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Understanding Data Types and Arithmetic Operations in Fortran

Learn about data types in Fortran, arithmetic errors, operations, functions, testing tips, file I/O, and more. Covering integer, real, double precision, complex, strings, logical values, and arithmetic functions.

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Understanding Data Types and Arithmetic Operations in Fortran

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  1. CS1001 Lecture 5 • Completion of Lecture 4 • Talked about Data Types & Arithmetic Errors • Continue with Operations and Functions • Program Testing Tips • File Input and Outputs

  2. Data Types In Fortran • Integer (0, 137, -2516, +17745) • Real or Single Precision (0.0, -0.01536, 123.4, 1.234E2, -1.536E-2) • Double Precision (1.234D-6, 0.1111111D3) • Complex (3+4i) • Character Strings (‘A’, ‘JOHN DOE’) • Logical (.TRUE., .FALSE.)

  3. Arithmetic Operations Binary Unary + Addition + positive - Subtraction - negative * Multiplication e.g., 5.0 ** (-1) / Division ** Exponentiation Precedence Rules: 0. Parenthesis 1. Exponentiation, right to left 2. Multiplication and Division, left to right 3. Addition and subtraction, left to right

  4. Operations • Operations result in same type as operands 6/5 = 1 integer operation (Division of integers produces an integer) 6.0/5.0 = 1.2 • Mixed-Mode expressions -- combine integer and real data e.g. 1.0/4 => 1.0/4.0 => 0.25 3.0+8/5 => 3.0+1 => 3.0+1.0 => 4.0 3.0+8.0/5 => 3.0+1.6=>4.6 • Generally poor practice

  5. Assignment Statement variable = expression e.g., Height = 0.5*acceleration*time**2 & + initialvelocity*time+initialheight Velocity=acceleration*time+initialvelocity • NOT an algebraic equality, but a replacement statement sum = sum + x means add the value of x to the value of sum and store the result in sum.

  6. Arithmetic Functions • Perform standard operations on variables which are referenced as an argument • Standard arithmetic functions do not have to be declared, merely used (see page 60 of text) • Examples: COS(X), SQRT(X), LOG(X) PROGRAM MiddleOfRange Print *, “enter 10 measures” Read *, x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 MidRange= ( MAX(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) + & MIN(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10) ) / 2. Print *, “Mid Range is ” , MidRange END PROGRAM MiddleOfRange

  7. PROGRAM QuadraticEquations_1 !------------------------------------------- ! Program to solve a quadratic equation ! using the quadratic formula. ! Variables used are: ! A, B, C : the coefficients of ! the quadratic equation ! Discriminant : the discriminant, ! B**2 - 4.0*A*C ! Root_1, Root_2 : the two roots of the ! equation ! ! Input: The coefficients A, B, and C ! Output: The two roots of the equation or ! the (negative) discriminant and a ! message indicating that there are ! no real roots !---------------------------------------------

  8. IMPLICIT NONE REAL A, B, C, Discriminant, Root_1, Root_2 ! Get the coefficients PRINT *, "Enter the coefficients of the & &quadratic equation:" READ *, A, B, C ! Calculate the discriminant Discriminant = B**2 - 4.0*A*C

  9. Preview of next lecture Control flow Sequential execution Statement_1 Statement_1 Statement_2 If . . . Statement_n Statement_2 Statement_3 Statement_4

  10. ! Check if discriminant is nonnegative. If ! it is, calculate and display the roots. ! Otherwise display the value of the ! Discriminant and a no-real-roots message. IF (Discriminant >= 0) THEN Discriminant = SQRT(Discriminant) Root_1 = (-B + Discriminant) / (2.0 * A) Root_2 = (-B - Discriminant) / (2.0 * A) PRINT *, "The roots are", Root_1, Root_2 ELSE PRINT *, "Discriminant is", Discriminant PRINT *, "There are no real roots" END IF END PROGRAM QuadraticEquations_1

  11. Consider Hungarian Notation • iName for INTEGER variables/constants • rName for REAL • dName for DOUBLE PRECISION • xName for COMPLEX • cName for CHARACTER strings • bName for LOGICAL (boolean) • Constants are all caps except type (rVAL)

  12. Simple List-Directed Output • PRINT *, output-listwhere output-list is: • output-list can contain multiple items • A constant such as ‘ENTER TIME’ • A variable such as OUTPUT • A formula or function such as SQRT(INP) • The “*” indicates that the output format is free-form, or whatever the memory holds for that value, which may be truncated • e.g., PRINT *, ‘Square root of ’, x, ‘ = ’, SQRT(x) Square root of 4.00 = 2.00

  13. Simple List-Directed Input • READ *, input-list, where input-list is: • A variable or variables • The user should be prompted for all inputs with a PRINT statement, and units and/or ranges should also be specified to the user inputing the data

  14. File I/O (Input/Output) • So far, free form READ and PRINT -- input from keyboard and output to display • For input and output of larger amount of data, file I/O may be used. • First, must let computer know what the files are: OPEN (UNIT=unit_number,FILE=file_name,STATUS=status) unit_number is an integer to be used by READ and WRITE file_name is string of the name of file status is string “OLD” for existing files or “NEW” for new file e.g., OPEN(UNIT=10,FILE=“input_data”,STATUS=“OLD”) OPEN(UNIT=11,FILE=“out_data”,STATUS=“NEW”)

  15. File I/O • Input READ (unit_number,*) input_list unit_number is digit specified in OPEN statement e.g., File input_data contains three resistance values and one voltage value 1.0, 1.0, 1.0 6.0 OPEN(UNIT=10,FILE=“input_data”,STATUS=“OLD”) …. READ(10,*) resistance_1, resistance_2, resistance_3 READ(10,*) voltage

  16. File I/O • Output WRITE (unit_number,*) output_list unit_number is digit specified in OPEN statement e.g., File “current_data” is the output file OPEN(UNIT=11,FILE=“current_data”,STATUS=“NEW”) …. WRITE(11,*) “The current is”, current, “amps” File current_data is created and contains the line The current is 18.0000000 amps

  17. PROGRAM Projectile_2 !------------------------------------------------ ! This program calculates the velocity and height ! of a projectile given its initial height, ! initial velocity, and constant acceleration. ! Identifiers used are: !InitialHeight:initial height of projectile (meters) !Height :height at any time (meters) !InitialVelocity : initial vertical velocity (m/sec) !Velocity :vertical velocity at any time (m/sec) !Acceleration:constant vertical acceleration ! (m/sec/sec) !Time : time since launch (seconds) ! ! Input (file): InitialHeight, InitialVelocity, Time ! Output (file): Velocity, Height !-----------------------------------------------------

  18. Specification IMPLICIT NONE REAL :: InitialHeight, Height, InitialVelocity, & Velocity, Time REAL, PARAMETER :: Acceleration = -9.80665 ! Open disk files FIG2-6.DAT and FIG2-6.OUT OPEN(UNIT = 12, FILE = "FIG2-6.DAT", STATUS = "OLD") OPEN(UNIT = 13, FILE = "FIG2-6.OUT", STATUS = "NEW") ! Read values for InitialHeight, InitialVeloc, ! and Time READ (12, *) InitialHeight, InitialVelocity, Time ! Calculate the height and velocity Height = 0.5 * Acceleration * Time ** 2 & + InitialVelocity* Time + InitialHeight Velocity = Acceleration * Time + InitialVelocity Execution

  19. ! Write values of Time, Velocity, and Height ! to FIG2-6.OUT WRITE (13, *) "At time", Time, "seconds" WRITE (13, *) "the vertical velocity is", & Velocity, "m/sec" WRITE (13, *) "and the height is", Height, "meters" ! Signal user that program is finished PRINT *, "*** Program is finished ***" END PROGRAM Projectile_2

  20. Arithmetic Errors • Overflow and underflow errors • 8 bit exponent restricts range to about 38 to -38 10**(-38) -10**38 -10**-38 0 10**38 overflow overflow underflow

  21. Roundoff errors • Due to binary representation and finite number of bits (A+B)+C = (1000. + 0.4)+0.3 = 1000.7 (A+B) => 1000. + 0.4000 => 1000. The result of (A+B) added to C => 1000. + 0.3000 => 1000. A + (B+C) = 1000. +( 0.4000 +0.3000) (B+C) = .4000 + .3000 => .7000 Add A to (B+C) => 1000. + .7000 => 1001. (rounding up) (A+B) + C = A + (B+C)

  22. Program Testing Tips • Boundary/bounds check all inputs • 1-100 input range, check 1, 100, 101, 0 • Check upper and lower case if applicable • Quadrant test in all four quadrants • 45, 135, 225, 315 degrees • Type test data inputs • Enter 10.5 for an INT, 56 for a REAL, etc. • Have someone else test your program, and reciprocate

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