3.4 Numeric Expressions

A numeric expression evaluates to data with any of the numeric data types (that is, INTEGER, SHORTINTEGER, DECIMAL, SHORTDECIMAL, and NUMBER). The data in a numeric expression can be any combination of the following:

Numeric literals
Numeric variables or formulas
Dimensions
Functions that yield numeric results
Date literals, variables, formulas, or functions

In addition, you can join any of these three-part expressions with the arithmetic operators for a more complex numeric expression. You use arithmetic operators in numeric expressions with numeric data, which returns a numeric result. You can also use some arithmetic operators in date expressions with a mix of date and numeric data, to retrieve either a date or numeric result.

3.4.1 Numeric Options

A number of options determine how Oracle OLAP handles numeric expressions. These options are listed in Table 3-2, "Numeric Options".

Table 3-2 Numeric Options

Option	Description
DECIMALOVERFLOW	Controls the result of arithmetic operations that produce out-of-range numbers. Decimal numbers are stored as a mantissa and an exponent. Decimal overflow occurs when the result of a calculation is very large and can no longer be represented by the exponent portion of the decimal representation.
DIVIDEBYZERO	Controls the result of division by zero.
RANDOM.SEED.1 and RANDOM.SEED.2	(Set only) Options that specify values used by RANDOM when computing random numbers. Typically, you only set values for these options when you are developing and debugging your application programs.
ROOTOFNEGATIVE	A flag that allows or disallows any attempt to obtain a root of a negative number.

3.4.2 Mixing Numeric Data Types

You can include any type of numeric data in the same numeric expression.

The data type of the result is determined according to the following rules:

When all the data in the expression is INTEGER or SHORTINTEGER, and the only operations are addition, subtraction, and multiplication, then the result is INTEGER.
When any of the data is NUMBER, then the result is NUMBER.
When any of the data is DECIMAL or SHORTDECIMAL, and no data is NUMBER, then the result is DECIMAL.
When you perform any division or exponentiation operations, then the result is DECIMAL.

3.4.3 Automatic Conversion of Numeric Data Types

Oracle OLAP automatically converts numeric data types according to the following rules:

When you use a value with the SHORTINTEGER or SHORTDECIMAL data type in an expression, then the value is converted to its long counterpart before using it. See "Boolean Expressions" for information about problems that can occur when you mix SHORTDECIMAL and DECIMAL data types in a comparison expression.
When you save the results of a calculation as a value with the SHORTINTEGER data type, then NA is stored when the result is outside the range of a SHORTINTEGER (-32768 to 32767).
When you assign the value of a DECIMAL expression to an object with the INTEGER data type, then the value is rounded before storing or using it.

Note:
When the decimal value is outside the range of an integer (approximately plus or minus 2 billion), then an NA is stored.
When you use a decimal value where a value with the INTEGER data type is required, then the value is rounded before storing or using it.

Note:
When the decimal value is outside the range of an integer (approximately plus or minus 2 billion), then an NA is stored.
When you assign the value of a decimal expression to a variable with the SHORTDECIMAL data type, then only the first 7 significant digits are stored.
When you combine NUMBER values with other numeric data types, then all values are converted to NUMBER.

When these conversions are not what you want, then you can use the CONVERT,
TO_CHAR, TO_NCHAR, TO_NUMBER, or TO_DATE functions to get different results.

3.4.4 Using Dimensions in Arithmetic Expressions

When you use a dimension with a data type of TEXT in a numeric expression, the dimension value is treated as a position (an INTEGER) and is used numerically. The position number is based on the default status list, not on current status.

3.4.5 Using Dates in Arithmetic Expressions

When you use dates in arithmetic expressions, the result can be numeric or it can be a date. The legal operations for dates and the data type of the result are outlined in Table 3-3, "Legal Operations for Dates".

Table 3-3 Legal Operations for Dates

Operation	Result
Add or subtract a number from a date	Future or prior date
Subtract a date from a date	The number of days between the dates.
Add or subtract a number from a time period.	The time period at the appropriate interval in the future or the past, similar to the return values of the LEAD or LAG function. The result is NA when there is no dimension value that corresponds to the result. The calculation is made based on the positions of the values in the default status list of the dimension.

3.4.6 Limitations of Floating Point Calculations

All decimal data is converted to floating point format, both for storing and for calculations. In floating point format, a number is represented by means of a mantissa and an exponent. The mantissa and the exponent are stored as binary numbers. The mantissa is a binary fraction which, when multiplied by a number equal to 2 raised to the exponent, produces a number that equals or closely approximates the original decimal number.

Because there is not always an exact binary representation for a fractional decimal number, just as there is not an exact representation for the decimal value of 1/3, fractional parts of decimal numbers cannot always be represented exactly as binary fractions. Arithmetic operations on floating point numbers can result in further approximations, and the inaccuracy gradually increases with the number of operations. In addition to the approximation factor, the available number of significant digits affects the exactness of the result.

For all of these reasons, a result computed by the TOTAL, AVERAGE, or other aggregation functions on a DECIMAL or SHORTDECIMAL variable can differ in the least significant digits from a result you compute by hand. Because the SHORTDECIMAL data type provides a maximum of only seven significant digits, you see more of these differences with SHORTDECIMAL data. Therefore, you might want to use the NUMBER data type when accuracy is more important than computational speed, such as variables that contain currency amounts.

Another result of the fact that some fractional decimal numbers cannot be exactly represented by binary fractions is that for such numbers, the DECIMAL data type offers a different and closer approximation than the SHORTDECIMAL data type, because it has more significant digits. This can lead to problems when SHORTDECIMAL and DECIMAL data types are mixed in a comparison expression. For information on how to handle such comparisons, see "Boolean Expressions" .

3.4.7 Controlling Errors During Calculations

You can control the following types of errors:

Division by zero. When you divide an NA value by zero, then the result is NA; no error occurs. Dividing a non-NA value by zero normally produces an error. When a divide-by-zero error occurs when you are making a calculation on dimensioned data, then you can end up with partial results. When you use REPORT or an assignment statement (SET), values are reported or stored as they are calculated, so the division by zero halts the loop before it has gone through all the values.

When you want to suppress the divide-by-zero error, then you can change the value of the DIVIDEBYZERO option to YES. This means that the result of any division by zero is NA and no error occurs. This allows the calculation of the other values of a dimensioned expression to continue.
Root of negative numbers. It is normally an error to try to take the root of a negative number (which includes raising a number to a non-integer power). When you want to suppress the error message and allow the calculation of roots for non-negative values of the expression to continue, then set the ROOTOFNEGATIVE option to YES.
Overflow errors. The DECIMALOVERFLOW option works in a similar manner to DIVIDEBYZERO. It lets you control whether an error is generated when a calculation produces a decimal result larger than it can handle.