SIMSCRIPT II.5 Programming Language

SIMSCRIPT II.5 Programming Language
1.5 Arithmetic Expressions
Arithmetic expressions are formed by combining variables and constants with arithmetic operators.
The arithmetic operators are + (add), - (subtract), * (multiply), / (divide), and ** (exponentiate).
Two of these operators, plus and minus, can be used as unary operators, that is, with a single variable
or constant. The constants +1 and -1 are examples of the use of plus and minus as unary operators
on the constant 1. All of the operators can be used as binary operators, that is, with two
variables (or constants or a variable and constant). If we let A and B represent either a variable or a
constant, then + A and - A are examples of plus and minus as unary operators, and A + B, A **
B are examples of arithmetic expressions that use binary operators.
The simplest expression consists of a single constant, or a single variable, perhaps preceded by a
unary plus or minus operator. An expression, + A, may be written as A, with the unary plus implied.
This is not possible, of course, with the unary minus operator.
All binary operators must be explicitly expressed, and no two operators can appear consecutively.
For example, multiplication of the variables A and B must be written as A * B, and not AB. The
latter would be interpreted as the value of a variable called AB. Addition of the expressions A and
-B can be written as A + (-B) or A - B, but not A + -B. This last example shows that parentheses
must be used to separate unary and binary operators. Parentheses may also be used (1) to clarify
the operations in an expression to make it more readable, or (2) to specify the order in which the
operations in an expression are to be performed.
Simple expressions can be connected by any of the arithmetic operators (+, -, *, /, **) to
form compound expressions. The "parentheses rule" states that expressions are evaluated from left
to right, removing parentheses before applying operator hierarchy rules. Imbedded parentheses are
evaluated from the inside out. Thus:
a + (b*c) + d
is evaluated by first computing the value of (b*c) and then adding this value to a and d.
When parentheses are omitted, the hierarchy of operations is:
1. Exponentiation **
2. Multiplication and division * and /
3. Addition and subtraction + and -
This hierarchy specifies the order in which the different operations are performed relative to one
another. Exponentiation is performed before multiplication or division, and either of these before
addition or subtraction. For example, the expression A + B/C + D**E * F - G is taken to mean
A + (B/C) + (D E * F) - G. If precedence is not completely specified by these rules, the
operation specified farthest to the left in the expression is performed first, as in A * B/C, which is
computed as (A * B) / C.
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