SQL Server 2008 - Query to get result in fraction format

Question

I have a table which contains data like this:

MinFormat(int)  MaxFormat(int)  Precision(nvarchar)
   -2              3             1/2

The

Answer 1

Sorry, now I'm late, but this was my approach:

I'd wrap this in a TVF actually and call it like

SELECT * FROM dbo.FractalStepper(-2,1,'1/4');

or join it with your actual table like

SELECT *
FROM SomeTable
CROSS APPLY dbo.MyFractalSteller(MinFormat,MaxFormat,[Precision]) AS Steps

But anyway, this was the code:

DECLARE @tbl TABLE (ID INT, MinFormat INT,MaxFormat INT,Precision NVARCHAR(100));

--Inserting two examples
INSERT INTO @tbl VALUES(1,-2,3,'1/2')
                      ,(2,-4,-1,'1/4');

--Test with example 1, just set it to 2 if you want to try the other example
DECLARE @ID INT=1;

--If you want to get your steps numbered, just de-comment the tree occurencies of "Step"
WITH RecursiveCTE as
(
    SELECT  CAST(tbl.MinFormat AS FLOAT) AS RunningValue
           ,CAST(tbl.MaxFormat AS FLOAT) AS MaxF
           ,1/CAST(SUBSTRING(LTRIM(RTRIM(tbl.Precision)),3,10) AS FLOAT) AS Prec
           --,1 AS Step
    FROM @tbl AS tbl
    WHERE tbl.ID=@ID

    UNION ALL

    SELECT RunningValue + Prec
          ,MaxF 
          ,Prec
          --,Step + 1
    FROM RecursiveCTE
    WHERE RunningValue + Prec <= MaxF
)
SELECT RunningValue --,Step 
      ,CASE WHEN CAST(RunningValue AS INT)<>RunningValue 
            THEN CAST(RunningValue / Prec AS VARCHAR(10)) + '/' + CAST(CAST(1/Prec AS INT) AS VARCHAR(MAX))
            ELSE CAST(RunningValue AS VARCHAR(10))
       END AS RunningValueFractal
FROM RecursiveCTE;

The result

Value   ValueFractal
-2      -2
-1,5    -3/2
-1      -1
-0,5    -1/2
0        0
0,5      1/2
1        1
1,5      3/2
2        2
2,5      5/2
3        3

Answer 2

Note this will only work for Precision 1/1, 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64

DECLARE @t table(MinFormat int, MaxFormat int, Precision varchar(4))
INSERT @t values(-2, 3, '1/2')

DECLARE @numerator INT, @denominator DECIMAL(9,7)
DECLARE @MinFormat INT, @MaxFormat INT

-- put a where clause on this to get the needed row

SELECT @numerator   = 1,
       @denominator = STUFF(Precision, 1, charindex('/', Precision), ''),
       @MinFormat = MinFormat,
       @MaxFormat = MaxFormat
FROM @t


;WITH N(N)AS 
(SELECT 1 FROM(VALUES(1),(1),(1),(1),(1),(1),(1),(1),(1),(1))M(N)),
tally(N)AS(SELECT ROW_NUMBER()OVER(ORDER BY N.N)FROM N,N a,N b,N c,N d,N e,N f)
SELECT top(cast((@MaxFormat- @MinFormat)  / (@numerator/@denominator) as int) + 1) 
CASE WHEN val % 1 = 0 THEN cast(cast(val as int) as varchar(10))
     WHEN val*2 % 1 = 0 THEN cast(cast(val*2 as int) as varchar(10)) + '/2'
     WHEN val*4 % 1 = 0 THEN cast(cast(val*4 as int) as varchar(10)) + '/4'
     WHEN val*8 % 1 = 0 THEN  cast(cast(val*8 as int) as varchar(10)) + '/8'
     WHEN val*16 % 1 = 0 THEN cast(cast(val*16 as int) as varchar(10)) + '/16'
     WHEN val*32 % 1 = 0 THEN cast(cast(val*32 as int) as varchar(10)) + '/32'
     WHEN val*64 % 1 = 0 THEN cast(cast(val*64 as int) as varchar(10)) + '/64'
END
FROM tally
CROSS APPLY
(SELECT @MinFormat +(N-1) *(@numerator/@denominator) val) x

Answer 3

Mine is a bit different others. I perform the addition on fraction and at the end, simplified the fraction.

-- This solution uses CTE
-- it breaks the @min, @max number into fraction
-- perform the addition in terms of fraction
-- at result, it attemp to convert the fraction to simpliest form

declare @min        int,
    @max        int,
    @step       varchar(10),
    @step_n     int,    -- precision step numerator portion
    @step_d     int -- precision step denominator portion

select  @min    = -2,
    @max    = 3,
    @step   = '1/16'

select  @step_n = left(@step, charindex('/', @step) - 1),
    @step_d = stuff(@step, 1, charindex('/', @step), '')

; with rcte as
(
    -- Anchor member
    select  n = @min,   -- numerator
        d = 1,      -- denominator
        v = convert(decimal(10,5), @min)

    union all

    -- Recursive member
    select  n = case when ( (r.n * @step_d) + (r.d * @step_n) ) % @step_d = 0 
             and  (r.d * @step_d) % @step_d = 0
             then ( (r.n * @step_d) + (r.d * @step_n) ) / @step_d
             else (r.n * @step_d) + (r.d * @step_n)
             end, 
        d = case when ( (r.n * @step_d) + (r.d * @step_n) ) % @step_d = 0
             and  (r.d * @step_d) % @step_d = 0
             then (r.d * @step_d) / @step_d
             else (r.d * @step_d)
             end,
        v =  convert(decimal(10,5), ((r.n * @step_d) + (r.d * @step_n)) / (r.d * @step_d * 1.0))
    from    rcte r
    where   r.v < @max
)
select  *,
    fraction    = case  when    n = 0
                then    '0'
                when    coalesce(d2, d) = 1
                then    convert(varchar(10), coalesce(n2, n))
                else    convert(varchar(10), coalesce(n2, n)) + '/' + convert(varchar(10), coalesce(d2, d))
                end
from    rcte r
    cross apply -- use to simplify the fraction result
    (
        select  n2 = case when n % 32 = 0 and d % 32 = 0 then n / 32
                  when n % 16 = 0 and d % 16 = 0 then n / 16
                  when n % 8 = 0 and d % 8 = 0 then n / 8
                  when n % 4 = 0 and d % 4 = 0 then n / 4
                  when n % 2 = 0 and d % 2 = 0 then n / 2
                  end,
            d2 = case when n % 32 = 0 and d % 32 = 0 then d / 32
                  when n % 16 = 0 and d % 16 = 0 then d / 16
                  when n % 8 = 0 and d % 8 = 0 then d / 8
                  when n % 4 = 0 and d % 4 = 0 then d / 4
                  when n % 2 = 0 and d % 2 = 0 then d / 2
                  end
    ) s
order by v
option (MAXRECURSION 0)