Why Can C Calculations with Floating-Point Numbers Result in Significant Errors?

Understanding Floating Point Error: A C Example

Floating point errors arise when computers represent real numbers using a limited number of bits, leading to precision loss. To illustrate this, let's consider an example in C :

Scenario:
Calculate the probability of exactly two successes in ten independent experiments with probability p.

Code:

double p_2x_success = pow(1-p, (double)8) * pow(p, (double)2) * (double)choose(8, 2);

Potential for Floating Point Error:

Each operation (exponentiation, multiplication, binomial coefficient) introduces some rounding error. While individual errors may be negligible, their accumulation can become significant, especially when dealing with large numbers or precise calculations.

Graphical Representation:

As mentioned in the answer, the function f(k), where k is the number of successes, can be graphed. The ideal graph would show a flat line at zero, indicating no error. However, due to floating point error, the actual graph resembles an exponential curve, with increasing error for higher values of k.

Mitigation Techniques:

To minimize floating point error, consider using:

• Double precision (64-bit) variables instead of single (32-bit) ones
• Libraries that specifically address floating point precision
• Techniques like fixed-point arithmetic or interval arithmetic

Understanding and mitigating floating point error is crucial for ensuring accurate computations, especially in scientific, financial, and engineering applications.

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