A very useful custom function (to determine whether a natural number contains a specified power of 2)

Function
/*           Name:    Fun_WheIncluded            function:    Determine whether the selected number is in the given integer              can know that any natural number can be split into a number of 2 powers and, such as:                 1 = 2^0                 2 = 2^1                 3 = 2^0 + 2^ 1                4 =  2^2                5  = 2^0 + 2^2                 6 = 2^1 + 2^4                7  = 2^0 + 2^1 + 2^2                 8 = 2^3                 9 = 2^0 + 2^3                 10 = 2^1 + 2^3                 11 = 2^0 + 2^1 + 2^3                 12 = 2^2  + 2^3                13  = 2^0 + 2^2 + 2^3                 14 = 2^1 + 2^2 + 2^3                 15 = 2^0 + 2^1 + 2^2 + 2^3                 16 = 2^4                 17 = 2^0 + 2^4           a method that resolves any number to a power sum of 2--recursive      law:                  as given  14                   ∵ 2^3 < < 2^4                 There must be 8--2^3              in the   ∴ 14.       14-8 = 6                   ∵ 2^2 < 6 < 2^3             There must be 4--2^2          in the       ∴ 6.          6-4 = 2                          ∵ 2 = 2                   ∴ 14 = 2^3 + 2^2 + 2^1

Parameters: @TotalNum type:int @SpecifiedNum type:int Steps: Author:waxdoll Cheung date:2005-03-21*/

The CREATE FUNCTION dbo. fun_wheincluded (@TotalNum int, @SpecifiedNum int) RETURNS BIT as BEGIN

DECLARE @varRet BIT

DECLARE @varLoop INT

SET @varLoop = 0

while (@TotalNum >= CAST (Power (2, @VarLoop) as INT)) SET @varLoop = @varLoop + 1

SET @TotalNum = @TotalNum-cast (Power (2, @varLoop-1) as INT)

if (@varLoop = @SpecifiedNum + 1) SET @varRet = 1 ELSE BEGIN IF (@TotalNum >= 1) return to dbo. Fun_wheincluded (@TotalNum, @SpecifiedNum) ELSE SET @varRet = 0 End

Return @varRetEND