### 6.3 FFTW Accuracy on Cell

The SPEs are fully IEEE-754 compliant in double precision. In single precision, they only implement round-towards-zero as opposed to the standard round-to-even mode. (The PPE is fully IEEE-754 compliant like all other PowerPC implementations.) Because of the rounding mode, FFTW is less accurate when running on the SPEs than on the PPE. The accuracy loss is hard to quantify in general, but as a rough guideline, the L2 norm of the relative roundoff error for random inputs is 4 to 8 times larger than the corresponding calculation in round-to-even arithmetic. In other words, expect to lose 2 to 3 bits of accuracy.

FFTW currently does not use any algorithm that degrades accuracy to gain performance on the SPE. One implication of this choice is that large 1D transforms run slower than they would if we were willing to sacrifice another bit or so of accuracy.