Floating Point - Precision Of Arithmetic Calculations On Server

Dec 4, 2013

I am trying to understand why SQL Server gives me significantly lower precision than many of the other sources that have tried when using the POWER function. My environment is 2008 R2 SP2 (10.50.4000.0 X64, Standard edition) on Windows 2008 X64 SP1

DECLARE @x FLOAT(53) = 1.0004;
DECLARE @y FLOAT(53) = 1.0/12.0;
SELECT POWER(@x,@y)-1; -- Answer: 3.33270904724348E-05
GO
DECLARE @x FLOAT(24) = 1.0004;
DECLARE @y FLOAT(24) = 1.0/12.0;

[URL] ....

Answer: 3.33272237835747E-05

I also tried using Windows Calculator.Answer:3.3327223783495255846580902358195e-5

And an online "high-precision" calculator from [URL] ...

Answer: 3.332722378349525584658E-5

The best SQL results compare only to the fourth digit with other results. Everything else agrees to the 10th or 12th digit.

Is the precision of arithmetic calculations on SQL Server that bad, or am I doing something wrong here? Is there another more precise alternative?

I did the following. The results speak for themselves

DECLARE @x FLOAT(53) = 1.0004;
DECLARE @y FLOAT(53) = 1.0/12.0;
DECLARE @z FLOAT(53) = POWER(@x,@y)-1; -- Answer: 3.33270904724348E-05
SELECT POWER((1+@z),12); -- 1.00039999839968

-- using results from other sources (c#, windows calc, casio.com)
SELECT POWER((1+3.33272237835747E-05),12) -- 1.0004
SELECT POWER((1+3.3327223783495255846580902358195e-5),12)-- 1.0004
SELECT POWER((1+3.332722378349525584658E-5),12) -- 1.0004

It is not important what I am trying to do, but in case it will work, I am trying to calculate the monthly return for a 90-day T-bill given the compounded annual return. x is the annualized return.

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Nov 9, 2001

Hello all,

I can't see any reason for this error, not having a high level understanding of maths I thought I'd post it and hope someone could share some light on it.

I yesterday got called by a client who said that a payment for £15 + VAT was being passed to their payment gateway as 17.62 when it should be 17.63. The VAT calculation is performed in a SQL Server 2000 stored procedure. In the end I tracked it down and it wasn't a propblem with my calculation.

The price was coming out as 17.63 fine. The stored procedure then had to return this price in pence (17.63 * 100 = 17.63). When I put in a print statement with this calculation it was correct but when I output the variable that the result was assigned to it was coming out as 1762.

The variable that the result was being put into was of real datatype.

I then wrote a udf to test this. Here is the function:

CREATE FUNCTION dbo.POUNDS_TO_PENCE
(
@POUNDVALUE real
)
RETURNS INTEGER
AS
BEGIN

RETURN @POUNDVALUE * 100

END

As you can see nothing very special.

If you run this runction and pass in 17.63 it will return 1762!!!

The bit I don't get is if I change the @POUNDSVALUE intput variable to type float it returns the correct amount.

I've also found that the same problem occurs when passing in £30 + VAT (35.25) + 1pence. So, 35.26 comes out as 3525 instead of 3526. This is the case if you keep doubling the number (and adding a few pence here and there).

Does anyone know why this is or is it a bug in the processor?

The SQL books online say the following about the float and real data types:

--------------------------------------------------------
float and real (T-SQL)
Approximate number data types for use with floating point numeric data. Floating point data is approximate; not all values in the data type range can be precisely represented.

Syntax
float[(n)]
Is a floating point number data from - 1.79E + 308 through 1.79E + 308. n is the number of bits used to store the mantissa of the float number in scientific notation and thus dictates the precision and storage size. n must be a value from 1 through 53.


n is Precision Storage size
1-24 7 digits 4 bytes
25-53 15 digits 8 bytes


The Microsoft® SQL Server™ float[(n)] data type conforms to the SQL-92 standard for all values of n from 1 to 53. The synonym for double precision is float(53).

real
Floating point number data from –3.40E + 38 through 3.40E + 38. Storage size is 4 bytes. In SQL Server, the synonym for real is float(24).


--------------------------------------------------------

Apart from the fact that it says 'Approximate number data types' I can't see any difference between the data type apart from the ranges.

Anyone any ideas?
Thanks
Tom Holder

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Column_2,
Column_3,
10*Column_1 AS Column_4,
10*Column_2 AS Column_5,

-- I am not being able to understand how to do this particular step Column_1*Column_5 As Column_6

FROM Table_1
First 3 Columns are available within the Original Table_1
The Column_4 and Column_5 have been created by me, by doing some Calculations related to the original columns.

Now, when I try to do FURTHER CALCULATION on these newly created columns, then SQL Server does not allows that.

I was hoping that I will be able to use the Newly Created Columns 4 and 5 within this same query to do further more calculations, but that does not seems to be the case, or am I doing something wrong here ?

If I have to create a new column by the name of Column_6, which is actually a multiplication of Original Column_1 and Newly Created Column_5 "I tried this - Column_1*Column_5 As Column_6", then what is the possible solution for me ?

I have tried to present my problem in the simplest possible manner. The actual query has many original columns from Table_1 and many Calculated columns that are created by me. And now I have to do various calculations that involve making use of both these type of columns.

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