Why do Floating-Point Calculations Differ with Compiler Optimization Enabled?

Different Floating Point Result with Optimization Enabled: A Deeper Dive into Compiler Behavior

When working with floating-point operations, it is essential to understand the nuances that can arise due to compiler optimizations. As demonstrated in the provided code snippet, different optimization levels can yield unexpected results in the precision of floating-point calculations.

Investigation and Explanation

The code aims to round a double-precision floating-point value to a specified digit. However, with optimizations enabled in g , the results deviate from the expected output. This behavior stems from the fact that Intel x86 processors internally utilize extended precision (80-bit) for floating-point calculations. In contrast, double-precision variables typically occupy 64 bits.

When optimization is disabled (O0), the compiler stores floating-point values in memory, ensuring that the 80-bit precision is preserved. However, with optimization enabled (O1-O3), the compiler takes advantage of the processor's extended precision by keeping values in registers. This optimization can lead to rounding errors when the values are eventually stored back in memory and converted from 80-bit to 64-bit precision.

Resolution Options

To mitigate this issue, the following solutions are recommended:

• Utilize the -ffloat-store GCC option: This option forces the compiler to store floating-point values in memory, preventing precision loss due to optimizations.
• Employ the long double type: This datatype occupies 80 bits on gcc platforms, eliminating the need for conversion between 80-bit and 64-bit precision.

Further Considerations:

• On x86_64 systems, compilers automatically use SSE registers for floating-point operations, avoiding the extended precision issue.
• GCC provides the -mfpmath option to control the compiler's handling of floating-point math.

Regarding Visual Studio 2008

The curious observation that the code produces correct results even with the /fp:fast optimization enabled in Visual Studio 2008 is a testament to the compiler's reliability in this context. While it is generally recommended to use the -ffloat-store option for g , Visual Studio 2008 seems to handle this issue more effectively.

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