Understanding Floating Point Data Types and the Impact of Parallelism on Query Results
In the realm of SQL development, data precision and accuracy are paramount. However, there are cases where seemingly straightforward operations on static tables can yield unexpected results. One such scenario involves the use of the float data type and the interaction between query parallelism and the associative property of mathematical operations.
The Mysterious Behavior of Float Data Types
Float data types are known for their inherent imprecision due to the way computers represent real numbers using binary approximations. Despite this, one might assume that a static, unmodified table should yield consistent results when performing the same operation repeatedly. However, this assumption can be challenged, as demonstrated by an intriguing phenomenon where summing a float column produces slightly varying results on subsequent runs.
The Non-Associative Property
The behavior in question can be attributed to the non-associative property of floating-point arithmetic. Unlike other numeric data types, such as integers, where the order of addition does not affect the outcome, float data types do not obey this property. In other words, the result of (a + b) + c might not be the same as a + (b + c). This discrepancy is often linked to the inherent imprecision of float data types, causing values to be rounded differently during intermediate steps of computation.
An excellent resource on this topic is the article “What Every Computer Scientist Should Know About Floating-Point Arithmetic.” This work provides valuable insights into the intricacies of floating-point arithmetic, shedding light on why float data types behave the way they do. See the bottom of this page for links.
The Parallelism Factor
Parallelism, a feature used to accelerate query processing by executing tasks concurrently, adds another layer of complexity to the mix. While parallelism can significantly enhance performance, it can also lead to unexpected variations in query results, even on static tables. This phenomenon becomes particularly apparent when performing summations on float columns.
Queries that involve parallel execution introduce the possibility of different threads processing rows in varying orders. This inherent parallelism-induced row processing variability, combined with the non-associative property of float arithmetic, can magnify the discrepancies in query results. Consequently, even when running the same query seconds apart, the outcomes may diverge due to the order in which rows are processed by parallel threads. Note that because relations are not inherently ordered, even without parallelism this effect can be noticed, but the likelihood of observing this effect is reduced without some other external factor causing a change in the row-fetching behavior. This external factor could be, however, something as simple as index maintenance happening in the background!
The Intersection of Float Data Types and Parallelism
The interaction between float data types and parallelism creates a unique challenge in ensuring consistent query results. For example, an experiment conducted on SQL Server demonstrates that running the same query with different degrees of parallelism can lead to varied outcomes. This behavior is especially pronounced when dealing with multiple copies of a table lacking unique clustered indexes.
Embracing the Complexity and Finding Solutions
While the behavior of float data types and parallelism may initially seem perplexing, understanding the underlying factors enables SQL developers to tackle these challenges effectively. The use of query hints, such as OPTION (MAXDOP 1), can mitigate some of the variability introduced by parallelism. However, in cases where parallel execution is necessary, developers should be aware of the potential for fluctuating results and strive to design queries that minimize the impact of the non-associative property of float arithmetic. For this reason, it is often recommended in software development to avoid using float data types, and instead define precise decimals for your numeric data.
BFAP
In conclusion, when the question is “why do my sums keep changing slightly?” then “Because Float And Parallelism” is the answer.
Additional Resources
What Every Computer Scientist Should Know About Floating-Point Arithmetic
More “Wrong” SQL Server Math - Floating Point Errors