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DQL Statements › SET Statements › Arithmetic Result Syntax Diagram › Evaluation of Arithmetic Expressions

Evaluation of Arithmetic Expressions

CA Dataquery evaluates arithmetic expressions according to the arithmetic operator it finds. This standard processing sequence is called the hierarchy of operations and is performed in the following order.

  1. Expressions within parentheses (innermost parentheses first)
  2. Expressions within parentheses (same level of parentheses, performing from left to right)
  3. Mathematical functions
  4. Unary + and unary -
  5. * and /
  6. + and -

CA Dataquery evaluates expressions within parentheses first. When expressions are contained within nested parentheses, evaluation proceeds from the least inclusive (innermost) to the most inclusive (outermost) set.

When the order of consecutive operations on the same hierarchic level is not completely specified, the order of operation is left-to-right; for example, the following two expressions are evaluated the same.

         A + B / C - D / C * F + G * C / H + I

         A + (B/C) - ((D / C) * F) + ((G * C) / H) + I

Note: There must be a one-to-one correspondence between left and right parentheses in an arithmetic expression.

Sample

The result of an arithmetic expression is dependent on the precision of the result and the arithmetic operation which is performed. The following example illustrates how CA Dataquery calculates the value for FLDX, using the following expression.

         FLDX (3.3) = ((2. + 3) * (4 + (5 / 6 + (7 - 8)))) + 9

Explanation

The following chart shows the hierarchy of operations, the part of the expression which is evaluated in each step, and the result of that evaluation. After each step, we show the expression with the value from the just completed step replacing the part that was evaluated.

Step

Part

Result

Comments

1

(7 - 8)

-1

CA Dataquery evaluates the innermost parenthetical expression first.

 

 

FLDX (3.3) = ((2. + 3) * (4 + (5 / 6 + (-1)))) + 9

2

5 / 6

0.833

CA Dataquery evaluates the part of the inner parenthetical expression involving division, since division has a higher precedence than addition.

 

 

FLDX (3.3) = ((2. + 3) * (4 + (0.833 + (-1)))) + 9

3

(0.833 + (-1))

-.167

CA Dataquery uses the results from the evaluation in Steps 1 and 2 to evaluate the second innermost parenthetical expression.

 

 

FLDX (3.3) = ((2. + 3) * (4 + (-.167))) + 9

4

(2 + 3)

5

The two remaining inner parenthetical expressions both involve addition and are at the same level, so CA Dataquery evaluates the left expression first.

 

 

FLDX (3.3) = ((5) * (4 + (-.167))) + 9

5

(4 + (-.167))

3.833

CA Dataquery evaluates the inner parenthetical expression on the right.

 

 

FLDX (3.3) = (5 * 3.833) + 9

6

(5 * 3.833)

19.165

CA Dataquery completes the evaluation of the multilevel parenthetical expression by multiplying the values within parentheses of FLDX, (3.3), designates the number of digits CA Dataquery calculates on either side of the decimal point. The precision (3.3) indicates that the value has three digits to the left and right of the decimal point.

 

 

FLDX (3.3) = 28.165

You can also define FLDX with a precision different from (3.3), as in the following alternative formats:

 FLDX (7.5) = +0000028.16665
 FLDX (2.4) = +28.1665
 FLDX (2.0) = +28
 FLDX (1.0) = ***E3***  (Display indicates error because of overflow.)