/4 = 2

Sec. 2.6.2 Real Arithmetic (or floating-point arithmetic)

e.g.,

3./4. = 0.75, 6./4. = 1.50 7./4. = 1.75, 9./4. = 2.25

Sec. 2.6.3 Hierarchy (order) of Operators

e.g.,

x = 0.5 * a * t **2 is equal to

x = 0.5 * a * (t **2) ? or

x = (0.5 * a * t ) **2 ? Order:

1. Parentheses, from inward to outward.

2. Exponentials, from right to left.

3. Multiplications and divisions, from left to right.

4. Additions and subtractions, from left to right.

Example 2-1

a = 3. b = 2. c=5. d=4.

e = 10. f = 2. g= 3.

(1) output = a * b + c * d + e / f **g (2) output = a * (b + c) * d + (e / f) **g (3) output = a * (b + c) * (d + e) / f **g Sol.

(1) output = 3. * 2. + 5. * 4. + 10. / 2. ** 3.

= 6. + 20. + 1.25 = 27.25

(2) output = 3. * (2. + 5.) * 4. + (10. / 2.) ** 3.

= 84. + 125.

= 209.

(3) output = 3. * (2. + 5.) * (4. + 10.) / 2. ** 3.

= 3. * 7. * 14. / 8.

= 294. / 8.

= 36.75

Example 2-2

a = 3. b = 2. c=3.

(1) output = a ** (b ** c) (2) output = (a ** b) ** c (3) output = a ** b ** c Sol.

(1) output = 3. ** (2. ** 3.) = 3. ** 8.

= 6561.

(2) output = (3. ** 2.) ** 3.

= 9. ** 3.

= 729.

(3) output = 3. ** 2. ** 3.

= 3. ** 8.

= 6561.

Sec. 2.6.4 Mixed-Mode Arithmetic

e.g.,

3. / 2 = 1.5 1 + 1/4 = 1 1. + 1/4 = 1.

1 + 1./4 = 1.25

Automatic type conversion:

e.g.,

nres = 1.25 + 9/4 ave = (5 + 2) / 2 = 1.25 + 2 = 7/2

= 3.25 = 3.

= 3

(a integer variable) (a real variable)

Logarithm

• Base 10:

If 10^x = N, then x = ? log N = x

e.g., N = 100 log 100 = log (10²) = 2 N = 3 log 3 = 0.47712…

• Base e (=2.71828…): (Natural logarithm)

If e^x = N, then x = ? ln N = x

e.g., N = e² ln (e²) = 2

N = 3 ln 3 = 1.09861…

* If N < 0 ( log N ) or ( ln N ) is undefined !

Sec. 2.6.5 Mixed-Mode Arithmetic and Exponentiation

If result and y are real, and n is an integer, result = y ** n

= y * y * y…*y

(real arithmetic, not mixed-mode) But if result, y and x are real,

result = y ** x = ?

use

y

= e

( e ∵

= e

= y

)

e.g.,

(4.0) ** 1.5 = 8.

(8.0)**(1./3)=2.

(-2.0) ** 2 = 4. [ (-2.0) * (-2.0) = 4.]∵

(-2.0) ** 2.0 [X, ln (-2.0) is undefined!]∵

Sec. 2.7 Assignment Statements and Logical Calculations

Assignment statements:

logical variable name = logical expression Logical operators:

• relational operators

• combinational operators

Sec. 2.7.1 Relational Operators

a₁ op a₂

a₁, a₂: arithmetic expressions, variables, constants, or character strings.

op: the relational logical operators. (see Table 2-3)

Table 2-3

operation meaning = = equal to

/ = not equal to > greater than

> = greater than or equal to < less than

< = less than or equal to e.g.,

operation result 3 < 4 .TRUE.

3 < = 4 .TRUE.

3 = = 4 .FALSE.

‘A’ < ‘B’ .TRUE. (in ASCII, A 65, B 66, p.493) 7+3 < 2+11 .TRUE.

Sec. 2.7.2 Combinational Logic Operators

l₁ .op. l2 and .NOT. l₁ (.NOT. is a unary operator) l₁, l₂: logical expressions, variables, or constants.

op: the binary operators. (see Table 2-4) Table 2-4

operation meaning

.AND. logical AND .OR. logical OR

.EQV. logical equivalence

.NEQV. logical non-equivalence .NOT. logical NOT

The order of operations:

1. Arithmetic operators.

2. All relational operators, from left to right.

3. All .NOT. operators.

4. All .AND. operators, from left to right.

5. All .OR. operators, from left to right.

6. All .EQV. And .NEQV. operators, from left to right.

Example 2-3

L1 = .TRUE., L2 = .TRUE., L3 = .FALSE.

(a) .NOT. L₁ .FALSE.

(b) L₁ .OR. L₃ .TRUE.

(c) L₁ .AND. L₃ .FALSE.

(d) L₂ .NEQV. L₃ .TRUE.

(e) L₁ .AND. L₂ .OR. L₃ .TRUE.

(f) L₁ .OR. L₂ .AND. L₃ .TRUE.

(g) .NOT. (L₁ .EQV. L₂) .FALSE.

Sec. 2.7.3 The Significance of Logical Variables and Expressions

Most of the major branching and looping structures of Fortran are controlled by logical values.

Sec. 2.8 Assignment Statements and Character Variables

character variables name = character expression Character operators:

1. substring specifications 2. concatenation

Sec. 2.8.1 Substring Specifications

E.g.,

str1 = ‘123456’ str1(2:4) contains the string ‘234’.

Example 2-4

PROGRAM substring

CHARACTER (len=8) :: a,b,c a = ‘ABCDEFGHIJ’

b = ‘12345678’

c = a(5:7)

b(7:8) = a(2:6)

WRITE(*,*) 'a=', a WRITE(*,*) 'b=', b WRITE(*,*) 'c=', c END PROGRAM

a = ? b = ? c = ? (Try it out!)

Solu:

a = ‘ABCDEFGH’ ( len = 8)∵ ∵ b(7:8) = a(2:6) = ‘BC’

b = ‘123456BC’

c = a(5:7) = ‘EFG’

= ‘EFG□□□□□‘ ( len = 8)∵

(Cont.)

Sec. 2.8.2 The Concatenation Operator

E.g.,

PROGRAM concate

CHARACTER (len=10) :: a CHARACTER (len=8) :: b,c a = ‘ABCDEFGHIJ’

b = ‘12345678’

c = a(1:3) // b(4:5) // a(6:8) WRITE(*,*)’c=‘,c

END PROGRAM

c = ? (Try it out: c =‘ABC45FGH’)

Sec. 2.8.3 Relational Operators with Character Data

E.g.,

‘123’ = = ‘123’ (true) ‘123’ = = ‘1234’ (false)

‘A’ < ‘B’ (true, ASCII, A 65, B 66)∵ ‘a’ < ‘A’ (false, a 97)∵

‘AAAAAB’ > ‘AAAAAA’ (true) ‘AB’ > ‘AAAA’ (true)

‘AAAAA’ > ‘AAAA’ (true)

Sec. 2.9 Intrinsic Functions

• Intrinsic functions are the most common functions built directly into the Fortran language. ( see Table 2-6 and App. B)

• External functions are supplied by the user. (see Ch. 6) e.g.,

y = sin(3.141593) INT(2.9995) = 2

(truncates the real number) y = sin(x)

y = sin(pi*x) NINT(2.9995) = 3

(rounds the real number) y = sin(SQRT(x))

Generic functions: (can use more than one type of input data) e.g.,

If x is a real number, ABS(x) is real.

If x is an integer,

ABS(x) is integer.

Specific functions: (can use only one specific type of input data) e.g.,

IABS(i)

(integer only)

*See Appendix B for a complete list of all intrinsic functions.

Sec. 2.10 List-directed (or free-format) Input and Output Statements

• The list-directed input statement:

READ (*,*) input_list I/O unit format

• The list-directed output statement:

WRITE (*,*) output_list I/O unit format

e.g.,

PROGRAM input_example INTEGER :: i, j

REAL :: a

CHARACTER (len=12) :: chars READ(*,*) i, j, a, chars

WRITE(*,*) i, j, a, chars END PROGRAM

Input: 1, 2, 3., ‘This one.’ (or 1 2 3. ‘This one.’) Output: 1 2 3.00000 This one.

(Try it out!)

Sec. 2.11 Initialization of Variables

E.g.,

PROGRAM init INTEGER :: i WRITE(*,*) I

END PROGRAM

Output: i = ??? (uninitialized variable)

Run-time error! (depends on machines)

(Try it out!)

Three ways to initialize variables:

1. Assignment statements:

e.g.,

PROGRAM init_1 INTEGER :: i

i = 1

WRITE(*,*) i

END PROGRAM 2. READ statements:

e.g.,

PROGRAM init_2 INTEGER :: i

READ(*,*) i WRITE(*,*) i

END PROGRAM

3. Type declaration Statements:

type :: var1 = value1, [var2 = value2, …]

e.g.,

REAL :: time = 0.0, distance = 5128.

INTEGER :: loop = 10

LOGICAL :: done = .FALSE.

CARACTER (len=12) :: string = ‘characters’

or

PROGRAM init_3 INTEGER :: i = 1 WRITE(*,*) i

END PROGRAM

Sec. 2.12 The IMPLICIT NONE Statement

When the IMPLICIT NONE statement is included in a program, any variable that does not appear in an explicit type declaration statement is considered an error.

e.g.,

PROGRAM test_1 REAL :: time

time = 10.0

WRITE(*,*) ‘Time=‘, tmie END PROGRAM

Output:

Run-time error! (depends on machines)

+ IMPLICIT NONE,

PROGRAM test_1 IMPLICIT NONE REAL :: time

time = 10.0

WRITE(*,*) ‘Time=‘, tmie END PROGRAM

Output:

Compile-time error! (depends on machines)

Sec. 2.13 Program Examples

Example 2-5 (Temperature conversion) T (⁰F) = (9/5) T(⁰C) + 32

Fig. 2-6

PROGRAM temp IMPLICIT NONE

REAL :: temp_c, temp_f

WRITE(*,*) ’Enter T in degrees C:’

READ(*,*) temp_c

temp_f = (9./5.) * temp_c + 32.

WRITE(*,*) temp_c,’ degrees C =‘, temp_f, &

‘degrees F’

END PROGRAM (Try it out!)

Example (extra)

Write a program for converting a 4 bits integer into a base 10 number, e.g.,

1 0 1 1 = 1 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2⁰ = 11

Ch. 3 Control Structures and Program Design

Ch. 2: Sequential programs (simple and fixed order)

Here: Complex programs (using two control statements)

Sec. 3.1 Introduction to Top-down Design Techniques

Start

State the problem

Design the algorithm

Convert algorithm into Fortran statements

Test the program

Finished !

Fig. 3-1 (a formal program design process)

Sec. 3.2 Pseudocode and Flowcharts

(1) Pseudocode : a mixture of Fortran and English (2) Flowcharts : graphical symbolsl

e.g.,

(1) The pseudocode for Example 2-5:

Prompt user to enter temp. in degree Farenheit Read temp. in degree Farenheit

temp_k in Kelvins (5./9.)*(temp_f-32.)+273.15 Write temp. in Kelvins

(2) The flowcharts for Example 2-5:

Start Tell user to enter temp_f

Get temp_f

Calculate

temp_k Write temp_k Stop

(an oval for start or stop)

(a parallelogram for I/O)

(a rectangle for computation)

Sec. 3.3 Control Constructs: Branches

• IF Statement

• SELECT CASE

Branches are Fortran statements that permit us to select and execute specific sections of code (called blocks) while skipping other sections of code.

Sec. 3.3.1 The Block IF Construct

This construct specifies that a block of code will be executed if and only if a certain logical expression is true.

IF (logical_expr) THEN Statement 1

Statement 2 .

. . END IF

a block

Fig . 3-5 (Flowchart for a simple block IF construct)

logical_expr

Statement 1 Statement 2 .

.

.TRUE.

.FALSE.

(a diamond for choice)

Example:

ax² + bx + c = 0,

x = -b ± ( b² – 4ac )^1/2 2a

If b² – 4ac = 0 b² – 4ac > 0

b² – 4ac < 0

two distinct real roots

two complex roots a single repeated root

Fig . 3-6 (Flowchart)

.TRUE.

.FALSE.

Problem: Tell the user if the eq. has complex roots.

b² – 4ac < 0

WRITE ‘two complex roots’

Fortran:

IF ( (b**2 – 4.*a*c) < 0. ) THEN

WRITE(*,*) ‘Two complex roots!’

END IF

Sec. 3.3.2 The ELSE and ELSE IF Clauses

For many different options to consider,

IF + ELSE IF (one or more) + an ELSE

IF (logical_expr_1) THEN Statement 1

Statement 2 .

.

ELSE IF (logical_expr_2) THEN Statement 1

Statement 2 .

. ELSE

Statement 1 Statement 2 .

. END IF

Block 1

Block 2

Block 3

Fig . 3-7 (flowchart)

.TRUE.

.FALSE.

logical_expr_1

Block 1

logical_expr_2

Block 2

.TRUE.

.FALSE.

Block 3

Fig . 3-8 (flowchart)

.TRUE.

.FALSE.

b² - 4ac < 0

WRITE ‘two complex roots’

.TRUE.

.FALSE.

Example: Tell the user whether the eq. has two complex roots, two identical real roots, or two distinct real roots.

b² - 4ac = 0

WRITE ‘two identical real roots’

WRITE ‘two distinct real roots’

Fortran:

IF ( (b**2 – 4.*a*c) < 0. ) THEN

WRITE(*,*) ‘two complex roots’

ELSE IF ( (b**2 – 4.*a*c) == 0. ) THEN WRITE(*,*) ‘two identical real roots’

ELSE

WRITE(*,*) ‘two distinct real roots’

END IF

Write a complete Fortran program for a quadratic equation ax² + bx + c = 0.

Input: a, b, c (e.g., 1., 5., 6.

or 1., 4., 4.

or 1., 2., 5.)

Output: ‘distinct real’

or ‘identical real’

or ‘complex roots’

(Try it out!)

PROGRAM abc IMPLICIT NONE REAL :: a, b, c

WRITE(*,*)'Enter the coeffs. a, b, and c:‘

READ(*,*) a, b, c

IF ( (b**2-4.*a*c) < 0. ) THEN WRITE(*,*) 'two complex root‘

ELSE IF ( (b**2-4.*a*c) == 0. ) THEN WRITE(*,*) 'two identical real roots‘

ELSE

WRITE(*,*) 'two distinct real roots‘

END IF

END PROGRAM

Sec. 3.3.3 Examples Using Block IF Constructs

Example 3-1 The Quadratic Equation: (ax² + bx + c =0) Write a program to solve for the roots of a quadratic equation, regardless of type.

Input: a, b, c

Output: roots

real

repeated real complex

PROGRAM root IMPLICIT NONE

REAL :: a, b, c, d, re, im, x1, x2

WRITE(*,*)'Enter the coeffs. a, b, and c:‘

READ(*,*) a, b, c d = b**2 – 4.*a*c IF ( d < 0. ) THEN

WRITE(*,*) 'two complex root:‘

re = (-b)/(2.*a)

im = sqrt(abs(d))/(2.*a)

WRITE(*,*) ’x1=‘, re, ‘+ i’, im WRITE(*,*) ’x2=‘, re, ‘- i’, im ELSE IF ( d == 0. ) THEN

WRITE(*,*) 'two identical real roots:‘

x1 = (-b) / (2.*a)

WRITE(*,*) ’x1=x2=‘, x1

ELSE

WRITE(*,*) 'two distinct real roots:‘

x1 = (-b + sqrt(d)) / (2.*a) x2 = (-b – sqrt(d)) / (2.*a) WRITE(*,*) ’x1=‘, x1

WRITE(*,*) ‘x2=‘, x2 END IF

END PROGRAM Test: (Try it out!)

x² + 5x + 6 = 0, x_1,2 = -2, -3 x² + 4x + 4 = 0, x_1,2 = -2

x² + 2x + 5 = 0, x_1,2 = -1 ± i 2

Example 3-2 Evaluation a Function of Two Variables:

f(x,y) =

x + y, x 0 ≧ and y 0≧ x + y², x 0 ≧ and y < 0 x² + y, x < 0 and y 0≧ x² + y², x < 0 and y < 0

Input: x, y

Output: f

Fig . 3-11 (flowchart)

.TRUE.

.FALSE.

x ≧ 0 &

y 0≧

f = x + y

x 0 ≧ &

y < 0

f = x² + y

.TRUE.

.FALSE.

f = x² + y² f = x + y²

x < 0 &

y 0≧

.TRUE.

.FALSE.

WRITE f Stop Start

READ x, y

PROGRAM funxy IMPLICIT NONE REAL :: x, y, f

WRITE(*,*)'Enter x and y:‘

READ(*,*) x, y

IF ((x >= 0.) .AND. (y >= 0. )) THEN f = x + y

ELSE IF ((x >= 0.) .AND. (y < 0. )) THEN f = x + y**2

ELSE IF ((x < 0.) .AND. (y >= 0. )) THEN f = x**2 + y

ELSE

f = x**2 + y**2 END IF

WRITE(*,*) ‘f = ‘, f END PROGRAM

Test: (Try it out!) x y f 2. 3. 5.

2. -3. 11.

-2. 3. 7.

-2. -3. 13.

[name:] IF (logical_expr_1) THEN Statement 1

Statement 2 .

.

ELSE IF (logical_expr_2) THEN [name]

Statement 1 Statement 2 .

.

ELSE [name]

Statement 1 Statement 2 .

.

END IF [name]

Block 1

Block 2

Block 3

Sec. 3.3.4 Named Block IF Constructs

optional

optional

Sec. 3.3.5 Notes Concerning the Use of Logical IF Constructs

Nested IF Constructs:

outer: IF ( x > 0. ) THEN .

.

inner: IF ( y < 0. ) THEN .

. END IF inner .

.

END IF outer

Example 3-3 Assigning Letter Grades:

95 < GRADE A 86 < GRADE < 95 B 76 < GRADE < 86 C 66 < GRADE < 76 D 0 < GRADE < 66 F

Input: grade

Output: ‘The grade is A.’

or ‘The grade is B.’

or ‘The grade is C.’

or ‘The grade is D.’

or ‘The grade is F.’

Method (a): IF + ELSE IF IF (grade > 95.) THEN

WRITE(*,*) ‘The grade is A.’

ELSE IF (grade > 86.) THEN

WRITE(*,*) ‘The grade is B.’

ELSE IF (grade > 76.) THEN

WRITE(*,*) ‘The grade is C.’

ELSE IF (grade > 66.) THEN

WRITE(*,*) ‘The grade is D.’

ELSE

WRITE(*,*) ‘The grade is F.’

END IF

Method (b): nested IF

if1: IF (grade > 95.) THEN

WRITE(*,*) ‘The grade is A.’

ELSE

if2: IF (grade > 86.) THEN

WRITE(*,*) ‘The grade is B.’

ELSE

if3: IF (grade > 76.) THEN

WRITE(*,*) ‘The grade is C.’

ELSE

if4: IF (grade > 66.) THEN

WRITE(*,*) ‘The grade is D.’

ELSE

WRITE(*,*) ‘The grade is F.’

END IF if4 END IF if3 END IF if2 END IF if1

Sec. 3.3.6 The Logical IF Statement

IF (logical_expr) Statement

e.g.,

IF ( (x >= 0.) .AND. (y >= 0.) ) f = x + y

[name:] SELECT CASE (case_expr) CASE (case_selector_1) [name]

Statement 1 Statement 2 . . .

CASE (case_selector_2) [name]

Statement 1 Statement 2 . . .

CASE DEFAULT [name]

Statement 1 Statement 2 . . .

END SELECT [name]

Block 1

Block 2

Block 3

Sec. 3.3.7 The CASE Construct

optional

optional

optional

case_expr: an integer, character, or logical expression.

The case_selector can take one of four forms:

1. case_value Execute block if case_value == case_expr 2. low_value: Execute block if low_value <= case_expr 3. : high_value: Execute block if case_expr <= high_value 4. low value: high_value

Execute block if low_value <= case_expr <= high_value

Fig . 3-13 (flowchart for a CASE construct)

In range Not

in range

case_sel_1

Block 1

case_sel_2

Block n

In range Not

In range

Default Block Block 2

case_sel_n

In range Not

in range

e.g., (modified)

REAL :: temp_c . . .

temp: SELECT CASE (temp_c) CASE (: -1.0)

WRITE (*,*) ‘ It’s below freezing today!’

CASE (0.0)

WRITE (*,*) ‘ It’s exactly at the freezing point!’

CASE (1.0:20.0)

WRITE (*,*) ‘ It’s cool today!’

CASE (21.0:33.0)

WRITE (*,*) ‘ It’s warm today!’

CASE (34.0:)

WRITE (*,*) ‘ It’s hot today!’

END SELECT temp

PROGRAM selectc IMPLICIT NONE INTEGER :: temp_c

WRITE(*,*) “Enter today’s temp. in degree C:”

READ(*,*) temp_c

temp: SELECT CASE (temp_c) CASE (: -1)

WRITE (*,*) “It’s below freezing today!”

CASE (0)

WRITE (*,*) “It’s exactly at the freezing point!”

CASE (1:20)

WRITE (*,*) “It’s cool today!”

CASE (21:33)

WRITE (*,*) “It’s warm today!”

CASE (34:)

WRITE (*,*) “It’s hot today!”

END SELECT temp END PROGRAM

Problem: Determine whether an integer between 1 and 10 is even or odd. (Try it out!)

PROGRAM selectv INTEGER :: value

WRITE(*,*) 'Enter an inter between 1-10:' READ(*,*) value

SELECT CASE (value) CASE (1,3,5,7,9)

WRITE(*,*) 'The value is odd.' CASE (2,4,6,8,10)

WRITE(*,*) 'The value is even.' CASE (11:)

WRITE(*,*) 'The value is too high' CASE DEFAULT

WRITE(*,*) 'The value is negative or zero.' END SELECT

END PROGRAM

Sec. 3.4 Control Constructs: Loops

• while loops

• iterative (or counting) loops

Sec. 3.4.1 The While Loop

DO . . .

IF (logical_expr) EXIT . . .

END DO

a code block

Fig . 3-14 (Flowchart for a while loop)

.TRUE.

.FALSE.

logical_expr Statement 1 . . .

Statement 1 . . .

Example 3-4 Statiscal Analysis:

Average:

x_ave =

Σ

i=1 N

N Standard deviation:

S =

N

Σ

i=1 i=1

N ^N

Σ

1/2

Input: x (i.e., x_i , i = 1, 2, …, N) 0 ≧ Output: x_ave and S

Fig . 3-15 (Flowchart for Example 3-4)

.TRUE.

.FALSE.

x < 0 READ x

n = n + 1

sum_x = sum_x + x sum_x2=sum_x2 + x²

Start

1

1

Calculate x_ave, s

Stop WRITE x_ave, s, n Initial values:

n = 0

sum_x = 0 Sum_x2 = 0

Fig . 3-16 PROGRAM stats_1 IMPLICIT NONE INTEGER :: n = 0

REAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.

DO

WRITE(*,*) ‘Enter the value x:’

READ (*,*) x

IF ( x < 0. ) EXIT n = n + 1

sum_x = sum_x + x

sum_x2 = sum_x2 + x**2 END DO

x_ave = sum_x / n

s = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1))) WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, &

‘ s = ‘, s END PROGRAM

Test:

Input: 3.

4.

5.

-1.

Output: n = 3 x_ave = 4.00000 s = 1.00000

Sec. 3.4.2 The Iterative Counting Loop

DO index = istart, iend, incr Statement 1

. . .

Statement n END DO

e.g.,

(1) Do i = 1, 10 Statement 1 . . .

Statement n END DO

( incr = 1 by default)

(2) Do i = 1, 10, 2 Statement 1 . . .

Statement n END DO

( i = 1, 3, 5, 7, 9 )

Fig. 3-18 (Flowchart for a Do loop construct)

index*incr

≦iend * incr index =

istart incr

Statement 1 Statement 2 . . .

.TRUE.

.FALSE.

Example 3-5 The Factorial Function:

N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.

0 ! = 1 e.g.,

4 ! = 4 × 3 × 2 × 1 = 24 5 ! = 5 × 4 × 3 × 2 × 1 = 120

Fortran Code: n_factorial = 1 DO i = 1, n

n_factorial = n_factorial * i END DO

Problem: Write a complete Fortran program for the factorial function.

Input: n ( n > = 0 )

N ! = N × (N-1) × (N-2) … × 3 × 2 × 1, N > 0.

0 ! = 1

Output: n!

PROGRAM factorial IMPLICIT NONE

INTEGER :: i, n, n_fact

WRITE(*,*) ’Enter an integer n ( > = 0 ):’

READ(*,*) n n_fact = 1

IF ( n > 0 ) THEN DO i = 1, n

n_fact = n_fact * i END DO

END IF

WRITE(*,*) n, ‘! = ‘, n_fact END PROGRAM

Fig . 3-20

.TRUE. .FALSE.

n < 2 READ n

sum_x =

sum_x + x sum_x2 =

sum_x2+x² Start

1

1

Calculate x_ave, s

Stop

WRITE x_ave, s, n

Initial values:

sum_x = 0 sum_x2 = 0

Example 3-7 Statistical Analysis: (modified)

WRITE

‘At least 2 values!’

i=1

i=i+1 i n≦ ?

READ x

.FALSE. .TRUE.

Fig . 3-21

PROGRAM stats_3 IMPLICIT NONE INTEGER :: i, n

REAL :: x, x_ave, s , sum_x = 0., sum_x2 = 0.

WRITE(*,*) ‘Enter the number of points n:’

READ(*,*) n

IF ( n < 2 ) THEN

WRITE(*,*) ‘ At least 2 values!’

ELSE

DO i = 1, n

WRITE(*,*) ‘Enter the value x:’

READ (*,*) x

sum_x = sum_x + x

sum_x2 = sum_x2 + x**2 END DO

x_ave = sum_x / n

s = sqrt (( n*sum_x2 – sum_x**2) / (n*(n-1))) WRITE(*,*) ‘n = ‘ , n, ‘ x_ave = ‘, x_ave, &

‘ s = ‘, s END IF

END PROGRAM Test:

Input: 3 3.

4.

5.

Output: n = 3 x_ave = 4.00000 s = 1.00000

Sec. 3.4.3 The CYCLE and EXIT Statements

E.g.,

PROGRAM test_cycle INTEGER :: i

DO i = 1, 5

IF ( i == 3 ) CYCLE WRITE(*,*) i

END DO

WRITE(*,*) ‘End of loop!’

END PROGRAM

Output: 1

2 4 5 End of loop!

PROGRAM test_exit INTEGER :: I

DO i = 1, 5

IF ( i == 3 ) EXIT WRITE(*,*) i

END DO

WRITE(*,*) ‘End of loop!’

END PROGRAM

Output: 1

2 End of loop!

[name:] DO . . .

IF (logical_expr) CYCLE [name]

. . .

IF (logical_expr) EXIT [name]

. . .

END DO [name]

Sec. 3.4.4 Named Loops

While loop:

optional

[name:] DO index = istart, iend, incr . . .

IF (logical_expr) CYCLE [name]

. . .

END DO [name]

Counting loop:

optional

Sec. 3.4.5 Nesting Loops and Block IF Construct

e.g.,

PROGRAM nested_loops INTEGER :: i, j, product DO i = 1, 3

DO j = 1, 3

product = i * j

WRITE(*,*) i, ‘*’, j, ‘=‘, product END DO

END DO

END PROGRAM

Output:

1 * 1 = 1 1 * 2 = 2 1 * 3 = 3 2 * 1 = 2 2 * 2 = 4 2 * 3 = 6 3 * 1 = 3 3 * 2 = 6 3 * 3 = 9

PROGRAM test_cycle_1 INTEGER :: i, j, product DO i = 1, 3

DO j = 1, 3

IF ( j == 2 ) CYCLE product = i * j

WRITE(*,*) i, ‘*’, j, ‘=‘, product END DO

END DO

END PROGRAM Output: 1 * 1 = 1

1 * 3 = 3 2 * 1 = 2 2 * 3 = 6 3 * 1 = 3 3 * 3 = 9

PROGRAM test_cycle_2 INTEGER :: i, j, product outer: DO i = 1, 3

inner: DO j = 1, 3

IF ( j == 2 ) CYCLE outer product = i * j

WRITE(*,*) i, ‘*’, j, ‘=‘, product END DO inner

END DO outer END PROGRAM Output:

1 * 1 = 1 2 * 1 = 2 3 * 1 = 3

Nesting loops within IF constructs and vice versa:

e.g.,

outer: IF ( a < b ) THEN . . .

inner: DO i = 1, 3 . . .

ELSE

. . .

END DO inner END IF outer

illegal!

outer: IF ( a < b ) THEN . . .

inner: DO i = 1, 3 . . .

END DO inner . . .

ELSE

. . .

END IF outer legal:

Ch. 4 Basic I/O Concepts

Sec. 4.1 FORMATS and FORMETED WRITE STATEMENTS

READ (*,*) Not always convenient!

WRITE (*,*) Not always pretty!

e.g,. PROGRAM free_format INTEGER :: i = 21

REAL :: result = 3.141593 WRITE(*,100) i, result

100 FORMAT (‘□The□result□for□iteration□’, &

I3, ‘□is□’, F7.3) END PROGRAM

Output: □The□result□for□iteration□□21□is□□□3.142

∵ I3 ∵ F7.3

The following three WRITE statements are equivalent:

• WRITE (*, 100) i, result 100 FORMAT (I6, F10.2)

• CHARACTER ( len=20 ) :: string string = ‘(I6, F10.2)’

WRITE(*,string) i, result

• WRITE(*, ‘(I6,F10.2)’) i, result

Output: □□□□21□□□□□□3.14

I6 F10.2

PROGRAM format INTEGER :: i = 21

REAL :: result = 3.141593

CHARACTER ( len=20 ) :: string WRITE (*, 100) i, result

100 FORMAT (I6, F10.2) string = '(I6, F10.2)'

WRITE(*,string) i, result

WRITE(*, '(I6,F10.2)') i, result END PROGRAM

Output: □□□□21□□□□□□3.14

Sec. 4.2 Output Devices

Line printers, laser printers, and terminals.

Sec. 4.3 Format Descriptors

Table 4-2 (Symbols used with format descriptors) Symbol meaning

c column number

d # of digits to the right of the decimal point m min. # of digit

r repeat count w field width

Sec. 4.3.1 Integer Output – The I Descriptor

rIw or rIw.m e.g.,

INTEGER :: index = -12, junk = 4, number = -12345 WRITE(*,200) index, index+12, junk, number

WRITE(*,210) index, index+12, junk, number WRITE(*,220) index, index+12, junk, number 200 FORMAT ( 2I5, I6, I10)

210 FORMAT (2I5.0, I6, I10.8) 220 FORMAT (2I5.3, I6, I5)

Output:

□□-12□□□□0□□□□□4□□□□-12345 □□-12□□□□□□□□□□4□-00012345 □-012□□000□□□□4*****

(Not in scale!)

I5 I5 I6 I10

PROGRAM iformat IMPLICIT NONE

INTEGER :: index = -12, junk = 4, number = -12345 WRITE(*,200) index, index+12, junk, number

WRITE(*,210) index, index+12, junk, number WRITE(*,220) index, index+12, junk, number 200 FORMAT ( 2I5, I6, I10)

210 FORMAT (2I5.0, I6, I10.8) 220FORMAT (2I5.3, I6, I5)

END PROGRAM

Output: -12 0 4 -12345 -12 4 -00012345 -012 000 4*****

(Not in scale!)

Sec. 4.3.2 Real Output – The F Descriptor

rFw.d e.g.,

REAL :: a = -12.3, b = .123, c = 123.456 WRITE(*,200) a, b, c

WRITE(*,210) a, b, c

200 FORMAT (2F6.3, F8.3) 210 FORMAT (3F10.2)

Output: ******□0.123□123.456

□□□□-12.30□□□□□□0.12□□□□123.46

(Not in scale!) F6.3 F6.3 F8.3

F10.2 F10.2 F10.2

PROGRAM rformat IMPLICIT NONE

REAL :: a = -12.3, b = .123, c = 123.456 WRITE(*,200) a, b, c

WRITE(*,210) a, b, c

200 FORMAT (2F6.3, F8.3) 210 FORMAT (3F10.2)

END PROGRAM

Output: ****** 0.123 123.456

-12.30 0.12 123.46 (Not in scale!)

Sec. 4.3.3 Real Output – The E Descriptor

(Expomential notation) Scientific notation: 6.02 × 10²³

Exponential notation: 0.602 × 10²⁴ (E Descriptor)

0.602 E+24 rFw.d ( w d + ≧ 7 )

e.g., REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10 WRITE (*,200) a, b, c, d

200 FORMAT (2E14.4, E13.6, E11.6)

□□□□0.1235E+07□□□□0.1000E-02-0.777000E+12***********

E14.4 E14.4 E13.6 E11.6

Output:

( ‘E+**’ , ‘0.’, and ‘-’)∵

( 11 < 6 + 7)∵

PROGRAM routput IMPLICIT NONE

REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10, d = -77.7E10 WRITE (*, 200) a, b, c, d

200 FORMAT (2E14.4, E13.6, E11.6) END PROGRAM

Sec. 4.3.4 True Scientific Notation – The ES Descriptor

rESw.d ( w d + ≧ 7 ) e.g.,

REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10 WRITE (*,200) a, b, c

200 FORMAT (2ES14.4, ES12.6)

□□□□1.2346E+06□□□□1.0000E-03************

ES14.4 ES14.4 ES12.6

Output:

PROGRAM esformat IMPLICIT NONE

REAL :: a = 1.2346E6, b = 0.001, c = -77.7E10 WRITE (*, 200) a, b, c

200 FORMAT (2ES14.4, ES12.6) END PROGRAM

Sec. 4.3.5 Logical Output – The L Descriptor

rLw e.g.,

LOGICAL :: output = .TRUE., debug = .FALSE.

WRITE (*, 200) output, debug 200 FORMAT (2L5)

□□□□T□□□□F

L5 L5

Output:

PROGRAM loutput IMPLICIT NONE

LOGICAL :: output = .TRUE., debug = .FALSE.

WRITE (*, 200) output, debug 200 FORMAT (2L5)

END PROGRAM

Sec. 4.3.6 Character Output – The A Descriptor

rAw or rA e.g.,

CHARACTER (len = 17) :: string = ‘This□is□a□string.’

WRITE (*, 10) string WRITE (*, 11) string WRITE (*, 12) string 10 FORMAT (A) 11 FORMAT (A20) 12 FORMAT (A6) Output:

(i.e., the width is the same as the # of characters being displayed.)

17 characters

This□is□a□string.

□□□This□is□a□string.

This□i

PROGRAM aoutput IMPLICIT NONE

CHARACTER (len = 17) :: string = 'This is a string.‘

WRITE (*, 10) string WRITE (*, 11) string WRITE (*, 12) string 10 FORMAT (A)

11 FORMAT (A20) 12 FORMAT (A6) END PROGRAM

Sec. 4.3.7 Horizontal Position – The X and T Descriptors

X descriptor:

nX

(the # of blanks to insert) T descriptor:

Tc

(the column # to go to)

e.g,.

CHARACTER (len = 10) :: first_name = ‘James□’

CHARACTER :: initial = ‘R’

CHARACTER (len = 16) :: last_name = ‘Johnson□’

CAHRACTER (len = 9) :: class = ‘COSC□2301’

INTEGER :: grade = 92

WRITE(*,100) first_name, initial, last_name, grade, class 100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9) Output:

James□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301

A10 1X A1 1X A10 4X I3 A9

(51^th column, T51)∵

or

CHARACTER (len = 10) :: first_name = ‘James□’

CHARACTER :: initial = ‘R’

CHARACTER (len = 16) :: last_name = ‘Johnson□’

CHARACTER (len = 9) :: class = ‘COSC□2301’

INTEGER :: grade = 92

WRITE(*,100) first_name, initial, last_name, class, grade 100 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3) Output:

James□□□□□□□R□Johnson□□□□□□□□92 . . . COSC□2301

A10 A1 A10 I3 A9

(13^th column, T13)∵

(15^th column, T15)∵ (29^th column, T29)∵

(51^th column, T51)∵

or

CHARACTER (len = 10) :: first_name = ‘James□’

CHARACTER :: initial = ‘R’

CHARACTER (len = 16) :: last_name = ‘Johnson□’

CAHRACTER (len = 9) :: class = ‘COSC□2301’

INTEGER :: grade = 92

WRITE(*,100) first_name, initial, last_name, class, grade 100 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3) Output:

James□□□□□□□R□JoCOSC□2301□□□□92

A10 A1 A10 I3

(13^th column, T13)∵

(15^th column, T15)∵

(29^th column, T29)∵ (17^th column, T17)∵

PROGRAM tformat

CHARACTER (len = 10) :: first_name = 'James ' CHARACTER :: initial = 'R'

CHARACTER (len = 16) :: last_name = 'Johnson ' CHARACTER (len = 9) :: class ='COSC 2301'

INTEGER :: grade = 92

WRITE(*,100) first_name, initial, last_name, grade, class WRITE(*,110) first_name, initial, last_name, class, grade WRITE(*,120) first_name, initial, last_name, class, grade 100 FORMAT (A10, 1X, A1, 1X, A10, 4X, I3, T51, A9) 110 FORMAT (A10, T13, A1, T15, A10, T51, A9, T29, I3) 120 FORMAT (A10, T13, A1, T15, A10, T17, A9, T29, I3) END PROGRAM

Sec. 4.3.8 Repeating Groups of Format Descriptors

E.g.,

320 FORMAT (1X, I6, I6, F10.2, F10.2, I6, F10.2, F10.2) 321 FORMAT (1X, I6, 2(I6, 2F10.2))

320 FORMAT (1X, I6, F10.2, A, F10.2, A, I6, F10.2, A, F10.2, A) 321 FORMAT (1X, 2(I6, 2(F10.2, A)))

Sec. 4.3.9 Changing Output Lines – The Slash ( / ) Descriptor

e.g.,

WRITE (*, 100) index, time, depth, amplitude, phase

100 FORMAT (T20, ‘Results for Test Number ‘, I3, ///, &

1X, ‘Time = ‘, F7.0/, &

1X, ‘Depth = ‘, F7.1, ‘ meters’, / , &

1X, ‘Amplitude = ‘, F8.2/, &

1X, ‘Phase = ‘, F7.1) Output:

Results for Test Number . . .

Time = . . . Depth = . . . Amplitude = . . . Phase = . . . (skip 2 lines)

Sec. 4.3.10 How Format Statements Are Used during WRITES

Example 4-1 Generating a Table of Information

Output:

Table of Square Roots, Squares, and Cubes Number Square Root Square Cube

====== ========== ====== ====

1 1.000000 1 1 2 1.414214 4 8 . . . . . . . . . . . . 9 3.000000 81 729 10 3.162278 100 1000

PROGRAM table IMPLICIT NONE

INTEGER :: i, square, cube REAL :: square_root

WRITE(*, 100)

100 FORMAT(T4, ‘Table of Square Roots, Squares, and Cubes’/ ) WRITE(*, 110)

110 FORMAT(T4, ‘Number’, T13, ‘Square Root’, T29, ‘Square’, T39, ‘Cube’) WRITE(*, 120)

120 FORMAT(T4, ‘======‘, T13, ‘===========‘, T29, &

‘======‘, T39, ‘====‘) DO i = 1, 10

square_root = SQRT(REAL(i)) square = i**2

cube = i**3

WRITE(*, 130) i, square_root, square, cube

130 FORMAT(T4, I4, T13, F10.6, T27, I6, T37, I6) END DO

END PROGRAM

Sec. 4.4 Formatted READ Statements e.g., READ (*,100) increment

100 FORMAT (6X, I6) (skip the 1^st six column)

(col. 7~12: an integer)

Sec. 4.4.1 Integer Input – The I Descriptor rIw

e.g.,

READ(*, 100) a, b, c 100 FORMAT(3I5) Input:

□□□15□□15□□15□□

I5 I5 I5

a = 15 b = 15 c = 15

PROGRAM iinput IMPLICIT NONE INTEGER :: a, b, c READ(*, 100) a, b, c 100 FORMAT(3I5) WRITE(*,*) 'a= ', a WRITE(*,*) 'b= ', b WRITE(*,*) 'c= ', c END PROGRAM

Sec. 4.4.2 Real Input – The F Descriptor

rFw.d e.g.,

READ (*, ‘(3F10.4)’ ) a, b, c Input:

1.5□□□□□□□□0.15E+01□□□15.0E-01

F10.4 F10.4 F10.4

a = 1.5 b = 1.5 c = 1.5

PROGRAM rinput IMPLICIT NONE REAL :: a, b, c

READ (*, '(3F10.4)' ) a, b, c WRITE(*,*) 'a= ', a

WRITE(*,*) 'b= ', b WRITE(*,*) 'c= ', c END PROGRAM

If a number without a decimal point appears in the

field, then a decimal point is assumed to be in the position specified by the d term of the format descriptor.

e.g.,

READ (*, ‘(3F10.4)’ ) a, b, c Input:

□□□□□□□□15□□□150□□□□□□15000□□□

F10.4 F10.4 F10.4

a = 0.0015 b = 0.0150 c = 1.5000

*The E and ES format descriptors are identical to the F descriptor.