Why Do Floating-Point Calculations Produce Unexpected Results?

Dealing with Accuracy Limitations in Floating-Point Calculations

Floating-point numbers are widely used in computing, but they come with inherent accuracy limitations. One such issue is the inability to represent all real numbers precisely, leading to rounding errors during calculations.

Issue with Floating-Point Representation

Consider the following code that attempts to calculate the number of columns based on certain values:

double mw = 4.5999999999999996; // Represented as 4.6 internally
double p = 0.2;
double g = 0.2;
int h = 1;
int columns = (int) ((mw - (h * 11 * p)) / ((h * 11 * p) + g)) + 1;

Despite having a desired result of 2, the program incorrectly outputs 1. This is because the internal floating-point representation of 4.6 (4.5999999999999996) causes rounding errors in the calculations.

Addressing the Accuracy Issue

Overcoming this accuracy issue requires acknowledging the limitations of floating-point arithmetic:

• Avoid Strict Equality: Instead of checking for exact equality to a specific value, use a range of acceptable values to account for rounding errors.
• Consider Different Number Representations: Exploring alternative number representations such as fixed-point numbers can provide more precise calculations for specific use cases.
• Understand the Floating-Point Arithmetic: Familiarizing yourself with the principles of floating-point arithmetic helps in understanding potential accuracy limitations and developing strategies to mitigate them.

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