ggml-common.h

// adapted from
// https://github.com/vllm-project/vllm/blob/4492e3a55428e161ca8db381edc28263e5da4c8d/csrc/quantization/gguf/ggml-common.h
// copied from https://github.com/ggerganov/llama.cpp/blob/b2899/ggml-common.h
#define QK_K 256
#define K_QUANTS_PER_ITERATION 2
#define WARP_SIZE_GGUF 64
#define K_SCALE_SIZE 12
#define CUDA_DEQUANTIZE_BLOCK_SIZE 256
#define CUDA_QUANTIZE_BLOCK_SIZE 256
#define GGML_CUDA_DMMV_X 32
#define GGML_CUDA_MMV_Y 1

// Data Structures
// QK = number of values after dequantization
// QR = QK / number of values before dequantization
// QI = number of 32 bit integers before dequantization

#define QK4_0 32
#define QR4_0 2
#define QI4_0 (QK4_0 / (4 * QR4_0))
typedef struct {
  half d;                 // delta
  uint8_t qs[QK4_0 / 2];  // nibbles / quants
} block_q4_0;

#define QK4_1 32
#define QR4_1 2
#define QI4_1 (QK4_1 / (4 * QR4_1))
typedef struct {
  half2 dm;               // dm.x = delta, dm.y = min
  uint8_t qs[QK4_1 / 2];  // nibbles / quants
} block_q4_1;

#define QK5_0 32
#define QR5_0 2
#define QI5_0 (QK5_0 / (4 * QR5_0))
typedef struct {
  half d;                 // delta
  uint8_t qh[4];          // 5-th bit of quants
  uint8_t qs[QK5_0 / 2];  // nibbles / quants
} block_q5_0;

#define QK5_1 32
#define QR5_1 2
#define QI5_1 (QK5_1 / (4 * QR5_1))
typedef struct {
  half2 dm;               // dm.x = delta, dm.y = min
  uint8_t qh[4];          // 5-th bit of quants
  uint8_t qs[QK5_1 / 2];  // nibbles / quants
} block_q5_1;

#define QK8_0 32
#define QR8_0 1
#define QI8_0 (QK8_0 / (4 * QR8_0))
typedef struct {
  half d;            // delta
  int8_t qs[QK8_0];  // quants
} block_q8_0;

#define QK8_1 32
#define QR8_1 1
#define QI8_1 (QK8_1 / (4 * QR8_1))
typedef struct {
  half2 ds;          // ds.x = delta, ds.y = sum
  int8_t qs[QK8_0];  // quants
} block_q8_1;

#define QR2_K 4
#define QI2_K (QK_K / (4 * QR2_K))
typedef struct {
  uint8_t scales[QK_K / 16];  // scales and mins, quantized with 4 bits
  uint8_t qs[QK_K / 4];       // quants
  half2 dm;                   // super-block scale for quantized scales/mins
} block_q2_K;

#define QR3_K 4
#define QI3_K (QK_K / (4 * QR3_K))
typedef struct {
  uint8_t hmask[QK_K / 8];       // quants - high bit
  uint8_t qs[QK_K / 4];          // quants - low 2 bits
  uint8_t scales[K_SCALE_SIZE];  // scales, quantized with 6 bits
  half d;                        // super-block scale
} block_q3_K;

#define QR4_K 2
#define QI4_K (QK_K / (4 * QR4_K))
typedef struct {
  half2 dm;                       // super-block scale for quantized scales/mins
  uint8_t scales[3 * QK_K / 64];  // scales, quantized with 6 bits
  uint8_t qs[QK_K / 2];           // 4--bit quants
} block_q4_K;

#define QR5_K 2
#define QI5_K (QK_K / (4 * QR5_K))
typedef struct {
  half2 dm;                      // super-block scale for quantized scales/mins
  uint8_t scales[K_SCALE_SIZE];  // scales and mins, quantized with 6 bits
  uint8_t qh[QK_K / 8];          // quants, high bit
  uint8_t qs[QK_K / 2];          // quants, low 4 bits
} block_q5_K;

#define QR6_K 2
#define QI6_K (QK_K / (4 * QR6_K))
typedef struct {
  uint8_t ql[QK_K / 2];      // quants, lower 4 bits
  uint8_t qh[QK_K / 4];      // quants, upper 2 bits
  int8_t scales[QK_K / 16];  // scales
  half d;                    // delta
} block_q6_K;

#define QR2_XXS 8
#define QI2_XXS (QK_K / (4 * QR2_XXS))
typedef struct {
  half d;
  uint16_t qs[QK_K / 8];
} block_iq2_xxs;

#define QR2_XS 8
#define QI2_XS (QK_K / (4 * QR2_XS))
typedef struct {
  half d;
  uint16_t qs[QK_K / 8];
  uint8_t scales[QK_K / 32];
} block_iq2_xs;

#define QR2_S 8
#define QI2_S (QK_K / (4 * QR2_S))
typedef struct {
  half d;
  uint8_t qs[QK_K / 4];
  uint8_t qh[QK_K / 32];
  uint8_t scales[QK_K / 32];
} block_iq2_s;

#define QR3_XXS 8
#define QI3_XXS (QK_K / (4 * QR3_XXS))
typedef struct {
  half d;
  uint8_t qs[3 * (QK_K / 8)];
} block_iq3_xxs;

#define QR3_XS 8
#define QI3_XS (QK_K / (4 * QR3_XS))
#define IQ3S_N_SCALE QK_K / 64
typedef struct {
  half d;
  uint8_t qs[QK_K / 4];
  uint8_t qh[QK_K / 32];
  uint8_t signs[QK_K / 8];
  uint8_t scales[IQ3S_N_SCALE];
} block_iq3_s;

// 1.5625 bpw
#define QR1_S 8
#define QI1_S (QK_K / (4 * QR1_S))
typedef struct {
  half d;
  uint8_t qs[QK_K / 8];
  uint16_t qh[QK_K / 32];
} block_iq1_s;

// 1.75 bpw
#define QR1_M 8
#define QI1_M (QK_K / (4 * QR1_M))
typedef struct {
  uint8_t qs[QK_K / 8];       // grid index, low 8 bits
  uint8_t qh[QK_K / 16];      // grid index, high 3 bits + grid shift bit (for two groups of 8)
  uint8_t scales[QK_K / 32];  // 3-bit block scales (4-bit if QK_K == 64)
} block_iq1_m;

// Used by IQ1_M quants
typedef union {
  half f16;
  uint16_t u16;
} iq1m_scale_t;

#define QK4_NL 32
#define QR4_NL 2
#define QI4_NL (QK4_NL / (4 * QR4_NL))
typedef struct {
  half d;
  uint8_t qs[QK4_NL / 2];
} block_iq4_nl;

#define QR4_XS 8
#define QI4_XS (QK_K / (4 * QR4_XS))
typedef struct {
  half d;
  uint16_t scales_h;
  uint8_t scales_l[QK_K / 64];
  uint8_t qs[QK_K / 2];
} block_iq4_xs;

static const __device__ uint64_t iq2xxs_grid[256] = {
    0x0808080808080808, 0x080808080808082b, 0x0808080808081919, 0x0808080808082b08, 0x0808080808082b2b,
    0x0808080808190819, 0x0808080808191908, 0x08080808082b0808, 0x08080808082b082b, 0x08080808082b2b08,
    0x08080808082b2b2b, 0x0808080819080819, 0x0808080819081908, 0x0808080819190808, 0x0808080819192b08,
    0x08080808192b0819, 0x08080808192b1908, 0x080808082b080808, 0x080808082b08082b, 0x080808082b082b2b,
    0x080808082b2b082b, 0x0808081908080819, 0x0808081908081908, 0x0808081908190808, 0x0808081908191919,
    0x0808081919080808, 0x080808192b081908, 0x080808192b192b08, 0x0808082b08080808, 0x0808082b0808082b,
    0x0808082b082b082b, 0x0808082b2b08082b, 0x0808190808080819, 0x0808190808081908, 0x0808190808190808,
    0x08081908082b0819, 0x08081908082b1908, 0x0808190819080808, 0x080819081908082b, 0x0808190819082b08,
    0x08081908192b0808, 0x080819082b080819, 0x080819082b081908, 0x080819082b190808, 0x080819082b2b1908,
    0x0808191908080808, 0x080819190808082b, 0x0808191908082b08, 0x08081919082b0808, 0x080819191908192b,
    0x08081919192b2b19, 0x080819192b080808, 0x080819192b190819, 0x0808192b08082b19, 0x0808192b08190808,
    0x0808192b19080808, 0x0808192b2b081908, 0x0808192b2b2b1908, 0x08082b0808080808, 0x08082b0808081919,
    0x08082b0808082b08, 0x08082b0808191908, 0x08082b08082b2b08, 0x08082b0819080819, 0x08082b0819081908,
    0x08082b0819190808, 0x08082b081919082b, 0x08082b082b082b08, 0x08082b1908081908, 0x08082b1919080808,
    0x08082b2b0808082b, 0x08082b2b08191908, 0x0819080808080819, 0x0819080808081908, 0x0819080808190808,
    0x08190808082b0819, 0x0819080819080808, 0x08190808192b0808, 0x081908082b081908, 0x081908082b190808,
    0x081908082b191919, 0x0819081908080808, 0x0819081908082b08, 0x08190819082b0808, 0x0819081919190808,
    0x0819081919192b2b, 0x081908192b080808, 0x0819082b082b1908, 0x0819082b19081919, 0x0819190808080808,
    0x0819190808082b08, 0x08191908082b0808, 0x08191908082b1919, 0x0819190819082b19, 0x081919082b080808,
    0x0819191908192b08, 0x08191919192b082b, 0x0819192b08080808, 0x0819192b0819192b, 0x08192b0808080819,
    0x08192b0808081908, 0x08192b0808190808, 0x08192b0819080808, 0x08192b082b080819, 0x08192b1908080808,
    0x08192b1908081919, 0x08192b192b2b0808, 0x08192b2b19190819, 0x082b080808080808, 0x082b08080808082b,
    0x082b080808082b2b, 0x082b080819081908, 0x082b0808192b0819, 0x082b08082b080808, 0x082b08082b08082b,
    0x082b0819082b2b19, 0x082b081919082b08, 0x082b082b08080808, 0x082b082b0808082b, 0x082b190808080819,
    0x082b190808081908, 0x082b190808190808, 0x082b190819080808, 0x082b19081919192b, 0x082b191908080808,
    0x082b191919080819, 0x082b1919192b1908, 0x082b192b2b190808, 0x082b2b0808082b08, 0x082b2b08082b0808,
    0x082b2b082b191908, 0x082b2b2b19081908, 0x1908080808080819, 0x1908080808081908, 0x1908080808190808,
    0x1908080808192b08, 0x19080808082b0819, 0x19080808082b1908, 0x1908080819080808, 0x1908080819082b08,
    0x190808081919192b, 0x19080808192b0808, 0x190808082b080819, 0x190808082b081908, 0x190808082b190808,
    0x1908081908080808, 0x19080819082b0808, 0x19080819192b0819, 0x190808192b080808, 0x190808192b081919,
    0x1908082b08080819, 0x1908082b08190808, 0x1908082b19082b08, 0x1908082b1919192b, 0x1908082b192b2b08,
    0x1908190808080808, 0x1908190808082b08, 0x19081908082b0808, 0x190819082b080808, 0x190819082b192b19,
    0x190819190819082b, 0x19081919082b1908, 0x1908192b08080808, 0x19082b0808080819, 0x19082b0808081908,
    0x19082b0808190808, 0x19082b0819080808, 0x19082b0819081919, 0x19082b1908080808, 0x19082b1919192b08,
    0x19082b19192b0819, 0x19082b192b08082b, 0x19082b2b19081919, 0x19082b2b2b190808, 0x1919080808080808,
    0x1919080808082b08, 0x1919080808190819, 0x1919080808192b19, 0x19190808082b0808, 0x191908082b080808,
    0x191908082b082b08, 0x1919081908081908, 0x191908191908082b, 0x191908192b2b1908, 0x1919082b2b190819,
    0x191919082b190808, 0x191919082b19082b, 0x1919191908082b2b, 0x1919192b08080819, 0x1919192b19191908,
    0x19192b0808080808, 0x19192b0808190819, 0x19192b0808192b19, 0x19192b08192b1908, 0x19192b1919080808,
    0x19192b2b08082b08, 0x192b080808081908, 0x192b080808190808, 0x192b080819080808, 0x192b0808192b2b08,
    0x192b081908080808, 0x192b081919191919, 0x192b082b08192b08, 0x192b082b192b0808, 0x192b190808080808,
    0x192b190808081919, 0x192b191908190808, 0x192b19190819082b, 0x192b19192b081908, 0x192b2b081908082b,
    0x2b08080808080808, 0x2b0808080808082b, 0x2b08080808082b2b, 0x2b08080819080819, 0x2b0808082b08082b,
    0x2b08081908081908, 0x2b08081908192b08, 0x2b08081919080808, 0x2b08082b08190819, 0x2b08190808080819,
    0x2b08190808081908, 0x2b08190808190808, 0x2b08190808191919, 0x2b08190819080808, 0x2b081908192b0808,
    0x2b08191908080808, 0x2b0819191908192b, 0x2b0819192b191908, 0x2b08192b08082b19, 0x2b08192b19080808,
    0x2b08192b192b0808, 0x2b082b080808082b, 0x2b082b1908081908, 0x2b082b2b08190819, 0x2b19080808081908,
    0x2b19080808190808, 0x2b190808082b1908, 0x2b19080819080808, 0x2b1908082b2b0819, 0x2b1908190819192b,
    0x2b1908192b080808, 0x2b19082b19081919, 0x2b19190808080808, 0x2b191908082b082b, 0x2b19190819081908,
    0x2b19191919190819, 0x2b192b082b080819, 0x2b192b19082b0808, 0x2b2b08080808082b, 0x2b2b080819190808,
    0x2b2b08082b081919, 0x2b2b081908082b19, 0x2b2b082b08080808, 0x2b2b190808192b08, 0x2b2b2b0819190808,
    0x2b2b2b1908081908,
};

static const __device__ uint64_t iq2xs_grid[512] = {
    0x0808080808080808, 0x080808080808082b, 0x0808080808081919, 0x0808080808082b08, 0x0808080808082b2b,
    0x0808080808190819, 0x0808080808191908, 0x080808080819192b, 0x0808080808192b19, 0x08080808082b0808,
    0x08080808082b082b, 0x08080808082b1919, 0x08080808082b2b08, 0x0808080819080819, 0x0808080819081908,
    0x080808081908192b, 0x0808080819082b19, 0x0808080819190808, 0x080808081919082b, 0x0808080819191919,
    0x0808080819192b08, 0x08080808192b0819, 0x08080808192b1908, 0x080808082b080808, 0x080808082b08082b,
    0x080808082b081919, 0x080808082b082b08, 0x080808082b190819, 0x080808082b191908, 0x080808082b192b19,
    0x080808082b2b0808, 0x0808081908080819, 0x0808081908081908, 0x080808190808192b, 0x0808081908082b19,
    0x0808081908190808, 0x080808190819082b, 0x0808081908191919, 0x0808081908192b08, 0x0808081908192b2b,
    0x08080819082b0819, 0x08080819082b1908, 0x0808081919080808, 0x080808191908082b, 0x0808081919081919,
    0x0808081919082b08, 0x0808081919190819, 0x0808081919191908, 0x08080819192b0808, 0x08080819192b2b08,
    0x080808192b080819, 0x080808192b081908, 0x080808192b190808, 0x0808082b08080808, 0x0808082b0808082b,
    0x0808082b08081919, 0x0808082b08082b08, 0x0808082b08190819, 0x0808082b08191908, 0x0808082b082b0808,
    0x0808082b19080819, 0x0808082b19081908, 0x0808082b19190808, 0x0808082b19191919, 0x0808082b2b080808,
    0x0808082b2b082b2b, 0x0808190808080819, 0x0808190808081908, 0x080819080808192b, 0x0808190808082b19,
    0x0808190808190808, 0x080819080819082b, 0x0808190808191919, 0x0808190808192b08, 0x08081908082b0819,
    0x08081908082b1908, 0x0808190819080808, 0x080819081908082b, 0x0808190819081919, 0x0808190819082b08,
    0x0808190819190819, 0x0808190819191908, 0x080819081919192b, 0x08081908192b0808, 0x080819082b080819,
    0x080819082b081908, 0x080819082b190808, 0x0808191908080808, 0x080819190808082b, 0x0808191908081919,
    0x0808191908082b08, 0x0808191908190819, 0x0808191908191908, 0x08081919082b0808, 0x0808191919080819,
    0x0808191919081908, 0x0808191919190808, 0x08081919192b0819, 0x080819192b080808, 0x0808192b08080819,
    0x0808192b08081908, 0x0808192b08190808, 0x0808192b082b192b, 0x0808192b19080808, 0x0808192b1908082b,
    0x0808192b2b081908, 0x08082b0808080808, 0x08082b080808082b, 0x08082b0808081919, 0x08082b0808082b08,
    0x08082b0808082b2b, 0x08082b0808190819, 0x08082b0808191908, 0x08082b08082b0808, 0x08082b08082b1919,
    0x08082b0819080819, 0x08082b0819081908, 0x08082b0819190808, 0x08082b0819192b08, 0x08082b082b080808,
    0x08082b082b2b0808, 0x08082b082b2b2b2b, 0x08082b1908080819, 0x08082b1908081908, 0x08082b1908190808,
    0x08082b1919080808, 0x08082b192b080819, 0x08082b192b082b19, 0x08082b2b08080808, 0x08082b2b082b0808,
    0x08082b2b082b2b08, 0x08082b2b2b19192b, 0x08082b2b2b2b0808, 0x0819080808080819, 0x0819080808081908,
    0x081908080808192b, 0x0819080808082b19, 0x0819080808190808, 0x081908080819082b, 0x0819080808191919,
    0x0819080808192b08, 0x08190808082b0819, 0x08190808082b1908, 0x0819080819080808, 0x081908081908082b,
    0x0819080819081919, 0x0819080819082b08, 0x0819080819190819, 0x0819080819191908, 0x08190808192b0808,
    0x08190808192b2b2b, 0x081908082b080819, 0x081908082b081908, 0x081908082b190808, 0x0819081908080808,
    0x081908190808082b, 0x0819081908081919, 0x0819081908082b08, 0x0819081908190819, 0x0819081908191908,
    0x08190819082b0808, 0x0819081919080819, 0x0819081919081908, 0x0819081919190808, 0x081908192b080808,
    0x081908192b191908, 0x081908192b19192b, 0x0819082b08080819, 0x0819082b08081908, 0x0819082b0808192b,
    0x0819082b08190808, 0x0819082b19080808, 0x0819082b192b0808, 0x0819190808080808, 0x081919080808082b,
    0x0819190808081919, 0x0819190808082b08, 0x0819190808190819, 0x0819190808191908, 0x08191908082b0808,
    0x0819190819080819, 0x0819190819081908, 0x0819190819082b19, 0x0819190819190808, 0x08191908192b1908,
    0x081919082b080808, 0x0819191908080819, 0x0819191908081908, 0x0819191908190808, 0x0819191919080808,
    0x0819192b08080808, 0x0819192b08191908, 0x0819192b19082b19, 0x08192b0808080819, 0x08192b0808081908,
    0x08192b0808190808, 0x08192b080819082b, 0x08192b0819080808, 0x08192b0819191908, 0x08192b082b08192b,
    0x08192b1908080808, 0x08192b1908081919, 0x08192b19192b192b, 0x08192b2b19190819, 0x08192b2b2b2b2b19,
    0x082b080808080808, 0x082b08080808082b, 0x082b080808081919, 0x082b080808082b08, 0x082b080808082b2b,
    0x082b080808190819, 0x082b080808191908, 0x082b0808082b0808, 0x082b080819080819, 0x082b080819081908,
    0x082b080819190808, 0x082b08082b080808, 0x082b08082b2b0808, 0x082b081908080819, 0x082b081908081908,
    0x082b081908190808, 0x082b081919080808, 0x082b081919082b08, 0x082b0819192b1919, 0x082b082b08080808,
    0x082b082b082b082b, 0x082b082b2b080808, 0x082b082b2b2b2b08, 0x082b190808080819, 0x082b190808081908,
    0x082b190808190808, 0x082b1908082b2b19, 0x082b190819080808, 0x082b191908080808, 0x082b191919080819,
    0x082b19191919082b, 0x082b19192b192b19, 0x082b192b08080819, 0x082b192b08192b2b, 0x082b192b2b2b192b,
    0x082b2b0808080808, 0x082b2b0808082b08, 0x082b2b0808082b2b, 0x082b2b08082b0808, 0x082b2b0819191919,
    0x082b2b082b082b08, 0x082b2b082b2b082b, 0x082b2b19192b2b08, 0x082b2b192b190808, 0x082b2b2b08082b08,
    0x082b2b2b082b0808, 0x082b2b2b2b08082b, 0x082b2b2b2b082b08, 0x082b2b2b2b082b2b, 0x1908080808080819,
    0x1908080808081908, 0x190808080808192b, 0x1908080808082b19, 0x1908080808190808, 0x190808080819082b,
    0x1908080808191919, 0x1908080808192b08, 0x19080808082b0819, 0x19080808082b1908, 0x1908080819080808,
    0x190808081908082b, 0x1908080819081919, 0x1908080819082b08, 0x1908080819082b2b, 0x1908080819190819,
    0x1908080819191908, 0x19080808192b0808, 0x19080808192b1919, 0x190808082b080819, 0x190808082b081908,
    0x190808082b190808, 0x1908081908080808, 0x190808190808082b, 0x1908081908081919, 0x1908081908082b08,
    0x1908081908190819, 0x1908081908191908, 0x19080819082b0808, 0x1908081919080819, 0x1908081919081908,
    0x1908081919190808, 0x190808192b080808, 0x190808192b081919, 0x190808192b2b082b, 0x1908082b08080819,
    0x1908082b08081908, 0x1908082b08190808, 0x1908082b0819082b, 0x1908082b082b2b19, 0x1908082b19080808,
    0x1908190808080808, 0x190819080808082b, 0x1908190808081919, 0x1908190808082b08, 0x1908190808190819,
    0x1908190808191908, 0x1908190808192b19, 0x19081908082b0808, 0x1908190819080819, 0x1908190819081908,
    0x1908190819190808, 0x190819082b080808, 0x190819082b191908, 0x1908191908080819, 0x1908191908081908,
    0x1908191908190808, 0x19081919082b1908, 0x1908191919080808, 0x190819192b192b2b, 0x1908192b08080808,
    0x1908192b08082b2b, 0x1908192b19081908, 0x1908192b19190808, 0x19082b0808080819, 0x19082b0808081908,
    0x19082b0808190808, 0x19082b0819080808, 0x19082b0819081919, 0x19082b0819191908, 0x19082b08192b082b,
    0x19082b1908080808, 0x19082b1908190819, 0x19082b1919081908, 0x19082b1919190808, 0x19082b19192b2b19,
    0x19082b2b08081908, 0x1919080808080808, 0x191908080808082b, 0x1919080808081919, 0x1919080808082b08,
    0x1919080808190819, 0x1919080808191908, 0x19190808082b0808, 0x19190808082b2b08, 0x1919080819080819,
    0x1919080819081908, 0x1919080819190808, 0x191908082b080808, 0x1919081908080819, 0x1919081908081908,
    0x1919081908190808, 0x1919081908191919, 0x1919081919080808, 0x191908191908082b, 0x1919082b08080808,
    0x1919082b19081908, 0x1919082b2b2b2b2b, 0x1919190808080819, 0x1919190808081908, 0x1919190808190808,
    0x19191908082b0819, 0x1919190819080808, 0x19191908192b0808, 0x191919082b080819, 0x191919082b2b0819,
    0x1919191908080808, 0x1919191908082b08, 0x191919192b080808, 0x191919192b082b08, 0x1919192b082b0819,
    0x1919192b192b2b08, 0x1919192b2b2b0819, 0x19192b0808080808, 0x19192b0808191908, 0x19192b0819080819,
    0x19192b0819190808, 0x19192b082b192b19, 0x19192b1908192b2b, 0x19192b1919080808, 0x19192b191908082b,
    0x19192b2b2b081919, 0x192b080808080819, 0x192b080808081908, 0x192b080808190808, 0x192b080819080808,
    0x192b080819191908, 0x192b0808192b082b, 0x192b08082b08192b, 0x192b08082b2b2b19, 0x192b081908080808,
    0x192b082b082b1908, 0x192b082b19082b2b, 0x192b082b2b19082b, 0x192b190808080808, 0x192b19080819192b,
    0x192b191908190808, 0x192b191919080808, 0x192b191919081919, 0x192b19192b2b1908, 0x192b2b0808080819,
    0x192b2b08192b2b2b, 0x192b2b19082b1919, 0x192b2b2b0808192b, 0x192b2b2b19191908, 0x192b2b2b192b082b,
    0x2b08080808080808, 0x2b0808080808082b, 0x2b08080808081919, 0x2b08080808082b08, 0x2b08080808190819,
    0x2b08080808191908, 0x2b080808082b0808, 0x2b080808082b2b2b, 0x2b08080819080819, 0x2b08080819081908,
    0x2b08080819190808, 0x2b0808082b080808, 0x2b0808082b08082b, 0x2b0808082b2b2b08, 0x2b0808082b2b2b2b,
    0x2b08081908080819, 0x2b08081908081908, 0x2b0808190808192b, 0x2b08081908190808, 0x2b08081919080808,
    0x2b08081919190819, 0x2b08081919192b19, 0x2b08082b08080808, 0x2b08082b082b0808, 0x2b08082b2b080808,
    0x2b08082b2b08082b, 0x2b08082b2b2b0808, 0x2b08082b2b2b2b08, 0x2b08190808080819, 0x2b08190808081908,
    0x2b08190808190808, 0x2b0819080819082b, 0x2b08190808191919, 0x2b08190819080808, 0x2b081908192b0808,
    0x2b0819082b082b19, 0x2b08191908080808, 0x2b08191919081908, 0x2b0819192b2b1919, 0x2b08192b08192b08,
    0x2b08192b192b2b2b, 0x2b082b0808080808, 0x2b082b0808082b08, 0x2b082b08082b1919, 0x2b082b0819192b2b,
    0x2b082b082b080808, 0x2b082b082b08082b, 0x2b082b082b2b2b08, 0x2b082b190808192b, 0x2b082b2b082b082b,
    0x2b082b2b2b080808, 0x2b082b2b2b082b08, 0x2b082b2b2b19192b, 0x2b082b2b2b2b2b08, 0x2b19080808080819,
    0x2b19080808081908, 0x2b19080808190808, 0x2b19080819080808, 0x2b1908081919192b, 0x2b1908082b081908,
    0x2b19081908080808, 0x2b190819082b082b, 0x2b190819192b1908, 0x2b19082b1919192b, 0x2b19082b2b082b19,
    0x2b19190808080808, 0x2b19190808081919, 0x2b19190819081908, 0x2b19190819190808, 0x2b19190819192b08,
    0x2b191919082b2b19, 0x2b1919192b190808, 0x2b1919192b19082b, 0x2b19192b19080819, 0x2b192b0819190819,
    0x2b192b082b2b192b, 0x2b192b1919082b19, 0x2b192b2b08191919, 0x2b192b2b192b0808, 0x2b2b080808080808,
    0x2b2b08080808082b, 0x2b2b080808082b08, 0x2b2b080808082b2b, 0x2b2b0808082b0808, 0x2b2b0808082b2b2b,
    0x2b2b08082b2b0808, 0x2b2b081919190819, 0x2b2b081919192b19, 0x2b2b08192b2b192b, 0x2b2b082b08080808,
    0x2b2b082b0808082b, 0x2b2b082b08082b08, 0x2b2b082b082b2b2b, 0x2b2b082b2b080808, 0x2b2b082b2b2b0808,
    0x2b2b190819080808, 0x2b2b19082b191919, 0x2b2b192b192b1919, 0x2b2b192b2b192b08, 0x2b2b2b0808082b2b,
    0x2b2b2b08082b0808, 0x2b2b2b08082b082b, 0x2b2b2b08082b2b08, 0x2b2b2b082b2b0808, 0x2b2b2b082b2b2b08,
    0x2b2b2b1908081908, 0x2b2b2b192b081908, 0x2b2b2b192b08192b, 0x2b2b2b2b082b2b08, 0x2b2b2b2b082b2b2b,
    0x2b2b2b2b2b190819, 0x2b2b2b2b2b2b2b2b,
};

static const __device__ uint64_t iq2s_grid[1024] = {
    0x0808080808080808, 0x080808080808082b, 0x0808080808081919, 0x0808080808082b08, 0x0808080808082b2b,
    0x0808080808190819, 0x0808080808191908, 0x080808080819192b, 0x0808080808192b19, 0x08080808082b0808,
    0x08080808082b082b, 0x08080808082b1919, 0x08080808082b2b08, 0x0808080819080819, 0x0808080819081908,
    0x080808081908192b, 0x0808080819082b19, 0x0808080819190808, 0x080808081919082b, 0x0808080819191919,
    0x0808080819192b08, 0x08080808192b0819, 0x08080808192b1908, 0x08080808192b192b, 0x08080808192b2b19,
    0x080808082b080808, 0x080808082b08082b, 0x080808082b081919, 0x080808082b082b08, 0x080808082b190819,
    0x080808082b191908, 0x080808082b2b0808, 0x080808082b2b1919, 0x080808082b2b2b2b, 0x0808081908080819,
    0x0808081908081908, 0x080808190808192b, 0x0808081908082b19, 0x0808081908190808, 0x080808190819082b,
    0x0808081908191919, 0x0808081908192b08, 0x08080819082b0819, 0x08080819082b1908, 0x0808081919080808,
    0x080808191908082b, 0x0808081919081919, 0x0808081919082b08, 0x0808081919190819, 0x0808081919191908,
    0x080808191919192b, 0x0808081919192b19, 0x08080819192b0808, 0x08080819192b1919, 0x08080819192b2b08,
    0x080808192b080819, 0x080808192b081908, 0x080808192b190808, 0x080808192b19082b, 0x080808192b191919,
    0x080808192b2b0819, 0x080808192b2b1908, 0x0808082b08080808, 0x0808082b0808082b, 0x0808082b08081919,
    0x0808082b08082b08, 0x0808082b08190819, 0x0808082b08191908, 0x0808082b082b0808, 0x0808082b082b2b2b,
    0x0808082b19080819, 0x0808082b19081908, 0x0808082b1908192b, 0x0808082b19082b19, 0x0808082b19190808,
    0x0808082b19191919, 0x0808082b2b080808, 0x0808082b2b081919, 0x0808082b2b082b2b, 0x0808082b2b191908,
    0x0808082b2b2b082b, 0x0808190808080819, 0x0808190808081908, 0x080819080808192b, 0x0808190808082b19,
    0x0808190808190808, 0x080819080819082b, 0x0808190808191919, 0x0808190808192b08, 0x08081908082b0819,
    0x08081908082b1908, 0x08081908082b192b, 0x08081908082b2b19, 0x0808190819080808, 0x080819081908082b,
    0x0808190819081919, 0x0808190819082b08, 0x0808190819082b2b, 0x0808190819190819, 0x0808190819191908,
    0x080819081919192b, 0x0808190819192b19, 0x08081908192b0808, 0x08081908192b082b, 0x08081908192b1919,
    0x080819082b080819, 0x080819082b081908, 0x080819082b08192b, 0x080819082b082b19, 0x080819082b190808,
    0x080819082b191919, 0x080819082b192b08, 0x080819082b2b0819, 0x080819082b2b1908, 0x0808191908080808,
    0x080819190808082b, 0x0808191908081919, 0x0808191908082b08, 0x0808191908082b2b, 0x0808191908190819,
    0x0808191908191908, 0x080819190819192b, 0x0808191908192b19, 0x08081919082b0808, 0x08081919082b1919,
    0x08081919082b2b08, 0x0808191919080819, 0x0808191919081908, 0x080819191908192b, 0x0808191919082b19,
    0x0808191919190808, 0x080819191919082b, 0x0808191919191919, 0x0808191919192b08, 0x08081919192b0819,
    0x08081919192b1908, 0x080819192b080808, 0x080819192b08082b, 0x080819192b081919, 0x080819192b082b08,
    0x080819192b190819, 0x080819192b191908, 0x080819192b2b0808, 0x0808192b08080819, 0x0808192b08081908,
    0x0808192b0808192b, 0x0808192b08082b19, 0x0808192b08190808, 0x0808192b08191919, 0x0808192b19080808,
    0x0808192b19081919, 0x0808192b19082b08, 0x0808192b19190819, 0x0808192b19191908, 0x0808192b192b0808,
    0x0808192b2b080819, 0x0808192b2b081908, 0x0808192b2b190808, 0x08082b0808080808, 0x08082b080808082b,
    0x08082b0808081919, 0x08082b0808082b08, 0x08082b0808190819, 0x08082b0808191908, 0x08082b080819192b,
    0x08082b0808192b19, 0x08082b08082b0808, 0x08082b08082b1919, 0x08082b08082b2b2b, 0x08082b0819080819,
    0x08082b0819081908, 0x08082b081908192b, 0x08082b0819082b19, 0x08082b0819190808, 0x08082b081919082b,
    0x08082b0819191919, 0x08082b0819192b08, 0x08082b08192b0819, 0x08082b08192b1908, 0x08082b082b080808,
    0x08082b082b081919, 0x08082b082b191908, 0x08082b082b2b2b2b, 0x08082b1908080819, 0x08082b1908081908,
    0x08082b1908190808, 0x08082b190819082b, 0x08082b1908191919, 0x08082b1908192b08, 0x08082b19082b0819,
    0x08082b1919080808, 0x08082b1919081919, 0x08082b1919082b08, 0x08082b1919190819, 0x08082b1919191908,
    0x08082b19192b0808, 0x08082b192b080819, 0x08082b192b190808, 0x08082b2b08080808, 0x08082b2b08190819,
    0x08082b2b08191908, 0x08082b2b082b082b, 0x08082b2b082b2b08, 0x08082b2b082b2b2b, 0x08082b2b19190808,
    0x08082b2b2b192b19, 0x0819080808080819, 0x0819080808081908, 0x081908080808192b, 0x0819080808082b19,
    0x0819080808190808, 0x081908080819082b, 0x0819080808191919, 0x0819080808192b08, 0x08190808082b0819,
    0x08190808082b1908, 0x08190808082b192b, 0x0819080819080808, 0x081908081908082b, 0x0819080819081919,
    0x0819080819082b08, 0x0819080819190819, 0x0819080819191908, 0x081908081919192b, 0x0819080819192b19,
    0x08190808192b0808, 0x08190808192b082b, 0x08190808192b1919, 0x08190808192b2b08, 0x081908082b080819,
    0x081908082b081908, 0x081908082b08192b, 0x081908082b190808, 0x081908082b191919, 0x081908082b192b08,
    0x081908082b2b0819, 0x081908082b2b1908, 0x0819081908080808, 0x081908190808082b, 0x0819081908081919,
    0x0819081908082b08, 0x0819081908082b2b, 0x0819081908190819, 0x0819081908191908, 0x081908190819192b,
    0x0819081908192b19, 0x08190819082b0808, 0x08190819082b082b, 0x08190819082b1919, 0x08190819082b2b08,
    0x0819081919080819, 0x0819081919081908, 0x081908191908192b, 0x0819081919082b19, 0x0819081919190808,
    0x081908191919082b, 0x0819081919191919, 0x0819081919192b08, 0x08190819192b0819, 0x08190819192b1908,
    0x081908192b080808, 0x081908192b08082b, 0x081908192b081919, 0x081908192b082b08, 0x081908192b190819,
    0x081908192b191908, 0x0819082b08080819, 0x0819082b08081908, 0x0819082b08082b19, 0x0819082b08190808,
    0x0819082b08191919, 0x0819082b082b0819, 0x0819082b082b1908, 0x0819082b19080808, 0x0819082b19081919,
    0x0819082b19190819, 0x0819082b19191908, 0x0819082b2b080819, 0x0819082b2b081908, 0x0819082b2b190808,
    0x0819190808080808, 0x081919080808082b, 0x0819190808081919, 0x0819190808082b08, 0x0819190808190819,
    0x0819190808191908, 0x081919080819192b, 0x0819190808192b19, 0x08191908082b0808, 0x08191908082b1919,
    0x08191908082b2b08, 0x0819190819080819, 0x0819190819081908, 0x081919081908192b, 0x0819190819082b19,
    0x0819190819190808, 0x081919081919082b, 0x0819190819191919, 0x0819190819192b08, 0x08191908192b0819,
    0x08191908192b1908, 0x081919082b080808, 0x081919082b08082b, 0x081919082b081919, 0x081919082b082b08,
    0x081919082b190819, 0x081919082b191908, 0x081919082b2b0808, 0x0819191908080819, 0x0819191908081908,
    0x081919190808192b, 0x0819191908082b19, 0x0819191908190808, 0x081919190819082b, 0x0819191908191919,
    0x0819191908192b08, 0x08191919082b0819, 0x08191919082b1908, 0x0819191919080808, 0x081919191908082b,
    0x0819191919081919, 0x0819191919082b08, 0x0819191919190819, 0x0819191919191908, 0x08191919192b0808,
    0x081919192b080819, 0x081919192b081908, 0x081919192b190808, 0x0819192b08080808, 0x0819192b08081919,
    0x0819192b08082b08, 0x0819192b08190819, 0x0819192b08191908, 0x0819192b082b0808, 0x0819192b19080819,
    0x0819192b19081908, 0x0819192b19190808, 0x0819192b2b080808, 0x0819192b2b2b2b2b, 0x08192b0808080819,
    0x08192b0808081908, 0x08192b080808192b, 0x08192b0808082b19, 0x08192b0808190808, 0x08192b0808191919,
    0x08192b0808192b08, 0x08192b08082b0819, 0x08192b0819080808, 0x08192b081908082b, 0x08192b0819081919,
    0x08192b0819082b08, 0x08192b0819190819, 0x08192b0819191908, 0x08192b08192b0808, 0x08192b082b080819,
    0x08192b082b081908, 0x08192b1908080808, 0x08192b190808082b, 0x08192b1908081919, 0x08192b1908082b08,
    0x08192b1908190819, 0x08192b1908191908, 0x08192b19082b0808, 0x08192b1919080819, 0x08192b1919081908,
    0x08192b1919190808, 0x08192b19192b2b19, 0x08192b192b2b082b, 0x08192b2b08081908, 0x08192b2b08190808,
    0x08192b2b19080808, 0x08192b2b1919192b, 0x082b080808080808, 0x082b08080808082b, 0x082b080808081919,
    0x082b080808082b08, 0x082b080808190819, 0x082b080808191908, 0x082b08080819192b, 0x082b080808192b19,
    0x082b0808082b0808, 0x082b0808082b1919, 0x082b0808082b2b2b, 0x082b080819080819, 0x082b080819081908,
    0x082b080819190808, 0x082b08081919082b, 0x082b080819191919, 0x082b0808192b1908, 0x082b08082b080808,
    0x082b08082b082b2b, 0x082b08082b191908, 0x082b08082b2b2b2b, 0x082b081908080819, 0x082b081908081908,
    0x082b081908190808, 0x082b08190819082b, 0x082b081908191919, 0x082b0819082b0819, 0x082b081919080808,
    0x082b08191908082b, 0x082b081919081919, 0x082b081919190819, 0x082b081919191908, 0x082b0819192b0808,
    0x082b08192b080819, 0x082b08192b081908, 0x082b08192b190808, 0x082b082b08080808, 0x082b082b08082b2b,
    0x082b082b082b082b, 0x082b082b082b2b08, 0x082b082b082b2b2b, 0x082b082b19081908, 0x082b082b19190808,
    0x082b082b2b082b08, 0x082b082b2b082b2b, 0x082b082b2b2b2b08, 0x082b190808080819, 0x082b190808081908,
    0x082b19080808192b, 0x082b190808082b19, 0x082b190808190808, 0x082b190808191919, 0x082b190808192b08,
    0x082b1908082b0819, 0x082b1908082b1908, 0x082b190819080808, 0x082b19081908082b, 0x082b190819081919,
    0x082b190819082b08, 0x082b190819190819, 0x082b190819191908, 0x082b1908192b0808, 0x082b19082b080819,
    0x082b19082b081908, 0x082b19082b190808, 0x082b191908080808, 0x082b191908081919, 0x082b191908082b08,
    0x082b191908190819, 0x082b191908191908, 0x082b1919082b0808, 0x082b191919080819, 0x082b191919081908,
    0x082b191919190808, 0x082b1919192b192b, 0x082b19192b080808, 0x082b192b08080819, 0x082b192b08081908,
    0x082b192b08190808, 0x082b192b19080808, 0x082b192b19192b19, 0x082b2b0808080808, 0x082b2b0808081919,
    0x082b2b0808190819, 0x082b2b0808191908, 0x082b2b0819080819, 0x082b2b0819081908, 0x082b2b0819190808,
    0x082b2b082b082b2b, 0x082b2b082b2b2b2b, 0x082b2b1908080819, 0x082b2b1908081908, 0x082b2b1908190808,
    0x082b2b192b191919, 0x082b2b2b08082b2b, 0x082b2b2b082b082b, 0x082b2b2b192b1908, 0x082b2b2b2b082b08,
    0x082b2b2b2b082b2b, 0x1908080808080819, 0x1908080808081908, 0x190808080808192b, 0x1908080808082b19,
    0x1908080808190808, 0x190808080819082b, 0x1908080808191919, 0x1908080808192b08, 0x1908080808192b2b,
    0x19080808082b0819, 0x19080808082b1908, 0x19080808082b192b, 0x1908080819080808, 0x190808081908082b,
    0x1908080819081919, 0x1908080819082b08, 0x1908080819082b2b, 0x1908080819190819, 0x1908080819191908,
    0x190808081919192b, 0x1908080819192b19, 0x19080808192b0808, 0x19080808192b082b, 0x19080808192b1919,
    0x190808082b080819, 0x190808082b081908, 0x190808082b190808, 0x190808082b191919, 0x190808082b192b08,
    0x190808082b2b0819, 0x190808082b2b1908, 0x1908081908080808, 0x190808190808082b, 0x1908081908081919,
    0x1908081908082b08, 0x1908081908190819, 0x1908081908191908, 0x190808190819192b, 0x1908081908192b19,
    0x19080819082b0808, 0x19080819082b082b, 0x19080819082b1919, 0x1908081919080819, 0x1908081919081908,
    0x190808191908192b, 0x1908081919082b19, 0x1908081919190808, 0x190808191919082b, 0x1908081919191919,
    0x1908081919192b08, 0x19080819192b0819, 0x19080819192b1908, 0x190808192b080808, 0x190808192b08082b,
    0x190808192b081919, 0x190808192b082b08, 0x190808192b190819, 0x190808192b191908, 0x190808192b2b0808,
    0x1908082b08080819, 0x1908082b08081908, 0x1908082b08190808, 0x1908082b0819082b, 0x1908082b08191919,
    0x1908082b08192b08, 0x1908082b082b1908, 0x1908082b19080808, 0x1908082b19081919, 0x1908082b19082b08,
    0x1908082b19190819, 0x1908082b19191908, 0x1908082b192b0808, 0x1908082b2b080819, 0x1908082b2b081908,
    0x1908190808080808, 0x190819080808082b, 0x1908190808081919, 0x1908190808082b08, 0x1908190808082b2b,
    0x1908190808190819, 0x1908190808191908, 0x190819080819192b, 0x1908190808192b19, 0x19081908082b0808,
    0x19081908082b082b, 0x19081908082b1919, 0x19081908082b2b08, 0x1908190819080819, 0x1908190819081908,
    0x190819081908192b, 0x1908190819082b19, 0x1908190819190808, 0x190819081919082b, 0x1908190819191919,
    0x1908190819192b08, 0x19081908192b0819, 0x19081908192b1908, 0x190819082b080808, 0x190819082b08082b,
    0x190819082b081919, 0x190819082b082b08, 0x190819082b190819, 0x190819082b191908, 0x190819082b2b0808,
    0x1908191908080819, 0x1908191908081908, 0x190819190808192b, 0x1908191908082b19, 0x1908191908190808,
    0x190819190819082b, 0x1908191908191919, 0x1908191908192b08, 0x19081919082b0819, 0x19081919082b1908,
    0x1908191919080808, 0x190819191908082b, 0x1908191919081919, 0x1908191919082b08, 0x1908191919190819,
    0x1908191919191908, 0x19081919192b0808, 0x19081919192b2b2b, 0x190819192b080819, 0x190819192b081908,
    0x190819192b190808, 0x1908192b08080808, 0x1908192b0808082b, 0x1908192b08081919, 0x1908192b08082b08,
    0x1908192b08190819, 0x1908192b08191908, 0x1908192b082b0808, 0x1908192b19080819, 0x1908192b19081908,
    0x1908192b19190808, 0x1908192b2b080808, 0x1908192b2b2b1919, 0x19082b0808080819, 0x19082b0808081908,
    0x19082b0808082b19, 0x19082b0808190808, 0x19082b080819082b, 0x19082b0808191919, 0x19082b0808192b08,
    0x19082b08082b0819, 0x19082b08082b1908, 0x19082b0819080808, 0x19082b081908082b, 0x19082b0819081919,
    0x19082b0819082b08, 0x19082b0819190819, 0x19082b0819191908, 0x19082b08192b0808, 0x19082b082b081908,
    0x19082b082b190808, 0x19082b1908080808, 0x19082b190808082b, 0x19082b1908081919, 0x19082b1908082b08,
    0x19082b1908190819, 0x19082b1908191908, 0x19082b19082b0808, 0x19082b1919080819, 0x19082b1919081908,
    0x19082b1919190808, 0x19082b192b080808, 0x19082b192b19192b, 0x19082b2b08080819, 0x19082b2b08081908,
    0x19082b2b08190808, 0x19082b2b19080808, 0x1919080808080808, 0x191908080808082b, 0x1919080808081919,
    0x1919080808082b08, 0x1919080808190819, 0x1919080808191908, 0x191908080819192b, 0x1919080808192b19,
    0x19190808082b0808, 0x19190808082b082b, 0x19190808082b1919, 0x19190808082b2b08, 0x1919080819080819,
    0x1919080819081908, 0x191908081908192b, 0x1919080819082b19, 0x1919080819190808, 0x191908081919082b,
    0x1919080819191919, 0x1919080819192b08, 0x19190808192b0819, 0x19190808192b1908, 0x191908082b080808,
    0x191908082b08082b, 0x191908082b081919, 0x191908082b082b08, 0x191908082b190819, 0x191908082b191908,
    0x1919081908080819, 0x1919081908081908, 0x191908190808192b, 0x1919081908082b19, 0x1919081908190808,
    0x191908190819082b, 0x1919081908191919, 0x1919081908192b08, 0x19190819082b0819, 0x19190819082b1908,
    0x1919081919080808, 0x191908191908082b, 0x1919081919081919, 0x1919081919082b08, 0x1919081919190819,
    0x1919081919191908, 0x19190819192b0808, 0x191908192b080819, 0x191908192b081908, 0x191908192b190808,
    0x1919082b08080808, 0x1919082b08081919, 0x1919082b08082b08, 0x1919082b08190819, 0x1919082b08191908,
    0x1919082b082b0808, 0x1919082b19080819, 0x1919082b19081908, 0x1919082b19190808, 0x1919082b192b2b19,
    0x1919082b2b080808, 0x1919190808080819, 0x1919190808081908, 0x191919080808192b, 0x1919190808082b19,
    0x1919190808190808, 0x191919080819082b, 0x1919190808191919, 0x1919190808192b08, 0x19191908082b0819,
    0x19191908082b1908, 0x1919190819080808, 0x191919081908082b, 0x1919190819081919, 0x1919190819082b08,
    0x1919190819190819, 0x1919190819191908, 0x19191908192b0808, 0x191919082b080819, 0x191919082b081908,
    0x191919082b190808, 0x1919191908080808, 0x191919190808082b, 0x1919191908081919, 0x1919191908082b08,
    0x1919191908190819, 0x1919191908191908, 0x19191919082b0808, 0x1919191919080819, 0x1919191919081908,
    0x1919191919190808, 0x191919192b080808, 0x1919192b08080819, 0x1919192b08081908, 0x1919192b08190808,
    0x1919192b082b192b, 0x1919192b19080808, 0x19192b0808080808, 0x19192b080808082b, 0x19192b0808081919,
    0x19192b0808082b08, 0x19192b0808190819, 0x19192b0808191908, 0x19192b08082b0808, 0x19192b0819080819,
    0x19192b0819081908, 0x19192b0819190808, 0x19192b0819192b2b, 0x19192b082b080808, 0x19192b1908080819,
    0x19192b1908081908, 0x19192b1908190808, 0x19192b1919080808, 0x19192b2b08080808, 0x19192b2b08192b19,
    0x19192b2b2b081919, 0x19192b2b2b2b2b08, 0x192b080808080819, 0x192b080808081908, 0x192b08080808192b,
    0x192b080808190808, 0x192b08080819082b, 0x192b080808191919, 0x192b080808192b08, 0x192b0808082b0819,
    0x192b0808082b1908, 0x192b080819080808, 0x192b080819081919, 0x192b080819082b08, 0x192b080819190819,
    0x192b080819191908, 0x192b0808192b0808, 0x192b08082b081908, 0x192b08082b190808, 0x192b081908080808,
    0x192b08190808082b, 0x192b081908081919, 0x192b081908082b08, 0x192b081908190819, 0x192b081908191908,
    0x192b0819082b0808, 0x192b081919080819, 0x192b081919081908, 0x192b081919190808, 0x192b08192b080808,
    0x192b08192b192b19, 0x192b082b08081908, 0x192b082b08190808, 0x192b082b19080808, 0x192b082b1919192b,
    0x192b082b2b2b0819, 0x192b190808080808, 0x192b190808081919, 0x192b190808082b08, 0x192b190808190819,
    0x192b190808191908, 0x192b1908082b0808, 0x192b190819080819, 0x192b190819081908, 0x192b190819190808,
    0x192b19082b080808, 0x192b191908080819, 0x192b191908081908, 0x192b191908190808, 0x192b191919080808,
    0x192b191919082b2b, 0x192b1919192b2b08, 0x192b19192b19082b, 0x192b192b08080808, 0x192b192b2b191908,
    0x192b2b0808080819, 0x192b2b0808081908, 0x192b2b0808190808, 0x192b2b08192b1919, 0x192b2b082b192b08,
    0x192b2b1908080808, 0x192b2b19082b2b2b, 0x192b2b2b1908082b, 0x192b2b2b2b2b0819, 0x2b08080808080808,
    0x2b0808080808082b, 0x2b08080808081919, 0x2b08080808082b08, 0x2b08080808190819, 0x2b08080808191908,
    0x2b08080808192b19, 0x2b080808082b0808, 0x2b080808082b1919, 0x2b08080819080819, 0x2b08080819081908,
    0x2b08080819190808, 0x2b0808081919082b, 0x2b08080819191919, 0x2b08080819192b08, 0x2b080808192b0819,
    0x2b0808082b080808, 0x2b0808082b081919, 0x2b0808082b190819, 0x2b0808082b191908, 0x2b08081908080819,
    0x2b08081908081908, 0x2b08081908082b19, 0x2b08081908190808, 0x2b0808190819082b, 0x2b08081908191919,
    0x2b08081908192b08, 0x2b080819082b0819, 0x2b080819082b1908, 0x2b08081919080808, 0x2b0808191908082b,
    0x2b08081919081919, 0x2b08081919082b08, 0x2b08081919190819, 0x2b08081919191908, 0x2b0808192b080819,
    0x2b0808192b081908, 0x2b0808192b190808, 0x2b0808192b2b2b19, 0x2b08082b08080808, 0x2b08082b08081919,
    0x2b08082b08082b2b, 0x2b08082b08190819, 0x2b08082b08191908, 0x2b08082b19080819, 0x2b08082b19081908,
    0x2b08082b19190808, 0x2b08190808080819, 0x2b08190808081908, 0x2b0819080808192b, 0x2b08190808082b19,
    0x2b08190808190808, 0x2b0819080819082b, 0x2b08190808191919, 0x2b08190808192b08, 0x2b081908082b0819,
    0x2b08190819080808, 0x2b0819081908082b, 0x2b08190819081919, 0x2b08190819082b08, 0x2b08190819190819,
    0x2b08190819191908, 0x2b081908192b0808, 0x2b0819082b080819, 0x2b0819082b081908, 0x2b0819082b190808,
    0x2b08191908080808, 0x2b0819190808082b, 0x2b08191908081919, 0x2b08191908082b08, 0x2b08191908190819,
    0x2b08191908191908, 0x2b081919082b0808, 0x2b08191919080819, 0x2b08191919081908, 0x2b08191919190808,
    0x2b0819192b080808, 0x2b0819192b082b2b, 0x2b08192b08080819, 0x2b08192b08081908, 0x2b08192b08190808,
    0x2b08192b082b2b19, 0x2b08192b19080808, 0x2b082b0808080808, 0x2b082b0808081919, 0x2b082b0808190819,
    0x2b082b0808191908, 0x2b082b0819080819, 0x2b082b0819081908, 0x2b082b0819190808, 0x2b082b082b2b082b,
    0x2b082b1908080819, 0x2b082b1908081908, 0x2b082b1919080808, 0x2b082b19192b1919, 0x2b082b2b082b082b,
    0x2b082b2b19192b08, 0x2b082b2b19192b2b, 0x2b082b2b2b08082b, 0x2b082b2b2b2b082b, 0x2b19080808080819,
    0x2b19080808081908, 0x2b19080808082b19, 0x2b19080808190808, 0x2b1908080819082b, 0x2b19080808191919,
    0x2b19080808192b08, 0x2b190808082b1908, 0x2b19080819080808, 0x2b1908081908082b, 0x2b19080819081919,
    0x2b19080819082b08, 0x2b19080819190819, 0x2b19080819191908, 0x2b190808192b0808, 0x2b1908082b080819,
    0x2b1908082b081908, 0x2b1908082b190808, 0x2b19081908080808, 0x2b19081908081919, 0x2b19081908190819,
    0x2b19081908191908, 0x2b19081919080819, 0x2b19081919081908, 0x2b19081919190808, 0x2b19081919192b2b,
    0x2b19082b08080819, 0x2b19082b08081908, 0x2b19082b08190808, 0x2b19082b19080808, 0x2b19082b2b2b192b,
    0x2b19190808080808, 0x2b1919080808082b, 0x2b19190808081919, 0x2b19190808082b08, 0x2b19190808190819,
    0x2b19190808191908, 0x2b191908082b0808, 0x2b19190819080819, 0x2b19190819081908, 0x2b19190819190808,
    0x2b1919082b080808, 0x2b1919082b19192b, 0x2b19191908080819, 0x2b19191908081908, 0x2b19191908190808,
    0x2b19191919080808, 0x2b1919192b192b08, 0x2b1919192b2b0819, 0x2b19192b08080808, 0x2b19192b1908192b,
    0x2b19192b192b1908, 0x2b192b0808080819, 0x2b192b0808081908, 0x2b192b0808190808, 0x2b192b08082b192b,
    0x2b192b0819080808, 0x2b192b082b2b2b19, 0x2b192b1908080808, 0x2b192b1919082b19, 0x2b192b191919082b,
    0x2b192b2b2b190808, 0x2b2b080808080808, 0x2b2b080808081919, 0x2b2b080808082b2b, 0x2b2b080808191908,
    0x2b2b0808082b082b, 0x2b2b0808082b2b2b, 0x2b2b080819080819, 0x2b2b080819081908, 0x2b2b080819190808,
    0x2b2b08082b2b082b, 0x2b2b08082b2b2b2b, 0x2b2b081919080808, 0x2b2b0819192b1919, 0x2b2b082b0808082b,
    0x2b2b082b08082b2b, 0x2b2b082b082b082b, 0x2b2b082b082b2b08, 0x2b2b082b082b2b2b, 0x2b2b082b2b08082b,
    0x2b2b082b2b082b08, 0x2b2b082b2b082b2b, 0x2b2b082b2b2b2b08, 0x2b2b190808080819, 0x2b2b190808081908,
    0x2b2b190808190808, 0x2b2b190819080808, 0x2b2b19082b082b19, 0x2b2b19082b2b1908, 0x2b2b191908080808,
    0x2b2b191908192b19, 0x2b2b192b19190819, 0x2b2b2b0808082b2b, 0x2b2b2b08082b2b08, 0x2b2b2b082b2b082b,
    0x2b2b2b1919191908, 0x2b2b2b192b08192b, 0x2b2b2b2b08082b08, 0x2b2b2b2b08082b2b, 0x2b2b2b2b082b0808,
    0x2b2b2b2b082b082b, 0x2b2b2b2b082b2b08, 0x2b2b2b2b2b082b08, 0x2b2b2b2b2b2b2b2b,
};

static const __device__ uint32_t iq3xxs_grid[256] = {
    0x04040404, 0x04040414, 0x04040424, 0x04040c0c, 0x04040c1c, 0x04040c3e, 0x04041404, 0x04041414, 0x04041c0c,
    0x04042414, 0x04043e1c, 0x04043e2c, 0x040c040c, 0x040c041c, 0x040c0c04, 0x040c0c14, 0x040c140c, 0x040c142c,
    0x040c1c04, 0x040c1c14, 0x040c240c, 0x040c2c24, 0x040c3e04, 0x04140404, 0x04140414, 0x04140424, 0x04140c0c,
    0x04141404, 0x04141414, 0x04141c0c, 0x04141c1c, 0x04141c3e, 0x04142c0c, 0x04142c3e, 0x04143e2c, 0x041c040c,
    0x041c043e, 0x041c0c04, 0x041c0c14, 0x041c142c, 0x041c3e04, 0x04240c1c, 0x04241c3e, 0x04242424, 0x04242c3e,
    0x04243e1c, 0x04243e2c, 0x042c040c, 0x042c043e, 0x042c1c14, 0x042c2c14, 0x04341c2c, 0x04343424, 0x043e0c04,
    0x043e0c24, 0x043e0c34, 0x043e241c, 0x043e340c, 0x0c04040c, 0x0c04041c, 0x0c040c04, 0x0c040c14, 0x0c04140c,
    0x0c04141c, 0x0c041c04, 0x0c041c14, 0x0c041c24, 0x0c04243e, 0x0c042c04, 0x0c0c0404, 0x0c0c0414, 0x0c0c0c0c,
    0x0c0c1404, 0x0c0c1414, 0x0c14040c, 0x0c14041c, 0x0c140c04, 0x0c140c14, 0x0c14140c, 0x0c141c04, 0x0c143e14,
    0x0c1c0404, 0x0c1c0414, 0x0c1c1404, 0x0c1c1c0c, 0x0c1c2434, 0x0c1c3434, 0x0c24040c, 0x0c24042c, 0x0c242c04,
    0x0c2c1404, 0x0c2c1424, 0x0c2c2434, 0x0c2c3e0c, 0x0c34042c, 0x0c3e1414, 0x0c3e2404, 0x14040404, 0x14040414,
    0x14040c0c, 0x14040c1c, 0x14041404, 0x14041414, 0x14041434, 0x14041c0c, 0x14042414, 0x140c040c, 0x140c041c,
    0x140c042c, 0x140c0c04, 0x140c0c14, 0x140c140c, 0x140c1c04, 0x140c341c, 0x140c343e, 0x140c3e04, 0x14140404,
    0x14140414, 0x14140c0c, 0x14140c3e, 0x14141404, 0x14141414, 0x14141c3e, 0x14142404, 0x14142c2c, 0x141c040c,
    0x141c0c04, 0x141c0c24, 0x141c3e04, 0x141c3e24, 0x14241c2c, 0x14242c1c, 0x142c041c, 0x142c143e, 0x142c240c,
    0x142c3e24, 0x143e040c, 0x143e041c, 0x143e0c34, 0x143e242c, 0x1c04040c, 0x1c040c04, 0x1c040c14, 0x1c04140c,
    0x1c04141c, 0x1c042c04, 0x1c04342c, 0x1c043e14, 0x1c0c0404, 0x1c0c0414, 0x1c0c1404, 0x1c0c1c0c, 0x1c0c2424,
    0x1c0c2434, 0x1c14040c, 0x1c14041c, 0x1c140c04, 0x1c14142c, 0x1c142c14, 0x1c143e14, 0x1c1c0c0c, 0x1c1c1c1c,
    0x1c241c04, 0x1c24243e, 0x1c243e14, 0x1c2c0404, 0x1c2c0434, 0x1c2c1414, 0x1c2c2c2c, 0x1c340c24, 0x1c341c34,
    0x1c34341c, 0x1c3e1c1c, 0x1c3e3404, 0x24040424, 0x24040c3e, 0x24041c2c, 0x24041c3e, 0x24042c1c, 0x24042c3e,
    0x240c3e24, 0x24141404, 0x24141c3e, 0x24142404, 0x24143404, 0x24143434, 0x241c043e, 0x241c242c, 0x24240424,
    0x24242c0c, 0x24243424, 0x242c142c, 0x242c241c, 0x242c3e04, 0x243e042c, 0x243e0c04, 0x243e0c14, 0x243e1c04,
    0x2c040c14, 0x2c04240c, 0x2c043e04, 0x2c0c0404, 0x2c0c0434, 0x2c0c1434, 0x2c0c2c2c, 0x2c140c24, 0x2c141c14,
    0x2c143e14, 0x2c1c0414, 0x2c1c2c1c, 0x2c240c04, 0x2c24141c, 0x2c24143e, 0x2c243e14, 0x2c2c0414, 0x2c2c1c0c,
    0x2c342c04, 0x2c3e1424, 0x2c3e2414, 0x34041424, 0x34042424, 0x34042434, 0x34043424, 0x340c140c, 0x340c340c,
    0x34140c3e, 0x34143424, 0x341c1c04, 0x341c1c34, 0x34242424, 0x342c042c, 0x342c2c14, 0x34341c1c, 0x343e041c,
    0x343e140c, 0x3e04041c, 0x3e04042c, 0x3e04043e, 0x3e040c04, 0x3e041c14, 0x3e042c14, 0x3e0c1434, 0x3e0c2404,
    0x3e140c14, 0x3e14242c, 0x3e142c14, 0x3e1c0404, 0x3e1c0c2c, 0x3e1c1c1c, 0x3e1c3404, 0x3e24140c, 0x3e24240c,
    0x3e2c0404, 0x3e2c0414, 0x3e2c1424, 0x3e341c04,
};

static const __device__ uint32_t iq3xs_grid[512] = {
    0x04040404, 0x0404040c, 0x04040414, 0x0404042c, 0x0404043e, 0x04040c04, 0x04040c0c, 0x04040c14, 0x04040c24,
    0x04040c34, 0x04041404, 0x0404140c, 0x0404142c, 0x04041c1c, 0x04042404, 0x04042414, 0x0404242c, 0x0404243e,
    0x04042c0c, 0x04042c1c, 0x04043404, 0x04043414, 0x04043e0c, 0x04043e24, 0x04043e3e, 0x040c0404, 0x040c040c,
    0x040c0414, 0x040c0424, 0x040c0c04, 0x040c0c0c, 0x040c0c2c, 0x040c1404, 0x040c141c, 0x040c143e, 0x040c1c0c,
    0x040c1c2c, 0x040c2424, 0x040c340c, 0x040c342c, 0x040c3e14, 0x04140404, 0x0414040c, 0x0414042c, 0x0414043e,
    0x04140c04, 0x04140c1c, 0x04140c34, 0x0414140c, 0x0414142c, 0x04141c04, 0x04141c24, 0x04142414, 0x0414242c,
    0x0414243e, 0x04142c0c, 0x04142c1c, 0x04143e04, 0x04143e1c, 0x041c041c, 0x041c0c0c, 0x041c0c2c, 0x041c1404,
    0x041c1414, 0x041c1c0c, 0x041c1c1c, 0x041c1c34, 0x041c2424, 0x041c2c04, 0x041c2c14, 0x041c343e, 0x041c3e0c,
    0x041c3e2c, 0x04240404, 0x04240c1c, 0x04240c3e, 0x0424140c, 0x04241424, 0x04241c14, 0x04242404, 0x0424241c,
    0x04242c0c, 0x04243e04, 0x042c0414, 0x042c0424, 0x042c1404, 0x042c1414, 0x042c1434, 0x042c1c1c, 0x042c240c,
    0x042c242c, 0x042c243e, 0x042c3434, 0x042c3e1c, 0x04340434, 0x04340c0c, 0x04340c1c, 0x04341c0c, 0x04342c14,
    0x04343e0c, 0x043e0404, 0x043e0414, 0x043e0424, 0x043e1404, 0x043e1414, 0x043e1434, 0x043e1c1c, 0x043e2c04,
    0x043e2c24, 0x0c040404, 0x0c04040c, 0x0c040414, 0x0c040424, 0x0c040c04, 0x0c040c0c, 0x0c040c1c, 0x0c040c2c,
    0x0c040c3e, 0x0c041404, 0x0c041414, 0x0c041c0c, 0x0c041c24, 0x0c041c34, 0x0c042c24, 0x0c042c34, 0x0c04340c,
    0x0c043e14, 0x0c0c0404, 0x0c0c040c, 0x0c0c041c, 0x0c0c0434, 0x0c0c0c04, 0x0c0c0c24, 0x0c0c140c, 0x0c0c1c04,
    0x0c0c1c1c, 0x0c0c240c, 0x0c0c2c04, 0x0c0c2c14, 0x0c0c3e04, 0x0c0c3e34, 0x0c140404, 0x0c140c14, 0x0c140c2c,
    0x0c140c3e, 0x0c141404, 0x0c141424, 0x0c141c14, 0x0c142404, 0x0c14241c, 0x0c142c2c, 0x0c143404, 0x0c143e14,
    0x0c1c040c, 0x0c1c0424, 0x0c1c043e, 0x0c1c0c04, 0x0c1c0c1c, 0x0c1c140c, 0x0c1c143e, 0x0c1c1c04, 0x0c1c1c24,
    0x0c1c240c, 0x0c1c3414, 0x0c1c3e04, 0x0c24041c, 0x0c24042c, 0x0c240c14, 0x0c240c24, 0x0c241c0c, 0x0c241c1c,
    0x0c242414, 0x0c242434, 0x0c242c04, 0x0c242c24, 0x0c2c040c, 0x0c2c0c04, 0x0c2c0c1c, 0x0c2c140c, 0x0c2c1c04,
    0x0c2c1c14, 0x0c2c2c0c, 0x0c341404, 0x0c341424, 0x0c34143e, 0x0c342424, 0x0c342434, 0x0c3e040c, 0x0c3e041c,
    0x0c3e0c04, 0x0c3e0c14, 0x0c3e140c, 0x0c3e1c2c, 0x0c3e240c, 0x0c3e3414, 0x0c3e3e04, 0x14040404, 0x1404040c,
    0x1404041c, 0x1404042c, 0x1404043e, 0x14040c04, 0x14040c14, 0x14040c24, 0x14040c34, 0x1404140c, 0x1404141c,
    0x1404143e, 0x14041c04, 0x14041c14, 0x1404240c, 0x1404241c, 0x1404242c, 0x14042c04, 0x14042c14, 0x1404343e,
    0x14043e04, 0x14043e1c, 0x14043e2c, 0x140c0404, 0x140c0414, 0x140c0c04, 0x140c0c1c, 0x140c0c3e, 0x140c1414,
    0x140c142c, 0x140c1c0c, 0x140c1c24, 0x140c2414, 0x140c2c0c, 0x1414040c, 0x14140424, 0x1414043e, 0x1414140c,
    0x1414141c, 0x14141c04, 0x14141c3e, 0x1414240c, 0x14142c1c, 0x14142c3e, 0x14143e0c, 0x14143e24, 0x141c0404,
    0x141c0414, 0x141c042c, 0x141c0c0c, 0x141c1414, 0x141c1424, 0x141c1c0c, 0x141c1c1c, 0x141c2414, 0x141c2c04,
    0x141c3434, 0x1424040c, 0x1424043e, 0x14241404, 0x1424141c, 0x14241c14, 0x14241c2c, 0x1424240c, 0x14243e14,
    0x14243e2c, 0x142c0424, 0x142c0c0c, 0x142c1414, 0x142c1c3e, 0x142c2404, 0x142c2c1c, 0x142c3e04, 0x14340404,
    0x14340414, 0x1434043e, 0x1434140c, 0x14342c2c, 0x1434340c, 0x143e042c, 0x143e0c0c, 0x143e1434, 0x143e1c04,
    0x143e241c, 0x143e2c04, 0x1c040414, 0x1c040c0c, 0x1c040c1c, 0x1c040c2c, 0x1c040c3e, 0x1c041414, 0x1c041c0c,
    0x1c041c1c, 0x1c041c2c, 0x1c042414, 0x1c042424, 0x1c04243e, 0x1c042c0c, 0x1c04341c, 0x1c043e0c, 0x1c0c040c,
    0x1c0c041c, 0x1c0c042c, 0x1c0c0c24, 0x1c0c140c, 0x1c0c141c, 0x1c0c2404, 0x1c0c3404, 0x1c0c3e14, 0x1c0c3e34,
    0x1c140404, 0x1c140c14, 0x1c141404, 0x1c141c14, 0x1c141c24, 0x1c142c04, 0x1c1c040c, 0x1c1c0c04, 0x1c1c0c24,
    0x1c1c140c, 0x1c1c141c, 0x1c1c143e, 0x1c1c1c04, 0x1c1c240c, 0x1c1c241c, 0x1c1c243e, 0x1c1c2c2c, 0x1c1c3e1c,
    0x1c24041c, 0x1c240c0c, 0x1c240c34, 0x1c241414, 0x1c241c0c, 0x1c242c14, 0x1c243404, 0x1c243424, 0x1c2c040c,
    0x1c2c0c04, 0x1c2c0c14, 0x1c2c142c, 0x1c2c1c14, 0x1c2c2424, 0x1c2c2c34, 0x1c2c3e1c, 0x1c340c34, 0x1c34240c,
    0x1c3e040c, 0x1c3e041c, 0x1c3e1404, 0x1c3e1414, 0x1c3e1c2c, 0x24040404, 0x24040424, 0x24040c14, 0x24041404,
    0x24041424, 0x2404143e, 0x24041c14, 0x2404240c, 0x24042c04, 0x24043e04, 0x240c0414, 0x240c043e, 0x240c0c0c,
    0x240c0c1c, 0x240c1414, 0x240c1c04, 0x240c1c2c, 0x240c241c, 0x240c2c0c, 0x240c2c2c, 0x2414040c, 0x2414041c,
    0x24140c04, 0x24140c2c, 0x2414140c, 0x24141c1c, 0x24142404, 0x24142c3e, 0x24143414, 0x24143e04, 0x241c0424,
    0x241c0c0c, 0x241c0c1c, 0x241c1404, 0x241c1414, 0x241c1c0c, 0x241c1c2c, 0x24240404, 0x24240414, 0x24241424,
    0x24241c3e, 0x24242404, 0x24243e0c, 0x242c042c, 0x242c043e, 0x242c140c, 0x242c3414, 0x24340c1c, 0x24341c24,
    0x24343404, 0x243e0c04, 0x243e0c2c, 0x243e1c04, 0x243e241c, 0x243e2c0c, 0x2c040414, 0x2c040c04, 0x2c040c24,
    0x2c041414, 0x2c042404, 0x2c042424, 0x2c04243e, 0x2c042c14, 0x2c043434, 0x2c043e24, 0x2c0c040c, 0x2c0c041c,
    0x2c0c042c, 0x2c0c0c14, 0x2c0c140c, 0x2c0c1c14, 0x2c0c3e14, 0x2c140404, 0x2c140c0c, 0x2c14141c, 0x2c141c04,
    0x2c141c34, 0x2c142c1c, 0x2c1c0414, 0x2c1c043e, 0x2c1c0c04, 0x2c1c143e, 0x2c1c2424, 0x2c1c2c0c, 0x2c1c342c,
    0x2c1c3e1c, 0x2c24040c, 0x2c240424, 0x2c241404, 0x2c241c14, 0x2c242434, 0x2c2c0c14, 0x2c2c1434, 0x2c2c2c0c,
    0x2c2c2c1c, 0x2c342414, 0x2c3e0414, 0x2c3e0424, 0x2c3e1414, 0x34040c0c, 0x34040c1c, 0x34040c2c, 0x34041c0c,
    0x34041c1c, 0x34043404, 0x340c0404, 0x340c1404, 0x340c143e, 0x340c3424, 0x34140c14, 0x34141c24, 0x34142414,
    0x34142c2c, 0x34143414, 0x34143e04, 0x341c0404, 0x341c0c24, 0x341c140c, 0x341c2404, 0x3424142c, 0x3424241c,
    0x34243414, 0x342c0404, 0x342c041c, 0x342c1c24, 0x342c3404, 0x3434042c, 0x34342404, 0x343e0c0c, 0x343e0c1c,
    0x3e040404, 0x3e040424, 0x3e04043e, 0x3e041404, 0x3e041414, 0x3e041c34, 0x3e042404, 0x3e042c24, 0x3e043414,
    0x3e0c0414, 0x3e0c0c0c, 0x3e0c1424, 0x3e0c241c, 0x3e0c242c, 0x3e14040c, 0x3e140424, 0x3e140c04, 0x3e140c34,
    0x3e14140c, 0x3e141c04, 0x3e142c0c, 0x3e1c0414, 0x3e1c1c14, 0x3e1c1c2c, 0x3e1c2c1c, 0x3e24040c, 0x3e24042c,
    0x3e240c1c, 0x3e241404, 0x3e242c04, 0x3e2c1414, 0x3e2c2414, 0x3e340414, 0x3e341c0c, 0x3e3e0404,
};

#define IQ1S_DELTA 0.125f
#define IQ1M_DELTA 0.125f
static const __device__ uint64_t iq1s_grid_gpu[2048] = {
    0x00000000, 0x00000002, 0x00000101, 0x00000200, 0x00000202, 0x00010001, 0x00010101, 0x00020000, 0x00020002,
    0x00020200, 0x00020202, 0x01000101, 0x01010001, 0x01010100, 0x01010102, 0x01020101, 0x02000000, 0x02000002,
    0x02000200, 0x02000202, 0x02010101, 0x02020000, 0x02020002, 0x02020200, 0x02020202, 0x00000110, 0x00000111,
    0x00010011, 0x00010110, 0x00010112, 0x00010211, 0x00010212, 0x00020111, 0x01000011, 0x01000112, 0x01000211,
    0x01010012, 0x01010111, 0x01010212, 0x01020011, 0x01020110, 0x01020112, 0x01020210, 0x02000111, 0x02010011,
    0x02010110, 0x02010112, 0x02020111, 0x00000020, 0x00000022, 0x00000220, 0x00000222, 0x00010121, 0x00020020,
    0x00020022, 0x00020220, 0x00020222, 0x01000121, 0x01010021, 0x01010221, 0x01020120, 0x01020221, 0x02000020,
    0x02000022, 0x02000220, 0x02000222, 0x02010021, 0x02010121, 0x02010221, 0x02020020, 0x02020022, 0x02020220,
    0x02020222, 0x00011001, 0x00011100, 0x00011102, 0x00021101, 0x01001001, 0x01001201, 0x01011101, 0x01011202,
    0x01021100, 0x01021101, 0x02011001, 0x02011201, 0x02021101, 0x00001011, 0x00001110, 0x00001111, 0x00001112,
    0x00011111, 0x00011210, 0x00011212, 0x00021211, 0x01001010, 0x01001111, 0x01001212, 0x01011010, 0x01011011,
    0x01011110, 0x01011111, 0x01011112, 0x01011211, 0x01021010, 0x01021012, 0x01021111, 0x01021210, 0x01021212,
    0x02001011, 0x02011011, 0x02011111, 0x02011210, 0x02011212, 0x02021011, 0x02021110, 0x02021111, 0x02021112,
    0x02021211, 0x00011120, 0x00011221, 0x01001021, 0x01001120, 0x01011020, 0x01011022, 0x01011121, 0x01011220,
    0x01021020, 0x01021021, 0x01021122, 0x01021221, 0x02001121, 0x02011021, 0x02011120, 0x02011221, 0x00002000,
    0x00002002, 0x00002200, 0x00002202, 0x00012101, 0x00022000, 0x00022002, 0x00022200, 0x00022202, 0x01002101,
    0x01012001, 0x01012102, 0x01022101, 0x02002000, 0x02002002, 0x02002200, 0x02002202, 0x02012101, 0x02022000,
    0x02022002, 0x02022200, 0x02022202, 0x00002111, 0x00012011, 0x00012110, 0x00012211, 0x00022110, 0x00022111,
    0x01002011, 0x01012010, 0x01012011, 0x01012111, 0x01022011, 0x01022110, 0x01022211, 0x02012011, 0x02012110,
    0x02012112, 0x02012211, 0x02022111, 0x00002020, 0x00002022, 0x00002220, 0x00002222, 0x00012121, 0x00022020,
    0x00022022, 0x00022220, 0x00022222, 0x01002121, 0x01012021, 0x01012221, 0x01022021, 0x01022121, 0x02002020,
    0x02002022, 0x02002121, 0x02002220, 0x02002222, 0x02012121, 0x02022020, 0x02022022, 0x02022220, 0x02022222,
    0x00110000, 0x00110001, 0x00110100, 0x00110201, 0x00120100, 0x00120101, 0x01100001, 0x01100100, 0x01110000,
    0x01110101, 0x01110200, 0x01120001, 0x01120100, 0x01120101, 0x01120201, 0x02110001, 0x02110100, 0x02110102,
    0x02120001, 0x02120101, 0x00100011, 0x00100110, 0x00100112, 0x00100211, 0x00110010, 0x00110012, 0x00110111,
    0x00110210, 0x00120011, 0x00120110, 0x00120211, 0x01100111, 0x01100212, 0x01110010, 0x01110011, 0x01110012,
    0x01110110, 0x01110111, 0x01110112, 0x01110211, 0x01120010, 0x01120111, 0x02100110, 0x02110012, 0x02110111,
    0x02120011, 0x02120110, 0x00110021, 0x00110120, 0x00110122, 0x00120121, 0x01100020, 0x01100122, 0x01100221,
    0x01110022, 0x01110121, 0x01110220, 0x01110222, 0x01120120, 0x01120122, 0x02100121, 0x02110021, 0x02110120,
    0x02110122, 0x02120121, 0x00101001, 0x00101102, 0x00101201, 0x00111100, 0x00111101, 0x00111200, 0x00111201,
    0x00121001, 0x00121102, 0x01101001, 0x01101101, 0x01101102, 0x01101200, 0x01101202, 0x01111001, 0x01111100,
    0x01111101, 0x01111102, 0x01111201, 0x01121002, 0x01121101, 0x01121200, 0x02101100, 0x02101201, 0x02111000,
    0x02111100, 0x02111101, 0x02111200, 0x02111201, 0x02111202, 0x02121001, 0x02121100, 0x02121101, 0x02121201,
    0x00101012, 0x00101111, 0x00101212, 0x00111011, 0x00111110, 0x00111111, 0x00111112, 0x00111211, 0x00121010,
    0x00121012, 0x00121111, 0x00121210, 0x00121212, 0x01101011, 0x01101110, 0x01101111, 0x01101112, 0x01111011,
    0x01111012, 0x01111110, 0x01111111, 0x01111112, 0x01111211, 0x01111212, 0x01121011, 0x01121110, 0x01121111,
    0x01121112, 0x01121211, 0x02101010, 0x02101012, 0x02101110, 0x02101111, 0x02101210, 0x02101212, 0x02111010,
    0x02111011, 0x02111110, 0x02111111, 0x02111112, 0x02111211, 0x02111212, 0x02121010, 0x02121012, 0x02121111,
    0x00101021, 0x00101120, 0x00101121, 0x00101122, 0x00111121, 0x00111122, 0x00111220, 0x00111222, 0x00121021,
    0x00121122, 0x01101020, 0x01101022, 0x01101120, 0x01101121, 0x01101220, 0x01101222, 0x01111021, 0x01111121,
    0x01111122, 0x01111220, 0x01111221, 0x01121021, 0x01121120, 0x01121121, 0x01121220, 0x01121221, 0x01121222,
    0x02101122, 0x02101222, 0x02111022, 0x02111121, 0x02121120, 0x02121221, 0x00112001, 0x00112102, 0x00122101,
    0x01102001, 0x01102100, 0x01102102, 0x01102201, 0x01112000, 0x01112101, 0x01112200, 0x01112202, 0x01122000,
    0x01122001, 0x01122100, 0x01122102, 0x01122201, 0x02102101, 0x02112001, 0x02112100, 0x02122101, 0x00112010,
    0x00112012, 0x00112111, 0x00112212, 0x00122011, 0x00122111, 0x01102012, 0x01102110, 0x01102111, 0x01102210,
    0x01112011, 0x01112110, 0x01112111, 0x01112112, 0x01112211, 0x01112212, 0x01122010, 0x01122111, 0x01122212,
    0x02102211, 0x02112011, 0x02112012, 0x02112111, 0x02112210, 0x02122011, 0x02122112, 0x02122211, 0x00102221,
    0x00112122, 0x00122120, 0x00122122, 0x01102120, 0x01102122, 0x01102221, 0x01112020, 0x01112022, 0x01112121,
    0x01112220, 0x01122021, 0x01122122, 0x01122221, 0x02102121, 0x02112021, 0x02112122, 0x02112222, 0x00200000,
    0x00200002, 0x00200200, 0x00200202, 0x00210101, 0x00220000, 0x00220002, 0x00220101, 0x00220200, 0x00220202,
    0x01200101, 0x01210001, 0x01210201, 0x01220001, 0x01220101, 0x02200000, 0x02200002, 0x02200200, 0x02200202,
    0x02210101, 0x02220000, 0x02220002, 0x02220101, 0x02220200, 0x02220202, 0x00200111, 0x00210011, 0x00210110,
    0x00210211, 0x00220111, 0x01200012, 0x01200110, 0x01200211, 0x01210111, 0x01210210, 0x01210212, 0x01220011,
    0x01220110, 0x01220111, 0x01220112, 0x02200111, 0x02210010, 0x02210112, 0x02210211, 0x02220111, 0x00200021,
    0x00200220, 0x00200222, 0x00210021, 0x00210121, 0x00220020, 0x00220022, 0x00220220, 0x00220222, 0x01200121,
    0x01210021, 0x01210122, 0x01210221, 0x01220121, 0x02200021, 0x02200220, 0x02200222, 0x02210021, 0x02210121,
    0x02220020, 0x02220022, 0x02220220, 0x02220222, 0x00201101, 0x00211100, 0x00211102, 0x00211201, 0x00221101,
    0x01201100, 0x01201101, 0x01201102, 0x01201201, 0x01211002, 0x01211101, 0x01211200, 0x01211202, 0x01221102,
    0x02201101, 0x02211001, 0x02211100, 0x02211201, 0x02221001, 0x02221101, 0x00201211, 0x00211111, 0x00221011,
    0x00221211, 0x01201010, 0x01201111, 0x01201210, 0x01211011, 0x01211110, 0x01211111, 0x01211211, 0x01221012,
    0x01221111, 0x01221210, 0x02201211, 0x02211010, 0x02211110, 0x02211111, 0x02211210, 0x02211212, 0x02221011,
    0x02221110, 0x02221112, 0x02221211, 0x00201121, 0x00211020, 0x00211022, 0x00211221, 0x00221121, 0x01201021,
    0x01201221, 0x01211121, 0x01221020, 0x01221021, 0x01221221, 0x02201120, 0x02201122, 0x02211020, 0x02211222,
    0x00202000, 0x00202002, 0x00202200, 0x00202202, 0x00212101, 0x00222000, 0x00222002, 0x00222200, 0x00222202,
    0x01202101, 0x01212001, 0x01212100, 0x01222101, 0x02202000, 0x02202002, 0x02202200, 0x02202202, 0x02222000,
    0x02222002, 0x02222200, 0x02222202, 0x00202211, 0x00212011, 0x00212110, 0x00212211, 0x00222111, 0x01202112,
    0x01202211, 0x01212012, 0x01212111, 0x01222011, 0x01222110, 0x01222112, 0x01222211, 0x02202111, 0x02212010,
    0x02212112, 0x02212211, 0x02222110, 0x02222111, 0x00202020, 0x00202022, 0x00202220, 0x00202222, 0x00222020,
    0x00222022, 0x00222220, 0x00222222, 0x01202121, 0x01212021, 0x01212122, 0x01212221, 0x01222121, 0x02202020,
    0x02202022, 0x02202220, 0x02202222, 0x02212121, 0x02222020, 0x02222022, 0x02222220, 0x02222222, 0x10000101,
    0x10010001, 0x10010102, 0x10020101, 0x11000201, 0x11010002, 0x11010101, 0x11010200, 0x11010202, 0x11020001,
    0x11020100, 0x11020102, 0x12010100, 0x12010201, 0x12020001, 0x12020102, 0x10000010, 0x10000011, 0x10000110,
    0x10000112, 0x10000211, 0x10010012, 0x10010111, 0x10010112, 0x10010210, 0x10010212, 0x10020011, 0x10020112,
    0x10020211, 0x11000111, 0x11000210, 0x11000212, 0x11010011, 0x11010110, 0x11010111, 0x11010112, 0x11010211,
    0x11010212, 0x11020111, 0x11020210, 0x11020212, 0x12000011, 0x12000110, 0x12000112, 0x12010010, 0x12010012,
    0x12010111, 0x12020010, 0x12020011, 0x12020012, 0x10000121, 0x10010021, 0x10010120, 0x10010122, 0x10020121,
    0x11000021, 0x11010022, 0x11010121, 0x11010222, 0x11020120, 0x11020221, 0x12000221, 0x12010120, 0x12020121,
    0x10001001, 0x10011101, 0x10011201, 0x10021201, 0x11001101, 0x11001200, 0x11001202, 0x11011001, 0x11011100,
    0x11011101, 0x11011102, 0x11021001, 0x11021002, 0x11021101, 0x11021200, 0x11021202, 0x12001001, 0x12001102,
    0x12001201, 0x12011000, 0x12011002, 0x12011101, 0x12021000, 0x12021001, 0x12021201, 0x10001011, 0x10001012,
    0x10001111, 0x10001212, 0x10011011, 0x10011110, 0x10011111, 0x10011112, 0x10011211, 0x10021010, 0x10021111,
    0x10021212, 0x11001011, 0x11001110, 0x11001111, 0x11001112, 0x11001211, 0x11011010, 0x11011011, 0x11011110,
    0x11011111, 0x11011112, 0x11011210, 0x11011211, 0x11021011, 0x11021110, 0x11021111, 0x11021112, 0x11021211,
    0x12001012, 0x12001110, 0x12001111, 0x12001210, 0x12011011, 0x12011110, 0x12011111, 0x12011112, 0x12011211,
    0x12011212, 0x12021111, 0x12021210, 0x12021212, 0x10001021, 0x10001121, 0x10001221, 0x10011120, 0x10011121,
    0x10011220, 0x10011222, 0x10021021, 0x10021120, 0x10021221, 0x11001020, 0x11001022, 0x11001121, 0x11001220,
    0x11011020, 0x11011021, 0x11011022, 0x11011121, 0x11011122, 0x11011221, 0x11021022, 0x11021121, 0x11021220,
    0x12001021, 0x12001121, 0x12001222, 0x12011120, 0x12011121, 0x12021021, 0x12021120, 0x12021122, 0x10002101,
    0x10012001, 0x10012101, 0x10012202, 0x10022101, 0x11002002, 0x11002201, 0x11012000, 0x11012101, 0x11012200,
    0x11022001, 0x11022100, 0x11022102, 0x11022201, 0x12002101, 0x12012001, 0x12012100, 0x12012102, 0x12012201,
    0x12022101, 0x10002011, 0x10002111, 0x10002112, 0x10002212, 0x10012010, 0x10012110, 0x10012111, 0x10012210,
    0x10022011, 0x10022110, 0x10022112, 0x11002010, 0x11002111, 0x11002212, 0x11012011, 0x11012012, 0x11012110,
    0x11012111, 0x11012112, 0x11012211, 0x11022010, 0x11022012, 0x11022111, 0x11022112, 0x11022212, 0x12002112,
    0x12002211, 0x12012012, 0x12012111, 0x12012112, 0x12012210, 0x12022011, 0x12022110, 0x12022112, 0x12022211,
    0x10012122, 0x11002120, 0x11002122, 0x11002221, 0x11012121, 0x11012220, 0x11012222, 0x11022120, 0x11022221,
    0x12012120, 0x12022121, 0x10100001, 0x10100100, 0x10100101, 0x10100102, 0x10100201, 0x10110002, 0x10110101,
    0x10110202, 0x10120001, 0x10120100, 0x10120201, 0x11100000, 0x11100101, 0x11100200, 0x11110001, 0x11110100,
    0x11110101, 0x11110102, 0x11110201, 0x11120101, 0x11120200, 0x12100102, 0x12100201, 0x12110101, 0x12110200,
    0x12120000, 0x12120001, 0x12120102, 0x12120201, 0x10100111, 0x10100210, 0x10100211, 0x10100212, 0x10110011,
    0x10110110, 0x10110111, 0x10110112, 0x10110210, 0x10110211, 0x10120010, 0x10120111, 0x10120112, 0x10120210,
    0x10120212, 0x11100011, 0x11100110, 0x11100111, 0x11100112, 0x11100211, 0x11110010, 0x11110011, 0x11110012,
    0x11110110, 0x11110111, 0x11110112, 0x11110210, 0x11110211, 0x11110212, 0x11120011, 0x11120110, 0x11120111,
    0x11120112, 0x11120211, 0x12100012, 0x12100111, 0x12110011, 0x12110110, 0x12110111, 0x12110112, 0x12110211,
    0x12120010, 0x12120111, 0x12120212, 0x10100021, 0x10100122, 0x10110022, 0x10110121, 0x10110222, 0x10120021,
    0x10120120, 0x11100022, 0x11100121, 0x11100222, 0x11110021, 0x11110120, 0x11110121, 0x11110122, 0x11110221,
    0x11120022, 0x11120121, 0x12100121, 0x12110020, 0x12110022, 0x12110121, 0x12110221, 0x12110222, 0x12120120,
    0x10101100, 0x10101101, 0x10111001, 0x10111100, 0x10111101, 0x10111102, 0x10111200, 0x10111201, 0x10121001,
    0x10121101, 0x10121200, 0x10121202, 0x11101001, 0x11101100, 0x11101101, 0x11101102, 0x11101201, 0x11101202,
    0x11111000, 0x11111001, 0x11111100, 0x11111101, 0x11111102, 0x11111200, 0x11111201, 0x11111202, 0x11121001,
    0x11121002, 0x11121100, 0x11121101, 0x11121102, 0x11121201, 0x12101000, 0x12101200, 0x12101202, 0x12111001,
    0x12111100, 0x12111101, 0x12111102, 0x12111201, 0x12121001, 0x12121100, 0x12121101, 0x12121202, 0x10101011,
    0x10101012, 0x10101110, 0x10101111, 0x10101112, 0x10101211, 0x10111010, 0x10111011, 0x10111012, 0x10111110,
    0x10111111, 0x10111112, 0x10111211, 0x10111212, 0x10121011, 0x10121110, 0x10121111, 0x10121112, 0x10121211,
    0x11101010, 0x11101011, 0x11101012, 0x11101110, 0x11101111, 0x11101112, 0x11101210, 0x11101211, 0x11111010,
    0x11111011, 0x11111012, 0x11111110, 0x11111111, 0x11111112, 0x11111210, 0x11111211, 0x11111212, 0x11121010,
    0x11121011, 0x11121110, 0x11121111, 0x11121112, 0x11121210, 0x11121211, 0x11121212, 0x12101011, 0x12101110,
    0x12101111, 0x12101211, 0x12101212, 0x12111010, 0x12111011, 0x12111110, 0x12111111, 0x12111112, 0x12111210,
    0x12111211, 0x12121011, 0x12121110, 0x12121111, 0x12121112, 0x12121211, 0x10101020, 0x10101021, 0x10101022,
    0x10101120, 0x10101122, 0x10101220, 0x10101221, 0x10111021, 0x10111120, 0x10111121, 0x10111220, 0x10111221,
    0x10121020, 0x10121021, 0x10121022, 0x10121120, 0x10121121, 0x10121122, 0x10121220, 0x10121221, 0x11101021,
    0x11101121, 0x11101122, 0x11101220, 0x11101221, 0x11101222, 0x11111020, 0x11111021, 0x11111022, 0x11111120,
    0x11111121, 0x11111122, 0x11111220, 0x11111221, 0x11111222, 0x11121021, 0x11121120, 0x11121121, 0x11121221,
    0x12101022, 0x12101121, 0x12101122, 0x12101220, 0x12101221, 0x12101222, 0x12111021, 0x12111121, 0x12111222,
    0x12121022, 0x12121121, 0x12121122, 0x12121220, 0x12121221, 0x10102100, 0x10102101, 0x10102102, 0x10102201,
    0x10112000, 0x10112101, 0x10112200, 0x10122001, 0x10122202, 0x11102101, 0x11102200, 0x11102202, 0x11112001,
    0x11112100, 0x11112101, 0x11112102, 0x11112200, 0x11112201, 0x11122000, 0x11122002, 0x11122100, 0x11122101,
    0x12102002, 0x12102201, 0x12112000, 0x12112002, 0x12112101, 0x12112200, 0x12122001, 0x12122201, 0x10102011,
    0x10102012, 0x10102111, 0x10102212, 0x10112011, 0x10112110, 0x10112111, 0x10112112, 0x10112211, 0x10122111,
    0x11102011, 0x11102110, 0x11102111, 0x11102112, 0x11102211, 0x11112010, 0x11112011, 0x11112012, 0x11112110,
    0x11112111, 0x11112112, 0x11112210, 0x11112211, 0x11112212, 0x11122011, 0x11122110, 0x11122111, 0x11122112,
    0x11122211, 0x12102011, 0x12102111, 0x12102211, 0x12112011, 0x12112110, 0x12112111, 0x12112112, 0x12112210,
    0x12112211, 0x12122111, 0x10102120, 0x10102220, 0x10112121, 0x10112222, 0x10122020, 0x10122121, 0x10122122,
    0x10122221, 0x11102121, 0x11102220, 0x11102221, 0x11112021, 0x11112121, 0x11112122, 0x11112220, 0x11112221,
    0x11122022, 0x11122121, 0x11122220, 0x11122222, 0x12102021, 0x12102222, 0x12112022, 0x12112121, 0x12112122,
    0x12112220, 0x12112222, 0x12122021, 0x10200101, 0x10210100, 0x10210102, 0x10210201, 0x10220101, 0x11200100,
    0x11210000, 0x11210101, 0x11210102, 0x11210200, 0x11210202, 0x11220001, 0x11220100, 0x11220102, 0x11220201,
    0x12200001, 0x12210102, 0x12220101, 0x10200011, 0x10200110, 0x10200112, 0x10200211, 0x10210012, 0x10210111,
    0x10220011, 0x10220012, 0x10220112, 0x10220211, 0x11200111, 0x11200211, 0x11210011, 0x11210111, 0x11210112,
    0x11210211, 0x11220111, 0x11220112, 0x11220212, 0x12200110, 0x12200212, 0x12210012, 0x12210111, 0x12220011,
    0x12220112, 0x12220211, 0x10210021, 0x10210122, 0x10210221, 0x11200020, 0x11200021, 0x11200122, 0x11210121,
    0x11210122, 0x11210220, 0x11220020, 0x12200121, 0x12210021, 0x12210122, 0x12220121, 0x10211001, 0x10211002,
    0x10211101, 0x10211102, 0x10211202, 0x10221001, 0x10221102, 0x10221201, 0x11201000, 0x11201002, 0x11201101,
    0x11201200, 0x11201202, 0x11211001, 0x11211100, 0x11211101, 0x11211102, 0x11211201, 0x11211202, 0x11221000,
    0x11221002, 0x11221101, 0x12201100, 0x12201101, 0x12201201, 0x12211000, 0x12211002, 0x12211100, 0x12211101,
    0x12211102, 0x12211200, 0x12211202, 0x12221001, 0x12221100, 0x12221201, 0x10201111, 0x10201210, 0x10201212,
    0x10211011, 0x10211111, 0x10211112, 0x10211211, 0x11201110, 0x11201111, 0x11201112, 0x11201211, 0x11211010,
    0x11211011, 0x11211110, 0x11211111, 0x11211112, 0x11211211, 0x11221011, 0x11221110, 0x11221111, 0x11221112,
    0x11221211, 0x12201112, 0x12201211, 0x12201212, 0x12211011, 0x12211111, 0x12211112, 0x12211211, 0x12211212,
    0x12221012, 0x12221111, 0x12221112, 0x12221210, 0x10201022, 0x10201221, 0x10211121, 0x10221020, 0x10221122,
    0x10221220, 0x10221221, 0x11201020, 0x11201121, 0x11201220, 0x11201222, 0x11211021, 0x11211120, 0x11211121,
    0x11211122, 0x11211220, 0x11211222, 0x11221020, 0x11221121, 0x11221220, 0x12201020, 0x12201022, 0x12201121,
    0x12201222, 0x12211120, 0x12211122, 0x12211220, 0x12211221, 0x12221020, 0x12221120, 0x12221122, 0x12221222,
    0x10212102, 0x10212201, 0x10222101, 0x11202001, 0x11212002, 0x11212101, 0x11212202, 0x11222001, 0x11222201,
    0x12202101, 0x12212001, 0x12212200, 0x12222102, 0x10202011, 0x10202110, 0x10212010, 0x10212111, 0x10222011,
    0x10222110, 0x10222112, 0x10222211, 0x11202010, 0x11202011, 0x11202111, 0x11202112, 0x11202210, 0x11212011,
    0x11212110, 0x11212111, 0x11212112, 0x11212211, 0x11222010, 0x11222111, 0x11222212, 0x12202012, 0x12202110,
    0x12202212, 0x12212111, 0x12222011, 0x12222110, 0x12222111, 0x12222211, 0x10212021, 0x10212122, 0x10212220,
    0x11202021, 0x11202120, 0x11202221, 0x11212020, 0x11212121, 0x11212220, 0x11212222, 0x11222120, 0x11222121,
    0x11222221, 0x12202122, 0x12212120, 0x12212220, 0x12212222, 0x12222122, 0x20000000, 0x20000002, 0x20000200,
    0x20000202, 0x20020000, 0x20020002, 0x20020200, 0x20020202, 0x21000101, 0x21010000, 0x21010001, 0x21010100,
    0x21010102, 0x21010201, 0x21020101, 0x22000000, 0x22000002, 0x22000200, 0x22000202, 0x22010101, 0x22020000,
    0x22020002, 0x22020200, 0x22020202, 0x20000111, 0x20010011, 0x20010110, 0x20010112, 0x20010211, 0x20020111,
    0x21000011, 0x21000110, 0x21000211, 0x21010010, 0x21010012, 0x21010111, 0x21010112, 0x21010210, 0x21010211,
    0x21020110, 0x21020112, 0x21020211, 0x22000111, 0x22000211, 0x22010110, 0x22010112, 0x22010211, 0x22020111,
    0x20000020, 0x20000022, 0x20000220, 0x20000222, 0x20010121, 0x20020020, 0x20020022, 0x20020220, 0x20020222,
    0x21010021, 0x21010120, 0x21010221, 0x21020121, 0x22000020, 0x22000022, 0x22000220, 0x22000222, 0x22010121,
    0x22020020, 0x22020022, 0x22020220, 0x22020222, 0x20011100, 0x20011201, 0x21001001, 0x21001100, 0x21011001,
    0x21011101, 0x21011202, 0x21021001, 0x21021100, 0x21021201, 0x22011100, 0x22011201, 0x20001011, 0x20001211,
    0x20011012, 0x20011111, 0x20011212, 0x20021112, 0x20021211, 0x21001010, 0x21001011, 0x21001111, 0x21001210,
    0x21011011, 0x21011110, 0x21011111, 0x21011112, 0x21011211, 0x21011212, 0x21021111, 0x21021112, 0x21021210,
    0x21021212, 0x22001011, 0x22001110, 0x22001112, 0x22001211, 0x22011010, 0x22011012, 0x22011111, 0x22011210,
    0x22021112, 0x20011021, 0x20011122, 0x20011221, 0x20021121, 0x21001021, 0x21001120, 0x21001221, 0x21001222,
    0x21011020, 0x21011121, 0x21011221, 0x21011222, 0x21021021, 0x21021122, 0x21021222, 0x22001121, 0x22011021,
    0x22011222, 0x22021120, 0x20002000, 0x20002002, 0x20002200, 0x20002202, 0x20012101, 0x20022000, 0x20022002,
    0x20022200, 0x20022202, 0x21002001, 0x21002101, 0x21012001, 0x21012100, 0x21012201, 0x21022101, 0x21022201,
    0x22002000, 0x22002002, 0x22002200, 0x22002202, 0x22012101, 0x22022000, 0x22022002, 0x22022200, 0x22022202,
    0x20002111, 0x20002112, 0x20012011, 0x20012110, 0x20012112, 0x20022111, 0x21002011, 0x21002110, 0x21002112,
    0x21002211, 0x21012010, 0x21012012, 0x21012111, 0x21012212, 0x21022011, 0x21022110, 0x22002111, 0x22012112,
    0x22012211, 0x22022111, 0x20002020, 0x20002022, 0x20002220, 0x20002222, 0x20012121, 0x20022020, 0x20022022,
    0x20022220, 0x20022222, 0x21002121, 0x21012021, 0x21012120, 0x21012122, 0x22002020, 0x22002022, 0x22002220,
    0x22002222, 0x22012121, 0x22022020, 0x22022022, 0x22022220, 0x22022222, 0x20100101, 0x20110001, 0x20110102,
    0x20110200, 0x20110201, 0x20120101, 0x21100001, 0x21100102, 0x21100201, 0x21110101, 0x21110200, 0x21110202,
    0x21120201, 0x21120202, 0x22100101, 0x22110001, 0x22110100, 0x22110102, 0x22110201, 0x22120101, 0x20100011,
    0x20100110, 0x20100112, 0x20100211, 0x20110010, 0x20110111, 0x20110210, 0x20110212, 0x20120011, 0x20120110,
    0x20120112, 0x20120211, 0x21100010, 0x21100111, 0x21110010, 0x21110011, 0x21110110, 0x21110111, 0x21110112,
    0x21110211, 0x21120012, 0x21120111, 0x22100110, 0x22100112, 0x22110012, 0x22110111, 0x22110210, 0x22120011,
    0x22120110, 0x22120112, 0x22120211, 0x20100121, 0x20110021, 0x20110120, 0x20110221, 0x20120121, 0x21100120,
    0x21100122, 0x21100221, 0x21110020, 0x21110022, 0x21110121, 0x21110220, 0x21120122, 0x21120221, 0x22100121,
    0x22110120, 0x22110122, 0x22120221, 0x20101001, 0x20101100, 0x20101102, 0x20111000, 0x20111101, 0x20111200,
    0x20121102, 0x21101000, 0x21101202, 0x21111001, 0x21111100, 0x21111101, 0x21111102, 0x21111200, 0x21111201,
    0x21121000, 0x21121001, 0x21121002, 0x21121101, 0x22101100, 0x22101102, 0x22111002, 0x22111100, 0x22111101,
    0x22111200, 0x22121001, 0x22121201, 0x20101010, 0x20101111, 0x20101210, 0x20101212, 0x20111010, 0x20111011,
    0x20111110, 0x20111111, 0x20111112, 0x20111211, 0x20121011, 0x20121111, 0x20121211, 0x20121212, 0x21101011,
    0x21101110, 0x21101111, 0x21101112, 0x21101211, 0x21111010, 0x21111011, 0x21111012, 0x21111110, 0x21111111,
    0x21111112, 0x21111210, 0x21111211, 0x21111212, 0x21121011, 0x21121110, 0x21121111, 0x21121112, 0x21121211,
    0x22101011, 0x22101111, 0x22101210, 0x22111011, 0x22111012, 0x22111110, 0x22111111, 0x22111112, 0x22111211,
    0x22111212, 0x22121010, 0x22121012, 0x22121111, 0x22121210, 0x22121212, 0x20101021, 0x20101120, 0x20111020,
    0x20111121, 0x20111221, 0x20121020, 0x20121122, 0x20121221, 0x21101121, 0x21101220, 0x21101221, 0x21111021,
    0x21111022, 0x21111121, 0x21111122, 0x21111221, 0x21121121, 0x21121220, 0x22101022, 0x22101120, 0x22101221,
    0x22101222, 0x22111022, 0x22111120, 0x22111121, 0x22121120, 0x22121122, 0x22121221, 0x20102101, 0x20112102,
    0x20112201, 0x20122101, 0x21102001, 0x21102102, 0x21112000, 0x21112002, 0x21112101, 0x21112102, 0x21112202,
    0x21122100, 0x21122101, 0x22102101, 0x22112001, 0x22112102, 0x22112201, 0x22122101, 0x20102110, 0x20102112,
    0x20102211, 0x20112010, 0x20112012, 0x20112111, 0x20112210, 0x20112212, 0x20122010, 0x20122011, 0x20122110,
    0x20122112, 0x21102010, 0x21102012, 0x21102111, 0x21102210, 0x21102212, 0x21112011, 0x21112110, 0x21112111,
    0x21112112, 0x21112211, 0x21122012, 0x21122111, 0x21122112, 0x21122212, 0x22102011, 0x22102110, 0x22112010,
    0x22112012, 0x22112111, 0x22112212, 0x22122011, 0x22122112, 0x20102121, 0x20112121, 0x20122121, 0x21102120,
    0x21102122, 0x21102221, 0x21112020, 0x21112121, 0x21112220, 0x21122021, 0x22102121, 0x22112021, 0x22112120,
    0x22112121, 0x22112122, 0x20200000, 0x20200002, 0x20200200, 0x20200202, 0x20210101, 0x20220000, 0x20220002,
    0x20220200, 0x20220202, 0x21200101, 0x21210001, 0x21210100, 0x21210102, 0x21210201, 0x22200000, 0x22200002,
    0x22200200, 0x22200202, 0x22210101, 0x22220000, 0x22220002, 0x22220200, 0x22220202, 0x20200111, 0x20200211,
    0x20210011, 0x20210110, 0x20210112, 0x20210211, 0x20210212, 0x21200112, 0x21200211, 0x21210011, 0x21210111,
    0x21210210, 0x21210212, 0x21220011, 0x21220110, 0x22200111, 0x22210010, 0x22210012, 0x22210112, 0x22210211,
    0x20200022, 0x20200220, 0x20200222, 0x20210020, 0x20210221, 0x20220022, 0x20220220, 0x20220222, 0x21200121,
    0x21210021, 0x21210122, 0x21210221, 0x21220121, 0x22200020, 0x22200022, 0x22200220, 0x22200222, 0x22210121,
    0x22220020, 0x22220022, 0x22220220, 0x22220222, 0x20211201, 0x20221101, 0x21201001, 0x21201100, 0x21211000,
    0x21211100, 0x21211101, 0x21211200, 0x21211202, 0x21221001, 0x21221101, 0x21221102, 0x21221200, 0x21221201,
    0x22201101, 0x20201112, 0x20201211, 0x20211010, 0x20211012, 0x20211111, 0x20211210, 0x20221112, 0x20221211,
    0x21201012, 0x21201111, 0x21211011, 0x21211110, 0x21211111, 0x21211112, 0x21211211, 0x21221111, 0x21221212,
    0x22201011, 0x22201110, 0x22201111, 0x22201112, 0x22201211, 0x22211012, 0x22211111, 0x22211210, 0x20201121,
    0x20211021, 0x20211122, 0x20211222, 0x20221021, 0x20221121, 0x21201120, 0x21201122, 0x21201222, 0x21211022,
    0x21211121, 0x21211122, 0x21211220, 0x21221020, 0x21221022, 0x22201122, 0x22211020, 0x22211121, 0x22211122,
    0x22211221, 0x22221021, 0x22221120, 0x22221122, 0x20202000, 0x20202002, 0x20202200, 0x20202202, 0x20222000,
    0x20222002, 0x20222200, 0x20222202, 0x21212001, 0x21212100, 0x21212102, 0x21212201, 0x22202000, 0x22202002,
    0x22202200, 0x22202202, 0x22212101, 0x22222000, 0x22222002, 0x22222200, 0x22222202, 0x20202111, 0x20212110,
    0x20212211, 0x20222011, 0x20222111, 0x21202011, 0x21212010, 0x21212111, 0x21212212, 0x21222011, 0x21222112,
    0x21222211, 0x22212010, 0x22212112, 0x20202020, 0x20202022, 0x20202220, 0x20202222, 0x20222020, 0x20222022,
    0x20222220, 0x20222222, 0x21212021, 0x21212120, 0x21212122, 0x22202020, 0x22202022, 0x22202220, 0x22202222,
    0x22212121, 0x22222020, 0x22222022, 0x22222220, 0x22222222,
};

static const __device__ uint8_t ksigns_iq2xs[128] = {
    0,   129, 130, 3,   132, 5,   6,   135, 136, 9,   10,  139, 12,  141, 142, 15,  144, 17,  18,  147, 20,  149,
    150, 23,  24,  153, 154, 27,  156, 29,  30,  159, 160, 33,  34,  163, 36,  165, 166, 39,  40,  169, 170, 43,
    172, 45,  46,  175, 48,  177, 178, 51,  180, 53,  54,  183, 184, 57,  58,  187, 60,  189, 190, 63,  192, 65,
    66,  195, 68,  197, 198, 71,  72,  201, 202, 75,  204, 77,  78,  207, 80,  209, 210, 83,  212, 85,  86,  215,
    216, 89,  90,  219, 92,  221, 222, 95,  96,  225, 226, 99,  228, 101, 102, 231, 232, 105, 106, 235, 108, 237,
    238, 111, 240, 113, 114, 243, 116, 245, 246, 119, 120, 249, 250, 123, 252, 125, 126, 255,
};

static const __device__ uint64_t ksigns64[128] = {
    0x0000000000000000, 0xff000000000000ff, 0xff0000000000ff00, 0x000000000000ffff, 0xff00000000ff0000,
    0x0000000000ff00ff, 0x0000000000ffff00, 0xff00000000ffffff, 0xff000000ff000000, 0x00000000ff0000ff,
    0x00000000ff00ff00, 0xff000000ff00ffff, 0x00000000ffff0000, 0xff000000ffff00ff, 0xff000000ffffff00,
    0x00000000ffffffff, 0xff0000ff00000000, 0x000000ff000000ff, 0x000000ff0000ff00, 0xff0000ff0000ffff,
    0x000000ff00ff0000, 0xff0000ff00ff00ff, 0xff0000ff00ffff00, 0x000000ff00ffffff, 0x000000ffff000000,
    0xff0000ffff0000ff, 0xff0000ffff00ff00, 0x000000ffff00ffff, 0xff0000ffffff0000, 0x000000ffffff00ff,
    0x000000ffffffff00, 0xff0000ffffffffff, 0xff00ff0000000000, 0x0000ff00000000ff, 0x0000ff000000ff00,
    0xff00ff000000ffff, 0x0000ff0000ff0000, 0xff00ff0000ff00ff, 0xff00ff0000ffff00, 0x0000ff0000ffffff,
    0x0000ff00ff000000, 0xff00ff00ff0000ff, 0xff00ff00ff00ff00, 0x0000ff00ff00ffff, 0xff00ff00ffff0000,
    0x0000ff00ffff00ff, 0x0000ff00ffffff00, 0xff00ff00ffffffff, 0x0000ffff00000000, 0xff00ffff000000ff,
    0xff00ffff0000ff00, 0x0000ffff0000ffff, 0xff00ffff00ff0000, 0x0000ffff00ff00ff, 0x0000ffff00ffff00,
    0xff00ffff00ffffff, 0xff00ffffff000000, 0x0000ffffff0000ff, 0x0000ffffff00ff00, 0xff00ffffff00ffff,
    0x0000ffffffff0000, 0xff00ffffffff00ff, 0xff00ffffffffff00, 0x0000ffffffffffff, 0xffff000000000000,
    0x00ff0000000000ff, 0x00ff00000000ff00, 0xffff00000000ffff, 0x00ff000000ff0000, 0xffff000000ff00ff,
    0xffff000000ffff00, 0x00ff000000ffffff, 0x00ff0000ff000000, 0xffff0000ff0000ff, 0xffff0000ff00ff00,
    0x00ff0000ff00ffff, 0xffff0000ffff0000, 0x00ff0000ffff00ff, 0x00ff0000ffffff00, 0xffff0000ffffffff,
    0x00ff00ff00000000, 0xffff00ff000000ff, 0xffff00ff0000ff00, 0x00ff00ff0000ffff, 0xffff00ff00ff0000,
    0x00ff00ff00ff00ff, 0x00ff00ff00ffff00, 0xffff00ff00ffffff, 0xffff00ffff000000, 0x00ff00ffff0000ff,
    0x00ff00ffff00ff00, 0xffff00ffff00ffff, 0x00ff00ffffff0000, 0xffff00ffffff00ff, 0xffff00ffffffff00,
    0x00ff00ffffffffff, 0x00ffff0000000000, 0xffffff00000000ff, 0xffffff000000ff00, 0x00ffff000000ffff,
    0xffffff0000ff0000, 0x00ffff0000ff00ff, 0x00ffff0000ffff00, 0xffffff0000ffffff, 0xffffff00ff000000,
    0x00ffff00ff0000ff, 0x00ffff00ff00ff00, 0xffffff00ff00ffff, 0x00ffff00ffff0000, 0xffffff00ffff00ff,
    0xffffff00ffffff00, 0x00ffff00ffffffff, 0xffffffff00000000, 0x00ffffff000000ff, 0x00ffffff0000ff00,
    0xffffffff0000ffff, 0x00ffffff00ff0000, 0xffffffff00ff00ff, 0xffffffff00ffff00, 0x00ffffff00ffffff,
    0x00ffffffff000000, 0xffffffffff0000ff, 0xffffffffff00ff00, 0x00ffffffff00ffff, 0xffffffffffff0000,
    0x00ffffffffff00ff, 0x00ffffffffffff00, 0xffffffffffffffff,
};

static const __device__ uint8_t kmask_iq2xs[8] = {1, 2, 4, 8, 16, 32, 64, 128};
static const __device__ int8_t kvalues_iq4nl[16] = {
    -127, -104, -83, -65, -49, -35, -22, -10, 1, 13, 25, 38, 53, 69, 89, 113};

typedef half dfloat;  // dequantize float
typedef half2 dfloat2;
typedef void (*dequantize_kernel_t)(const void* vx, const int ib, const int iqs, dfloat2& v);
template <typename dst_t>
using to_cuda_ggml_t = void (*)(const void* __restrict__ x, dst_t* __restrict__ y, int k, cudaStream_t stream);
typedef float (*vec_dot_q_cuda_t)(const void* __restrict__ vbq, const block_q8_1* __restrict__ bq8_1, const int& iqs);
typedef void (*allocate_tiles_cuda_t)(int** x_ql, half2** x_dm, int** x_qh, int** x_sc);
typedef void (*load_tiles_cuda_t)(
    const void* __restrict__ vx,
    int* __restrict__ x_ql,
    half2* __restrict__ x_dm,
    int* __restrict__ x_qh,
    int* __restrict__ x_sc,
    const int& i_offset,
    const int& i_max,
    const int& k,
    const int& blocks_per_row);
typedef float (*vec_dot_q_mul_mat_cuda_t)(
    const int* __restrict__ x_ql,
    const half2* __restrict__ x_dm,
    const int* __restrict__ x_qh,
    const int* __restrict__ x_sc,
    const int* __restrict__ y_qs,
    const half2* __restrict__ y_ms,
    const int& i,
    const int& j,
    const int& k);

// Utility function

template <typename dst_t>
static __device__ __forceinline__ dst_t convert_from_half(half val) {
  return val;
}

template <>
__device__ __forceinline__ c10::BFloat16 convert_from_half<c10::BFloat16>(half val) {
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
  return __float2bfloat16(__half2float(val));
#else
  return __half2float(val);
#endif  // defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
}

template <>
__device__ __forceinline__ float convert_from_half<float>(half val) {
  return __half2float(val);
}

#if defined(USE_ROCM)

#ifndef __has_builtin
#define __has_builtin(x) 0
#endif

typedef int8_t int8x4_t __attribute__((ext_vector_type(4)));
static __device__ __forceinline__ int __vsubss4(const int a, const int b) {
  const int8x4_t va = reinterpret_cast<const int8x4_t&>(a);
  const int8x4_t vb = reinterpret_cast<const int8x4_t&>(b);
#if __has_builtin(__builtin_elementwise_sub_sat)
  const int8x4_t c = __builtin_elementwise_sub_sat(va, vb);
  return reinterpret_cast<const int&>(c);
#else
  int8x4_t c;
  int16_t tmp;
#pragma unroll
  for (int i = 0; i < 4; i++) {
    tmp = va[i] - vb[i];
    if (tmp > std::numeric_limits<int8_t>::max()) tmp = std::numeric_limits<int8_t>::max();
    if (tmp < std::numeric_limits<int8_t>::min()) tmp = std::numeric_limits<int8_t>::min();
    c[i] = tmp;
  }
  return reinterpret_cast<int&>(c);
#endif  // __has_builtin(__builtin_elementwise_sub_sat)
}

static __device__ __forceinline__ int __dp4a(const int a, const int b, int c) {
#if __has_builtin(__builtin_amdgcn_sdot4)
  c = __builtin_amdgcn_sdot4(a, b, c, false);
#else
  const int8x4_t va = reinterpret_cast<const int8x4_t&>(a);
  const int8x4_t vb = reinterpret_cast<const int8x4_t&>(b);
  c += va[0] * vb[0] + va[1] * vb[1] + va[2] * vb[2] + va[3] * vb[3];
#endif
  return c;
}

static __device__ __forceinline__ uint32_t __vcmpeq4(const uint32_t a, const uint32_t b) {
  uint32_t neq = a ^ b;
  return !(neq & 0xff000000) * 0xff000000 | !(neq & 0x00ff0000) * 0x00ff0000 | !(neq & 0x0000ff00) * 0x0000ff00 |
         !(neq & 0x000000ff) * 0x000000ff;
}

static __device__ __forceinline__ uint32_t __vsub4(const uint32_t a, const uint32_t b) {
  return (static_cast<uint8_t>(((a & 0xff000000) >> 24) - ((b & 0xff000000) >> 24)) << 24) +
         (static_cast<uint8_t>(((a & 0x00ff0000) >> 16) - ((b & 0x00ff0000) >> 16)) << 16) +
         (static_cast<uint8_t>(((a & 0x0000ff00) >> 8) - ((b & 0x0000ff00) >> 8)) << 8) +
         (static_cast<uint8_t>(((a & 0x000000ff) >> 0) - ((b & 0x000000ff) >> 0)) << 0);
}
#endif  // defined(USE_ROCM)