SQL Functions - factorial

Question

I am a beginner in SQL Functions. What is the best way to create a function for factorial in SQL Server- Say 10!

Answer 1

-- Iterative method. -- Why Iterative? It is simpler and faster. -- For @N from 0 to 20 this gives an exact result. -- 21 will give an overflow.

DECLARE @N Bigint = 20
DECLARE @F Bigint = 1
WHILE @N > 0 BEGIN
  SET @F = @f*@n
  SET @N = @N-1
END
SELECT @F AS FACTORIAL

-- Change the datatype to float and you can get the factorial up to 170. -- 171 will result in an overflow. -- Remark the result will only be accurate over a limited number of positions.

DECLARE @N FLOAT = 170
DECLARE @F FLOAT = 1
WHILE @N > 0 BEGIN
  SET @F = @f*@n
  SET @N = @N-1
END
SELECT @F AS FACTORIAL

-- Ben

Answer 2

Another way:

create function Fact(@num int)
returns bigint
as
begin
declare @i int = 1

 while @num>1
 begin
  set @i = @num *  @i
  set @num=@num-1
  end

return @i
end

select dbo.Fact(5)

Answer 3

MS-SQL: Factorial from 0 to 88:

with tb1 as (
select 10000000 as b, 1 as n, 
0 as t18, 0 as t17, 0 as t16, 0 as t15, 0 as t14, 0 as t13, 0 as t12, 0 as t11, 0 as t10, 0 as t9, 0 as t8, 0 as t7, 0 as t6, 0 as t5, 0 as t4, 0 as t3, 0 as t2, 0 as t1, 1 as t0
union all 
select 
tb1.b,
tb1.n + 1,
(tb1.t18 * tb1.n) + ((tb1.t17 * tb1.n) + ((tb1.t16 * tb1.n) + ((tb1.t15 * tb1.n) + ((tb1.t14 * tb1.n) + ((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b,
((tb1.t17 * tb1.n) + ((tb1.t16 * tb1.n) + ((tb1.t15 * tb1.n) + ((tb1.t14 * tb1.n) + ((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t16 * tb1.n) + ((tb1.t15 * tb1.n) + ((tb1.t14 * tb1.n) + ((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t15 * tb1.n) + ((tb1.t14 * tb1.n) + ((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t14 * tb1.n) + ((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t13 * tb1.n) + ((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t12 * tb1.n) + ((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t11 * tb1.n) + ((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t10 * tb1.n) + ((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t9 * tb1.n) + ((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t8 * tb1.n) + ((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t7 * tb1.n) + ((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t6 * tb1.n) + ((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b, 
((tb1.t5 * tb1.n) + ((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t4 * tb1.n) + ((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t3 * tb1.n) + ((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)/tb1.b)%tb1.b,
((tb1.t2 * tb1.n) + ((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)/tb1.b)%tb1.b,
((tb1.t1 * tb1.n) + (tb1.t0 * tb1.n) / tb1.b)%tb1.b,
(tb1.t0 * tb1.n) % tb1.b
from tb1 where tb1.n < 89
)
, t2 as (
select  tb1.n - 1 as N,
        FORMAT(tb1.t18, '0000000') + 
        FORMAT(tb1.t17, '0000000') + FORMAT(tb1.t16, '0000000') + FORMAT(tb1.t15, '0000000') + 
        FORMAT(tb1.t14, '0000000') + FORMAT(tb1.t13, '0000000') + FORMAT(tb1.t12, '0000000') +
        FORMAT(tb1.t11, '0000000') + FORMAT(tb1.t10, '0000000') + FORMAT(tb1.t9, '0000000') +
        FORMAT(tb1.t8, '0000000') + FORMAT(tb1.t7, '0000000') + FORMAT(tb1.t6, '0000000') +
        FORMAT(tb1.t5, '0000000') + FORMAT(tb1.t4, '0000000') + FORMAT(tb1.t3, '0000000') +
        FORMAT(tb1.t2, '0000000') + FORMAT(tb1.t1, '0000000') + FORMAT(tb1.t0, '0000000') as FACT
from tb1
)

select  t2.N, SUBSTRING(t2.FACT, PATINDEX('%[^0]%', t2.FACT+'.'), LEN(t2.FACT))
from t2
order by t2.N 

Answer 4

A non recursive way

;With Nums As
(
select ROW_NUMBER() OVER (ORDER BY (SELECT 0)) AS RN
FROM sys.objects
)
SELECT  POWER(10.0, SUM(LOG10(RN)))
FROM Nums
WHERE RN <= 10

And a recursive way

declare @target int
set @target=10;

WITH N AS
     (SELECT 1 AS i,
           1 AS f

     UNION ALL

     SELECT i+1,
            f*(i+1)
     FROM   N
     WHERE  i < @target
     )
SELECT f FROM N
WHERE i=@target

Answer 5

Here is an other method to calculate factorial value of an integer in SQL Server

 create function sqlFactorial (@int int)
 returns int
 begin
  declare @factorial bigint = 1
  select @factorial = @factorial * i from dbo.NumbersTable(1,@int,1)
  return @factorial
 end

You need to use a SQL numbers table for this solution. The Select statement updates the declared integer variable for each row in the FROM part with multiplying it with the ordered integer values

Answer 6

Here is a recursive solution:

CREATE FUNCTION dbo.Factorial ( @iNumber int )
RETURNS INT
AS
BEGIN
DECLARE @i  int

    IF @iNumber <= 1
        SET @i = 1
    ELSE
        SET @i = @iNumber * dbo.Factorial( @iNumber - 1 )
RETURN (@i)
END