04-arithmetic_operations

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CE 311 K - Introduction to

Computer Methods

Arithmetic Operations and

Intrinsic Functions



Assignment Statements

Assigns a value to a variable

vari abl e=const ant, arithmetic expression, or string

When a variable has not yet been assigned a value in the program, it is

said to be ³undefined´.

After the first value is assigned, the variable is said to be ³initialized´.

A variable can only store one value or string at a time. If a new value or

string is assigned to the variable after it is first initialized in a program,

the new value replaces the old one.



Character Strings

ExampleCHARCTER (LEN=6):: STATE49, STATE50

STATE50=µHAWAII¶

STATE49=µMICHIGAN´

When a variable does not yet have a value, it is said to be ³undefined´

Rules: ± If the declared length and the string size are the same, all characters are

stored in the character variable

± If the declared length is longer than the string, then blank ³padding´ will beadded to the right of the string to equalize the lengths.

± If the declared length is shorter than the string length, the string is truncated.

± No arithmetic operations

± So what is stored for STATE50 and STATE49?



Arithmetic Expressions

All ( ) are evaluated first. Innermost () are evaluated first in

expressions that contain nested ( ).

Operator Precedence1. exponentiation (**)

2. multiplication and division (*,/)

3. addition and subtraction (+,-) : Can be used as a sign, but standard

Fortran 90 does not allow two operands to appear side by side

Left Associative: Operators at the same precedence level are evaluated

from left to right, but consecutive exponentiation operators are

evaluated from right to left.

No division by zero or raising a zero value operand to a negative orzero valued ower.



Truncation vs. Rounding

Truncation: When computer stores a realnumber in an integer variable, it ignores thefractional portion and stores only the wholenumber portion of that real number.

e.g.) If Integer = 3.75, then Integer = 3

Rounding: The approximation of a real

number to an integer closest in value to thethat real number when writing to an output.

e.g.) If Real = 3.75 (F4.0), then Real = 4.e.g.) If Real = 3.75 (F4.1), then Real = 3.8



Mixed-mode Operation

The result of an operation involving two integer

numbers is an integer number.

e.g.) MEAN= (N1+N2)/2

If N1= 2 and N2= 3, then MEAN = 2

The result of an operation involving two real

numbers is a real number.

e.g.) AVE= (N1+N2)/2.0If N1= 2.0 and N2= 3.0, then AVE = 2.5

If N1= 2 and N2= 3, then AVE = 2.5 (= 5/2.0)



Mixed-mode Operation

Mixed-mode operation is an operation

involving both an integer value and a real

value. The intermediate results is a realvalue.

e.g.) P E R IM= 4×SIDE

If SIDE =2.2, then P

E R

IM = 8.8e.g.) ROOT = NUM**0.5

If NUM = 9, then ROOT = 3.0



A Case where Mixed-mode Operation is

Desired

A R EA=SIDE**2

Calculated as

SIDE×SIDE

If SIDE = 5.0, then

A R EA= 25.0

A R EA=SIDE**2.0

Performed by arithmetic

logic unit (ALU) using³logarithm.´

Calculated as

antilog(2.0×log( SIDE ))

If SIDE = 5.0, then A R

EA= 24.99999 (small error

introduced with logarithm)



Another Case where Mixed-mode

Operation is Desired

(-2.0)**2 is a valid

operation.

Performed as:

(-2.0)*(-2.0)= 4.0

(-2.0)**(2.0) is not a

valid operation.

Performed as:

antilog(2.0×log(-2.0))

Does not exist!



A Case where Mixed-mode Operation is

NOT Desired

V OLUM= (4/3)*3.14159* R**3

Final result (V OLUM ) will be a real

number.

Intermediate result of (4/3) is an integer

number (4/3= 1 but not 1.3333)

Solution: useV OLUM=(4.0/3.0)*3.14159* R**3 instead



Intrinsic Functions

³Built-in´ module of code provided with theFortran compiler

Certain operations that are used frequently

variable=NAME OF FUNCTION(argument)

± Argument can be a constant, variable, or expression

± Separate arguments by commas if there is morethan one

± Some functions are generic, others are data typespecific

± Can nest functions, but enclose in parentheses

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