Why Do My Double-Precision Floating Point Calculations Change With Optimization?

Floating Point Precision Discrepancies Under Optimization: A Compiler Bug?

Problem Statement:

In certain cases, code using floating point calculations may produce different results when optimization is enabled compared to when it is disabled. This is particularly observed in the case of double variables, where optimization seems to affect the precision of calculations.

Analysis:

The issue arises due to the internal handling of floating point values in Intel x86 processors. These processors use an 80-bit extended precision internally, while double variables are typically stored in 64-bit registers. When optimization is enabled, the compiler may optimize code to store floating point values in registers to improve performance. However, this optimization can lead to rounding errors when values are transferred from the 80-bit extended precision registers to the 64-bit registers.

Resolution:

To resolve this issue, there are several options:

1. Use the -ffloat-store GCC Option: This option explicitly instructs the compiler not to store floating point variables in registers, preventing the rounding errors caused by precision differences.
2. Utilize long double Data Type: long double variables are typically 80-bit wide on GCC, eliminating the need for precision conversion between extended precision and double precision.

Further Considerations:

• In x86_64 builds, the compiler usually uses SSE registers for float and double, effectively eliminating the extended precision issue.
• The -mfpmath GCC compiler option allows fine-grained control over floating point precision handling.

Conclusion:

The observed discrepancy in floating point results under optimization is not necessarily a compiler bug but rather a result of the internal floating point handling in Intel x86 processors. By employing the provided solutions, developers can ensure that their floating point calculations produce consistent results regardless of optimization settings.

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