My query is relatively simple but would like to know the root cause
Sql query to convert Float to Decimal gives incorrect results.
Example:
Select CAST(CONVERT(DECIMAL(25,8), CONVERT(FLOAT,338193293.16))AS VARCHAR(255))
Expected result: 338193293.16000000
Actual Result: 338193293.16000003
Where did the extra 3come from?
The number of digits are too much - no matter that after decimal point they are only 2. Use shorter number e.g. 38193293.16 or use FLOAT(24). For normal FLOAT there is "Precision = 7 digits".
Related
I found weird or strange behavior of Round function in MSSQL for real column type. I have tested this issue in Azure SQL DB and SQL Server 2012
Why #number=201604.125 Return 201604.1 ?
Why round(1.12345,10) Return 1.1234500408 ?
-- For Float column it working as expected
-- Declare #number as float,#number1 as float;
Declare #number as real,#number1 as real;
set #number=201604.125;
set #number1=1.12345;
select #number as Realcolumn_Original
,round(#number,2) as Realcolumn_ROUND_2
,round(#number,3) as Realcolumn_ROUND_3
, #number1 as Realcolumn1_Original
,round(#number1,6) as Realcolumn1_ROUND_6
,round(#number1,7) as Realcolumn1_ROUND_7
,round(#number1,8) as Realcolumn1_ROUND_8
,round(#number1,9) as Realcolumn1_ROUND_9
,round(#number1,10) as Realcolumn1_ROUND_10
Output for real column type
I suspect what you are asking here is why does:
DECLARE #n real = 201604.125;
SELECT #n;
Return 201604.1?
First point of call for things like this should be the documentation: Let's start with float and real (Transact-SQL). Firstly we note that:
The ISO synonym for real is float(24).
If we then look further down:
float [ (n) ] Where n is the number of bits that are used to store the
mantissa of the float number in scientific notation and, therefore,
dictates the precision and storage size. If n is specified, it must be
a value between 1 and 53. The default value of n is 53. n value
Precision Storage size
1-24 7 digits 4 bytes
So, now we know that a real (aka a float(24)) has precision of 7. 201604.125 has a precision of 9, that's 2 too many; so off come that 2 and 5 in the return value.
Now, ROUND (Transact-SQL). That states:
Returns a numeric value, rounded to the specified length or precision.
When using real/float those digits aren't actually lost, as such, due to the floating point. When you use ROUND, you are specifically stating "I want this many decimal places". This is why you can then see the .13 and the .125, as you have specifically asked for those. When you just returned the value of #number it had a precision of 7, due to being a real, so 201604.1 was the value returned.
I have a number with two digits after the decimal point; I try to cast this number using CAST for example:
Select SUM(CAST((123345.56) as decimal(28, 2))) * 100 AS AMOUNT
I get the following result
12334556.00
but I want get only 12334556 without displaying two digits after the decimal point.
Thank you.
It is not clear what you really want to do, but
SELECT SUM(CAST((123345.56 * 100.0) AS DECIMAL(28,0))) AS AMOUNT
gives 12334556.
When you use a number in the format 1234.56 it is a decimal literal in SQL Server: see "decimal constants" in Constants (Transact-SQL).
Integer data type is whole numbers, so cast your calculated value as int.
Select SUM(CAST((123345.56 * 100) as int)) AS AMOUNT
I am looking for a division result that is extremely accurate.
This SQL returns the following results:
SELECT (CAST(297282.26 AS DECIMAL(38, 30)) / CAST(495470.44 AS DECIMAL(38, 30))) AS ResultDecimal
SELECT (CAST(297282.26 AS FLOAT) / CAST(495470.44 AS FLOAT)) AS ResultFloat
Here is the accurate result from WolframAlpha:
http://www.wolframalpha.com/input/?i=297282.26%2F495470.44
I was under the impression that DECIMAL would be more accurate than FLOAT:
"Because of the approximate nature of the float and real data types, do not use these data types when exact numeric behavior is required, such as in financial applications, in operations involving rounding, or in equality checks. Instead, use the integer, decimal, money, or smallmoney data types."
https://technet.microsoft.com/en-us/library/ms187912(v=sql.105).aspx
Why does the FLOAT calculation give me a result more accurate than when using DECIMAL?
I found the best precision to be when you use:
SELECT (CAST(297282.26 AS DECIMAL(15, 9)) / CAST(495470.44 AS DECIMAL(24, 2))) AS ResultDecimal
This gives a result of
0.599999991926864496699338915153
I think the actual value (to 100 digits) is:
0.5999999919268644966993389151530412187657451370862810705720405842980259326873264124495499670979362562...
Please bear in mind SQL Server defines the maximum precision and scale for division as:
max precision = (p1 - s1 + s2) + MAX(6, s1 + p2 + 1) -- up to 38
max scale = MAX(6, s1 + p2 + 1)
Where p1 & p2 are the precision of the two numbers and s1 & s2 are the scale of the numbers.
In this case the maximum precision is (15-9+2) + MAX(6, 9+24+1) = 8 + 34 = 42.
However SQL Server only allows a maximum precision of 38.
The maximum scale = MAX(6, 9+24+1) = 34
Hopefully you already understand that just because the FLOAT version presents more numbers after the decimal point, doesn't necessarily mean that those are the true numbers. This is about precision, not accuracy.
It is the CAST function itself that causes this loss of precision, not the difference between the FLOAT and DECIMAL data types.
To demonstrate this, compare your previous results to the result of this:
SELECT 297282.26 / 495470.44 AS ResultNoCast
In my version of the query, the presence of a decimal point in the literal numbers tells SQL Server to treat the values as DECIMAL datatype, with appropriate length and precision as determined by the server. The result is more precise than when you CAST explicitly to DECIMAL.
A clue to the reason for this can be found hidden in the official documentation of the CAST function, under Truncating and Rounding Results:
When you convert data types that differ in decimal places, sometimes the result value is truncated and at other times it is rounded. The following table shows the behavior.
From | To | Behavior
numeric | numeric | Round
So the fact that each separate literal value is treated as a NUMERIC (same thing as DECIMAL) on the way in, and is being casted to NUMERIC, causes rounding.
Anticipating your next question a little, if you want a more precise result from the NUMERIC/DECIMAL datatype, you just need to tell SQL Server that each component of the calculation is more precise:
SELECT 297282.26000000 / 495470.44000000 AS ResultSuperPrecise
This appears (from experimentation) to be the most precise I can get: either adding or removing a 0 from either the numerator or denominator makes the result less precise. I'm at a loss to explain why that is, because the result is only 23 digits to the right of the decimal point.
It doesn't give you a more accurate result. I say that because the value is an approximate and not all values will be available to stored in a float. On the other side of that coin though is that float has the possibility of a lot more precision. The maximum precision of a decimal/numeric is 38. https://msdn.microsoft.com/en-us/library/ms187746.aspx
When you look at float though the maximum precision is 53. https://msdn.microsoft.com/en-us/library/ms173773.aspx
Okay, here is what I think is going on.
#philosophicles - I think you are right in that the CAST is causing the problem, but not because I am trying to "convert data types that differ in decimal places".
When I execute the following statement
SELECT CAST((297282.26 / 495470.44) AS DECIMAL(38, 30)) AS ResultDecimal
The accurate result for the calculation is
This has way more than 30 digits after the decimal point, and my data type has scale set to 30. So the CAST rounds the value, then just adds zeros to the end until there are 30 digits. We end up with this:
So the interesting thing is how does the CAST determine up to how many decimals to round or truncate the output? I am not sure, but as #philosophicles pointed out, the scale of the input effects the rounding applied on the output.
SELECT CAST(((297282.26/10000) / (495470.44/10000)) AS DECIMAL(38, 30)) AS ResultDecimal
Thoughts?
Also interesting:
However, in simple terms, precision is lost when the input scales are
high because the result scales need to be dropped to 38 with a
matching precision drop.
https://dba.stackexchange.com/questions/41743/automatic-decimal-rounding-issue
The precision and scale of the numeric data types besides decimal are fixed.
https://dba.stackexchange.com/questions/41743/automatic-decimal-rounding-issue
It is really strange how auto convert between numeric data behaves in T-Sql
Declare #fdays as float(12)
Declare #mAmount As Money
Declare #fDaysi as float(12)
Set #fdays =3
Set #fdaysi =1
Set #mAmount=527228.52
Set #mAmount = #fdaysi * #mAmount/#fDays
Select #mAmount, 527228.52/3
The result of this computation is
175742.8281 175742.840000
Does this occur because money and float are not actually the same kind of numeric data? Float is Approximate Numeric and Money is Exact Numeric
Money and Decimal are fixed numeric datatypes while Float is an
approximate numeric datatype. Results of mathematical operations on
floating point numbers can seem unpredictable, especially when
rounding is involved. Be sure you understand the significance of the
difference before you use Float!
Also, Money doesn't provide any advantages over Decimal. If fractional
units up to 5 decimal places are not valid in your currency or
database schema, just use Decimal with the appropriate precision and
scale.
ref link : http://www.sqlservercentral.com/Forums/Topic1408159-391-1.aspx
Should you choose the MONEY or DECIMAL(x,y) datatypes in SQL Server?
https://dba.stackexchange.com/questions/12916/datatypes-in-sql-server-difference-between-similar-dataypes-numeric-money
float [ (n) ]
Where n is the number of bits that are used to store the mantissa of the float number in scientific notation and, therefore, dictates the precision and storage size. If n is specified, it must be a value between 1 and 53. The default value of n is 53.
When n in 1-24 then precision is 7 digits.
When n in 25-53 then precision is 15 digits.
So in your example precision is 7 digits, thus first part #fdaysi * #mAmount
rounds result to 7 digits 527228.5. The second part returns 527228.5/3=175742.828 and casting 175742.828 to Money results in 175742.8281. So FLOAT and REAL are approximate data types and sometimes you get such surprises.
DECLARE #f AS FLOAT = '29545428.022495';
SELECT CAST(#f AS NUMERIC(28, 14)) AS value;
The result of this is 29545428.02249500200000 with just a casting.
I have really simply question about DECIMAL (and maybe NUMERIC) type in SQL Server 2008 R2.
MSDN said:
(scale)
The maximum number of decimal digits that can be stored to the right of the decimal point. Scale must be a value from 0 through p.
I understand this following way:
if I have DECIMAL(10, 5) - I am able to store 12345.12345 or 12345678.91.
if I have DECIMAL(5, 5) - I can have 12345 or 1234.5 or 1.2345, etc...
Is it clear?
But I got this error message:
SELECT CAST(2.8514 AS DECIMAL(5,5))
Arithmetic overflow error converting numeric to data type numeric.
I thought 5,5 means I can have up to 5 digits and up to 5 CAN BE right of the decimal point.
As I tried:
SELECT CAST(12.851 AS DECIMAL(6,5)) - overflows too
however
SELECT CAST(1.23456 AS DECIMAL(6,5)) - is OK.
So what's the truth?
DECIMAL(a,b) says that I can have up to a digits and JUST b of them are right to the decimal point (and there rest a-b to the left to the dec. point)?
I'm really confused about statement in doc which is copied everywhere. Please take a while and explain me this simple thing.
Lot of thanks!
The easiest way to think of it (for me) is that precision is the total number of digits, of which scale is the number of digits to the right of the decimal point. So DECIMAL(p,s) means p-s digits to the left of the point, and s digits to the right of the point.
That explains all the conversion errors you're seeing: the 2.8514 cannot be decimal(5,5) because p-s = 0; 12.851 cannot be decimal(6,5) because p-s = 1 and so on.