Why Does My Floating-Point Rounding Code Produce Different Results with Compiler Optimizations Enabled?

Floating Point Rounding Disparities with Optimization Enabled: A Compiler Bug or Optimization Dilemma?

Floating point computations can often exhibit unexpected behavior, especially when compiler optimizations are enabled. Consider the following code snippet:

#include <cstdlib>
#include <iostream>
#include <cmath>

double round(double v, double digit)
{
    double pow = std::pow(10.0, digit);
    double t = v * pow;
    double r = std::floor(t + 0.5);
    return r / pow;
}

int main()
{
    std::cout << round(4.45, 1) << std::endl;
    std::cout << round(4.55, 1) << std::endl;
}

Expected output:

4.5
4.6

However, when this code is compiled using g with optimizations (O1 - O3), the output becomes:

4.5
4.5

Cause of Disparity:

This inconsistency stems from the fact that x86 processors internally use 80-bit extended precision for floating point calculations. However, double variables are typically 64-bit wide. When floating point values are stored from the CPU registers to memory, they are rounded from 80-bit precision to 64-bit precision. This rounding can introduce slight errors.

Impact of Optimization Levels:

Different optimization levels can affect the frequency with which floating point values are saved into memory. With higher optimization levels, this happens more frequently. As a result, the rounding error becomes more pronounced.

Solutions:

1. Use the -ffloat-store GCC Option: This option instructs the compiler to store floating point variables in memory instead of registers. This forces the rounding to occur consistently across different optimization levels.
2. Use the long double Type: long double is typically 80-bit wide on g . Using this type can avoid the rounding issue entirely.
3. Modify Variable Storage: Store intermediate computation results into variables to minimize the rounding error.

Further Considerations:

• Intel x86_64 builds are less affected by this issue because compilers use SSE registers for float and double by default, eliminating the need for extended precision.
• -mfpmath compiler option can be used to control the floating point precision used in x86_64 builds.
• Whether to always turn on the -ffloat-store option depends on the specific application and its sensitivity to floating point accuracy. For critical applications, it may be wise to use this option to ensure consistent results.
• Investigating existing C code and libraries for potential issues can be time-consuming. Consider using tools or implementing tests to detect and address any floating point precision problems.

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