How are floating point values in JSON data columns rounded in MySQL (5.7)?
I am having trouble finding a good resource to know how to solve my issue.
Here's what happens:
CREATE TABLE someTable (jdoc JSON);
INSERT INTO someTable VALUES('{"data":14970.911769838869}');
Then select the rows:
SELECT * from someTable;
I get data back with a different final digit:
'{"data": 14970.911769838867}'
Any idea why this happens? Can I adjust the data in a way to prevent this or is there a rounding precision issue?
Double precision floating point has about 16 decimal digits of precision. Your number has 17 digits, so it can't be represented exactly in floating point, and you get round-off error in the last digit.
See How many significant digits have floats and doubles in java?
The question is about Java, but just about everything uses the same IEEE 754 floating point format, so the answer applies pretty generally.
Related
I am inserting data from one table into another in a MariaDB database, where the column in the first table is FLOAT, and in the second it's DOUBLE. The data can have values of any size, precision and decimal places.
Here is what happens to the values when I do a straight-forward copy:
INSERT INTO data2 (value) SELECT value FROM data1
The values are given random extra significant figures:
FLOAT in data1 DOUBLE in data2
-0.000000000000454747 -0.0000000000004547473508864641
-122.319 -122.31932830810547
14864199700 14864220160
CAST(value AS DECIMAL(65,30)) generates exactly the same values as col 2 above, except I see trailing zeroes.
Yet when I just do
UPDATE data2 SET value = 14867199700 WHERE id = 133025046;
the DOUBLE value is accepted.
Do I have to export all the value to an SQL script and re-import them? Isn't there a better way?
Despite hours trying to experimenting with the issue, I'm not much closer to a solution, despite its limited nature. I can see this is problem that besets all technologies, not just MariaDB or databases, so I have probably just missed the answer somewhere. Stackoverflow is desperately trying to guide to a solution with new suggestion features I hadn't seen before, but unfortunately they are no help, like the other suggested answers.
Your test case is flawed. You are feeding in decimal digits, and not testing just the transfer of FLOAT to DOUBLE.
UPDATE tbl SET double_col = float_col will always copy exactly the same value. This because the DOUBLE representation is a superset of the FLOAT representation (53 vs 24 bits of precision; etc).
Literal, with decimal places: UPDATE tbl SET double_col = 123.456 will mangle the number because of rounding from decimal to DOUBLE. Ditto for float_col. Furthermore, the mangled results will be different!
Hole number literal: UPDATE tbl SET double_col = 14867199700 will be stored exactly. But if you put that same literal into a FLOAT, it will be rounded to 24 bits, so it cannot be stored exactly. You lose exactness at about 7 significant digits for FLOAT and about 16 for DOUBLE. The literal in this example has 9 significant digits (after ignoring trailing zeros).
That's just a sampling of the nightmares you can get into.
You must consider FLOAT and DOUBLE to be approximate. You should never compare for equality; you don't know what might have messed with the last bit of the value.
Also, you should not try to guess when MySQL will perform expressions in DECIMAL instead of DOUBLE.
And, keep in mind that division is usually imprecise due to rounding to some number of bits or decimals.
The "mantissa" of 14864199700 is
1.10111010111111001101100 (binary of FLOAT : 24 bits including 'hidden' leading bit)
1.1011101011111100110110000000101000000000000000000000 (binary of DOUBLE)
^ ^ (lost in FLOAT)
Each of those is multiplied by the same power of 2. The DOUBLE gets exactly 14864199700. The FLOAT lost the bits pointed to.
You can play around with such at https://gregstoll.dyndns.org/~gregstoll/floattohex/
Believe it or not, things used to be worse. People would be billed for $0.00 -- due to rounding errors. Or results of what should have been 1+1 showed as 1.99999999.
I spotted some rounding bug in MySQL. Here is my query:
SELECT /*debugz*/ ROUND((SUM(grade)/2),0) AS grade, SUM(grade) FROM entry.computed_grade a WHERE a.stud_id='7901159' AND a.sy='2014' AND a.term=01 AND a.terms=01 AND a.catalog_no='Christian Life Formation';
and the result is this:
grade sum(grade)
------ ------------
92 185
The grade result should be 93, not 92 because 185/2 = 92.5
Try this
SELECT CEIL((SUM(grade)/2),0) AS grade, SUM(grade) FROM entry.computed_grade a WHERE ((a.stud_id='7901159') AND (a.sy='2014') AND (a.term=01) AND (a.terms=01) AND (a.catalog_no='Christian Life Formation'));
Try to use ceil instead of round.
e.g ceil(1.45) = 2
You should check rounding behavior artickle for mysql. I believe here is the reason of your problem:
For approximate-value numbers, the result depends on the C library. On
many systems, this means that ROUND() uses the “round to nearest even”
rule: A value with any fractional part is rounded to the nearest even
integer.
By the way it's IEEE standard for float point rounding, so you might want stay with it
Do not "patch" this problem by tweaking the query. Actually fix your database. If you are not storing the "grade" column as the DECIMAL data type, and are instead using FLOAT or DOUBLE, your design is inherently broken.
Because floating-point values are approximate and not stored as exact values, attempts to treat them as exact in comparisons may lead to problems.
http://dev.mysql.com/doc/refman/5.6/en/floating-point-types.html
This is not a bug in MySQL. It is an inherent limitation in industry-standard floating point number storage. Use DECIMAL columns to store meaningful, precise numbers, and the other two types only when low storage space or a wide range of allowable values are more important than precision.
Why Subtraction of two equal values in mysql does not equal zero?
both field type are double. See image below
That's known as a approximate precision . This isn't an error, floating point data types are intended to work such way. They can not store data precisely. So if that matters, you should use fixed-point data types, such as DECIMAL in MySQL.
On the other hand, you can always use precision delta for comparisons for floating point, like:
SELECT
`foo`,
`bar`,
IF(ABS(`foo`-`bar`)<1E-13, 0, `foo`-`bar`) AS zero_compared
FROM
t
as you can see, here delta is 1E-13 (normally, that will be enough)
This problem is due to floating point precision and calculations on them.
You can also refer this Issue for clarity on your problem:
MySQL floating point comparison issues
I am creating for fun, but I still want to approach it seriously, a site which hosts various tests. With these tests I hope to collect statistical data.
Some of the data will include the percentage of the completeness of the tests as they are timed. I can easily compute the percentage of the tests but I would like true data to be returned as I store the various different values concerning the tests on completion.
Most of the values are, in PHP floats, so my question is, if I want true statistical data should I store them in MYSQL as FLOAT, DOUBLE or DECIMAL.
I would like to utilize MYSQL'S functions such as AVG() and LOG10() as well as TRUNCATE(). For MYSQL to return true data based off of my values that I insert, what should I use as the database column choice.
I ask because some numbers may or may not be floats such as, 10, 10.89, 99.09, or simply 0.
But I would like true and valid statistical data to be returned.
Can I rely on floating point math for this?
EDIT
I know this is a generic question, and I apologise extensively, but for non mathematicians like myself, also I am not a MYSQL expert, I would like an opinion of an expert in this field.
I have done my research but I still feel I have a clouded judgement on the matter. Again I apologise if my question is off topic or not suitable for this site.
This link does a good job of explaining what you are looking for. Here is what is says:
All these three Types, can be specified by the following Parameters (size, d). Where size is the total size of the String, and d represents precision. E.g To store a Number like 1234.567, you will set the Datatype to DOUBLE(7, 3) where 7 is the total number of digits and 3 is the number of digits to follow the decimal point.
FLOAT and DOUBLE, both represent floating point numbers. A FLOAT is for single-precision, while a DOUBLE is for double-precision numbers. A precision from 0 to 23 results in a 4-byte single-precision FLOAT column. A precision from 24 to 53 results in an 8-byte double-precision DOUBLE column. FLOAT is accurate to approximately 7 decimal places, and DOUBLE upto 14.
Decimal’s declaration and functioning is similar to Double. But there is one big difference between floating point values and decimal (numeric) values. We use DECIMAL data type to store exact numeric values, where we do not want precision but exact and accurate values. A Decimal type can store a Maximum of 65 Digits, with 30 digits after decimal point.
So, for the most accurate and precise value, Decimal would be the best option.
Unless you are storing decimal data (i.e. currency), you should use a standard floating point type (FLOAT or DOUBLE). DECIMAL is a fixed point type, so can overflow when computing things like SUM, and will be ridiculously inaccurate for LOG10.
There is nothing "less precise" about binary floating point types, in fact, they will be much more accurate (and faster) for your needs. Go with DOUBLE.
Decimal : Fixed-Point Types (Exact Value). Use it when you care about exact precision like money.
Example: salary DECIMAL(8,2), 8 is the total number of digits, 2 is the number of decimal places. salary will be in the range of -999999.99 to 999999.99
Float, Double : Floating-Point Types (Approximate Value). Float uses 4 bytes to represent value, Double uses 8 bytes to represent value.
Example: percentage FLOAT(5,2), same as the type decimal, 5 is total digits and 2 is the decimal places. percentage will store values between -999.99 to 999.99.
Note that they are approximate value, in this case:
Value like 1 / 3.0 = 0.3333333... will be stored as 0.33 (2 decimal place)
Value like 33.009 will be stored as 33.01 (rounding to 2 decimal place)
Put it simply, Float and double are not as precise as decimal. decimal is recommended for money related number input.(currency and salary).
Another point need to point out is: Do NOT compare float number using "=","<>", because float numbers are not precise.
Linger: The website you mention and quote has IMO some imprecise info that made me confused. In the docs I read that when you declare a float or a double, the decimal point is in fact NOT included in the number. So it is not the number of chars in a string but all digits used.
Compare the docs:
"DOUBLE PRECISION(M,D).. Here, “(M,D)” means than values can be stored with up to M digits in total, of which D digits may be after the decimal point. For example, a column defined as FLOAT(7,4) will look like -999.9999 when displayed"
http://dev.mysql.com/doc/refman/5.1/en/floating-point-types.html
Also the nomenclature in misleading - acc to docs: M is 'precision' and D is 'scale', whereas the website takes 'scale' for 'precision'.
Thought it would be useful in case sb like me was trying to get a picture.
Correct me if I'm wrong, hope I haven't read some outdated docs:)
Float and Double are Floating point data types, which means that the numbers they store can be precise up to a certain number of digits only.
For example for a table with a column of float type if you store 7.6543219 it will be stored as 7.65432.
Similarly the Double data type approximates values but it has more precision than Float.
When creating a table with a column of Decimal data type, you specify the total number of digits and number of digits after decimal to store, and if the number you store is within the range you specified it will be stored exactly.
When you want to store exact values, Decimal is the way to go, it is what is known as a fixed data type.
Simply use FLOAT. And do not tack on '(m,n)'. Do display numbers to a suitable precision with formatting options. Do not expect to get correct answers with "="; for example, float_col = 0.12 will always return FALSE.
For display purposes, use formatting to round the results as needed.
Percentages, averages, etc are all rounded (at least in some cases). That any choice you make will sometimes have issues.
Use DECIMAL(m,n) for currency; use ...INT for whole numbers; use DOUBLE for scientific stuff that needs more than 7 digits of precision; use FLOAT` for everything else.
Transcendentals (such as the LOG10 that you mentioned) will do their work in DOUBLE; they will essentially never be exact. It is OK to feed it a FLOAT arg and store the result in FLOAT.
This Answer applies not just to MySQL, but to essentially any database or programming language. (The details may vary.)
PS: (m,n) has been removed from FLOAT and DOUBLE. It only added extra rounding and other things that were essentially no benefit.
i want to understand this:
i have a dump of a table (a sql script file) from a database that use float 9,2 as default type for numbers.
In the backup file i have a value like '4172.08'.
I restore this file in a new database and i convert the float to decimal 20,5.
Now the value in the field is 4172.08008
...where come from the 008??
tnx at all
where come from the 008??
Short answer:
In order to avoid the float inherent precision error, cast first to decimal(9,2), then to decimal(20,5).
Long answer:
Floating point numbers are prone to rounding errors in digital computers. It is a little hard to explain without throwing up a lot of math, but lets try: the same way 1/3 represented in decimal requires an infinite number of digits (it is 1.3333333...), some numbers that are "round" in decimal notation have infinite number of digits in binary. Because this format is stored in binary and has finite precision, there is an implicit rounding error and you may experience funny things like getting 0.30000000000000004 as the result of 1.1 + 1.2.
This is the difference between float and decimal. Float is a binary type, and can't represent that value exactly. So when you convert to decimal (as expected, a decimal type), its not exactly the original value.
See http://floating-point-gui.de/ for some more information.