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Elementary FORTRAN 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 Command structure rules FORTRAN 77 (and earlier versions) had a fixed-column method of structuring commands. Later versions of FORTRAN allow freeformat. Since the fixed format is so common in FORTRAN we will start out writing our programs that way. 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. 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 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 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. Program structure Comments Specification (variable declaration) Execution c c c This is a demo program by me integer num print*, “Enter a number” read*, num print*, “The number you entered is:” print*, num end Basic data types These are the data types supported by standard FORTRAN integers real numbers double precision (f77 only) complex (f90 only) character logical 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) 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. 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). 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) Binary representation of real numbers 100101000100001001001110000010010 00101101011000100110000100100 exponent 7,324,645,336 x 10 mantissa 31,254,355,218 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) 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 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. 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. 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) 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 Character declarations In FORTRAN 77 Character *10 name Character fname*10, lname*20 In FORTRAN 90 Character(10) :: name Character(10) :: name, lname*20 Logical data Logical means true or false We will use logical data later in the course and spend more time on it then. Mixed types Some types can be mixed REAL num1 INTEGER num2 num2 = 5 num1 = num2 Others cannot character*10 name num1 = name 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 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. 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. 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. 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. 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 Memory allocation Memory cells 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. 1345243 1345244 1345245 1345246 1345247 1345248 1345249 1345250 1345251 1345252 1345253 1345254 1345255 Memory allocation Memory cells REAL length, angle, period length angle period 1345243 1345244 1345245 1345246 1345247 1345248 1345249 1345250 1345251 1345252 1345253 1345254 1345255 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 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. 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 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 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 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. 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. Arithmetic Operators ** exponentiation * multiplication / division + addition - subtraction a = 2**3 a=2*3 a=2/3 a = 2 / 3.0 a = 2 / real(3) a=2+3 a=2-3 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. 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 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. Examples 2 + 4 ** 2 / 2 2 + 16 / 2 2 + 8 10 Example 5 * 11 - 5 ** 2 * 4 + 9 5 * 11 - 25 * 4 + 9 55 - 25 * 4 + 9 55 100 + 9 -45 +9 -36 Example with parentheses (5 * (11 - 5) ** 2) * 4 + 9 (5 * (6) ** 2) * 4 + 9 (5 * 36) * 4 + 9 (180) * 4 + 9 720 + 9 729 Expression trees 4 - 7 ** 2 / 4 * 3 + 2 49 12 36 -32 -30 Functions INT( arg ) NINT ( arg ) REAL ( arg ) ABS ( arg ) IABS ( arg ) SQRT ( arg ) integer - drops fraction integer - rounds arg converts to real absolute value - real absolute value - integer square root Functions EXP (arg) ALOG (arg) ALOG10 (arg) SIN (arg) COS (arg) TAN (arg) natural exponent e^arg natural logarithm logarithm arg in radians arg in radians arg in radians Functions MOD (A1, A2) MAX0 (A1,...An) AMAX1 (A1,...An) MIN0 (A1,...An) AMIN1 (A1,...An) remainder of A1/A2 largest value - integer largest value - real smallest value - integer smallest value - real Examples of function use Calculate the volume of an oblate spheroid. The formula is: 2 V = (4/3)a b Fortran version parameter (pi = 3.14159) v = (4/real(3))*pi*a**2*b Other examples Algorithm if num goes into 100 evenly then … Fortran version if (MOD(100, num) .eq. 0) then MOD MOD stands for modulo It is a mathematical term used to denote the integer remainder from integer division. In other words, mod takes two integer arguments. It then divides the first one by the second and finds the integer remainder. This integer remainder is what MOD sends back to the program. MOD in action PRINT*, MOD(14,3) will print the value 2 3 goes in to 14 four times with 2 left over 2 is the integer remainder from integer division. 4r2 3 14 12 2 Examples continued a = SQRT(b) b cannot be negative t = TAN(angle) angle must be in radians i = INT(4.7) sets i to 4 i = NINT(4.7) sets i to 5 Note: to use SIN, COS, TAN, you must convert the angle from degrees to radians. This is done by multiplying the angle by pi and then dividing by 180. Integer division and MOD This example will construct a program to determine the smallest number of coins to dispense as change. Useful if you are a vending machine. Rules: amount of change is always < $1.00 valid coins are quarters, dimes, nickels, pennies Alogorithm 1. 2. 3. 4. 5. 6. Declare variables Prompt for amount of change to give back Read amount Figure out how many quarters can be taken out of it Subtract the quarters from the amount Figure out how many dimes can be taken out of the remaining amount 7. Subtract the dimes from the amount 8. Figure out how many nickels can be taken out of the remaining amount 9. Subtract the nickels from it and all you have left are the number of pennies 10. Add up the number of quarters, dimes, nickels and pennies you took out to get the number of coins 11. Print out the number of coins. 12. END Program example: Vending machine change c c This program figures out the fewest number of coins to dispense as change in a vending machine INTEGER amount, coins, numq, numd, numn, nump PRINT*, “How much change should you give? <$1” READ*, amount numq = amount / 25 amount = MOD(amount, 25) numd = amount / 10 amount = MOD(amount, 10) numn = amount / 5 nump = MOD(amount, 5) coins = numq + numd + numn + nump PRINT*, “The machine will dispense”, coins, “coins” END Trace of vending machine program: statement numbering 1 2 3 4 5 6 7 8 9 10 11 12 INTEGER amount, coins, numq, numd, numn, nump PRINT*, “How much change should you give? <$1” READ*, amount numq = amount / 25 amount = MOD(amount, 25) numd = amount / 10 amount = MOD(amount, 10) numn = amount / 5 nump = MOD(amount, 5) coins = numq + numd + numn + nump PRINT*, “The machine will dispense”, coins, “coins” END Trace of 99 cents 1 2 3 4 5 6 7 8 9 10 11 12 Declare vars. Prompt for amount Read amount Compute # of quarters Compute new amount Compute # of dimes Compute new amount Compute # of nickels Compute # of pennies Add up coins print results END amount coins numq numd numn nump ? ? ? ? ? ? 99 3 24 2 4 0 4 9 Assignment statements Assignment statements are the very heart of this, and all, computer languages. They assign a value to a variable Example: angle = angle * pi / 180 The assignment operator (=) Assigns the value on the right hand side of the = to the location on the left. Do not think of it as ‘equals’ Think of it as ‘assigns’ or ‘is set to’ Example: count = count + 1 (see next slide) The nature of assignment The rvalue is put into the left-hand location (a variable) UMDid = 2123456 UMDid 2123456 The nature of assignment DO NOT read = as ‘equals’ or you will encounter algebraic nonsense. Count = Count + 1 5 = 5 + 1 Count 5 Count 6 6 Mixed mode assignments If an integer is assigned to a real variable it becomes a real If a real is assigned to an integer you will get an error message. Be careful to only assign data of the correct type Input statements: READ The READ statement gets it’s input from the keyboard. Later in the semester we will learn how to read data from files. The format is READ*, var1, var2, var3 The * simply means ‘use the default method of getting data from input Output statements: PRINT To print a message on the screen use the PRINT statement. To write your output to a file use the WRITE statement (covered later in the semester) PRINT*, var1, var2, var3 The *, indicates that you are printing to the default output device PRINT considerations You may print the contents of a variable or character strings or both. PRINT*, “Please enter an integer” READ*, num PRINT*, num PRINT*, “You entered”, num PRINT*, “num is: “, num, “cm” Output control Unfortunately, right now we cannot control what happens with our output very well. Num is 4.00000 Later we will learn how to control everything (like the number of decimal points, etc.) Files Chapter 2, section 10 deals with files. We will not do this until much later in the course.