Different floating point result with optimization enabled – compiler bug?

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Intel x86 processors use 80-bit extended precision internally, whereas double is normally 64-bit wide. Different optimization levels affect how often floating point values from CPU get saved into memory and thus rounded from 80-bit precision to 64-bit precision.

Use the -ffloat-store gcc option to get the same floating point results with different optimization levels.

Alternatively, use the long double type, which is normally 80-bit wide on gcc to avoid rounding from 80-bit to 64-bit precision.

man gcc says it all:

   -ffloat-store
       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 prevents undesirable excess precision on machines such
       as the 68000 where the floating registers (of the 68881) keep more
       precision than a "double" is supposed to have.  Similarly for the
       x86 architecture.  For most programs, the excess precision does
       only good, but a few programs rely on the precise definition of
       IEEE floating point.  Use -ffloat-store for such programs, after
       modifying them to store all pertinent intermediate computations
       into variables.

In x86_64 builds compilers use SSE registers for float and double by default, so that no extended precision is used and this issue doesn’t occur.

gcc compiler option -mfpmath controls that.

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