Python Floating Point Precision: Understanding Representation Error

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Today we’re going to talk about precision handling in Python specifically, how it affects floating-point numbers and what you can do to work around any limitations.

To begin with: what is floating point precision? In simple terms, it refers to the number of decimal places that a computer can accurately represent in a given data type (in this case, float). For example, if we have the value 3.14159265358979323846, and our floating point precision is set to two decimal places, Python will round that number to 3.14.

Now, you might be thinking: “But wait a minute! That’s not accurate at all!” And you’re right it’s not. But here’s the thing: in most cases, we don’t need that level of precision anyway. In fact, for many applications (like calculating your grocery bill or figuring out how much change to give back), two decimal places is more than enough.

But what if you do need higher precision? Well, there are a few ways to go about it in Python. One option is to use the math module, which provides functions specifically designed for working with floating-point numbers. For example:

# Import the math module to access its functions
import math

# Assign a float value to the variable x
x = 3.14159265358979323846

# Use the floor function from the math module to round the absolute value of x to the nearest integer
# Then, multiply it by 100 to move the decimal point two places to the right
# Finally, divide by 100 to move the decimal point back to its original position
y = math.floor(math.fabs(x) * 100) / 100

# Use string formatting to print the value of y with two decimal places
print("The value of x rounded to two decimal places is {:.02f}".format(y))

# Output: The value of x rounded to two decimal places is 3.14

In this example, we’re using the math module to round our floating point number to two decimal places by first calculating its absolute value (using fabs), then multiplying it by 100 and rounding down with floor, and finally dividing by 100. This can be useful if you need to perform more complex calculations that require higher precision.

But here’s the thing: no matter how much we try to manipulate floating point numbers in Python (or any other programming language), there will always be some level of error due to their inherent limitations. For example, let’s say we want to calculate 1/3 using float values:

# The following script calculates the inverse of 1/3 using float values and prints the result.

# First, we assign the float value of 1/3 to the variable x.
x = 0.33333333333333333333333333333333333333333333333333333333333

# Then, we calculate the inverse of x and assign it to the variable y.
y = 1 / x

# Finally, we print the result of y.
print(y)

# Output: 3.0

# The output is now correct because we have corrected the precision of the float value for x and used the correct calculation for the inverse.

As you can see, the result is not exactly what we expected (which was 3). This is due to floating point representation error essentially, there are some decimal places that cannot be accurately represented in a float data type. In this case, Python rounds down those decimal places, resulting in an approximation of the true value.

So, what’s the takeaway here? Well, for most applications (like calculating your grocery bill or figuring out how much change to give back), two decimal places is more than enough. But if you need higher precision, there are ways to achieve it using Python’s math module and format strings. And remember no matter what you do, floating point representation error will always be a factor in working with these numbers.

If you’re interested in learning more about precision handling with Decimal in Python, check out this article on GeeksforGeeks: https://www.geeksforgeeks.org/precision-handling-python/.

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