1. Basic Scientific Programming
Computer Arithmetic
Eyad Taqieddin
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2. Arithmetic Operations and Functions
Operator
Operation
Fortran Notation
+
Addition,Unary Plus
a+b , +b
-
Subtraction,Unary
Minus
a-b , -b
*
Multiplication
a*b
/
Division
a/b
Exponentiation
a**b
**
Eyad Taqieddin
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3. Integer Arithmetic




Int
Int
Int
Int
+ Int = Int
- Int = Int
* Int = Int
/ Int = Int
5+2=7
5 -2=3
5 * 2 = 10
5 / 2 = 2 why?
Division is a special case, because the result
must be an integer. So, the fraction part is
truncated, and only the integer is stored.
Eyad Taqieddin
3

4. Example
what is the result of the following?
1) program example
Implicit none
Real :: x= 2.0 , y
Integer :: n = 2, j
y= 1/x
j= 1/n
print *, ‘y=‘ , y
print *, ‘j=‘, j
end program example
Eyad Taqieddin
4

5. Priority Rules
1) Parenthesis
2) All exponentiations are performed first, consecutive
exponentiations are performed from right to left.
3) All Multiplications and divisions are performed next,
in the order in which they appear from left to right.
4) The additions and subtractions are performed last,
in the order in which they appear from left to right.
Eyad Taqieddin
5

6. Example

2**3**2 = 2**9 = 512

10-8-2 = 2 – 2 = 0

2+4/2 +5**3 = 2+ 4/2+125=2+2+125
= 129
Eyad Taqieddin
6

7. Example


((-b) + sqrt( B**2 – 4*a*c))/(2*a)
((-b) + sqrt( B**2 – 4*a*c))/2*a
do u think these expressions are equal??
Eyad Taqieddin
7

8. Mixed Mode Expressions
Expressions that involve different types of
numeric operands
Int + Real = Real
Int - Real = Real
Int * Real = Real
Int / Real = Real
The integer value is converted to its real
equivalent.
Eyad Taqieddin
8

9. Example



2.0/5  2.0/5.0  0.4
3.0 + 6/4  3.0 + 1  3.0 +1.0  4.0
3.0 + 6.0/4 3.0+ 6.0/4.0  3.0 +1.5
 4.5
from the second and third expressions we see
why it is not a good programming practice to
use mixed mode operations.
Eyad Taqieddin
9

10. Functions
Fortran provides library functions for many
mathematical operations and functions.
Ex:
ABS(X) returns the absolute value of X
Sqrt(X) returns the square root of X
Sin(X) returns the sine of X radians
Eyad Taqieddin
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11. The Assignment Statement
Form
Variable = Expression


Variable is a valid Fortran identifier.
Expression may be a constant, another
varialble to which a value has previously been
assigned or a formula to be evaluated.
Eyad Taqieddin
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12. Example



Length = 6
assigns the value 6 to the memory location length.
C= x**2 + 5*x + 7
calculates the expressions (x**2 + 5*x + 7) and
assigns the result to the memory location C.
Salary = Salary + 1000
adds the value 1000 to the value stored in the
memory location salary and then stores the result in
the same memory location.
The previous value of salary is lost.
Eyad Taqieddin
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13. Integer Vs. Real


If an integer-valued expression is assigned to a real
variable, the integer value is converted to a real
constant and then assigned to the variable.
temp = (6+2)/4 “assuming temp is real”
temp will be assigned the value 2.0 not 2
If a real-valued expression is assigned to an integer
variable, the fractional part is truncated and the
integer part is assigned to the variable.
temp = 2.36 / 2 “assuming temp is integer”
temp will be assigned the value 1 not 1.18
Eyad Taqieddin
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