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Using Mathematical Functions (Transact-SQL)

A mathematical function performs a mathematical operation on numeric expressions and returns the result of the operation. Mathematical functions operate on the SQL Server system-supplied numeric data: decimal, integer, float, real, money, smallmoney, smallint, and tinyint. By default, the precision of built-in operations on float data type data is six decimal places.

By default, a number passed to a mathematical function will be interpreted as a decimal data type. The CAST or CONVERT functions can be used to change the data type to something else, such as a float. For example, the value returned by the FLOOR function has the data type of the input value. The input of the following SELECT statement is a decimal. FLOOR returns 123. This is a decimal value.

SELECT FLOOR(123.45);

---------------------
123

(1 row(s) affected)

But, the following example uses a float value and FLOOR returns a float value:

SELECT FLOOR (CONVERT (float, 123.45));

-------------------------------------
123.000000

(1 row(s) affected)

A floating point underflow error occurs when the float or real result of a mathematical function is too small to display. A result of 0.0 is returned and no error message is displayed. For example, the mathematical calculation of 2 to the -100.0 power has a result 0.0.

Domain errors occur when the value provided in the mathematical function is not a valid value. For example, values specified for the ASIN function must be from -1.00 through 1.00. If a range of -2 is specified, a domain error occurs.

Range errors occur when the value specified is outside the allowed values. For example, POWER(10.0, 400) is out of the range of the maximum of ~2e+308 of the float data type, and POWER(-10.0, 401) is out of the range of the minimum of ~ -2e+308 of the float data type.

The following table shows mathematical functions that produce either a domain or range error.

Mathematical function

Result

SQRT(-1)

Domain error.

POWER(10.0, 400)

Arithmetic Overflow error.

POWER(10.0, -400)

Value of 0.0 (floating point underflow).

Error traps are provided to handle domain or range errors of these functions. You can use the following:

  • SET ARITHABORT ON. This terminates the query and ends the user-defined transaction. The SET ARITHABORT setting overrides the setting for SET ANSI_WARNINGS.

  • SET ANSI_WARNINGS ON. This stops the command.

  • SET ARITHIGNORE ON. This prevents the display of a warning message. Both the SET ARITHABORT and SET ANSI_WARNINGS settings override the SET ARITHIGNORE setting.

If none of these options is set, SQL Server returns NULL and returns a warning message after the query is executed. For more information: 

SET ARITHABORT (Transact-SQL)

SET ANSI_WARNINGS (Transact-SQL)

SET ARITHIGNORE (Transact-SQL)

Internal conversion to float can cause loss of precision if either the money or numeric data types are used.

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