Mathematical User-Defined Functions

Introduction

In this article, I wrote some useful Mathematical User-Defined Functions.

Mathematical UDFs

These scalar User-Defined Functions perform a calculation, usually
based on input values provided as arguments, and return a numeric
value.

To download Mathematical User-Defined Functions click this link:
Download Mathematical UDFs

Factorial

Returns the factorial value of the given number.

Syntax

Factorial ( number )

Arguments

number

Is the integer value.

Return Types

bigint

The function's text:


CREATE FUNCTION Factorial
  ( @number int )
RETURNS bigint
AS
BEGIN
  DECLARE @i int, @factorial bigint
  IF @number > 20 RETURN 0
  SET @i = 1
  SET @factorial = 1
  WHILE @i <= @number
    BEGIN
      SET @factorial = @factorial * @i
      SET @i = @i + 1
    END
  RETURN @factorial
END
GO




Examples

This example returns the factorial value of the number 5:


SELECT dbo.Factorial(5)
GO




Here is the result set:

--------------------
120

(1 row(s) affected)

PercentFrom

Returns the percent of the expression1 in the expression2.

Syntax

PercentFrom ( expression1, expression2 )

Arguments

expression1

Is an expression of the exact numeric or approximate numeric
data type category.

expression2

Is an expression of the exact numeric or approximate numeric
data type category.

Return Types

float

The function's text:


CREATE FUNCTION PercentFrom
  ( @expression1 SQL_VARIANT,
    @expression2 SQL_VARIANT )
RETURNS float
AS
BEGIN
  RETURN (CAST(@expression1 AS FLOAT)/CAST(@expression2 AS FLOAT)*100)
END
GO




Examples

This example returns the percent of the 137 in the 273:


SELECT dbo.PercentFrom(137, 273)
GO




Here is the result set:

-----------------------------------------------------
50.183150183150182

(1 row(s) affected)

PercentValue

Returns the percent's value from the given expression for the
given percent.

Syntax

PercentValue ( expression, percent )

Arguments

expression

Is an expression of the exact numeric or approximate numeric
data type category.

percent

Is the integer value.

Return Types

float

The function's text:


CREATE FUNCTION PercentValue
  ( @expression SQL_VARIANT,
    @percent int )
RETURNS float
AS
BEGIN
  RETURN ( CAST(@expression AS FLOAT) / 100 * @percent )
END
GO




Examples

Returns the percent's value from the number 137 for the percent 11:


SELECT dbo.PercentValue (137, 11)
GO




Here is the result set:

-----------------------------------------------------
15.07

(1 row(s) affected)

Degree

Returns the degree for the given number and degree value.

Syntax

Degree ( number, degree )

Arguments

number

Is an expression of the exact numeric or approximate numeric
data type category.

degree

Is the integer value.

Return Types

float

The function's text:


CREATE FUNCTION Degree
  ( @number SQL_VARIANT,
    @degree int )
RETURNS float
AS
BEGIN
  DECLARE @i int, @res float
  SET @i = 1
  SET @res = 1
  WHILE @i <= @degree
    BEGIN
      SET @res = CAST(@number AS FLOAT) * @res
      SET @i = @i + 1
    END
  RETURN @res
END
GO




Examples

Returns the degree 4 for the number 3:


SELECT dbo.Degree(3, 4)
GO




Here is the result set:

-----------------------------------------------------
81.0

(1 row(s) affected)

Allocation

Returns the allocation from the m by n.

Syntax

Allocation ( m, n )

Arguments

m

Is the integer value.

n

Is the integer value.

Return Types

int

The function's text:


CREATE FUNCTION Allocation
  ( @m int,
    @n int )
RETURNS int
AS
BEGIN
  RETURN (dbo.Factorial(@m)/dbo.Factorial(@m-@n))
END
GO




Examples

Returns the allocation from the 5 by 3:


SELECT dbo.Allocation(5,3)
GO




Here is the result set:

-----------
60

(1 row(s) affected)

Combination

Returns the combination from the m by n.

Syntax

Combination ( m, n )

Arguments

m

Is the integer value.

n

Is the integer value.

Return Types

int

The function's text:


CREATE FUNCTION Combination
  ( @m int,
    @n int )
RETURNS int
AS
BEGIN
  RETURN (dbo.Factorial(@m)/(dbo.Factorial(@m-@n)*dbo.Factorial(@n)))
END
GO




Examples

Returns the combination from the 5 by 3:


SELECT dbo.Combination(5,3)
GO




Here is the result set:

-----------
10

(1 row(s) affected)