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copied!<p>You are encountering what is often called the 'x87 excess-precision "bug"'.</p> <p>In short: historically, (nearly) all floating-point computation on x86 processors was done using the x87 instruction set, which by default operates on an 80-bit floating-point type, but can be set to operate in either single- or double-precision (almost) by some bits in a control register.</p> <p>If single-precision operations are performed while the precision of the x87 control register is set to double- or extended-precision, then the results will differ from what would be produced if the same operations were performed in single-precision (unless the compiler is extraordinarily careful and stores the result of every computation and reloads it to force rounding to occur in the correct place.)</p> <p>Your code running on 32-bit is using the x87 unit for floating-point computation (apparently with the control register set for double-precision), and thus encountering the issue described above. Your code running on 64-bit is using the SSE[2,3,...] instructions for floating-point computation, which provide native single- and double-precision operations, and therefore does not carry excess-precision. This is why your results differ.</p> <p>You can work around this (to a point) by telling your compiler to use SSE for floating-point computation even on 32-bit (<code>-mfpmath=sse</code> with GCC). Even then, bit-exact results are not guaranteed because the various libraries that you link against may use x87, or simply use different algorithms depending on the architecture.</p>

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