SQL Server 2008 - Query to get result in fraction format - sql

Question

I have a table which contains data like this:
MinFormat(int) MaxFormat(int) Precision(nvarchar)
-2 3 1/2
The values in precision can be 1/2, 1/4, 1/8, 1/16, 1/32, 1/64 only.
Now I want result from query as -
-2
-3/2
-1
-1/2
0
1/2
1
3/2
2
5/2
3
Any query to get the result as follows?
Idea is to create result based onMinimum boundary (MinFomrat col value which is integer) to Maximum boundary (MaxFormat Col value which is integer) accordingly to the precision value.
Hence, in above example, value should start from -2 and generate the next values based on the precision value (1/2) till it comes to 3

Answer 1

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 2

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 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)