// IQ2_XS codebook, stored as pairs of four packed magnitudes.
constant uint iq2_xs_grid[1024] = {
0x08080808, 0x08080808, 0x0808082b, 0x08080808, 0x08081919, 0x08080808, 0x08082b08, 0x08080808,
0x08082b2b, 0x08080808, 0x08190819, 0x08080808, 0x08191908, 0x08080808, 0x0819192b, 0x08080808,
0x08192b19, 0x08080808, 0x082b0808, 0x08080808, 0x082b082b, 0x08080808, 0x082b1919, 0x08080808,
0x082b2b08, 0x08080808, 0x19080819, 0x08080808, 0x19081908, 0x08080808, 0x1908192b, 0x08080808,
0x19082b19, 0x08080808, 0x19190808, 0x08080808, 0x1919082b, 0x08080808, 0x19191919, 0x08080808,
0x19192b08, 0x08080808, 0x192b0819, 0x08080808, 0x192b1908, 0x08080808, 0x2b080808, 0x08080808,
0x2b08082b, 0x08080808, 0x2b081919, 0x08080808, 0x2b082b08, 0x08080808, 0x2b190819, 0x08080808,
0x2b191908, 0x08080808, 0x2b192b19, 0x08080808, 0x2b2b0808, 0x08080808, 0x08080819, 0x08080819,
0x08081908, 0x08080819, 0x0808192b, 0x08080819, 0x08082b19, 0x08080819, 0x08190808, 0x08080819,
0x0819082b, 0x08080819, 0x08191919, 0x08080819, 0x08192b08, 0x08080819, 0x08192b2b, 0x08080819,
0x082b0819, 0x08080819, 0x082b1908, 0x08080819, 0x19080808, 0x08080819, 0x1908082b, 0x08080819,
0x19081919, 0x08080819, 0x19082b08, 0x08080819, 0x19190819, 0x08080819, 0x19191908, 0x08080819,
0x192b0808, 0x08080819, 0x192b2b08, 0x08080819, 0x2b080819, 0x08080819, 0x2b081908, 0x08080819,
0x2b190808, 0x08080819, 0x08080808, 0x0808082b, 0x0808082b, 0x0808082b, 0x08081919, 0x0808082b,
0x08082b08, 0x0808082b, 0x08190819, 0x0808082b, 0x08191908, 0x0808082b, 0x082b0808, 0x0808082b,
0x19080819, 0x0808082b, 0x19081908, 0x0808082b, 0x19190808, 0x0808082b, 0x19191919, 0x0808082b,
0x2b080808, 0x0808082b, 0x2b082b2b, 0x0808082b, 0x08080819, 0x08081908, 0x08081908, 0x08081908,
0x0808192b, 0x08081908, 0x08082b19, 0x08081908, 0x08190808, 0x08081908, 0x0819082b, 0x08081908,
0x08191919, 0x08081908, 0x08192b08, 0x08081908, 0x082b0819, 0x08081908, 0x082b1908, 0x08081908,
0x19080808, 0x08081908, 0x1908082b, 0x08081908, 0x19081919, 0x08081908, 0x19082b08, 0x08081908,
0x19190819, 0x08081908, 0x19191908, 0x08081908, 0x1919192b, 0x08081908, 0x192b0808, 0x08081908,
0x2b080819, 0x08081908, 0x2b081908, 0x08081908, 0x2b190808, 0x08081908, 0x08080808, 0x08081919,
0x0808082b, 0x08081919, 0x08081919, 0x08081919, 0x08082b08, 0x08081919, 0x08190819, 0x08081919,
0x08191908, 0x08081919, 0x082b0808, 0x08081919, 0x19080819, 0x08081919, 0x19081908, 0x08081919,
0x19190808, 0x08081919, 0x192b0819, 0x08081919, 0x2b080808, 0x08081919, 0x08080819, 0x0808192b,
0x08081908, 0x0808192b, 0x08190808, 0x0808192b, 0x082b192b, 0x0808192b, 0x19080808, 0x0808192b,
0x1908082b, 0x0808192b, 0x2b081908, 0x0808192b, 0x08080808, 0x08082b08, 0x0808082b, 0x08082b08,
0x08081919, 0x08082b08, 0x08082b08, 0x08082b08, 0x08082b2b, 0x08082b08, 0x08190819, 0x08082b08,
0x08191908, 0x08082b08, 0x082b0808, 0x08082b08, 0x082b1919, 0x08082b08, 0x19080819, 0x08082b08,
0x19081908, 0x08082b08, 0x19190808, 0x08082b08, 0x19192b08, 0x08082b08, 0x2b080808, 0x08082b08,
0x2b2b0808, 0x08082b08, 0x2b2b2b2b, 0x08082b08, 0x08080819, 0x08082b19, 0x08081908, 0x08082b19,
0x08190808, 0x08082b19, 0x19080808, 0x08082b19, 0x2b080819, 0x08082b19, 0x2b082b19, 0x08082b19,
0x08080808, 0x08082b2b, 0x082b0808, 0x08082b2b, 0x082b2b08, 0x08082b2b, 0x2b19192b, 0x08082b2b,
0x2b2b0808, 0x08082b2b, 0x08080819, 0x08190808, 0x08081908, 0x08190808, 0x0808192b, 0x08190808,
0x08082b19, 0x08190808, 0x08190808, 0x08190808, 0x0819082b, 0x08190808, 0x08191919, 0x08190808,
0x08192b08, 0x08190808, 0x082b0819, 0x08190808, 0x082b1908, 0x08190808, 0x19080808, 0x08190808,
0x1908082b, 0x08190808, 0x19081919, 0x08190808, 0x19082b08, 0x08190808, 0x19190819, 0x08190808,
0x19191908, 0x08190808, 0x192b0808, 0x08190808, 0x192b2b2b, 0x08190808, 0x2b080819, 0x08190808,
0x2b081908, 0x08190808, 0x2b190808, 0x08190808, 0x08080808, 0x08190819, 0x0808082b, 0x08190819,
0x08081919, 0x08190819, 0x08082b08, 0x08190819, 0x08190819, 0x08190819, 0x08191908, 0x08190819,
0x082b0808, 0x08190819, 0x19080819, 0x08190819, 0x19081908, 0x08190819, 0x19190808, 0x08190819,
0x2b080808, 0x08190819, 0x2b191908, 0x08190819, 0x2b19192b, 0x08190819, 0x08080819, 0x0819082b,
0x08081908, 0x0819082b, 0x0808192b, 0x0819082b, 0x08190808, 0x0819082b, 0x19080808, 0x0819082b,
0x192b0808, 0x0819082b, 0x08080808, 0x08191908, 0x0808082b, 0x08191908, 0x08081919, 0x08191908,
0x08082b08, 0x08191908, 0x08190819, 0x08191908, 0x08191908, 0x08191908, 0x082b0808, 0x08191908,
0x19080819, 0x08191908, 0x19081908, 0x08191908, 0x19082b19, 0x08191908, 0x19190808, 0x08191908,
0x192b1908, 0x08191908, 0x2b080808, 0x08191908, 0x08080819, 0x08191919, 0x08081908, 0x08191919,
0x08190808, 0x08191919, 0x19080808, 0x08191919, 0x08080808, 0x0819192b, 0x08191908, 0x0819192b,
0x19082b19, 0x0819192b, 0x08080819, 0x08192b08, 0x08081908, 0x08192b08, 0x08190808, 0x08192b08,
0x0819082b, 0x08192b08, 0x19080808, 0x08192b08, 0x19191908, 0x08192b08, 0x2b08192b, 0x08192b08,
0x08080808, 0x08192b19, 0x08081919, 0x08192b19, 0x192b192b, 0x08192b19, 0x19190819, 0x08192b2b,
0x2b2b2b19, 0x08192b2b, 0x08080808, 0x082b0808, 0x0808082b, 0x082b0808, 0x08081919, 0x082b0808,
0x08082b08, 0x082b0808, 0x08082b2b, 0x082b0808, 0x08190819, 0x082b0808, 0x08191908, 0x082b0808,
0x082b0808, 0x082b0808, 0x19080819, 0x082b0808, 0x19081908, 0x082b0808, 0x19190808, 0x082b0808,
0x2b080808, 0x082b0808, 0x2b2b0808, 0x082b0808, 0x08080819, 0x082b0819, 0x08081908, 0x082b0819,
0x08190808, 0x082b0819, 0x19080808, 0x082b0819, 0x19082b08, 0x082b0819, 0x192b1919, 0x082b0819,
0x08080808, 0x082b082b, 0x082b082b, 0x082b082b, 0x2b080808, 0x082b082b, 0x2b2b2b08, 0x082b082b,
0x08080819, 0x082b1908, 0x08081908, 0x082b1908, 0x08190808, 0x082b1908, 0x082b2b19, 0x082b1908,
0x19080808, 0x082b1908, 0x08080808, 0x082b1919, 0x19080819, 0x082b1919, 0x1919082b, 0x082b1919,
0x2b192b19, 0x082b1919, 0x08080819, 0x082b192b, 0x08192b2b, 0x082b192b, 0x2b2b192b, 0x082b192b,
0x08080808, 0x082b2b08, 0x08082b08, 0x082b2b08, 0x08082b2b, 0x082b2b08, 0x082b0808, 0x082b2b08,
0x19191919, 0x082b2b08, 0x2b082b08, 0x082b2b08, 0x2b2b082b, 0x082b2b08, 0x192b2b08, 0x082b2b19,
0x2b190808, 0x082b2b19, 0x08082b08, 0x082b2b2b, 0x082b0808, 0x082b2b2b, 0x2b08082b, 0x082b2b2b,
0x2b082b08, 0x082b2b2b, 0x2b082b2b, 0x082b2b2b, 0x08080819, 0x19080808, 0x08081908, 0x19080808,
0x0808192b, 0x19080808, 0x08082b19, 0x19080808, 0x08190808, 0x19080808, 0x0819082b, 0x19080808,
0x08191919, 0x19080808, 0x08192b08, 0x19080808, 0x082b0819, 0x19080808, 0x082b1908, 0x19080808,
0x19080808, 0x19080808, 0x1908082b, 0x19080808, 0x19081919, 0x19080808, 0x19082b08, 0x19080808,
0x19082b2b, 0x19080808, 0x19190819, 0x19080808, 0x19191908, 0x19080808, 0x192b0808, 0x19080808,
0x192b1919, 0x19080808, 0x2b080819, 0x19080808, 0x2b081908, 0x19080808, 0x2b190808, 0x19080808,
0x08080808, 0x19080819, 0x0808082b, 0x19080819, 0x08081919, 0x19080819, 0x08082b08, 0x19080819,
0x08190819, 0x19080819, 0x08191908, 0x19080819, 0x082b0808, 0x19080819, 0x19080819, 0x19080819,
0x19081908, 0x19080819, 0x19190808, 0x19080819, 0x2b080808, 0x19080819, 0x2b081919, 0x19080819,
0x2b2b082b, 0x19080819, 0x08080819, 0x1908082b, 0x08081908, 0x1908082b, 0x08190808, 0x1908082b,
0x0819082b, 0x1908082b, 0x082b2b19, 0x1908082b, 0x19080808, 0x1908082b, 0x08080808, 0x19081908,
0x0808082b, 0x19081908, 0x08081919, 0x19081908, 0x08082b08, 0x19081908, 0x08190819, 0x19081908,
0x08191908, 0x19081908, 0x08192b19, 0x19081908, 0x082b0808, 0x19081908, 0x19080819, 0x19081908,
0x19081908, 0x19081908, 0x19190808, 0x19081908, 0x2b080808, 0x19081908, 0x2b191908, 0x19081908,
0x08080819, 0x19081919, 0x08081908, 0x19081919, 0x08190808, 0x19081919, 0x082b1908, 0x19081919,
0x19080808, 0x19081919, 0x2b192b2b, 0x19081919, 0x08080808, 0x1908192b, 0x08082b2b, 0x1908192b,
0x19081908, 0x1908192b, 0x19190808, 0x1908192b, 0x08080819, 0x19082b08, 0x08081908, 0x19082b08,
0x08190808, 0x19082b08, 0x19080808, 0x19082b08, 0x19081919, 0x19082b08, 0x19191908, 0x19082b08,
0x192b082b, 0x19082b08, 0x08080808, 0x19082b19, 0x08190819, 0x19082b19, 0x19081908, 0x19082b19,
0x19190808, 0x19082b19, 0x192b2b19, 0x19082b19, 0x08081908, 0x19082b2b, 0x08080808, 0x19190808,
0x0808082b, 0x19190808, 0x08081919, 0x19190808, 0x08082b08, 0x19190808, 0x08190819, 0x19190808,
0x08191908, 0x19190808, 0x082b0808, 0x19190808, 0x082b2b08, 0x19190808, 0x19080819, 0x19190808,
0x19081908, 0x19190808, 0x19190808, 0x19190808, 0x2b080808, 0x19190808, 0x08080819, 0x19190819,
0x08081908, 0x19190819, 0x08190808, 0x19190819, 0x08191919, 0x19190819, 0x19080808, 0x19190819,
0x1908082b, 0x19190819, 0x08080808, 0x1919082b, 0x19081908, 0x1919082b, 0x2b2b2b2b, 0x1919082b,
0x08080819, 0x19191908, 0x08081908, 0x19191908, 0x08190808, 0x19191908, 0x082b0819, 0x19191908,
0x19080808, 0x19191908, 0x192b0808, 0x19191908, 0x2b080819, 0x19191908, 0x2b2b0819, 0x19191908,
0x08080808, 0x19191919, 0x08082b08, 0x19191919, 0x2b080808, 0x19191919, 0x2b082b08, 0x19191919,
0x082b0819, 0x1919192b, 0x192b2b08, 0x1919192b, 0x2b2b0819, 0x1919192b, 0x08080808, 0x19192b08,
0x08191908, 0x19192b08, 0x19080819, 0x19192b08, 0x19190808, 0x19192b08, 0x2b192b19, 0x19192b08,
0x08192b2b, 0x19192b19, 0x19080808, 0x19192b19, 0x1908082b, 0x19192b19, 0x2b081919, 0x19192b2b,
0x08080819, 0x192b0808, 0x08081908, 0x192b0808, 0x08190808, 0x192b0808, 0x19080808, 0x192b0808,
0x19191908, 0x192b0808, 0x192b082b, 0x192b0808, 0x2b08192b, 0x192b0808, 0x2b2b2b19, 0x192b0808,
0x08080808, 0x192b0819, 0x082b1908, 0x192b082b, 0x19082b2b, 0x192b082b, 0x2b19082b, 0x192b082b,
0x08080808, 0x192b1908, 0x0819192b, 0x192b1908, 0x08190808, 0x192b1919, 0x19080808, 0x192b1919,
0x19081919, 0x192b1919, 0x2b2b1908, 0x192b1919, 0x08080819, 0x192b2b08, 0x192b2b2b, 0x192b2b08,
0x082b1919, 0x192b2b19, 0x0808192b, 0x192b2b2b, 0x19191908, 0x192b2b2b, 0x192b082b, 0x192b2b2b,
0x08080808, 0x2b080808, 0x0808082b, 0x2b080808, 0x08081919, 0x2b080808, 0x08082b08, 0x2b080808,
0x08190819, 0x2b080808, 0x08191908, 0x2b080808, 0x082b0808, 0x2b080808, 0x082b2b2b, 0x2b080808,
0x19080819, 0x2b080808, 0x19081908, 0x2b080808, 0x19190808, 0x2b080808, 0x2b080808, 0x2b080808,
0x2b08082b, 0x2b080808, 0x2b2b2b08, 0x2b080808, 0x2b2b2b2b, 0x2b080808, 0x08080819, 0x2b080819,
0x08081908, 0x2b080819, 0x0808192b, 0x2b080819, 0x08190808, 0x2b080819, 0x19080808, 0x2b080819,
0x19190819, 0x2b080819, 0x19192b19, 0x2b080819, 0x08080808, 0x2b08082b, 0x082b0808, 0x2b08082b,
0x2b080808, 0x2b08082b, 0x2b08082b, 0x2b08082b, 0x2b2b0808, 0x2b08082b, 0x2b2b2b08, 0x2b08082b,
0x08080819, 0x2b081908, 0x08081908, 0x2b081908, 0x08190808, 0x2b081908, 0x0819082b, 0x2b081908,
0x08191919, 0x2b081908, 0x19080808, 0x2b081908, 0x192b0808, 0x2b081908, 0x2b082b19, 0x2b081908,
0x08080808, 0x2b081919, 0x19081908, 0x2b081919, 0x2b2b1919, 0x2b081919, 0x08192b08, 0x2b08192b,
0x192b2b2b, 0x2b08192b, 0x08080808, 0x2b082b08, 0x08082b08, 0x2b082b08, 0x082b1919, 0x2b082b08,
0x19192b2b, 0x2b082b08, 0x2b080808, 0x2b082b08, 0x2b08082b, 0x2b082b08, 0x2b2b2b08, 0x2b082b08,
0x0808192b, 0x2b082b19, 0x082b082b, 0x2b082b2b, 0x2b080808, 0x2b082b2b, 0x2b082b08, 0x2b082b2b,
0x2b19192b, 0x2b082b2b, 0x2b2b2b08, 0x2b082b2b, 0x08080819, 0x2b190808, 0x08081908, 0x2b190808,
0x08190808, 0x2b190808, 0x19080808, 0x2b190808, 0x1919192b, 0x2b190808, 0x2b081908, 0x2b190808,
0x08080808, 0x2b190819, 0x082b082b, 0x2b190819, 0x192b1908, 0x2b190819, 0x1919192b, 0x2b19082b,
0x2b082b19, 0x2b19082b, 0x08080808, 0x2b191908, 0x08081919, 0x2b191908, 0x19081908, 0x2b191908,
0x19190808, 0x2b191908, 0x19192b08, 0x2b191908, 0x082b2b19, 0x2b191919, 0x2b190808, 0x2b191919,
0x2b19082b, 0x2b191919, 0x19080819, 0x2b19192b, 0x19190819, 0x2b192b08, 0x2b2b192b, 0x2b192b08,
0x19082b19, 0x2b192b19, 0x08191919, 0x2b192b2b, 0x192b0808, 0x2b192b2b, 0x08080808, 0x2b2b0808,
0x0808082b, 0x2b2b0808, 0x08082b08, 0x2b2b0808, 0x08082b2b, 0x2b2b0808, 0x082b0808, 0x2b2b0808,
0x082b2b2b, 0x2b2b0808, 0x2b2b0808, 0x2b2b0808, 0x19190819, 0x2b2b0819, 0x19192b19, 0x2b2b0819,
0x2b2b192b, 0x2b2b0819, 0x08080808, 0x2b2b082b, 0x0808082b, 0x2b2b082b, 0x08082b08, 0x2b2b082b,
0x082b2b2b, 0x2b2b082b, 0x2b080808, 0x2b2b082b, 0x2b2b0808, 0x2b2b082b, 0x19080808, 0x2b2b1908,
0x2b191919, 0x2b2b1908, 0x192b1919, 0x2b2b192b, 0x2b192b08, 0x2b2b192b, 0x08082b2b, 0x2b2b2b08,
0x082b0808, 0x2b2b2b08, 0x082b082b, 0x2b2b2b08, 0x082b2b08, 0x2b2b2b08, 0x2b2b0808, 0x2b2b2b08,
0x2b2b2b08, 0x2b2b2b08, 0x08081908, 0x2b2b2b19, 0x2b081908, 0x2b2b2b19, 0x2b08192b, 0x2b2b2b19,
0x082b2b08, 0x2b2b2b2b, 0x082b2b2b, 0x2b2b2b2b, 0x2b190819, 0x2b2b2b2b, 0x2b2b2b2b, 0x2b2b2b2b
}
inline uint iq2_xs_signs(uint code) {
return code | ((popcount(code) & 1u) << 7)}