To kick things off, let’s define what exactly is meant by “floating point” in this context. In computer science, a float (short for “floating-point number”) refers to any real number that can be represented using a finite set of digits with decimal points. This is different from an integer or whole number, which has no fractional component and can only take on specific values within its range.
Now, you might be wondering why we need floating point numbers in the first place. Well, for starters, they allow us to perform calculations that involve decimals without having to resort to cumbersome string manipulation or other workarounds. They also provide a more intuitive way of representing real-world data, such as measurements and financial figures, which often require decimal places beyond the scope of whole numbers.
However, there’s a catch floating point arithmetic is not perfect. In fact, it can be downright frustrating at times! This is because computers use binary (base-2) rather than decimal (base-10) to represent numbers, which means that certain values cannot be accurately represented using only 8 bytes of memory. As a result, we often encounter rounding errors and other anomalies when working with floats in Python or any other programming language.
In fact, there are several ways to mitigate them and ensure that your code is as accurate and reliable as possible. Here are a few tips:
1) Use the decimal module instead of floats whenever possible. This will allow you to perform calculations with greater precision and avoid common rounding errors. For example, instead of using float(3.14), try importing from decimal and using Decimal(‘3.14’) instead.
2) Avoid comparing floating point numbers for equality or inequality. Instead, use a tolerance threshold (e.g., 0.00001) to determine whether two values are close enough to be considered equal. This will help you avoid false positives and negatives due to rounding errors.
3) Be aware of the limitations of floating point arithmetic when working with large or small numbers. For example, if your program involves calculating the square root of a very large number (e.g., 10^20), you may encounter overflow or underflow errors due to the limited range and precision of floats.
4) Use scientific notation whenever possible to improve readability and reduce clutter in your code. For example, instead of writing out long strings of digits for large numbers (e.g., 1234567890), try using exponential notation (e.g., 1.23E+9) instead.