Mathematical User-Defined Functions

Introduction

Mathematical UDFs

Factorial

PercentFrom

PercentValue

Degree

Allocation

Combination

Introduction

I would like to write the series of articles about useful User-Defined
Functions grouped by the following categories:

Date and Time User-Defined Functions

Mathematical User-Defined Functions

Metadata User-Defined Functions

Security User-Defined Functions

String User-Defined Functions

System User-Defined Functions

Text and Image User-Defined Functions

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)

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