1. 21 March, 2000 CS1001 Lecture 4 Data Types + Algorithms = Programs Data Types & Arithmetic Errors Arithmetic Operators and Functions Program Testing Tips

2. 21 March, 2000 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. 21 March, 2000 INTEGER Data Type Limited to computer word size For a 16-bit word size: 0111111111111111 = 2 15 - 1 = 32767 1000000000000000 = -2 15 = -32768 For a 32-bit word size 2 31 - 1 = 2147483647 -2 31 = -2147483648

4. 21 March, 2000 REAL or Single Precision Data Separated into two parts: –Mantissa, or fractional part (24 bits of 32) –Exponent, or magnitude part (8 bits of 32) First bit of each part reserved for sign Overflow -- too large an exponent Underflow -- too small an exponent Range is approximately 10 -38 to 10 +38 Approximately 7 significant digits

5. 21 March, 2000 REAL Type (cont’d) Sometimes, the internal representation of REAL is not accurate enough e.g., 1.00/.1254 1.00e00/1.25e-01 = 8.00e00 instead of 7.97e00 Cumulating of these roundoffs errors can affect final results.

6. 21 March, 2000 DOUBLE Precision Data Type Instead of using one word, use two words. Separated into two parts: –Mantissa, or fractional part (instead if about 7 significant digits, you can have about 14) –Exponent, or magnitude part –Machine dependent First bit of each part reserved for sign Overflow -- too large an exponent Underflow -- too small an exponent

7. 21 March, 2000 Arithmetic Error Disaster Time in system’s internal clock was measured in tenths of seconds. System used 24 bits. 1/10 = 1/2**4+1/2**5+1/2**8 +… = 0.0001100110011001100110011001100… with 24 bits, 1/10 = 0.00011001100110011001100 error of 0.0000000000000000000000011001100... which is about 0.000000095 decimal In 100 hours, error = 0.000000095*100hr*60min/hr*60sec/min*10 = 0.34sec

8. 21 March, 2000 Arithmetic Error Disaster A Scud travels at about 1676 meters/sec 0.34 sec * 1676 meters/sec = 570 meters Patriot missile miss the Scud !

9. 21 March, 2000 COMPLEX Data Type Unique to Fortran Complex numbers are represented as a pair of real numbers -- (a, b) First number is the “real” part Second number is the “imaginary” part (6.2, 2.4) means 6.2 + 2.4i

10. 21 March, 2000 CHARACTER Data Type Has a specific length associated with it Default is length 1 (single character) Denoted by “ ” or ‘ ’ –“CS1001” character string of 6 characters long –‘All of you are super programmers’ Usually ASCII encoded which is only 7 bits, but stores as 8 bits –“A” is decimal 65 or 41 hex, and “a” is decimal 97 or 61 hex

11. 21 March, 2000 LOGICAL Data Types Boolean variables, or flags, 1-bit data Value is either.TRUE. or.FALSE. or more accurately, 0 or 1 Used for binary choices –True or False –Set or Clear –Yes or No

12. 21 March, 2000 Data Declaration Within the program “specification” part Uses type statement consisting of: –type-specifier –list type-specifier is INTEGER, REAL, COMPLEX, CHARACTER(n) where n is the number of characters to be stored in identifier, or LOGICAL list is a list of identifiers INTEGER:: Numvalues, Factorial, Sum CHARACTER(6) :: classnumber classnumber = ‘CS1001’

13. 21 March, 2000 Identifiers & Variables Identifiers are used to identify programs, constants, variables, and other entities. Variables are used to store computed values Constants are used to store fixed values Constants cannot be changed within a program If a value must change from an initial value, declare the variable, initialize it to an initial value, then change that value within the program where needed

14. 21 March, 2000 Named Constants The PARAMETER statement declares the variable as a constant and associates each specified constant with a constant value: –INTEGER, PARAMETER :: iLimit = 50 –REAL, PARAMETER :: PI = 3.14159 –or REAL, PARAMETER :: rPI = 3.14159

15. 21 March, 2000 Variable Initialization Data type and identifier (name) must first be declared with a type statement The DATA statement is no longer used Use an assignment statement for each variable: INTEGER :: iYear REAL :: rBodyTemperature iYear = 1997 rBodyTemperature = 98.6

16. 21 March, 2000 Arithmetic Operations BinaryUnary +Addition+positive -Subtraction-negative *Multiplicatione.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 Height = 0.5*acceleration*time**2 & + (initialvelocity*time)+initialheight

17. 21 March, 2000 Operations Operations result in same type as operands 6/5 = 1 integer operation 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

18. 21 March, 2000

19. Arithmetic Functions Perform standard operations on variables which are referenced as an argument Standard arithmetic functions do not have to be declared, merely used Examples: COS(X), SQRT(X)

20. 21 March, 2000 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.

21. 21 March, 2000 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)

22. 21 March, 2000 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