An arithmetic expression is one which is evaluated by performing a sequence of arithmetic operations to obtain a numeric value, which replaces the expression. Arithmetic operations are denoted by the following arithmetic operators
Operator Operation + Addition or unary + - Subtraction or unary - * Multiplication / Division ** Exponentiation
Figure 4 : Arithmetic operators
An operand of an arithmetic expression may be:
An arithmetic expression has the form:
operand [operator operand] ...
The square brackets indicate that the items operator operand are optional and the ellipsis (...) that they may be repeated indefinitely.
Spaces may be used to improve readability, but are ignored by the FORTRAN compiler.
3.14159 K (A+B)*(C+D) -1.0/X + Y/Z**2 2.0 * 3.14159*RADIUS
Example: A*-B is illegal. The second factor must be made into an expression by using parentheses, viz: A*(-B).
An arithmetic expression is evaluated by replacing variable operands and parenthesised expressions by their values, and performing the operations indicated in sequence, using the result of each operation as an operand of the next. Clearly, the sequence in which the operations are performed is significant, as shown by the example:
which evaluates to 20.0 if the addition is performed first, or 16.0 if the multiplication is performed first.
The sequence of operations is determined by the following precedence order, in which operators on any line have equal precedence and precedence decreases downwards.
+ - (binary and unary)
Using this precedence order, the rules for the evaluation of an arithmetic expression may be stated as follows:
Example: 2**3**2 evaluates to 512 (29).
4.0+6.0*2.0 evaluates to 16.0
(4.0+6.0)*2.0 evaluates to 20.0
Type rules for arithmetic expressions
Subject to the restrictions noted under 'Restrictions:' above, REAL and INTEGER operands may be freely mixed in an arithmetic expression. The type of the expression's value is determined by applying the following rules to each operation performed in its evaluation:
Rule (i) is inconsistent with the rules of arithmetic, in which dividing one integer by another (e.g. 7/5) or raising an integer to an integer power (e.g. 2-1) does not always result in an integer. FORTRAN deals with such cases by truncating, as described under 'Type rules' on page 5, to obtain an INTEGER value.
Value 99/100 0 7/3 2 -7/3 -2 N**(-1) 0 N**(1/2) 1 100*9/5 180 9/5*100 100
The last two examples show that the ordering of * and / operators with INTEGER operands is significant. It is usually best to avoid dividing one integer by another unless there are special reasons for doing so.
As noted at the beginning of the chapter, the value of an arithmetic expression is assigned to a numeric variable in a statement of the form:
numeric_variable = arithmetic_expression
If the type of the expression differs from that of the variable, the rules listed under 'Type rules' on page 5 are applied, i.e.
Expression Variable Rule type type INTEGER REAL Convert to REAL REAL INTEGER Truncate
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