// magic number is 2^n
const double FMOD_MAGIC_NUMBER = 4294967296.0;
const double FRAC_MAGIC_NUMBER = 268435456.0;   // 2^28

// these fmods won't work with negative numbers.
// if the input is negative, the magic number needs to be negated,
// but this support was omitted for speed.
double fmod64(double f_)
{
    M3Assert(0.0f <= f_ && f_ < FMOD_MAGIC_NUMBER);
    __m128d f = _mm_set_sd(f_);
    __m128d magic = _mm_set_sd(FMOD_MAGIC_NUMBER);
    f = _mm_add_sd(f, magic);
    // Hang on to the exponent, and to everything below 64.
    const M3uint64 mask_ = 0xFFF0000003FFFFFF;
    __m128d mask = _mm_set_sd(reinterpret_cast<const double&>(mask_));
    f = _mm_and_pd(f, mask);
    f = _mm_sub_sd(f, magic);
    _mm_store_sd(&f_, f);
    M3Assert(f.m128d_f64[0] < 64.0f);
    return f_;
}