![]() Some of this difference is coming from things other than overflow checking, but this gives you a sense of the performance cost of making integers safer in regular Python:Īnother oddity about how computers think about numbers is that while it seems like computers generate random numbers for you all time time - for example, your computer is happy to give you a random subsample of your data if you ask - the reality is that because computers are deterministic, they actually can’t generate truly random numbers. How much faster? Here’s a comparison of adding up all the integers from 1 to 1,000,000 using regular Python integers (which check for overflows) and using numpy tools (which do not). This makes them much faster, but if you add two really big integers in numpy (or add even small numbers to a really big number) and the result is bigger than what fits in the available bits, you’ll just end up with a negative number. That’s why libraries like numpy and pandas - which are designed for performance when working with huge datasets - don’t check for integer overflows. This makes adding integers in Python much, much slower than it could be. Asking Python to add two integers doesn’t just require the computer to add two integers it requires it to also check the size of the result, and if that size is so big it won’t fit in the existing number of bits that have been allocated, it has to allocate more bits. The problem with what Python does with integers is that, while convenient, it’s slow. See? No problem! Integer Overflows in numpy and pandas ¶ Python is meant to be a friendly language, and one manifestation of that is that in vanilla Python, you can’t overflow your integers! That’s because whenever Python does an integer computation, it stops to check whether you the integer in question has been allocated enough bits to store the result, and, if not, it just adds more bits! So if you do math with an integer that won’t fit in 64 bits, it will just allocate more bits to the integer!ħ237005577332262213973186563042994240829374041602535252466099000494570602496 ![]() ![]() The answer is that it depends on whether you’re using regular, vanilla Python, or numpy / pandas. įloating point numbers can only keep track of so many leading digits, meaning that you can’t work with BOTH very large and very small floating points at the same time (e.g., in Python, 2.32781**55 + 1 = 2.32781**55 returns True).īut when do we need to worry about these issues?.įloating point numbers are always imprecise, resulting in situations where apparently simple math breaks (e.g., in Python 0.1 + 0.1 + 0.1 = 0.3 returns False).Integers can overflow, resulting in situations where adding two big numbers produces a … negative number. So in general terms, the dangers with integers and floating points are: Read This Numeric Hazards in Python, Numpy, and Pandas ¶ To learn about floating point numbers, please: So how do we deal with decimals and really big numbers? Floating point numbers! But they also have their weaknesses: namely, they can’t represent numbers with decimal points (which we use all the time), and they can’t represent really big numbers. If after watching you would like to learn more, Chapters 7 and 8 of Code: The Hidden Language of Computer Hardware and Software by Charles Petzold get into integers in great detail. To see a great discussion of integers (and their major pitfall: integer overflow), please watch this video. Then continue to the section below on Python-specific hazards. To learn the ins-and-outs of how integers and floating point numbers work, please review the following materials (these explanations are very good, and there’s no reason to try to write my own explanations when these exist). But below the hood, integers and floating point numbers work in very different ways, and there are distinct hazards when working with both. In most intro computer science courses, students are taught that integers are for… well, integers (whole numbers), and floating point numbers are for numbers with decimal points. The Two Classes of Numbers: Integers and Floating Point Numbers ¶īroadly speaking, computers have two ways of representing numbers: integers and floating point numbers. In the second part, we’ll discuss when you need to worry about these hazards both (a) when using vanilla Python, and (b) when using numpy and pandas. In the first part, we’ll cover the basics of how computers think about numbers, and what issues can potentially arise with the two main numerical representations you’ll use. As a result, it pays to understand how numbers are represented in computers, and how those representations can get you into trouble. Numeric Hazards in Python, Numpy, and PandasĪs a data scientist, you will spend a lot more time playing with numbers than most programmers. ![]()
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