Elementary FORTRAN

1. Elementary FORTRAN

2. Elementary FORTRAN 77 • All FORTRAN programs consist of data that is manipulated by a set of control structures to produce a result. • Control structures are statements that implement the algorithm steps you have chosen when you designed the program. • Data + algorithms = programs

3. Command structure rules • FORTRAN 77 (and earlier versions) had a fixed-column method of structuring commands. • Later versions of FORTRAN allow free-format. • Since the fixed format is so common in FORTRAN we will start out writing our programs that way.

4. Column-based (fixed) structure (f77) 12345678901234567890123456789012345678901234567890123456789012345678901234567890 FORTRAN programs were originally punched on cards. Modern FORTRAN still supports the conventions that were used in that day. For example, every FORTRAN command must obey the following set of rules. Column 1: reserved for comment marks only. Valid comment marks are c, C or * in f77, f90 adds ! Columns 2-5: reserved for statement labels. These are integers used to mark a line so that other statements can get back to it. They are labels, not line numbers. Column 6: reserved for a continuation mark (either a + or a single digit integer 1,2,3,4..etc. These indicate that the line is a continuation of the previous one. Columns 7-72: Your executable FORTRAN statements go here Columns 73-80: For line sequence numbers. Not used any more.

5. Column-based structure (f77) 12345678901234567890123456789012345678901234567890123456789012345678901234567890 c this is a comment line, comments start in column 1 c * Either a c, C or * may be used to indicate a comment c *********************************************************************** INTEGER i PRINT *, “This long line continues on the next one. To indicate this I place a + in column 6 (the continuation column)” DO 10 (i=1,10) PRINT*, “Hello world!” 10 CONTINUE END +

6. Elementary FORTRAN 77 • All FORTRAN programs consist of data that is manipulated by a set of control structures to produce a result. • Control structures are statements that implement the algorithm steps you have chosen when you designed the program. • Data + algorithms = programs

7. Program structure • First you should put in comments • Then specify to the compiler what data items (variables) you program will need. • Give each a name • Tell what type of data it is • Specify how many (if more than 1) • Then perform the executable statements that act on the data to produce results.

8. Program structure Comments c This is a demo program c by me c integer num print*, “Enter a number” read*, num print*, “The number you entered is:” print*, num end Specification (variable declaration) Execution

9. Basic data types • These are the data types supported by standard FORTRAN • integers • real numbers • double precision (f77 only) • complex (f90 only) • character • logical

10. Integers • NOT intergers! • Integers consist of positive or negative whole numbers or 0 • …,-2, -1, 0, 1, 2, … • Declared as • INTEGER num (in f77 or f90) • INTEGER :: num (in f90, preferred)

11. Binary representation of integers 128 64 32 16 8 4 2 1 0 1 0 0 0 0 0 1 64 + 1 = 65 This is an 8-bit byte most PCs use 32 bit words (4 bytes) Often the first bit is a sign bit.

12. Sign bits 128 64 32 16 8 4 2 1 0 1 0 0 0 0 0 1 The first bit may be used as a sign bit and therefore unavailable to represent integers. This cuts the capacity for representing large integers in half (from 256 to 128).

13. Real numbers • Any number that might have a decimal point. • 3.14159, 4.0, -234.56 • If you enter a real number without a decimal point, one will be inserted automatically. (4 becomes 4.0)

14. Binary representation of real numbers 100101000100001001001110000010010 00101101011000100110000100100 mantissa exponent 31,254,355,218 7,324,645,336 x 10

15. Scientific notation • Often called exponential notation • 12345.6789 becomes • 12.3456789E3 (x 1000) • 1.23456789E4 (x 10000) • 0.123456789E5 (x 100000) • 123456789E-4 (x 0.0001)

16. For all numeric data • DO NOT include punctuation in input • Please enter a number • 1,234 is incorrect • $1234 is also incorrect • Real numbers can take integers but not vice versa. • Please enter a real number • 1234 is OK • Please enter an integer • 123.45 is incorrect

17. Double precision • Doubles the representational size of a real number. • Not used under FORTRAN 90 but common under FORTRAN 77 for some applications. • We will probably not need it.

18. Complex numbers • Contain both a real and an imaginary part. • This is not a standard data type in any other computer language. • Not supported in f77 • More on this later.

19. Character data • Much easier to handle in FORTRAN than in most other languages (Pascal, C, C++, etc.) • Valid characters are all standard ASCII and UNICODE characters • Character strings are enclosed in “” • “This is a line” • Above string has length of 14 (spaces count)

20. Special cases • Apostrophes work the same as quotes • ‘This is a sentence’ • but you cannot mix them: • ‘This is a sentence” • How do you handle embedded apostrophes or quotes? • ‘don’’t’ • “I said “”Hi””” • use two sets to produce one character

21. Character declarations • In FORTRAN 77 • Character *10 name • Character fname*10, lname*20 • In FORTRAN 90 • Character(10) :: name • Character(10) :: name, lname*20

22. Logical data • Logical means true or false • We will use logical data later in the course and spend more time on it then.

23. Mixed types • Some types can be mixed • REAL num1 • INTEGER num2 • num2 = 5 • num1 = num2 • Others cannot • character*10 name • num1 = name

24. Variable declarations • When a variable is declared you give the name and data type of the variable. • The compiler figures out the size that will be required. • If you use a variable in your program that you forgot to declare, the compiler has assigned it a type: integer or real • This assignment may not be appropriate

25. Implicit data type rule • Any variable that has not been declared and begins with the letters i through n automatically becomes an integer. • Variables beginning with any other character automatically become real numbers.

26. Implicit data typing problem • INTEGER sum, n • … program reads data, stores the count of how many in n and the total of them in sum • mean = sum / n • Since mean was not declared it becomes an integer. This is probably not what you want here.

27. Uses for implicit data typing • Loop control variables are variables that only exist to count the number of time a loop has executed. • They should be integers • A very common convention is to use the undeclared variables i, j, k, l, m and n for loop control variables because implicit typing makes them integers by default.

28. Turning off implicit typing • Most programming languages regard implicit typing as dangerous. • If it is turned off, then all variables must be explicitly declared by you. • f77 does not allow you to turn this off but f90 does. Like this… • IMPLICIT NONE • This command is placed at the top of the executable program statements.

29. The important points • When a variable is declared, three things happen. • 1. Space to store your data is allocated in memory • 2. That space is assigned a data type • 3. That space is assigned a name

30. Memory allocation Memory cells 1345243 1345244 1345245 1345246 1345247 1345248 1345249 1345250 1345251 1345252 1345253 1345254 1345255 REAL length, angle, period Variable declaration first must find available memory cells to store this data in. It then allocates them for the program and assigns your identifier names to them.

31. Memory allocation Memory cells 1345243 1345244 1345245 1345246 1345247 1345248 1345249 1345250 1345251 1345252 1345253 1345254 1345255 REAL length, angle, period length angle period

32. Identifiers • So, now that we are familiar with the built-in data types of this language, what do we do with them? • We will solve problems using data items that are of these basic types. • These items will be given names. • In fact, we will have to give names to many things in our programs. • Names are called identifiers

33. Naming conventions • Identifiers • must begin with a letter • cannot be longer than 31 characters (8 is the common standard practice in f77) • Only letters, digits or underscores (_) are allowed.

34. Valid and invalid identifiers • Valid identifiers • number, s1, name, speed_of_light • Invalid identifiers • 1stnum, soc-sec-num • A good rule of thumb is to keep the identifier names short and concise. • name, employee, id_num (good) • employee_name (too much typing?) • the_first_number_entered_by_the_user

35. Variable initialization • Initialization refers to the act of assigning a value to a variable. • Example: • integer num • num = 10 • The = sign is called the ‘assignment operator’ • Do not think of it as ‘equal to’. It really means assign the right-hand value to the left-hand variable

36. Constants • A constant is a data item whose value never changes after initialization. • Use the parameter statement • f77 • parameter (pi = 3.14159, g = 980) • f90 • real, parameter :: pi = 3.14159, g = 980

37. Mathematical expressions • FORTRAN comes from the phrase FORmula TRANslation • Coding mathematical formulas is an important part of the language. • Example: • y = a * x + b • The expression on the right is evaluated and the result is assigned to the variable on the left.

38. Arithmetic operators • In order to carry out mathematical expressions the computer must understand what operations to perform. • This means it needs to know a set of arithmetic symbols, what operations they stand for and which ones should be done before others.

39. Arithmetic Operators • ** exponentiation a = 2**3 • * multiplication a = 2 * 3 • / division a = 2 / 3 • a = 2 / 3.0 • a = 2 / real(3) • + addition a = 2 + 3 • - subtraction a = 2 - 3

40. Mixed mode expressions • Mixed mode expressions combine more than one data type. • Example: • a = 4 + 7 / 2 * 3 - 7 • a = 14/5.0 + 4 • Watch out for integer division! • Group expressions using parentheses rather than guessing about what will happen.

41. Integer division • An integer divided by an integer IS AN INTEGER • integer a • a = 14 / 3 • PRINT*, a • The output from this is 4 • not 4.666667 as you might expect

42. Precedence (priority) rules • Exponentiation is performed first. Multiple exponentiation is performed right to left. • A = 2 ** 3 ** 2 is same as a = 2 ** 9 • a = 5 - 3 ** 3 a becomes -22 • Multiplication and division are next. If more than one, go left to right. • Addition and subtraction are last. If more than one, go left to right.

43. Examples • 2 + 4 ** 2 / 2 • 2 + 16 / 2 • 2 + 8 • 10

44. Example • 5 * 11 - 5 ** 2 * 4 + 9 • 5 * 11 - 25 * 4 + 9 • 55 - 25 * 4 + 9 • 55 - 100 + 9 • -45 + 9 • -36

45. Example with parentheses • (5 * (11 - 5) ** 2) * 4 + 9 • (5 * (6) ** 2) * 4 + 9 • (5 * 36) * 4 + 9 • (180) * 4 + 9 • 720 + 9 • 729

46. Expression trees • 4 - 7 ** 2 / 4 * 3 + 2 49 12 36 -32 -30

47. Functions • INT( arg ) integer - drops fraction • NINT ( arg ) integer - rounds arg • REAL ( arg ) converts to real • ABS ( arg ) absolute value - real • IABS ( arg ) absolute value - integer • SQRT ( arg ) square root

48. Functions • EXP (arg) natural exponent e^arg • ALOG (arg) natural logarithm • ALOG10 (arg) logarithm • SIN (arg) arg in radians • COS (arg) arg in radians • TAN (arg) arg in radians

49. Functions • MOD (A1, A2) remainder of A1/A2 • MAX0 (A1,...An) largest value - integer • AMAX1 (A1,...An) largest value - real • MIN0 (A1,...An) smallest value - integer • AMIN1 (A1,...An) smallest value - real

50. Examples of function use • Calculate the volume of an oblate spheroid. The formula is: • V = (4/3)a b • Fortran version • parameter (pi = 3.14159) • v = (4/real(3))*pi*a**2*b 2