Why Do Floating-Point Rounding Discrepancies Occur During Optimization?

Floating Point Discrepancies Due to Optimization: Compiler Bug or Intrinsic Precision

The code provided, intended to round floating-point values, exhibits divergent behavior on different compilers and optimization settings. This discrepancy stems from discrepancies in floating-point precision handling during optimization.

Intel x86 processors employ 80-bit extended precision internally, while double is typically a 64-bit data type. Optimization levels influence how frequently floating-point values are stored in memory, which leads to rounding from 80-bit to 64-bit precision.

To mitigate this, the -ffloat-store gcc option can be used to maintain consistent floating-point outcomes across optimization levels. Alternatively, using the long double type, which is typically 80-bit wide on gcc, can avoid rounding issues between 80-bit and 64-bit precision.

As per the man gcc documentation, the -ffloat-store option:

Do not store floating point variables in registers, and inhibit
other options that might change whether a floating point value is
taken from a register or memory.

This option is often useful in scenarios where programs require precise definition of IEEE floating point and rely on intermediate computations stored in variables.

In x86_64 builds, compilers by default utilize SSE registers for float and double, eliminating the use of extended precision and mitigating the issue in question. The gcc compiler option -mfpmath controls this behavior.

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