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

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)