I am currently making a small MariaDB database and ran into the following problem:
I want to save a floatingpoint number with only 2 poistions after the decimal point but everything before the decimal point should be unaffected.
For example: 1.11; 56789.12; 9999.00; 999999999999.01 etc.
I have done some research and this is what I am using right now:
CREATE TABLE mytable (
mynumber DOUBLE(10, 2)
)
The problem with this solution is that I also have to limit the number of positions before the decimal point, what I don't want to do.
So is there a possibility to limit the number of positions after the decimal point without affecting the positions before the decimal point or is there a "default number" I can use for the positions before the decimal point?
Don't use (m,n) with FLOAT or DOUBLE. It does nothing useful; it does cause an extra round.
DECIMAL(10,2) is possible; that will store numbers precisely (to 2 decimal places).
See also ROUND() and FORMAT() for controlling the rounding for specific values.
You had a mistake -- 999999999999.01 won't fit in DOUBLE(10,2), nor DECIMAL(10,2). It can handle only 8 (=10-2) digits to the left of the decimal point.
You can create a trigger that intercepts INSERT and UPDATE statements and truncates their value to 2 decimal places. Note, however, that due to how floating point numbers work at machine level, the actual number may be different.
Double precision numbers are accurate up to 14 significant figures, not a certain number of decimal points. Realistically, you need to detemine what is the biggest value you might ever want to store. Once you have done that, the DECIMAL type may be more appropriate for what you are trying to do.
See here for more details:
https://dev.mysql.com/doc/refman/8.0/en/precision-math-decimal-characteristics.html
I'm doing geography calculations, and ultimately end up with a latitude and longitude to store in a Geography::Point object.
Both latitude and longitude can have 7 digits at most (which also gives precision up to 11 mm, which is plenty).
The problem is: if the value of a field cannot be stored correctly in a Double, MS SQL rounds towards the nearest number that can, but does so by adding a bunch of digits.
=> e.g. 5.9395772 is stored as 5.9395771999999996
The problem this creates, is that [Position].ToString() then exceeds the maximum amount of characters is allowed for that column (and no, I can't increase that limit).
Since we're dealing with Latitude, Longitude, Altitude and Accuracy, there's space for exactly 11 characters for Latitude and Longitude each:
String.Format(CultureInfo.InvariantCulture, "{0:##0.0######}", num)
I've tried simply Math.Round()ing to 6 digits, but then other numbers (e.g. 6.098163 to 6.0981629999999996) get the same problem.
How do I Math.Round towards the nearest 7-digit valid bit representation?
EDIT/ADD
Public Function ToString_LatLon(ByVal num As Double) As String
num = Math.Round(num, 7, MidpointRounding.AwayFromZero)
Return String.Format(CultureInfo.InvariantCulture, "{0:##0.0######}", num)
End Function 'IN = 5.9395772, OUT = 5.9395772
The above code receives a Double and correctly returns the String representation. I've checked it, this is correct also for troubling numbers.
It's stored in SQL Server through the framework we use. I think the problem occurs when storing the value
When I retrieve the value, I get an error in VB, saying the value is wider than the framework allows (max of 50 characters).
If I run a query in SSMS, I find e.g. POINT (X.0981629999999996 XX.664725 NULL 15602.707) (51 characters, anonimized).
EDIT 2
I've done some more research and some calculations. It seems that the stored value 5.9395772 is converted to binary and returned as 5.9395771999999996, which is stored as a double inside the database (in a binary Geography::Point object, not to worry.) Convert the binary 0 10000000001 0111110000100010000010000110100010000100010011011101 back to decimal, and you get 5.93957719999999955717839839053340256214141845703125, but abbreviated at 16 decimals - whereas I would like it abbreviated at 7 decimals.
Solutions:
Round the value down/up to the nearest value where everything from the 8th decimal onward is 0 (or enough zeroes before another nonzero digit is found)
Query for only so many decimals.
Query the actual (hexadecimal) value, and convert that (instead of the string representation)
Keep the string representation, but round the values before storing and after retrieving to the required amount of decimals.
Discussions:
Both in office and here (at #RobertBaron's answer): this is quite tricky, might have a huge decrease in precision, and is basically a lot of work.
Perhaps this is possible, I don't know.
This would be the cleanest solution, as my colleagues and I agree, however this is a lot of work in developing and testing.
Instead of caring about the value in memory to be equal to the value in the database, we don't care about the value in the database (too much).
In the end, after quite some whiteboard bit-calculations and a lengthy discussion, we've gone with option 4. After we retrieve the [Position].ToString() (for which we've increased the string limit) from the database, we convert that as we're already doing, and as additional step before using it anywhere we round the value to the required amount of decimals. When returning the value to the database, we once again round the value to the amount of decimals, and don't care what the database really does with it.
Essentially, this is option 2, but then on the program-side instead of database-side.
This is only a partial answer.
If by valid bit representation you mean exact bit representation, then this is possible. The decimal numbers that have exact bit representation are 1/2, 1/4, 3/4, 1/8, 3/8, 5/8, 7/8, 1/16, 3/16, ...
The challenge is to characterize among these powers of two, those whose base 10 representation has 7 digits or less, and then to round any base 10 number to the closest of these numbers.
I am posting this in the hope that it may get you one step further toward a solution.
If you cannot change the data type into a DECIMAL for whatever reasons, you have to cast it into a DECIMAL every time you need the value. It's that simple. And you can either do it on the SQL Server side or in VB.NET, but you need a DECIMAL. DOUBLEs are imprecise.
By the way, it is not the SQL Server that rounds towards the nearest number it recognizes by adding a bunch of digits - it's the processor that does it. That's also why you may get slightly different DOUBLE values after restoring your database on another server.
And never ever even think of using them as an ID: I know an application that uses FLOAT values containing the timestamp (<creation day since whatever>.<time as fractals of the day>) as part of the primary key (of nearly every table!). Every 10000th record or so cannot be addressed directly by its ID because the value differs somewhat on the client that sends the query and the server by some nanoseconds although the number looks exactly the same in SSMS on the client and the server.
I need to multiply a number which is like these 00000000001099 with 0.01 and then convert into two decimal places for e.g., 10.99 after multiplication in a derived column in SSIS package.
Right now I am using these expression (dt_numeric,2,2)((DT_CY)((dt_wstr,14)PRICE) * 0.01) but it is failing.
I get the column price with value 00000000001099 from a flat file after conversion I need to place the value back to a flat file again.
Since your string is 14 long you cannot use DT_I4 - it'll just figure out that this is very wrong and give you the error about potential loss of data. You could edit the error and ignore possible truncations, but a better way is to use a datatype that can hold your number
Your Derivation should look like this:
(DT_NUMERIC,X,2)((DT_NUMERIC,X+2,2)([InputColumn]))*0.01)
In your example
(DT_NUMERIC,14,2)(((DT_NUMERIC,16,2)([PRICE]))*0.01)
By using the extra step with x+2,2 makes you able to hold 99999999999999 into the numeric, then divide by 100 (or multiply with 0.01) and cast back to the minimum possible numeric (x,2) - you might want to use a bigger standardized numeric type - look at MSDN/BOL to see the storage requirements for each of them, and just pick the biggest type taking the same amount of bytes as your requirement.
This should work...
(DT_DECIMAL, 2 )(DT_WSTR, 20 )((DT_I4)#[User::Cost] * 0.01)
While the value 00000000001099 is a number, it cannot be represented this way in a numeric datatype. The leading zeros will be stripped. Because you are showing this number this way, I must presume the number is stored in a string datatype. In the dataflow before your derived column I would recommend the use of the "Data Conversion" component. Convert the string to a numeric type. In the downstream derived column component perform the mathematical multiplcation operation to get the decimal point in the correct place.
We are rewriting our legacy accounting system in VB.NET and SQL Server. We brought in a new team of .NET/ SQL Programmers to do the rewrite. Most of the system is already completed with the dollar amounts using floats. The legacy system language, I programmed in, did not have a float, so I probably would have used a decimal.
What is your recommendation?
Should the float or decimal data type be used for dollar amounts?
What are some of the pros and cons for either?
One con mentioned in our daily scrum was you have to be careful when you calculate an amount that returns a result that is over two decimal positions. It sounds like you will have to round the amount to two decimal positions.
Another con is all displays and printed amounts have to have a format statement that shows two decimal positions. I noticed a few times where this was not done and the amounts did not look correct. (i.e. 10.2 or 10.2546)
A pro is the float-only approach takes up eight bytes on disk where the decimal would take up nine bytes (decimal 12,2).
Should Float or Decimal data type be used for dollar amounts?
The answer is easy. Never floats. NEVER!
Floats were according to IEEE 754 always binary, only the new standard IEEE 754R defined decimal formats. Many of the fractional binary parts can never equal the exact decimal representation.
Any binary number can be written as m/2^n (m, n positive integers), any decimal number as m/(2^n*5^n).
As binaries lack the prime factor 5, all binary numbers can be exactly represented by decimals, but not vice versa.
0.3 = 3/(2^1 * 5^1) = 0.3
0.3 = [0.25/0.5] [0.25/0.375] [0.25/3.125] [0.2825/3.125]
1/4 1/8 1/16 1/32
So you end up with a number either higher or lower than the given decimal number. Always.
Why does that matter? Rounding.
Normal rounding means 0..4 down, 5..9 up. So it does matter if the result is
either 0.049999999999.... or 0.0500000000... You may know that it means 5 cent, but the the computer does not know that and rounds 0.4999... down (wrong) and 0.5000... up (right).
Given that the result of floating point computations always contain small error terms, the decision is pure luck. It gets hopeless if you want decimal round-to-even handling with binary numbers.
Unconvinced? You insist that in your account system everything is perfectly ok?
Assets and liabilities equal? Ok, then take each of the given formatted numbers of each entry, parse them and sum them with an independent decimal system!
Compare that with the formatted sum. Oops, there is something wrong, isn't it?
For that calculation, extreme accuracy and fidelity was required (we used Oracle's
FLOAT) so we could record the "billionth's of a penny" being accured.
It doesn't help against this error. Because all people automatically assume that the computer sums right, and practically no one checks independently.
This photo answers:
This is another situation: man from Northampton got a letter stating his home would be seized if he didn't pay up zero dollars and zero cents!
First you should read What Every Computer Scientist Should Know About Floating Point Arithmetic. Then you should really consider using some type of fixed point / arbitrary-precision number package (e.g., Java BigNum or Python decimal module). Otherwise, you'll be in for a world of hurt. Then figure out if using the native SQL decimal type is enough.
Floats and doubles exist(ed) to expose the fast x87 floating-point coprocessor that is now pretty much obsolete. Don't use them if you care about the accuracy of the computations and/or don't fully compensate for their limitations.
Just as an additional warning, SQL Server and the .NET framework use a different default algorithm for rounding. Make sure you check out the MidPointRounding parameter in Math.Round(). .NET framework uses bankers' rounding by default and SQL Server uses Symmetric Algorithmic Rounding. Check out the Wikipedia article here.
Ask your accountants! They will frown upon you for using float. Like David Singer said, use float only if you don't care for accuracy. Although I would always be against it when it comes to money.
In accounting software is not acceptable a float. Use decimal with four decimal points.
A bit of background here....
No number system can handle all real numbers accurately. All have their limitations, and this includes both the standard IEEE floating point and signed decimal. The IEEE floating point is more accurate per bit used, but that doesn't matter here.
Financial numbers are based on centuries of paper-and-pen practice, with associated conventions. They are reasonably accurate, but, more importantly, they're reproducible. Two accountants working with various numbers and rates should come up with the same number. Any room for discrepancy is room for fraud.
Therefore, for financial calculations, the right answer is whatever gives the same answer as a CPA who's good at arithmetic. This is decimal arithmetic, not IEEE floating point.
Floating points have unexpected irrational numbers.
For instance you can't store 1/3 as a decimal, it would be 0.3333333333... (and so on)
Floats are actually stored as a binary value and a power of 2 exponent.
So 1.5 is stored as 3 x 2 to the -1 (or 3/2)
Using these base-2 exponents create some odd irrational numbers, for instance:
Convert 1.1 to a float and then convert it back again, your result will be something like: 1.0999999999989
This is because the binary representation of 1.1 is actually 154811237190861 x 2^-47, more than a double can handle.
More about this issue on my blog, but basically, for storage, you're better off with decimals.
On Microsoft SQL server you have the money data type - this is usually best for financial storage. It is accurate to 4 decimal positions.
For calculations you have more of a problem - the inaccuracy is a tiny fraction, but put it into a power function and it quickly becomes significant.
However decimals aren't very good for any sort of maths - there's no native support for decimal powers, for instance.
I'd recommend using 64-bit integers that store the whole thing in cents.
Use SQL Server's decimal type.
Do not use money or float.
money uses four decimal places and is faster than using decimal, but suffers from some obvious and some not so obvious problems with rounding (see this connect issue).
The only reason to use Float for money is if you don't care about accurate answers.
Floats are not exact representations, precision issues are possible, for example when adding very large and very small values. That's why decimal types are recommended for currency, even though the precision issue may be sufficiently rare.
To clarify, the decimal 12,2 type will store those 14 digits exactly, whereas the float will not as it uses a binary representation internally. For example, 0.01 cannot be represented exactly by a floating point number - the closest representation is actually 0.0099999998
For a banking system I helped develop, I was responsible for the "interest accrual" part of the system. Each day, my code calculated how much interest had been accrued (earnt) on the balance that day.
For that calculation, extreme accuracy and fidelity was required (we used Oracle's FLOAT) so we could record the "billionth's of a penny" being accrued.
When it came to "capitalising" the interest (ie. paying the interest back into your account) the amount was rounded to the penny. The data type for the account balances was two decimal places. (In fact it was more complicated as it was a multi-currency system that could work in many decimal places - but we always rounded to the "penny" of that currency). Yes - there where "fractions" of loss and gain, but when the computers figures were actualised (money paid out or paid in) it was always REAL money values.
This satisfied the accountants, auditors and testers.
So, check with your customers. They will tell you their banking/accounting rules and practices.
Even better than using decimals is using just plain old integers (or maybe some kind of bigint). This way you always have the highest accuracy possible, but the precision can be specified. For example the number 100 could mean 1.00, which is formatted like this:
int cents = num % 100;
int dollars = (num - cents) / 100;
printf("%d.%02d", dollars, cents);
If you like to have more precision, you can change the 100 to a bigger value, like: 10 ^ n, where n is the number of decimals.
Another thing you should be aware of in accounting systems is that no one should have direct access to the tables. This means all access to the accounting system must be through stored procedures.
This is to prevent fraud, not just SQL injection attacks. An internal user who wants to commit fraud should not have the ability to directly change data in the database tables, ever. This is a critical internal control on your system.
Do you really want some disgruntled employee to go to the backend of your database and have it start writing them checks? Or hide that they approved an expense to an unauthorized vendor when they don't have approval authority? Only two people in your whole organization should be able to directly access data in your financial database, your database administrator (DBA) and his backup. If you have many DBAs, only two of them should have this access.
I mention this because if your programmers used float in an accounting system, likely they are completely unfamiliar with the idea of internal controls and did not consider them in their programming effort.
I had been using SQL's money type for storing monetary values. Recently, I've had to work with a number of online payment systems and have noticed that some of them use integers for storing monetary values. In my current and new projects I've started using integers and I'm pretty content with this solution.
Out of the 100 fractions n/100, where n is a natural number such that 0 <= n and n < 100, only four can be represented as floating point numbers. Take a look at the output of this C program:
#include <stdio.h>
int main()
{
printf("Mapping 100 numbers between 0 and 1 ");
printf("to their hexadecimal exponential form (HEF).\n");
printf("Most of them do not equal their HEFs. That means ");
printf("that their representations as floats ");
printf("differ from their actual values.\n");
double f = 0.01;
int i;
for (i = 0; i < 100; i++) {
printf("%1.2f -> %a\n",f*i,f*i);
}
printf("Printing 128 'float-compatible' numbers ");
printf("together with their HEFs for comparison.\n");
f = 0x1p-7; // ==0.0071825
for (i = 0; i < 0x80; i++) {
printf("%1.7f -> %a\n",f*i,f*i);
}
return 0;
}
You can always write something like a Money type for .NET.
Take a look at this article: A Money type for the CLR. The author did an excellent work in my opinion.
Whatever you do, you need to be careful of rounding errors. Calculate using a greater degree of precision than you display in.
Have you considered using the money-data type to store dollar-amounts?
Regarding the con that decimal takes up one more byte, I would say don't care about it. In 1 million rows you will only use 1 more MB and storage is very cheap these days.
You will probably want to use some form of fixed point representation for currency values. You will also want to investigate banker's rounding (also known as "round half to even"). It avoids bias that exist in the usual "round half up" method.
Always use Decimal. Float will give you inaccurate values due to rounding issues.
Floating point numbers can only represent numbers that are a sum of negative multiples of the base - for binary floating point, of course, that's two.
There are only four decimal fractions representable precisely in binary floating point: 0, 0.25, 0.5 and 0.75. Everything else is an approximation, in the same way that 0.3333... is an approximation for 1/3 in decimal arithmetic.
Floating point is a good choice for computations where the scale of the result is what is important. It's a bad choice where you're trying to be accurate to some number of decimal places.
This is an excellent article describing when to use float and decimal. Float stores an approximate value and decimal stores an exact value.
In summary, exact values like money should use decimal, and approximate values like scientific measurements should use float.
Here is an interesting example that shows that both float and decimal are capable of losing precision. When adding a number that is not an integer and then subtracting that same number float results in losing precision while decimal does not:
DECLARE #Float1 float, #Float2 float, #Float3 float, #Float4 float;
SET #Float1 = 54;
SET #Float2 = 3.1;
SET #Float3 = 0 + #Float1 + #Float2;
SELECT #Float3 - #Float1 - #Float2 AS "Should be 0";
Should be 0
----------------------
1.13797860024079E-15
When multiplying a non integer and dividing by that same number, decimals lose precision while floats do not.
DECLARE #Fixed1 decimal(8,4), #Fixed2 decimal(8,4), #Fixed3 decimal(8,4);
SET #Fixed1 = 54;
SET #Fixed2 = 0.03;
SET #Fixed3 = 1 * #Fixed1 / #Fixed2;
SELECT #Fixed3 / #Fixed1 * #Fixed2 AS "Should be 1";
Should be 1
---------------------------------------
0.99999999999999900
Your accountants will want to control how you round. Using float means that you'll be constantly rounding, usually with a FORMAT() type statement, which isn't the way you want to do it (use floor / ceiling instead).
You have currency datatypes (money, smallmoney), which should be used instead of float or real. Storing decimal (12,2) will eliminate your roundings, but will also eliminate them during intermediate steps - which really isn't what you'll want at all in a financial application.