Heresy on Bagel

inline mat4 inverse(const mat4& m)
{
    __m128 f1 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0xAA),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xFF), _mm_shuffle_ps(m.m4, m.m3, 0xFF), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xAA), _mm_shuffle_ps(m.m4, m.m3, 0xAA), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0xFF)));

    __m128 f2 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0x55),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xFF), _mm_shuffle_ps(m.m4, m.m3, 0xFF), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x55), _mm_shuffle_ps(m.m4, m.m3, 0x55), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0xFF)));

    __m128 f3 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0x55),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xAA), _mm_shuffle_ps(m.m4, m.m3, 0xAA), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x55), _mm_shuffle_ps(m.m4, m.m3, 0x55), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0xAA)));

    __m128 f4 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0x00),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xFF), _mm_shuffle_ps(m.m4, m.m3, 0xFF), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x00), _mm_shuffle_ps(m.m4, m.m3, 0x00), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0xFF)));

    __m128 f5 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0x00),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0xAA), _mm_shuffle_ps(m.m4, m.m3, 0xAA), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x00), _mm_shuffle_ps(m.m4, m.m3, 0x00), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0xAA)));

    __m128 f6 = _mm_sub_ps(_mm_mul_ps(_mm_shuffle_ps(m.m3, m.m2, 0x00),
        _mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x55), _mm_shuffle_ps(m.m4, m.m3, 0x55), 0x80)),
        _mm_mul_ps(_mm_shuffle_ps(_mm_shuffle_ps(m.m4, m.m3, 0x00), _mm_shuffle_ps(m.m4, m.m3, 0x00), 0x80),
            _mm_shuffle_ps(m.m3, m.m2, 0x55)));

    __m128 v1 = _mm_shuffle_ps(_mm_shuffle_ps(m.m2, m.m1, 0x00), _mm_shuffle_ps(m.m2, m.m1, 0x00), 0xA8);
    __m128 v2 = _mm_shuffle_ps(_mm_shuffle_ps(m.m2, m.m1, 0x55), _mm_shuffle_ps(m.m2, m.m1, 0x55), 0xA8);
    __m128 v3 = _mm_shuffle_ps(_mm_shuffle_ps(m.m2, m.m1, 0xAA), _mm_shuffle_ps(m.m2, m.m1, 0xAA), 0xA8);
    __m128 v4 = _mm_shuffle_ps(_mm_shuffle_ps(m.m2, m.m1, 0xFF), _mm_shuffle_ps(m.m2, m.m1, 0xFF), 0xA8);
    __m128 s1 = _mm_set_ps(-0.0f, 0.0f, -0.0f, 0.0f);
    __m128 s2 = _mm_set_ps(0.0f, -0.0f, 0.0f, -0.0f);
    __m128 i1 = _mm_xor_ps(s1, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v2, f1),
        _mm_mul_ps(v3, f2)),
        _mm_mul_ps(v4, f3)));
    __m128 i2 = _mm_xor_ps(s2, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f1),
        _mm_mul_ps(v3, f4)),
        _mm_mul_ps(v4, f5)));
    __m128 i3 = _mm_xor_ps(s1, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f2),
        _mm_mul_ps(v2, f4)),
        _mm_mul_ps(v4, f6)));
    __m128 i4 = _mm_xor_ps(s2, _mm_add_ps(_mm_sub_ps(_mm_mul_ps(v1, f3),
        _mm_mul_ps(v2, f5)),
        _mm_mul_ps(v3, f6)));
    __m128 d = _mm_mul_ps(m.m1, _mm_movelh_ps(_mm_unpacklo_ps(i1, i2), _mm_unpacklo_ps(i3, i4)));
    d = _mm_add_ps(d, _mm_shuffle_ps(d, d, 0x4E));
    d = _mm_add_ps(d, _mm_shuffle_ps(d, d, 0x11));
    d = _mm_div_ps(_mm_set1_ps(1.0f), d);
    return mat4(float4(_mm_mul_ps(i1, d)),
        float4(_mm_mul_ps(i2, d)),
        float4(_mm_mul_ps(i3, d)),
        float4(_mm_mul_ps(i4, d)));
}