#define GGML_COMMON_DECL_METAL
#define GGML_COMMON_IMPL_METAL
#if defined(GGML_METAL_EMBED_LIBRARY)
__embed_ggml-common.h__
#else
#include "ggml-common.h"
#endif
#include "ggml-metal-impl.h"

#include <metal_stdlib>

#ifdef GGML_METAL_HAS_TENSOR
#include <metal_tensor>

#include <MetalPerformancePrimitives/MetalPerformancePrimitives.h>
#endif

using namespace metal;

#define MAX(x, y) ((x) > (y) ? (x) : (y))
#define MIN(x, y) ((x) < (y) ? (x) : (y))
#define SWAP(x, y) { auto tmp = (x); (x) = (y); (y) = tmp; }

#define PAD2(x, n) (((x) + (n) - 1) & ~((n) - 1))

#define FOR_UNROLL(x) _Pragma("clang loop unroll(full)") for (x)

#define N_SIMDWIDTH 32 // assuming SIMD group size is 32

// ref: https://developer.apple.com/metal/Metal-Shading-Language-Specification.pdf
//
// cmd:
//   .../usr/bin/metal -dM -E -c                             ggml/src/ggml-metal/ggml-metal.metal
//   .../usr/bin/metal -dM -E -c -target air64-apple-ios14.0 ggml/src/ggml-metal/ggml-metal.metal
//
#if __METAL_VERSION__ < 310 && defined(GGML_METAL_HAS_BF16)
#undef GGML_METAL_HAS_BF16
#endif

#if defined(GGML_METAL_HAS_BF16)
typedef matrix<bfloat, 4, 4> bfloat4x4;
typedef matrix<bfloat, 2, 4> bfloat2x4;
#endif

constexpr constant static float kvalues_iq4nl_f[16] = {
    -127.f, -104.f, -83.f, -65.f, -49.f, -35.f, -22.f, -10.f, 1.f, 13.f, 25.f, 38.f, 53.f, 69.f, 89.f, 113.f
};

constexpr constant static float kvalues_mxfp4_f[16] = {
    0, .5f, 1.f, 1.5f, 2.f, 3.f, 4.f, 6.f, -0, -.5f, -1.f, -1.5f, -2.f, -3.f, -4.f, -6.f
};

static inline int best_index_int8(int n, constant float * val, float x) {
    if (x <= val[0]) return 0;
    if (x >= val[n-1]) return n-1;
    int ml = 0, mu = n-1;
    while (mu-ml > 1) {
        int mav = (ml+mu)/2;
        if (x < val[mav]) mu = mav; else ml = mav;
    }
    return x - val[mu-1] < val[mu] - x ? mu-1 : mu;
}

static inline float e8m0_to_fp32(uint8_t x) {
    uint32_t bits;

    if (x == 0) {
        bits = 0x00400000;
    } else {
        bits = (uint32_t) x << 23;
    }

    return as_type<float>(bits);
}

static inline float dot(float x, float y) {
    return x*y;
}

// NOTE: this is not dequantizing - we are simply fitting the template
template <typename type4x4>
void dequantize_f32(device const float4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4>
void dequantize_f32_t4(device const float4 * src, short il, thread type4 & reg) {
    reg = (type4)(*src);
}

template <typename type4x4>
void dequantize_f16(device const half4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4>
void dequantize_f16_t4(device const half4 * src, short il, thread type4 & reg) {
    reg = (type4)(*(src));
}

#if defined(GGML_METAL_HAS_BF16)
template <typename type4x4>
void dequantize_bf16(device const bfloat4x4 * src, short il, thread type4x4 & reg) {
    reg = (type4x4)(*src);
}

template <typename type4>
void dequantize_bf16_t4(device const bfloat4 * src, short il, thread type4 & reg) {
    reg = (type4)(*(src));
}
#endif

template <typename type4x4>
void dequantize_q4_0(device const block_q4_0 * xb, short il, thread type4x4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 1);
    const float d1 = il ? (xb->d / 16.h) : xb->d;
    const float d2 = d1 / 256.f;
    const float md = -8.h * xb->d;
    const ushort mask0 = il ? 0x00F0 : 0x000F;
    const ushort mask1 = mask0 << 8;

    float4x4 reg_f;

    for (int i = 0; i < 8; i++) {
        reg_f[i/2][2*(i%2) + 0] = d1 * (qs[i] & mask0) + md;
        reg_f[i/2][2*(i%2) + 1] = d2 * (qs[i] & mask1) + md;
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q4_0_t4(device const block_q4_0 * xb, short il, thread type4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 1);
    const float d1 = (il/4) ? (xb->d / 16.h) : xb->d;
    const float d2 = d1 / 256.f;
    const float md = -8.h * xb->d;
    const ushort mask0 = (il/4) ? 0x00F0 : 0x000F;
    const ushort mask1 = mask0 << 8;

    for (int i = 0; i < 2; i++) {
        reg[2*i + 0] = d1 * (qs[2*(il%4) + i] & mask0) + md;
        reg[2*i + 1] = d2 * (qs[2*(il%4) + i] & mask1) + md;
    }
}

void quantize_q4_0(device const float * src, device block_q4_0 & dst) {
#pragma METAL fp math_mode(safe)
    float amax = 0.0f; // absolute max
    float max  = 0.0f;

    for (int j = 0; j < QK4_0; j++) {
        const float v = src[j];
        if (amax < fabs(v)) {
            amax = fabs(v);
            max  = v;
        }
    }

    const float d = max / -8;
    const float id = d ? 1.0f/d : 0.0f;

    dst.d = d;

    for (int j = 0; j < QK4_0/2; ++j) {
        const float x0 = src[0       + j]*id;
        const float x1 = src[QK4_0/2 + j]*id;

        const uint8_t xi0 = MIN(15, (int8_t)(x0 + 8.5f));
        const uint8_t xi1 = MIN(15, (int8_t)(x1 + 8.5f));

        dst.qs[j]  = xi0;
        dst.qs[j] |= xi1 << 4;
    }
}

void quantize_q4_1(device const float * src, device block_q4_1 & dst) {
#pragma METAL fp math_mode(safe)
    float min = FLT_MAX;
    float max = -FLT_MAX;

    for (int j = 0; j < QK4_1; j++) {
        const float v = src[j];
        if (min > v) min = v;
        if (max < v) max = v;
    }

    const float d = (max - min) / ((1 << 4) - 1);
    const float id = d ? 1.0f/d : 0.0f;

    dst.d = d;
    dst.m = min;

    for (int j = 0; j < QK4_1/2; ++j) {
        const float x0 = (src[0       + j] - min)*id;
        const float x1 = (src[QK4_1/2 + j] - min)*id;

        const uint8_t xi0 = MIN(15, (int8_t)(x0 + 0.5f));
        const uint8_t xi1 = MIN(15, (int8_t)(x1 + 0.5f));

        dst.qs[j]  = xi0;
        dst.qs[j] |= xi1 << 4;
    }
}

void quantize_q5_0(device const float * src, device block_q5_0 & dst) {
#pragma METAL fp math_mode(safe)
    float amax = 0.0f; // absolute max
    float max  = 0.0f;

    for (int j = 0; j < QK5_0; j++) {
        const float v = src[j];
        if (amax < fabs(v)) {
            amax = fabs(v);
            max  = v;
        }
    }

    const float d = max / -16;
    const float id = d ? 1.0f/d : 0.0f;

    dst.d = d;

    uint32_t qh = 0;
    for (int j = 0; j < QK5_0/2; ++j) {
        const float x0 = src[0       + j]*id;
        const float x1 = src[QK5_0/2 + j]*id;

        const uint8_t xi0 = MIN(31, (int8_t)(x0 + 16.5f));
        const uint8_t xi1 = MIN(31, (int8_t)(x1 + 16.5f));

        dst.qs[j] = (xi0 & 0xf) | ((xi1 & 0xf) << 4);
        qh |= ((xi0 & 0x10u) >> 4) << (j + 0);
        qh |= ((xi1 & 0x10u) >> 4) << (j + QK5_0/2);
    }

    thread const uint8_t * qh8 = (thread const uint8_t *)&qh;

    for (int j = 0; j < 4; ++j) {
        dst.qh[j] = qh8[j];
    }
}

void quantize_q5_1(device const float * src, device block_q5_1 & dst) {
#pragma METAL fp math_mode(safe)
    float max = src[0];
    float min = src[0];

    for (int j = 1; j < QK5_1; j++) {
        const float v = src[j];
        min = v < min ? v : min;
        max = v > max ? v : max;
    }

    const float d = (max - min) / 31;
    const float id = d ? 1.0f/d : 0.0f;

    dst.d = d;
    dst.m = min;

    uint32_t qh = 0;
    for (int j = 0; j < QK5_1/2; ++j) {
        const float x0 = (src[0       + j] - min)*id;
        const float x1 = (src[QK5_1/2 + j] - min)*id;

        const uint8_t xi0 = (uint8_t)(x0 + 0.5f);
        const uint8_t xi1 = (uint8_t)(x1 + 0.5f);

        dst.qs[j] = (xi0 & 0xf) | ((xi1 & 0xf) << 4);
        qh |= ((xi0 & 0x10u) >> 4) << (j + 0);
        qh |= ((xi1 & 0x10u) >> 4) << (j + QK5_1/2);
    }

    thread const uint8_t * qh8 = (thread const uint8_t *)&qh;

    for (int j = 0; j < 4; ++j) {
        dst.qh[j] = qh8[j];
    }
}

void quantize_q8_0(device const float * src, device block_q8_0 & dst) {
#pragma METAL fp math_mode(safe)
    float amax = 0.0f; // absolute max

    for (int j = 0; j < QK8_0; j++) {
        const float v = src[j];
        amax = MAX(amax, fabs(v));
    }

    const float d = amax / ((1 << 7) - 1);
    const float id = d ? 1.0f/d : 0.0f;

    dst.d = d;

    for (int j = 0; j < QK8_0; ++j) {
        const float x0 = src[j]*id;

        dst.qs[j] = round(x0);
    }
}

void quantize_iq4_nl(device const float * src, device block_iq4_nl & dst) {
#pragma METAL fp math_mode(safe)
    float amax = 0.0f; // absolute max
    float max  = 0.0f;

    for (int j = 0; j < QK4_NL; j++) {
        const float v = src[j];
        if (amax < fabs(v)) {
            amax = fabs(v);
            max  = v;
        }
    }

    const float d = max / kvalues_iq4nl_f[0];
    const float id = d ? 1.0f/d : 0.0f;

    float sumqx = 0, sumq2 = 0;
    for (int j = 0; j < QK4_NL/2; ++j) {
        const float x0 = src[0        + j]*id;
        const float x1 = src[QK4_NL/2 + j]*id;

        const uint8_t xi0 = best_index_int8(16, kvalues_iq4nl_f, x0);
        const uint8_t xi1 = best_index_int8(16, kvalues_iq4nl_f, x1);

        dst.qs[j] = xi0 | (xi1 << 4);

        const float v0 = kvalues_iq4nl_f[xi0];
        const float v1 = kvalues_iq4nl_f[xi1];
        const float w0 = src[0        + j]*src[0        + j];
        const float w1 = src[QK4_NL/2 + j]*src[QK4_NL/2 + j];
        sumqx += w0*v0*src[j] + w1*v1*src[QK4_NL/2 + j];
        sumq2 += w0*v0*v0 + w1*v1*v1;

    }

    dst.d = sumq2 > 0 ? sumqx/sumq2 : d;
}

template <typename type4x4>
void dequantize_q4_1(device const block_q4_1 * xb, short il, thread type4x4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 2);
    const float d1 = il ? (xb->d / 16.h) : xb->d;
    const float d2 = d1 / 256.f;
    const float  m = xb->m;
    const ushort mask0 = il ? 0x00F0 : 0x000F;
    const ushort mask1 = mask0 << 8;

    float4x4 reg_f;

    for (int i = 0; i < 8; i++) {
        reg_f[i/2][2*(i%2) + 0] = ((qs[i] & mask0) * d1) + m;
        reg_f[i/2][2*(i%2) + 1] = ((qs[i] & mask1) * d2) + m;
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q4_1_t4(device const block_q4_1 * xb, short il, thread type4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 2);
    const float d1 = (il/4) ? (xb->d / 16.h) : xb->d;
    const float d2 = d1 / 256.f;
    const float  m = xb->m;
    const ushort mask0 = (il/4) ? 0x00F0 : 0x000F;
    const ushort mask1 = mask0 << 8;

    for (int i = 0; i < 2; i++) {
        reg[2*i + 0] = d1 * (qs[2*(il%4) + i] & mask0) + m;
        reg[2*i + 1] = d2 * (qs[2*(il%4) + i] & mask1) + m;
    }
}

template <typename type4x4>
void dequantize_q5_0(device const block_q5_0 * xb, short il, thread type4x4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 3);
    const float d = xb->d;
    const float md = -16.h * xb->d;
    const ushort mask = il ? 0x00F0 : 0x000F;

    const uint32_t qh = *((device const uint32_t *)xb->qh);

    const int x_mv = il ? 4 : 0;

    const int gh_mv = il ? 12 : 0;
    const int gh_bk = il ?  0 : 4;

    float4x4 reg_f;

    for (int i = 0; i < 8; i++) {
        // extract the 5-th bits for x0 and x1
        const uint8_t xh_0 = ((qh >> (gh_mv + 2*i  )) << gh_bk) & 0x10;
        const uint8_t xh_1 = ((qh >> (gh_mv + 2*i+1)) << gh_bk) & 0x10;

        // combine the 4-bits from qs with the 5th bit
        const int32_t x0 = ((((qs[i]     ) & mask) >> x_mv) | xh_0);
        const int32_t x1 = ((((qs[i] >> 8) & mask) >> x_mv) | xh_1);

        reg_f[i/2][2*(i%2) + 0] = d * x0 + md;
        reg_f[i/2][2*(i%2) + 1] = d * x1 + md;
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q5_0_t4(device const block_q5_0 * xb, short il, thread type4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 3);
    const float d = xb->d;
    const float md = -16.h * xb->d;
    const ushort mask = (il/4) ? 0x00F0 : 0x000F;

    const uint32_t qh = *((device const uint32_t *)xb->qh);

    const int x_mv = (il/4) ? 4 : 0;

    const int gh_mv = (il/4) ? 12 : 0;
    const int gh_bk = (il/4) ?  0 : 4;

    for (int ii = 0; ii < 2; ii++) {
        int i = 2*(il%4) + ii;

        // extract the 5-th bits for x0 and x1
        const uint8_t xh_0 = ((qh >> (gh_mv + 2*i  )) << gh_bk) & 0x10;
        const uint8_t xh_1 = ((qh >> (gh_mv + 2*i+1)) << gh_bk) & 0x10;

        // combine the 4-bits from qs with the 5th bit
        const int32_t x0 = ((((qs[i]     ) & mask) >> x_mv) | xh_0);
        const int32_t x1 = ((((qs[i] >> 8) & mask) >> x_mv) | xh_1);

        reg[2*ii + 0] = d * x0 + md;
        reg[2*ii + 1] = d * x1 + md;
    }
}

template <typename type4x4>
void dequantize_q5_1(device const block_q5_1 * xb, short il, thread type4x4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 4);
    const float d = xb->d;
    const float m = xb->m;
    const ushort mask = il ? 0x00F0 : 0x000F;

    const uint32_t qh = *((device const uint32_t *)xb->qh);

    const int x_mv = il ? 4 : 0;

    const int gh_mv = il ? 12 : 0;
    const int gh_bk = il ?  0 : 4;

    float4x4 reg_f;

    for (int i = 0; i < 8; i++) {
        // extract the 5-th bits for x0 and x1
        const uint8_t xh_0 = ((qh >> (gh_mv + 2*i  )) << gh_bk) & 0x10;
        const uint8_t xh_1 = ((qh >> (gh_mv + 2*i+1)) << gh_bk) & 0x10;

        // combine the 4-bits from qs with the 5th bit
        const int32_t x0 = ((((qs[i]     ) & mask) >> x_mv) | xh_0);
        const int32_t x1 = ((((qs[i] >> 8) & mask) >> x_mv) | xh_1);

        reg_f[i/2][2*(i%2) + 0] = d * x0 + m;
        reg_f[i/2][2*(i%2) + 1] = d * x1 + m;
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q5_1_t4(device const block_q5_1 * xb, short il, thread type4 & reg) {
    device const uint16_t * qs = ((device const uint16_t *)xb + 4);
    const float d = xb->d;
    const float m = xb->m;
    const ushort mask = (il/4) ? 0x00F0 : 0x000F;

    const uint32_t qh = *((device const uint32_t *)xb->qh);

    const int x_mv = (il/4) ? 4 : 0;

    const int gh_mv = (il/4) ? 12 : 0;
    const int gh_bk = (il/4) ?  0 : 4;

    for (int ii = 0; ii < 2; ii++) {
        int i = 2*(il%4) + ii;

        // extract the 5-th bits for x0 and x1
        const uint8_t xh_0 = ((qh >> (gh_mv + 2*i  )) << gh_bk) & 0x10;
        const uint8_t xh_1 = ((qh >> (gh_mv + 2*i+1)) << gh_bk) & 0x10;

        // combine the 4-bits from qs with the 5th bit
        const int32_t x0 = ((((qs[i]     ) & mask) >> x_mv) | xh_0);
        const int32_t x1 = ((((qs[i] >> 8) & mask) >> x_mv) | xh_1);

        reg[2*ii + 0] = d * x0 + m;
        reg[2*ii + 1] = d * x1 + m;
    }
}

template <typename type4x4>
void dequantize_q8_0(device const block_q8_0 *xb, short il, thread type4x4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    float4x4 reg_f;

    for (int i = 0; i < 16; i++) {
        reg_f[i/4][i%4] = (qs[i + 16*il] * d);
    }

    reg = (type4x4) reg_f;
}

template <typename type4>
void dequantize_q8_0_t4(device const block_q8_0 *xb, short il, thread type4 & reg) {
    device const int8_t * qs = ((device const int8_t *)xb->qs);
    const float d = xb->d;

    for (int i = 0; i < 4; i++) {
        reg[i] = (qs[4*(il%4) + i + 16*(il/4)] * d);
    }
}

template <typename type4x4>
void dequantize_mxfp4(device const block_mxfp4 * xb, short il, thread type4x4 & reg) {
    device const uint8_t * q2 = (device const uint8_t *)xb->qs;

    const float d = e8m0_to_fp32(xb->e);
    const uint8_t shr = il >= 1 ? 4 : 0;

    for (int i = 0; i < 4; ++i) {
        reg[i][0] = d * kvalues_mxfp4_f[(q2[4*i + 0] >> shr) & 0x0F];
        reg[i][1] = d * kvalues_mxfp4_f[(q2[4*i + 1] >> shr) & 0x0F];
        reg[i][2] = d * kvalues_mxfp4_f[(q2[4*i + 2] >> shr) & 0x0F];
        reg[i][3] = d * kvalues_mxfp4_f[(q2[4*i + 3] >> shr) & 0x0F];
    }
}

template <typename type4>
void dequantize_mxfp4_t4(device const block_mxfp4 * xb, short il, thread type4 & reg) {
    device const uint8_t * q2 = (device const uint8_t *)xb->qs;

    const float d = e8m0_to_fp32(xb->e);
    const short il4 = il%4;

    const uint8_t shr = il >= 4 ? 4 : 0;

    reg[0] = d * kvalues_mxfp4_f[(q2[4*il4 + 0] >> shr) & 0x0F];
    reg[1] = d * kvalues_mxfp4_f[(q2[4*il4 + 1] >> shr) & 0x0F];
    reg[2] = d * kvalues_mxfp4_f[(q2[4*il4 + 2] >> shr) & 0x0F];
    reg[3] = d * kvalues_mxfp4_f[(q2[4*il4 + 3] >> shr) & 0x0F];
}

template <typename type4x4>
void dequantize_q2_K(device const block_q2_K *xb, short il, thread type4x4 & reg) {
    const float d = xb->d;
    const float min = xb->dmin;
    device const uint8_t * q = (device const uint8_t *)xb->qs;
    float dl, ml;
    uint8_t sc = xb->scales[il];

    q = q + 32*(il/8) + 16*(il&1);
    il = (il/2)%4;

    half  coef = il>1 ? (il>2 ? 1/64.h : 1/16.h) : (il>0 ? 1/4.h : 1.h);
    uchar mask = il>1 ? (il>2 ? 192    : 48)     : (il>0 ? 12    : 3);
    dl = d * (sc & 0xF) * coef, ml = min * (sc >> 4);
    for (int i = 0; i < 16; ++i) {
        reg[i/4][i%4] = dl * (q[i] & mask) - ml;
    }
}

template <typename type4x4>
void dequantize_q3_K(device const block_q3_K *xb, short il, thread type4x4 & reg) {
    const half d_all = xb->d;
    device const uint8_t * q = (device const uint8_t *)xb->qs;
    device const uint8_t * h = (device const uint8_t *)xb->hmask;
    device const int8_t * scales = (device const int8_t *)xb->scales;

    q = q + 32 * (il/8) + 16 * (il&1);
    h = h + 16 * (il&1);
    uint8_t m = 1 << (il/2);
    uint16_t kmask1 = (il/4)>1 ? ((il/4)>2 ? 192 : 48) : \
                                 ((il/4)>0 ? 12  : 3);
    uint16_t kmask2 = il/8 ? 0xF0 : 0x0F;
    uint16_t scale_2 = scales[il%8], scale_1 = scales[8 + il%4];
    int16_t  dl_int = (il/4)&1 ? (scale_2&kmask2) | ((scale_1&kmask1) << 2)
                               : (scale_2&kmask2) | ((scale_1&kmask1) << 4);
    float dl = il<8 ? d_all * (dl_int - 32.f) : d_all * (dl_int / 16.f - 32.f);
    const float ml = 4.f * dl;

    il = (il/2) & 3;
    const half    coef = il>1 ? (il>2 ? 1/64.h : 1/16.h) : (il>0 ? 1/4.h : 1.h);
    const uint8_t mask = il>1 ? (il>2 ? 192    : 48)     : (il>0 ? 12    : 3);
    dl *= coef;

    for (int i = 0; i < 16; ++i) {
        reg[i/4][i%4] = dl * (q[i] & mask) - (h[i] & m ? 0 : ml);
    }
}

static inline uchar2 get_scale_min_k4_just2(int j, int k, device const uchar * q) {
    return j < 4 ? uchar2{uchar(q[j+0+k] & 63), uchar(q[j+4+k] & 63)}
                 : uchar2{uchar((q[j+4+k] & 0xF) | ((q[j-4+k] & 0xc0) >> 2)), uchar((q[j+4+k] >> 4) | ((q[j-0+k] & 0xc0) >> 2))};
}

template <typename type4x4>
void dequantize_q4_K(device const block_q4_K * xb, short il, thread type4x4 & reg) {
    device const uchar * q = xb->qs;

    short is = (il/4) * 2;
    q = q + (il/4) * 32 + 16 * (il&1);
    il = il & 3;
    const uchar2 sc = get_scale_min_k4_just2(is, il/2, xb->scales);
    const float d   = il < 2 ? xb->d : xb->d / 16.h;
    const float min = xb->dmin;
    const float dl = d * sc[0];
    const float ml = min * sc[1];

    const ushort mask = il < 2 ? 0x0F : 0xF0;
    for (int i = 0; i < 16; ++i) {
        reg[i/4][i%4] = dl * (q[i] & mask) - ml;
    }
}

template <typename type4x4>
void dequantize_q5_K(device const block_q5_K *xb, short il, thread type4x4 & reg) {
    device const uint8_t * q  = xb->qs;
    device const uint8_t * qh = xb->qh;

    short is = (il/4) * 2;
    q  = q + 32 * (il/4) + 16 * (il&1);
    qh = qh + 16 * (il&1);
    uint8_t ul = 1 << (il/2);
    il = il & 3;
    const uchar2 sc = get_scale_min_k4_just2(is, il/2, xb->scales);
    const float d = il < 2 ? xb->d : xb->d / 16.f;
    const float min = xb->dmin;
    const float dl = d * sc[0];
    const float ml = min * sc[1];

    const ushort mask  = il<2 ? 0x0F : 0xF0;
    const float qh_val = il<2 ? 16.f : 256.f;
    for (int i = 0; i < 16; ++i) {
        reg[i/4][i%4] = dl * ((q[i] & mask) + (qh[i] & ul ? qh_val : 0)) - ml;
    }
}

template <typename type4x4>
void dequantize_q6_K(device const block_q6_K *xb, short il, thread type4x4 & reg) {
    const half d_all = xb->d;
    device const uint16_t * ql = (device const uint16_t *)xb->ql;
    device const uint16_t * qh = (device const uint16_t *)xb->qh;
    device const int8_t * scales = (device const int8_t *)xb->scales;

    ql = ql + 32*(il/8) + 16*((il/2)&1) + 8*(il&1);
    qh = qh + 16*(il/8) + 8*(il&1);
    float sc = scales[(il%2) + 2 * ((il/2))];
    il = (il/2) & 3;

    const uint32_t kmask1 = il>1 ? (il>2 ? 0xC0C0C0C0 : 0x30303030) : (il>0 ? 0x0C0C0C0C : 0x03030303);
    const uint32_t kmask2 = il>1 ? 0xF0F0F0F0                       : 0x0F0F0F0F;
    const float ml = d_all * sc * 32.f;
    const float dl0 = d_all * sc;
    const float dl1 = dl0 / 256.f;
    const float dl2 = dl0 / (256.f * 256.f);
    const float dl3 = dl0 / (256.f * 256.f * 256.f);
    const uint8_t shr_h = il>2 ? 2 : 0;
    const uint8_t shl_h = il>1 ? 0 : (il>0 ? 2 : 4);
    const uint8_t shr_l = il>1 ? 4 : 0;
    for (int i = 0; i < 4; ++i) {
        const uint32_t  low = (ql[2*i] | (uint32_t)(ql[2*i+1] << 16)) & kmask2;
        const uint32_t high = (qh[2*i] | (uint32_t)(qh[2*i+1] << 16)) & kmask1;
        const uint32_t q = ((high << shl_h) >> shr_h) | (low >> shr_l);
        reg[i][0] = dl0 *  ((half)(q & 0xFF))       - ml;
        reg[i][1] = dl1 * ((float)(q & 0xFF00))     - ml;
        reg[i][2] = dl2 * ((float)(q & 0xFF0000))   - ml;
        reg[i][3] = dl3 * ((float)(q & 0xFF000000)) - ml;
    }
}

template <typename type4x4>
void dequantize_iq2_xxs(device const block_iq2_xxs * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const float d = xb->d;
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    // each block of 32 needs 2 uint32_t's for the quants & scale, so 4 uint16_t's.
    device const uint16_t * q2 = xb->qs + 4*ib32;
    const uint32_t aux32_g = q2[0] | (q2[1] << 16);
    const uint32_t aux32_s = q2[2] | (q2[3] << 16);
    thread const uint8_t * aux8 = (thread const uint8_t *)&aux32_g;
    const float dl = d * (0.5f + (aux32_s >> 28)) * 0.25f;
    constant uint8_t * grid = (constant uint8_t *)(iq2xxs_grid + aux8[2*il+0]);
    uint8_t signs = ksigns_iq2xs[(aux32_s >> 14*il) & 127];
    for (int i = 0; i < 8; ++i) {
        reg[i/4][i%4] = dl * grid[i] * (signs & kmask_iq2xs[i] ? -1.f : 1.f);
    }
    grid = (constant uint8_t *)(iq2xxs_grid + aux8[2*il+1]);
    signs = ksigns_iq2xs[(aux32_s >> (14*il+7)) & 127];
    for (int i = 0; i < 8; ++i) {
        reg[2+i/4][i%4] = dl * grid[i] * (signs & kmask_iq2xs[i] ? -1.f : 1.f);
    }
}

template <typename type4x4>
void dequantize_iq2_xs(device const block_iq2_xs * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const float d = xb->d;
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    device const uint16_t * q2 = xb->qs + 4*ib32;
    const float dl = d * (0.5f + ((xb->scales[ib32] >> 4*il) & 0xf)) * 0.25f;
    constant uint8_t * grid = (constant uint8_t *)(iq2xs_grid + (q2[2*il+0] & 511));
    uint8_t signs = ksigns_iq2xs[q2[2*il+0] >> 9];
    for (int i = 0; i < 8; ++i) {
        reg[i/4][i%4] = dl * grid[i] * (signs & kmask_iq2xs[i] ? -1.f : 1.f);
    }
    grid = (constant uint8_t *)(iq2xs_grid + (q2[2*il+1] & 511));
    signs = ksigns_iq2xs[q2[2*il+1] >> 9];
    for (int i = 0; i < 8; ++i) {
        reg[2+i/4][i%4] = dl * grid[i] * (signs & kmask_iq2xs[i] ? -1.f : 1.f);
    }
}

template <typename type4x4>
void dequantize_iq3_xxs(device const block_iq3_xxs * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const float d = xb->d;
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    device const uint8_t * q3 = xb->qs + 8*ib32;
    device const uint16_t * gas = (device const uint16_t *)(xb->qs + QK_K/4) + 2*ib32;
    const uint32_t aux32 = gas[0] | (gas[1] << 16);
    const float dl = d * (0.5f + (aux32 >> 28)) * 0.5f;
    constant uint8_t * grid1 = (constant uint8_t *)(iq3xxs_grid + q3[4*il+0]);
    constant uint8_t * grid2 = (constant uint8_t *)(iq3xxs_grid + q3[4*il+1]);
    uint8_t signs = ksigns_iq2xs[(aux32 >> 14*il) & 127];
    for (int i = 0; i < 4; ++i) {
        reg[0][i] = dl * grid1[i] * (signs & kmask_iq2xs[i+0] ? -1.f : 1.f);
        reg[1][i] = dl * grid2[i] * (signs & kmask_iq2xs[i+4] ? -1.f : 1.f);
    }
    grid1 = (constant uint8_t *)(iq3xxs_grid + q3[4*il+2]);
    grid2 = (constant uint8_t *)(iq3xxs_grid + q3[4*il+3]);
    signs = ksigns_iq2xs[(aux32 >> (14*il+7)) & 127];
    for (int i = 0; i < 4; ++i) {
        reg[2][i] = dl * grid1[i] * (signs & kmask_iq2xs[i+0] ? -1.f : 1.f);
        reg[3][i] = dl * grid2[i] * (signs & kmask_iq2xs[i+4] ? -1.f : 1.f);
    }
}

template <typename type4x4>
void dequantize_iq3_s(device const block_iq3_s * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const float d = xb->d;
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    device const uint8_t * qs = xb->qs + 8*ib32;
    device const uint8_t * signs = xb->signs + 4*ib32 + 2*il;
    const uint8_t qh = xb->qh[ib32] >> 4*il;
    const float dl = d * (1 + 2*((xb->scales[ib32/2] >> 4*(ib32%2)) & 0xf));
    constant uint8_t * grid1 = (constant uint8_t *)(iq3s_grid + (qs[4*il+0] | ((qh << 8) & 256)));
    constant uint8_t * grid2 = (constant uint8_t *)(iq3s_grid + (qs[4*il+1] | ((qh << 7) & 256)));
    for (int i = 0; i < 4; ++i) {
        reg[0][i] = dl * grid1[i] * select(1, -1, signs[0] & kmask_iq2xs[i+0]);
        reg[1][i] = dl * grid2[i] * select(1, -1, signs[0] & kmask_iq2xs[i+4]);
    }
    grid1 = (constant uint8_t *)(iq3s_grid + (qs[4*il+2] | ((qh << 6) & 256)));
    grid2 = (constant uint8_t *)(iq3s_grid + (qs[4*il+3] | ((qh << 5) & 256)));
    for (int i = 0; i < 4; ++i) {
        reg[2][i] = dl * grid1[i] * select(1, -1, signs[1] & kmask_iq2xs[i+0]);
        reg[3][i] = dl * grid2[i] * select(1, -1, signs[1] & kmask_iq2xs[i+4]);
    }
}

template <typename type4x4>
void dequantize_iq2_s(device const block_iq2_s * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const float d = xb->d;
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    device const uint8_t * qs = xb->qs + 4*ib32 + 2*il;
    device const uint8_t * signs = qs + QK_K/8;
    const uint8_t qh = xb->qh[ib32] >> 4*il;
    const float dl = d * (0.5f + ((xb->scales[ib32] >> 4*il) & 0xf)) * 0.25f;
    constant uint8_t * grid1 = (constant uint8_t *)(iq2s_grid + (qs[0] | ((qh << 8) & 0x300)));
    constant uint8_t * grid2 = (constant uint8_t *)(iq2s_grid + (qs[1] | ((qh << 6) & 0x300)));
    for (int i = 0; i < 8; ++i) {
        reg[i/4+0][i%4] = dl * grid1[i] * select(1, -1, signs[0] & kmask_iq2xs[i]);
        reg[i/4+2][i%4] = dl * grid2[i] * select(1, -1, signs[1] & kmask_iq2xs[i]);
    }
}

template <typename type4x4>
void dequantize_iq1_s(device const block_iq1_s * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const int ib32 = il/2;
    il = il%2;
    const float d = xb->d;
    device const uint8_t  * qs = xb->qs + 4*ib32 + 2*il;
    device const uint16_t * qh = xb->qh;
    const float dl = d * (2*((qh[ib32] >> 12) & 7) + 1);
    const float ml = dl * (qh[ib32] & 0x8000 ? -1 - IQ1S_DELTA : -1 + IQ1S_DELTA);
    const uint16_t h = qh[ib32] >> 6*il;
    constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | ((h << 8) & 0x700)));
    constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | ((h << 5) & 0x700)));
    for (int i = 0; i < 4; ++i) {
        reg[0][i] = dl * (grid1[i] & 0xf) + ml;
        reg[1][i] = dl * (grid1[i] >>  4) + ml;
        reg[2][i] = dl * (grid2[i] & 0xf) + ml;
        reg[3][i] = dl * (grid2[i] >>  4) + ml;
    }
}

template <typename type4x4>
void dequantize_iq1_m(device const block_iq1_m * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const int ib32 = il/2;
    il = il%2;
    device const uint16_t * sc = (device const uint16_t *)xb->scales;

    iq1m_scale_t scale;
    scale.u16 = (sc[0] >> 12) | ((sc[1] >> 8) & 0x00f0) | ((sc[2] >> 4) & 0x0f00) | (sc[3] & 0xf000);
    const float d = scale.f16;

    device const uint8_t * qs = xb->qs + 4*ib32 + 2*il;
    device const uint8_t * qh = xb->qh + 2*ib32 + il;

    const float dl  = d * (2*((sc[ib32/2] >> (6*(ib32%2)+3*il)) & 7) + 1);
    const float ml1 = dl * (qh[0] & 0x08 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA);
    const float ml2 = dl * (qh[0] & 0x80 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA);
    constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | ((qh[0] << 8) & 0x700)));
    constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | ((qh[0] << 4) & 0x700)));
    for (int i = 0; i < 4; ++i) {
        reg[0][i] = dl * (grid1[i] & 0xf) + ml1;
        reg[1][i] = dl * (grid1[i] >>  4) + ml1;
        reg[2][i] = dl * (grid2[i] & 0xf) + ml2;
        reg[3][i] = dl * (grid2[i] >>  4) + ml2;
    }
}

template <typename type4x4>
void dequantize_iq4_nl(device const block_iq4_nl * xb, short il, thread type4x4 & reg) {
    device const uint16_t * q4 = (device const uint16_t *)xb->qs;
    const float d = xb->d;
    uint32_t aux32;
    thread const uint8_t * q8 = (thread const uint8_t *)&aux32;
    for (int i = 0; i < 4; ++i) {
        aux32 = ((q4[2*i] | (q4[2*i+1] << 16)) >> 4*il) & 0x0f0f0f0f;
        reg[i][0] = d * kvalues_iq4nl_f[q8[0]];
        reg[i][1] = d * kvalues_iq4nl_f[q8[1]];
        reg[i][2] = d * kvalues_iq4nl_f[q8[2]];
        reg[i][3] = d * kvalues_iq4nl_f[q8[3]];
    }
}

template <typename type4>
void dequantize_iq4_nl_t4(device const block_iq4_nl * xb, short il, thread type4 & reg) {
    device const uint16_t * q4 = (device const uint16_t *)xb->qs;
    const float d = xb->d;
    uint32_t aux32;
    thread const uint8_t * q8 = (thread const uint8_t *)&aux32;
    aux32 = ((q4[2*(il%4)] | (q4[2*(il%4)+1] << 16)) >> 4*(il/4)) & 0x0f0f0f0f;
    reg[0] = d * kvalues_iq4nl_f[q8[0]];
    reg[1] = d * kvalues_iq4nl_f[q8[1]];
    reg[2] = d * kvalues_iq4nl_f[q8[2]];
    reg[3] = d * kvalues_iq4nl_f[q8[3]];
}

template <typename type4x4>
void dequantize_iq4_xs(device const block_iq4_xs * xb, short il, thread type4x4 & reg) {
    // il is 0...15 for QK_K = 256 => index of block of 32 is il/2
    const int ib32 = il/2;
    il = il%2;
    // il = 0 or 1. il = 0 processes the first 16 quants in a block of 32, il = 1 the second 16
    device const uint32_t * q4 = (device const uint32_t *)xb->qs + 4*ib32;
    const int ls = ((xb->scales_l[ib32/2] >> 4*(ib32%2)) & 0xf) | (((xb->scales_h >> 2*ib32) & 3) << 4);
    const float d = (float)xb->d * (ls - 32);
    uint32_t aux32;
    thread const uint8_t * q8 = (thread const uint8_t *)&aux32;
    for (int i = 0; i < 4; ++i) {
        aux32 = (q4[i] >> 4*il) & 0x0f0f0f0f;
        reg[i][0] = d * kvalues_iq4nl_f[q8[0]];
        reg[i][1] = d * kvalues_iq4nl_f[q8[1]];
        reg[i][2] = d * kvalues_iq4nl_f[q8[2]];
        reg[i][3] = d * kvalues_iq4nl_f[q8[3]];
    }
}

enum ggml_sort_order {
    GGML_SORT_ORDER_ASC,
    GGML_SORT_ORDER_DESC,
};

// general-purpose kernel for addition, subtraction, multiplication and division of two tensors
// pros: works for non-contiguous tensors, supports broadcast across all dims
// cons: not very efficient
template <int F>
kernel void kernel_add_fuse_impl(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig.z;
    const int i02 = tgpig.y;
    const int i01 = tgpig.x;

    const int i13 = i03%args.ne13;
    const int i12 = i02%args.ne12;
    const int i11 = i01%args.ne11;

    device const float * src0_ptr = (device const float *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs);
    device       float * dst_ptr  = (device       float *) (dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs);

    device const float * src1_ptr[F];
    for (short j = 0; j < F; ++j) {
        src1_ptr[j] = (device const float *) (src1 + args.o1[j] + i13*args.nb13 + i12*args.nb12 + i11*args.nb11);
    }

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        const int i10 = i0%args.ne10;

        float res = src0_ptr[i0];

#pragma unroll
        for (short j = 0; j < F; ++j) {
            res += src1_ptr[j][i10];
        }

        dst_ptr[i0] = res;
    }
}

typedef decltype(kernel_add_fuse_impl<2>) kernel_add_fuse_t;

template [[host_name("kernel_add_fuse_1")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<1>;
template [[host_name("kernel_add_fuse_2")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<2>;
template [[host_name("kernel_add_fuse_3")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<3>;
template [[host_name("kernel_add_fuse_4")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<4>;
template [[host_name("kernel_add_fuse_5")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<5>;
template [[host_name("kernel_add_fuse_6")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<6>;
template [[host_name("kernel_add_fuse_7")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<7>;
template [[host_name("kernel_add_fuse_8")]] kernel kernel_add_fuse_t kernel_add_fuse_impl<8>;

kernel void kernel_sub_fuse_1(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig.z;
    const int i02 = tgpig.y;
    const int i01 = tgpig.x;

    const int i13 = i03%args.ne13;
    const int i12 = i02%args.ne12;
    const int i11 = i01%args.ne11;

    device const char * src0_ptr = src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs;
    device const char * src1_ptr = src1 + i13*args.nb13 + i12*args.nb12 + i11*args.nb11 + args.o1[0];
    device       char * dst_ptr  = dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        const int i10 = i0%args.ne10;
        *((device float *)(dst_ptr + i0*args.nb0)) = *((device float *)(src0_ptr + i0*args.nb00)) - *((device float *)(src1_ptr + i10*args.nb10));
    }
}

kernel void kernel_mul_fuse_1(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig.z;
    const int i02 = tgpig.y;
    const int i01 = tgpig.x;

    const int i13 = i03%args.ne13;
    const int i12 = i02%args.ne12;
    const int i11 = i01%args.ne11;

    device const char * src0_ptr = src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs;
    device const char * src1_ptr = src1 + i13*args.nb13 + i12*args.nb12 + i11*args.nb11 + args.o1[0];
    device       char * dst_ptr  = dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs;

    if (args.ne10 == 1) {
        const float x = *((device float *)(src1_ptr));
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            *((device float *)(dst_ptr + i0*args.nb0)) = *((device float *)(src0_ptr + i0*args.nb00)) * x;
        }
    } else {
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            const int i10 = i0%args.ne10;
            *((device float *)(dst_ptr + i0*args.nb0)) = *((device float *)(src0_ptr + i0*args.nb00)) * *((device float *)(src1_ptr + i10*args.nb10));
        }
    }
}

kernel void kernel_div_fuse_1(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig.z;
    const int i02 = tgpig.y;
    const int i01 = tgpig.x;

    const int i13 = i03%args.ne13;
    const int i12 = i02%args.ne12;
    const int i11 = i01%args.ne11;

    device const char * src0_ptr = src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + args.offs;
    device const char * src1_ptr = src1 + i13*args.nb13 + i12*args.nb12 + i11*args.nb11 + args.o1[0];
    device       char * dst_ptr  = dst  + i03*args.nb3  + i02*args.nb2  + i01*args.nb1  + args.offs;

    if (args.ne10 == 1) {
        const float x = 1.0f / *((device float *)(src1_ptr));
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            *((device float *)(dst_ptr + i0*args.nb0)) = *((device float *)(src0_ptr + i0*args.nb00)) * x;
        }
    } else {
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            const int i10 = i0%args.ne10;
            *((device float *)(dst_ptr + i0*args.nb0)) = *((device float *)(src0_ptr + i0*args.nb00)) / *((device float *)(src1_ptr + i10*args.nb10));
        }
    }
}

kernel void kernel_add_id(
        constant ggml_metal_kargs_add_id & args,
        device const char * src0,
        device const char * src1,
        device const char * src2,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i1 = tgpig.x;
    const int i2 = tgpig.y;

    const int i11 = *((device const int32_t *) (src2 + i1*sizeof(int32_t) + i2*args.nb21));

    const size_t nb1 = args.ne0 * sizeof(float);
    const size_t nb2 = args.ne1 * nb1;

    device       float * dst_row  = (device       float *)((device char *)dst + i1*nb1 + i2*nb2);
    device const float * src0_row = (device const float *)((device char *)src0 +  i1*args.nb01 + i2*args.nb02);
    device const float * src1_row = (device const float *)((device char *)src1 + i11*args.nb11);

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        dst_row[i0] = src0_row[i0] + src1_row[i0];
    }
}

template<typename T>
kernel void kernel_repeat(
        constant ggml_metal_kargs_repeat & args,
        device const char * src0,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    const int i03 = i3%args.ne03;
    const int i02 = i2%args.ne02;
    const int i01 = i1%args.ne01;

    device const char * src0_ptr = src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01;
    device       char * dst_ptr  = dst  +  i3*args.nb3  +  i2*args.nb2  +  i1*args.nb1;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        const int i00 = i0%args.ne00;
        *((device T *)(dst_ptr + i0*args.nb0)) = *((device T *)(src0_ptr + i00*args.nb00));
    }
}

typedef decltype(kernel_repeat<float>) kernel_repeat_t;

template [[host_name("kernel_repeat_f32")]] kernel kernel_repeat_t kernel_repeat<float>;
template [[host_name("kernel_repeat_f16")]] kernel kernel_repeat_t kernel_repeat<half>;
template [[host_name("kernel_repeat_i32")]] kernel kernel_repeat_t kernel_repeat<int>;
template [[host_name("kernel_repeat_i16")]] kernel kernel_repeat_t kernel_repeat<short>;

// assumption: src1 is a row
// broadcast src1 into src0
template <short F>
kernel void kernel_add_row_c4_fuse_impl(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tpig[[thread_position_in_grid]]) {
    const uint nb = args.ne00/4;
    const uint i  = tpig % nb;

    device const float4 * src0_row = (device const float4 *) (src0);
    device       float4 *  dst_row = (device       float4 *) (dst);

    float4 res = src0_row[tpig];

#pragma unroll(F)
    for (short j = 0; j < F; ++j) {
        res += ((device const float4 *) (src1 + args.o1[j]))[i];
    }

    dst_row[tpig] = res;
}

typedef decltype(kernel_add_row_c4_fuse_impl<1>) kernel_add_row_c4_fuse_t;

template [[host_name("kernel_add_row_c4_fuse_1")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<1>;
template [[host_name("kernel_add_row_c4_fuse_2")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<2>;
template [[host_name("kernel_add_row_c4_fuse_3")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<3>;
template [[host_name("kernel_add_row_c4_fuse_4")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<4>;
template [[host_name("kernel_add_row_c4_fuse_5")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<5>;
template [[host_name("kernel_add_row_c4_fuse_6")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<6>;
template [[host_name("kernel_add_row_c4_fuse_7")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<7>;
template [[host_name("kernel_add_row_c4_fuse_8")]] kernel kernel_add_row_c4_fuse_t kernel_add_row_c4_fuse_impl<8>;

template <short F>
kernel void kernel_sub_row_c4_fuse_impl(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tpig[[thread_position_in_grid]]) {

    const uint nb = args.ne00/4;
    const uint i  = tpig % nb;

    device const float4 * src0_row = (device const float4 *) (src0);
    device       float4 *  dst_row = (device       float4 *) (dst);

    device const float4 * src1_row[F];
    for (short j = 0; j < F; ++j) {
        src1_row[j] = (device const float4 *) (src1 + args.o1[j]);
    }

    float4 res = src0_row[tpig];

#pragma unroll(F)
    for (short j = 0; j < F; ++j) {
        res -= src1_row[j][i];
    }

    dst_row[tpig] = res;
}

typedef decltype(kernel_sub_row_c4_fuse_impl<1>) kernel_sub_row_c4_fuse_t;

template [[host_name("kernel_sub_row_c4_fuse_1")]] kernel kernel_sub_row_c4_fuse_t kernel_sub_row_c4_fuse_impl<1>;

template <short F>
kernel void kernel_mul_row_c4_fuse_impl(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tpig[[thread_position_in_grid]]) {

    const uint nb = args.ne00/4;
    const uint i  = tpig % nb;

    device const float4 * src0_row = (device const float4 *) (src0);
    device       float4 *  dst_row = (device       float4 *) (dst);

    device const float4 * src1_row[F];
    for (short j = 0; j < F; ++j) {
        src1_row[j] = (device const float4 *) (src1 + args.o1[j]);
    }

    float4 res = src0_row[tpig];

#pragma unroll(F)
    for (short j = 0; j < F; ++j) {
        res *= src1_row[j][i];
    }

    dst_row[tpig] = res;
}

typedef decltype(kernel_mul_row_c4_fuse_impl<1>) kernel_mul_row_c4_fuse_t;

template [[host_name("kernel_mul_row_c4_fuse_1")]] kernel kernel_mul_row_c4_fuse_t kernel_mul_row_c4_fuse_impl<1>;

template <short F>
kernel void kernel_div_row_c4_fuse_impl(
        constant ggml_metal_kargs_bin & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tpig[[thread_position_in_grid]]) {

    const uint nb = args.ne00/4;
    const uint i  = tpig % nb;

    device const float4 * src0_row = (device const float4 *) (src0);
    device       float4 *  dst_row = (device       float4 *) (dst);

    device const float4 * src1_row[F];
    for (short j = 0; j < F; ++j) {
        src1_row[j] = (device const float4 *) (src1 + args.o1[j]);
    }

    float4 res = src0_row[tpig];

#pragma unroll(F)
    for (short j = 0; j < F; ++j) {
        res /= src1_row[j][i];
    }

    dst_row[tpig] = res;
}

typedef decltype(kernel_div_row_c4_fuse_impl<1>) kernel_div_row_c4_fuse_t;

template [[host_name("kernel_div_row_c4_fuse_1")]] kernel kernel_div_row_c4_fuse_t kernel_div_row_c4_fuse_impl<1>;

kernel void kernel_scale_f32(
        constant ggml_metal_kargs_scale & args,
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = src0[tpig] * args.scale + args.bias;
}

kernel void kernel_scale_f32_4(
        constant ggml_metal_kargs_scale & args,
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = src0[tpig] * args.scale + args.bias;
}

kernel void kernel_clamp_f32(
        constant ggml_metal_kargs_clamp & args,
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = clamp(src0[tpig], args.min, args.max);
}

kernel void kernel_clamp_f32_4(
        constant ggml_metal_kargs_clamp & args,
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = clamp(src0[tpig], args.min, args.max);
}

kernel void kernel_relu_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = max(0.0f, src0[tpig]);
}

kernel void kernel_relu_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = max(0.0f, src0[tpig]);
}

kernel void kernel_sigmoid_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = 1.0f / (1.0f + exp(-src0[tpig]));
}

kernel void kernel_sigmoid_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = 1.0f / (1.0f + exp(-src0[tpig]));
}

kernel void kernel_tanh_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = precise::tanh(src0[tpig]);
}

kernel void kernel_tanh_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = precise::tanh(src0[tpig]);
}

constant float GELU_COEF_A     = 0.044715f;
constant float GELU_QUICK_COEF = -1.702f;
constant float SQRT_2_OVER_PI  = 0.79788456080286535587989211986876f;
constant float SQRT_2_INV      = 0.70710678118654752440084436210484f;

kernel void kernel_gelu_f32(
    device const float * src0,
    device       float * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float & x = src0[tpig];

    dst[tpig] = 0.5f*x*(1.0f + precise::tanh(SQRT_2_OVER_PI*x*(1.0f + GELU_COEF_A*x*x)));
}

kernel void kernel_gelu_f32_4(
    device const float4 * src0,
    device       float4 * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float4 & x = src0[tpig];

    // BEWARE !!!
    // Simply using "tanh" instead of "precise::tanh" will sometimes results in NaNs!
    // This was observed with Falcon 7B and 40B models
    //
    dst[tpig] = 0.5f*x*(1.0f + precise::tanh(SQRT_2_OVER_PI*x*(1.0f + GELU_COEF_A*x*x)));
}

kernel void kernel_gelu_quick_f32(
    device const float * src0,
    device       float * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float & x = src0[tpig];

    dst[tpig] = x*(1.0f/(1.0f+exp(GELU_QUICK_COEF*x)));
}

kernel void kernel_gelu_quick_f32_4(
    device const float4 * src0,
    device       float4 * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float4 & x = src0[tpig];

    dst[tpig] = x*(1.0f/(1.0f+exp(GELU_QUICK_COEF*x)));
}

// based on Abramowitz and Stegun formula 7.1.26 or similar Hastings' approximation
// ref: https://www.johndcook.com/blog/python_erf/
constant float p_erf  = 0.3275911f;
constant float a1_erf = 0.254829592f;
constant float a2_erf = -0.284496736f;
constant float a3_erf = 1.421413741f;
constant float a4_erf = -1.453152027f;
constant float a5_erf = 1.061405429f;

template<typename T>
T erf_approx(T x) {
    T sign_x = sign(x);
    x = fabs(x);
    T t = 1.0f / (1.0f + p_erf * x);
    T y = 1.0f - (((((a5_erf * t + a4_erf) * t) + a3_erf) * t + a2_erf) * t + a1_erf) * t * exp(-x * x);
    return sign_x * y;
}

kernel void kernel_gelu_erf_f32(
    device const float * src0,
    device       float * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float & x = src0[tpig];

    dst[tpig] = 0.5f*x*(1.0f+erf_approx<float>(x*SQRT_2_INV));
}

kernel void kernel_gelu_erf_f32_4(
    device const float4 * src0,
    device       float4 * dst,
    uint tpig[[thread_position_in_grid]]) {
    device const float4 & x = src0[tpig];

    dst[tpig] = 0.5f*x*(1.0f+erf_approx<float4>(x*SQRT_2_INV));
}

kernel void kernel_silu_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    device const float & x = src0[tpig];
    dst[tpig] = x / (1.0f + exp(-x));
}

kernel void kernel_silu_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    device const float4 & x = src0[tpig];
    dst[tpig] = x / (1.0f + exp(-x));
}

kernel void kernel_elu_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float x = src0[tpig];
    dst[tpig] = (x > 0.0f) ? x : (exp(x) - 1.0f);
}

kernel void kernel_elu_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float4 x = src0[tpig];
    dst[tpig][0] = (x[0] > 0.0f) ? x[0] : (exp(x[0]) - 1.0f);
    dst[tpig][1] = (x[1] > 0.0f) ? x[1] : (exp(x[1]) - 1.0f);
    dst[tpig][2] = (x[2] > 0.0f) ? x[2] : (exp(x[2]) - 1.0f);
    dst[tpig][3] = (x[3] > 0.0f) ? x[3] : (exp(x[3]) - 1.0f);
}

kernel void kernel_sqr_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = src0[tpig] * src0[tpig];
}

kernel void kernel_sqr_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = src0[tpig] * src0[tpig];
}

kernel void kernel_sqrt_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sqrt(src0[tpig]);
}

kernel void kernel_sqrt_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sqrt(src0[tpig]);
}

kernel void kernel_sin_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sin(src0[tpig]);
}

kernel void kernel_sin_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sin(src0[tpig]);
}

kernel void kernel_cos_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = cos(src0[tpig]);
}

kernel void kernel_cos_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = cos(src0[tpig]);
}

kernel void kernel_log_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = log(src0[tpig]);
}

kernel void kernel_log_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = log(src0[tpig]);
}

kernel void kernel_neg_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = -src0[tpig];
}

kernel void kernel_neg_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = -src0[tpig];
}

kernel void kernel_abs_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = fabs(src0[tpig]);
}

kernel void kernel_abs_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = fabs(src0[tpig]);
}

kernel void kernel_sgn_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sign(src0[tpig]);
}

kernel void kernel_sgn_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = sign(src0[tpig]);
}

kernel void kernel_step_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = step(0.0f, src0[tpig]);
}

kernel void kernel_step_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = step(0.0f, src0[tpig]);
}

kernel void kernel_hardswish_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float x = src0[tpig];
    dst[tpig] = x * fmin(1.0f, fmax(0.0f, (x + 3.0f) / 6.0f));
}

kernel void kernel_hardswish_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float4 x = src0[tpig];
    dst[tpig] = x * fmin(1.0f, fmax(0.0f, (x + 3.0f) / 6.0f));
}

kernel void kernel_hardsigmoid_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float x = src0[tpig];
    dst[tpig] = fmin(1.0f, fmax(0.0f, (x + 3.0f) / 6.0f));
}

kernel void kernel_hardsigmoid_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float4 x = src0[tpig];
    dst[tpig] = fmin(1.0f, fmax(0.0f, (x + 3.0f) / 6.0f));
}

kernel void kernel_exp_f32(
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = exp(src0[tpig]);
}

kernel void kernel_exp_f32_4(
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    dst[tpig] = exp(src0[tpig]);
}

kernel void kernel_reglu_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        dst_row[i0] = x0*x1*(x0 > 0.0f);
    }
}

kernel void kernel_geglu_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float gelu = 0.5f*x0*(1.0f + precise::tanh(SQRT_2_OVER_PI*x0*(1.0f + GELU_COEF_A*x0*x0)));

        dst_row[i0] = gelu*x1;
    }
}

kernel void kernel_swiglu_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float silu = x0 / (1.0f + exp(-x0));

        dst_row[i0] = silu*x1;
    }
}

kernel void kernel_swiglu_oai_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        float x0 = src0_row[i0];
        float x1 = src1_row[i0];

        x0 = min(x0, args.limit);
        x1 = max(min(x1, args.limit), -args.limit);

        float out_glu = x0 / (1.0f + exp(-x0 * args.alpha));
        out_glu = out_glu * (1.0f + x1);

        dst_row[i0] = out_glu;
    }
}

kernel void kernel_geglu_erf_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float gelu_erf = 0.5f*x0*(1.0f+erf_approx<float>(x0*SQRT_2_INV));

        dst_row[i0] = gelu_erf*x1;
    }
}

kernel void kernel_geglu_quick_f32(
        constant ggml_metal_kargs_glu & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    device const float * src0_row = (device const float *) ((device const char *) src0 + tgpig*args.nb01) + args.i00;
    device const float * src1_row = (device const float *) ((device const char *) src1 + tgpig*args.nb11) + args.i10;
    device       float * dst_row  = (device       float *) ((device       char *) dst  + tgpig*args.nb1);

    for (int i0 = tpitg; i0 < args.ne0; i0 += ntg) {
        const float x0 = src0_row[i0];
        const float x1 = src1_row[i0];

        const float gelu_quick = x0*(1.0f/(1.0f+exp(GELU_QUICK_COEF*x0)));

        dst_row[i0] = gelu_quick*x1;
    }
}

kernel void kernel_op_sum_f32(
        constant ggml_metal_kargs_sum & args,
        device const float * src0,
        device       float * dst,
        threadgroup  float * shmem_f32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {

    if (args.np == 0) {
        return;
    }

    const uint nsg = (ntg.x + 31) / 32;

    float sumf = 0;

    for (uint64_t i0 = tpitg.x; i0 < args.np; i0 += ntg.x) {
        sumf += src0[i0];
    }

    sumf = simd_sum(sumf);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    float total = 0;

    if (sgitg == 0) {
        float v = 0;

        if (tpitg.x < nsg) {
            v = shmem_f32[tpitg.x];
        }

        total = simd_sum(v);

        if (tpitg.x == 0) {
            dst[0] = total;
        }
    }
}

template <bool norm>
kernel void kernel_sum_rows(
        constant ggml_metal_kargs_sum_rows & args,
        device const float * src0,
        device       float * dst,
        threadgroup  float * shmem_f32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    int64_t i3 = tgpig.z;
    int64_t i2 = tgpig.y;
    int64_t i1 = tgpig.x;

    if (i3 >= args.ne03 || i2 >= args.ne02 || i1 >= args.ne01) {
        return;
    }

    if (sgitg == 0) {
        shmem_f32[tiisg] = 0.0f;
    }

    device const float * src_row = (device const float *) ((device const char *) src0 + i1*args.nb01 + i2*args.nb02 + i3*args.nb03);
    device       float * dst_row = (device       float *) ((device       char *) dst  + i1*args.nb1  + i2*args.nb2  + i3*args.nb3);

    float sumf = 0;

    for (int64_t i0 = tpitg.x; i0 < args.ne00; i0 += ntg.x) {
        sumf += src_row[i0];
    }

    sumf = simd_sum(sumf);

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    sumf = shmem_f32[tiisg];
    sumf = simd_sum(sumf);

    if (tpitg.x == 0) {
        dst_row[0] = norm ? sumf / args.ne00 : sumf;
    }
}

typedef decltype(kernel_sum_rows<false>) kernel_sum_rows_t;

template [[host_name("kernel_sum_rows_f32")]] kernel kernel_sum_rows_t kernel_sum_rows<false>;
template [[host_name("kernel_mean_f32")]]     kernel kernel_sum_rows_t kernel_sum_rows<true>;

template<typename T>
kernel void kernel_cumsum_blk(
        constant ggml_metal_kargs_cumsum_blk & args,
        device const char * src0,
        device       char * tmp,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int ib = tgpig[0]/args.ne01;

    const int i00 = ib*ntg.x;
    const int i01 = tgpig[0]%args.ne01;
    const int i02 = tgpig[1];
    const int i03 = tgpig[2];

    device const float * src0_row = (device const float *) (src0 +
            args.nb01*i01 +
            args.nb02*i02 +
            args.nb03*i03);

    threadgroup float * shmem_f32 = (threadgroup float *) shmem;

    float v = 0.0f;

    if (i00 + tpitg.x < args.ne00) {
        v = src0_row[i00 + tpitg.x];
    }

    float s = simd_prefix_inclusive_sum(v);

    if (tiisg == N_SIMDWIDTH - 1) {
        shmem_f32[sgitg] = s;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (sgitg == 0) {
        shmem_f32[tiisg] = simd_prefix_exclusive_sum(shmem_f32[tiisg]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    s += shmem_f32[sgitg];

    device float * dst_row = (device float *) dst +
        args.ne00*i01 +
        args.ne00*args.ne01*i02 +
        args.ne00*args.ne01*args.ne02*i03;

    if (i00 + tpitg.x < args.ne00) {
        dst_row[i00 + tpitg.x] = s;
    }

    if (args.outb && tpitg.x == ntg.x - 1) {
        device float * tmp_row = (device float *) tmp +
            args.net0*i01 +
            args.net0*args.net1*i02 +
            args.net0*args.net1*args.net2*i03;

        tmp_row[ib] = s;
    }
}

typedef decltype(kernel_cumsum_blk<float>) kernel_cumsum_blk_t;

template [[host_name("kernel_cumsum_blk_f32")]] kernel kernel_cumsum_blk_t kernel_cumsum_blk<float>;

template<typename T>
kernel void kernel_cumsum_add(
        constant ggml_metal_kargs_cumsum_add & args,
        device const char * tmp,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int ib = tgpig[0]/args.ne01;

    if (ib == 0) {
        return;
    }

    const int i00 = ib*ntg.x;
    const int i01 = tgpig[0]%args.ne01;
    const int i02 = tgpig[1];
    const int i03 = tgpig[2];

    device const float * tmp_row = (device const float *) (tmp +
            args.nbt1*i01 +
            args.nbt2*i02 +
            args.nbt3*i03);

    device float * dst_row = (device float *) dst +
        args.ne00*i01 +
        args.ne00*args.ne01*i02 +
        args.ne00*args.ne01*args.ne02*i03;

    if (i00 + tpitg.x < args.ne00) {
        dst_row[i00 + tpitg.x] += tmp_row[ib - 1];
    }
}

typedef decltype(kernel_cumsum_add<float>) kernel_cumsum_add_t;

template [[host_name("kernel_cumsum_add_f32")]] kernel kernel_cumsum_add_t kernel_cumsum_add<float>;

template<typename T>
kernel void kernel_soft_max(
        constant ggml_metal_kargs_soft_max & args,
        device const  char * src0,
        device const  char * src1,
        device const  char * src2,
        device        char * dst,
        threadgroup  float * buf [[threadgroup(0)]],
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint  sgitg[[simdgroup_index_in_threadgroup]],
        uint  tiisg[[thread_index_in_simdgroup]],
        uint3  tptg[[threads_per_threadgroup]]) {
    const int32_t i03 = tgpig.z;
    const int32_t i02 = tgpig.y;
    const int32_t i01 = tgpig.x;

    const int32_t i13 = i03%args.ne13;
    const int32_t i12 = i02%args.ne12;
    const int32_t i11 = i01;

    device const float * psrc0 =                (device const float *) (src0 + i01*args.nb01 + i02*args.nb02 + i03*args.nb03);
    device const     T * pmask = src1 != src0 ? (device const T *    ) (src1 + i11*args.nb11 + i12*args.nb12 + i13*args.nb13) : nullptr;
    device const float * psrc2 = src2 != src0 ? (device const float *) (src2)                                                 : nullptr;
    device       float * pdst  =                (device       float *) (dst  + i01*args.nb1  + i02*args.nb2  + i03*args.nb3);

    float slope = 1.0f;

    // ALiBi
    if (args.max_bias > 0.0f) {
        const int32_t h = i02;

        const float base = h < args.n_head_log2 ? args.m0 : args.m1;
        const int   exp  = h < args.n_head_log2 ? h + 1 : 2*(h - args.n_head_log2) + 1;

        slope = pow(base, exp);
    }

    // parallel max
    float lmax = psrc2 ? psrc2[i02] : -INFINITY;

    for (int i00 = tpitg.x; i00 < args.ne00; i00 += tptg.x) {
        lmax = MAX(lmax, psrc0[i00]*args.scale + (pmask ? slope*pmask[i00] : 0.0f));
    }

    // find the max value in the block
    float max_val = simd_max(lmax);
    if (tptg.x > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = -INFINITY;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = max_val;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        max_val = buf[tiisg];
        max_val = simd_max(max_val);
    }

    // parallel sum
    float lsum = 0.0f;
    for (int i00 = tpitg.x; i00 < args.ne00; i00 += tptg.x) {
        const float exp_psrc0 = exp((psrc0[i00]*args.scale + (pmask ? slope*pmask[i00] : 0.0f)) - max_val);
        lsum += exp_psrc0;
        pdst[i00] = exp_psrc0;
    }

    // This barrier fixes a failing test
    // ref: https://github.com/ggml-org/ggml/pull/621#discussion_r1425156335
    threadgroup_barrier(mem_flags::mem_none);

    float sum = simd_sum(lsum);

    if (tptg.x > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = 0.0f;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = sum;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        sum = buf[tiisg];
        sum = simd_sum(sum);
    }

    if (psrc2) {
        sum += exp(psrc2[i02] - max_val);
    }

    const float inv_sum = 1.0f/sum;

    for (int i00 = tpitg.x; i00 < args.ne00; i00 += tptg.x) {
        pdst[i00] *= inv_sum;
    }
}

template<typename T>
kernel void kernel_soft_max_4(
        constant ggml_metal_kargs_soft_max & args,
        device const  char * src0,
        device const  char * src1,
        device const  char * src2,
        device        char * dst,
        threadgroup  float * buf [[threadgroup(0)]],
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint  sgitg[[simdgroup_index_in_threadgroup]],
        uint  tiisg[[thread_index_in_simdgroup]],
        uint3  tptg[[threads_per_threadgroup]]) {
    const int32_t i03 = tgpig.z;
    const int32_t i02 = tgpig.y;
    const int32_t i01 = tgpig.x;

    const int32_t i13 = i03%args.ne13;
    const int32_t i12 = i02%args.ne12;
    const int32_t i11 = i01;

    device const float4 * psrc4 =                (device const float4 *) (src0 + i01*args.nb01 + i02*args.nb02 + i03*args.nb03);
    device const      T * pmask = src1 != src0 ? (device const T *     ) (src1 + i11*args.nb11 + i12*args.nb12 + i13*args.nb13) : nullptr;
    device const float *  psrc2 = src2 != src0 ? (device const float * ) (src2)                                                 : nullptr;
    device       float4 * pdst4 =                (device       float4 *) (dst  + i01*args.nb1  + i02*args.nb2  + i03*args.nb3);

    float slope = 1.0f;

    if (args.max_bias > 0.0f) {
        const int32_t h = i02;

        const float base = h < args.n_head_log2 ? args.m0 : args.m1;
        const int   exp  = h < args.n_head_log2 ? h + 1 : 2*(h - args.n_head_log2) + 1;

        slope = pow(base, exp);
    }

    // parallel max
    float4 lmax4 = psrc2 ? psrc2[i02] : -INFINITY;

    for (int i00 = tpitg.x; i00 < args.ne00/4; i00 += tptg.x) {
        lmax4 = fmax(lmax4, psrc4[i00]*args.scale + (float4)((pmask ? slope*pmask[i00] : 0.0f)));
    }

    const float lmax = MAX(MAX(lmax4[0], lmax4[1]), MAX(lmax4[2], lmax4[3]));

    float max_val = simd_max(lmax);
    if (tptg.x > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = -INFINITY;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = max_val;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        max_val = buf[tiisg];
        max_val = simd_max(max_val);
    }

    // parallel sum
    float4 lsum4 = 0.0f;
    for (int i00 = tpitg.x; i00 < args.ne00/4; i00 += tptg.x) {
        const float4 exp_psrc4 = exp((psrc4[i00]*args.scale + (float4)((pmask ? slope*pmask[i00] : 0.0f))) - max_val);
        lsum4 += exp_psrc4;
        pdst4[i00] = exp_psrc4;
    }

    const float lsum = lsum4[0] + lsum4[1] + lsum4[2] + lsum4[3];

    // This barrier fixes a failing test
    // ref: https://github.com/ggml-org/ggml/pull/621#discussion_r1425156335
    threadgroup_barrier(mem_flags::mem_none);

    float sum = simd_sum(lsum);

    if (tptg.x > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = 0.0f;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = sum;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        sum = buf[tiisg];
        sum = simd_sum(sum);
    }

    if (psrc2) {
        sum += exp(psrc2[i02] - max_val);
    }

    const float inv_sum = 1.0f/sum;

    for (int i00 = tpitg.x; i00 < args.ne00/4; i00 += tptg.x) {
        pdst4[i00] *= inv_sum;
    }
}

typedef decltype(kernel_soft_max<float>)    kernel_soft_max_t;
typedef decltype(kernel_soft_max_4<float4>) kernel_soft_max_4_t;

template [[host_name("kernel_soft_max_f16")]]   kernel kernel_soft_max_t   kernel_soft_max<half>;
template [[host_name("kernel_soft_max_f32")]]   kernel kernel_soft_max_t   kernel_soft_max<float>;
template [[host_name("kernel_soft_max_f16_4")]] kernel kernel_soft_max_4_t kernel_soft_max_4<half4>;
template [[host_name("kernel_soft_max_f32_4")]] kernel kernel_soft_max_4_t kernel_soft_max_4<float4>;

// ref: ggml.c:ggml_compute_forward_ssm_conv_f32
kernel void kernel_ssm_conv_f32_f32(
        constant ggml_metal_kargs_ssm_conv & args,
        device const  void * src0,
        device const  void * src1,
        device       float * dst,
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint3   ntg[[threads_per_threadgroup]]) {
    const int64_t ir = tgpig.x;
    const int64_t i2 = tgpig.y;
    const int64_t i3 = tgpig.z;

    const int64_t nc  = args.ne10;
  //const int64_t ncs = args.ne00;
  //const int64_t nr  = args.ne01;
  //const int64_t n_t = args.ne1;
  //const int64_t n_s = args.ne2;

    device const float * s = (device const float *) ((device const char *) src0 + ir*args.nb01 + i2*args.nb00 + i3*args.nb02);
    device const float * c = (device const float *) ((device const char *) src1 + ir*args.nb11);
    device       float * x = (device       float *) ((device       char *) dst  + ir*args.nb0  + i2*args.nb1  + i3*args.nb2);

    float sumf = 0.0f;

    for (int64_t i0 = 0; i0 < nc; ++i0) {
        sumf += s[i0] * c[i0];
    }

    x[0] = sumf;
}

kernel void kernel_ssm_conv_f32_f32_4(
        constant ggml_metal_kargs_ssm_conv & args,
        device const  void * src0,
        device const  void * src1,
        device       float * dst,
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint3   ntg[[threads_per_threadgroup]]) {
    const int64_t ir = tgpig.x;
    const int64_t i2 = tgpig.y;
    const int64_t i3 = tgpig.z;

    const int64_t nc  = args.ne10;
  //const int64_t ncs = args.ne00;
  //const int64_t nr  = args.ne01;
  //const int64_t n_t = args.ne1;
  //const int64_t n_s = args.ne2;

    device const float4 * s = (device const float4 *) ((device const char *) src0 + ir*args.nb01 + i2*args.nb00 + i3*args.nb02);
    device const float4 * c = (device const float4 *) ((device const char *) src1 + ir*args.nb11);
    device       float  * x = (device       float  *) ((device       char *) dst  + ir*args.nb0  + i2*args.nb1  + i3*args.nb2);

    float sumf = 0.0f;

    for (int64_t i0 = 0; i0 < nc/4; ++i0) {
        sumf += dot(s[i0], c[i0]);
    }

    x[0] = sumf;
}

// ref: ggml.c:ggml_compute_forward_ssm_scan_f32, Mamba-2 part
kernel void kernel_ssm_scan_f32(
        constant ggml_metal_kargs_ssm_scan & args,
        device const void * src0,
        device const void * src1,
        device const void * src2,
        device const void * src3,
        device const void * src4,
        device const void * src5,
        device const void * src6,
        device      float * dst,
        threadgroup float * shared [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgptg[[simdgroups_per_threadgroup]],
        uint3    tgpg[[threadgroups_per_grid]]) {
    constexpr short NW = N_SIMDWIDTH;

    shared[tpitg.x] = 0.0f;

    const int32_t i0 = tpitg.x;
    const int32_t i1 = tgpig.x;
    const int32_t ir = tgpig.y; // current head
    const int32_t i3 = tgpig.z; // current seq

    const int32_t nc  = args.d_state;
    const int32_t nr  = args.d_inner;
    const int32_t nh  = args.n_head;
    const int32_t ng  = args.n_group;
    const int32_t n_t = args.n_seq_tokens;

    const int32_t s_off = args.s_off;

    device const int32_t * ids = (device const int32_t *) src6;

    device const float * s0_buff = (device const float *) ((device const char *) src0 + ir*args.nb02 + ids[i3]*args.nb03);
    device       float * s_buff  = (device       float *) ((device       char *) dst  + ir*args.nb02 +      i3*args.nb03 + s_off);

    const int32_t i = i0 + i1*nc;
    const int32_t g = ir / (nh / ng); // repeat_interleave

    float s0 = s0_buff[i];
    float s  = 0.0f;

    device const float * A = (device const float *) ((device const char *) src3 + ir*args.nb31); // {ne30, nh}

    const float A0 = A[i0%args.ne30];

    device const float * x  = (device const float *)((device const char *) src1 + i1*args.nb10  + ir*args.nb11 + i3*args.nb13); // {dim, nh, nt, ns}
    device const float * dt = (device const float *)((device const char *) src2 + ir*args.nb20  + i3*args.nb22);                // {nh, nt, ns}
    device const float * B  = (device const float *)((device const char *) src4 +  g*args.nb41  + i3*args.nb43);                // {d_state, ng, nt, ns}
    device const float * C  = (device const float *)((device const char *) src5 +  g*args.nb51  + i3*args.nb53);                // {d_state, ng, nt, ns}

    device float * y = dst + (i1 + ir*(nr) + i3*(n_t*nh*nr)); // {dim, nh, nt, ns}

    for (int i2 = 0; i2 < n_t; i2 += sgptg) {
        threadgroup_barrier(mem_flags::mem_threadgroup);

        for (int t = 0; t < sgptg && i2 + t < n_t; t++) {
            const float dt0  = dt[0];
            const float dtsp = dt0 <= 20.0f ? log(1.0f + exp(dt0)) : dt0;
            const float x_dt = x[0] * dtsp;
            const float dA   = exp(dtsp * A0);

            s = (s0 * dA) + (B[i0] * x_dt);

            const float sumf = simd_sum(s * C[i0]);

            if (tiisg == 0) {
                shared[t*NW + sgitg] = sumf;
            }

            // recurse
            s0 = s;

            x  += args.ns12;
            dt += args.ns21;
            B  += args.ns42;
            C  += args.ns52;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        const float sumf = simd_sum(shared[sgitg*NW + tiisg]);

        if (tiisg == 0 && i2 + sgitg < n_t) {
            y[sgitg*nh*nr] = sumf;
        }

        y += sgptg*nh*nr;
    }

    s_buff[i] = s;
}

kernel void kernel_rwkv_wkv6_f32(
    device const float * k,
    device const float * v,
    device const float * r,
    device const float * tf,
    device const float * td,
    device const float * state_in,
    device       float * dst,
    constant    uint & B,
    constant    uint & T,
    constant    uint & C,
    constant    uint & H,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]])  {

    const uint head_size = 64; // TODO: support head_size = 128
    const uint batch_id = tgpig.x / H;
    const uint head_id = tgpig.x % H;
    const uint tid = tpitg.x;

    if (batch_id >= B || head_id >= H) {
        return;
    }

    const uint state_size = C * head_size;
    const uint n_seq_tokens = T / B;

    threadgroup float _k[head_size];
    threadgroup float _r[head_size];
    threadgroup float _tf[head_size];
    threadgroup float _td[head_size];

    float state[head_size];

    for (uint i = 0; i < head_size; i++) {
        state[i] = state_in[batch_id * state_size + head_id * head_size * head_size
                          + i * head_size + tid];
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);
    _tf[tid] = tf[head_id * head_size + tid];
    threadgroup_barrier(mem_flags::mem_threadgroup);

    const uint start_t = batch_id * n_seq_tokens * C + head_id * head_size + tid;
    const uint end_t = (batch_id + 1) * n_seq_tokens * C + head_id * head_size + tid;

    for (uint t = start_t; t < end_t; t += C) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        _k[tid] = k[t];
        _r[tid] = r[t];
        _td[tid] = td[t];
        threadgroup_barrier(mem_flags::mem_threadgroup);

        const float v_val = v[t];
        float y = 0.0;

        for (uint j = 0; j < head_size; j += 4) {
            float4 k_vec = float4(_k[j], _k[j+1], _k[j+2], _k[j+3]);
            float4 r_vec = float4(_r[j], _r[j+1], _r[j+2], _r[j+3]);
            float4 tf_vec = float4(_tf[j], _tf[j+1], _tf[j+2], _tf[j+3]);
            float4 td_vec = float4(_td[j], _td[j+1], _td[j+2], _td[j+3]);
            float4 s_vec = float4(state[j], state[j+1], state[j+2], state[j+3]);

            float4 kv = k_vec * v_val;

            float4 temp = tf_vec * kv + s_vec;
            y += dot(r_vec, temp);

            s_vec = s_vec * td_vec + kv;
            state[j]   = s_vec[0];
            state[j+1] = s_vec[1];
            state[j+2] = s_vec[2];
            state[j+3] = s_vec[3];
        }

        dst[t] = y;
    }

    for (uint i = 0; i < head_size; i++) {
        dst[T * C + batch_id * state_size + head_id * head_size * head_size
            + i * head_size + tid] = state[i];
    }
}

kernel void kernel_rwkv_wkv7_f32(
    device const float * r,
    device const float * w,
    device const float * k,
    device const float * v,
    device const float * a,
    device const float * b,
    device const float * state_in,
    device       float * dst,
    constant    uint & B,
    constant    uint & T,
    constant    uint & C,
    constant    uint & H,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]])  {

    const uint head_size = 64; // TODO: support head_size = 128
    const uint batch_id = tgpig.x / H;
    const uint head_id = tgpig.x % H;
    const uint tid = tpitg.x;

    if (batch_id >= B || head_id >= H) {
        return;
    }

    const uint state_size = C * head_size;
    const uint n_seq_tokens = T / B;

    threadgroup float _r[head_size];
    threadgroup float _w[head_size];
    threadgroup float _k[head_size];
    threadgroup float _a[head_size];
    threadgroup float _b[head_size];

    float state[head_size];

    for (uint i = 0; i < head_size; i++) {
        state[i] = state_in[batch_id * state_size + head_id * head_size * head_size
                          + tid * head_size + i];
    }

    const uint start_t = batch_id * n_seq_tokens * C + head_id * head_size + tid;
    const uint end_t = (batch_id + 1) * n_seq_tokens * C + head_id * head_size + tid;

    for (uint t = start_t; t < end_t; t += C) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        _r[tid] = r[t];
        _w[tid] = w[t];
        _k[tid] = k[t];
        _a[tid] = a[t];
        _b[tid] = b[t];
        threadgroup_barrier(mem_flags::mem_threadgroup);

        const float v_val = v[t];
        float y = 0.0, sa = 0.0;

        float4 sa_vec(0.0);

        for (uint j = 0; j < head_size; j += 4) {
            float4 a_vec = float4(_a[j], _a[j+1], _a[j+2], _a[j+3]);
            float4 s_vec = float4(state[j], state[j+1], state[j+2], state[j+3]);
            sa_vec += a_vec * s_vec;
        }
        sa = sa_vec[0] + sa_vec[1] + sa_vec[2] + sa_vec[3];

        for (uint j = 0; j < head_size; j += 4) {
            float4 r_vec = float4(_r[j], _r[j+1], _r[j+2], _r[j+3]);
            float4 w_vec = float4(_w[j], _w[j+1], _w[j+2], _w[j+3]);
            float4 k_vec = float4(_k[j], _k[j+1], _k[j+2], _k[j+3]);
            float4 b_vec = float4(_b[j], _b[j+1], _b[j+2], _b[j+3]);
            float4 s_vec = float4(state[j], state[j+1], state[j+2], state[j+3]);

            float4 kv = k_vec * v_val;

            s_vec = s_vec * w_vec + kv + sa * b_vec;
            y += dot(s_vec, r_vec);

            state[j]   = s_vec[0];
            state[j+1] = s_vec[1];
            state[j+2] = s_vec[2];
            state[j+3] = s_vec[3];
        }

        dst[t] = y;
    }

    for (uint i = 0; i < head_size; i++) {
        dst[T * C + batch_id * state_size + head_id * head_size * head_size
            + tid * head_size + i] = state[i];
    }
}

kernel void kernel_argmax_f32(
        constant ggml_metal_kargs_argmax & args,
        device   const char * src0,
        device         char * dst,
        threadgroup    char * shmem [[threadgroup(0)]],
        uint  tgpig[[threadgroup_position_in_grid]],
        uint  tpitg[[thread_position_in_threadgroup]],
        uint  sgitg[[simdgroup_index_in_threadgroup]],
        uint  tiisg[[thread_index_in_simdgroup]],
        uint    ntg[[threads_per_threadgroup]]) {
    device const float * x_row = (device const float *) ((device const char *) src0 + tgpig * args.nb01);

    float   lmax = -INFINITY;
    int32_t larg = -1;

    for (int i00 = tpitg; i00 < args.ne00; i00 += ntg) {
        if (x_row[i00] > lmax) {
            lmax = x_row[i00];
            larg = i00;
        }
    }

    // find the argmax value in the block
    float max_val = simd_max(lmax);
    int32_t arg_val = simd_max(select(-1, larg, lmax == max_val));

    device int32_t * dst_i32 = (device int32_t *) dst;

    threadgroup   float * shared_maxval = (threadgroup   float *) shmem;
    threadgroup int32_t * shared_argmax = (threadgroup int32_t *) shmem + N_SIMDWIDTH;

    if (ntg > N_SIMDWIDTH) {
        if (sgitg == 0) {
            shared_maxval[tiisg] = -INFINITY;
            shared_argmax[tiisg] = -1;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            shared_maxval[sgitg] = max_val;
            shared_argmax[sgitg] = arg_val;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        max_val = shared_maxval[tiisg];
        arg_val = shared_argmax[tiisg];

        float max_val_reduced   = simd_max(max_val);
        int32_t arg_val_reduced = simd_max(select(-1, arg_val, max_val == max_val_reduced));

        dst_i32[tgpig] = arg_val_reduced;

        return;
    }

    dst_i32[tgpig] = arg_val;
}

// F == 1 : norm (no fuse)
// F == 2 : norm + mul
// F == 3 : norm + mul + add
template <typename T, short F>
kernel void kernel_norm_fuse_impl(
        constant ggml_metal_kargs_norm & args,
        device const char * src0,
        device const char * src1_0,
        device const char * src1_1,
        device       char * dst,
        threadgroup float * shmem_f32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    if (sgitg == 0) {
        shmem_f32[tiisg] = 0.0f;
    }

    const int i01 = tgpig.x;
    const int i02 = tgpig.y;
    const int i03 = tgpig.z;

    device const T * x = (device const T *) (src0 + i03*args.nbf3[0] + i02*args.nbf2[0] + i01*args.nbf1[0]);

    device const T * f0 = (device const T *) (src1_0 + (i03%args.nef3[1])*args.nbf3[1] + (i02%args.nef2[1])*args.nbf2[1] + (i01%args.nef1[1])*args.nbf1[1]);
    device const T * f1 = (device const T *) (src1_1 + (i03%args.nef3[2])*args.nbf3[2] + (i02%args.nef2[2])*args.nbf2[2] + (i01%args.nef1[2])*args.nbf1[2]);

    T sumft(0.0f);

    float sumf = 0.0f;

    for (int i00 = tpitg.x; i00 < args.ne00_t; i00 += ntg.x) {
        sumft += x[i00];
    }
    sumf = dot(sumft, T(1.0f));
    sumf = simd_sum(sumf);

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    sumf = shmem_f32[tiisg];
    sumf = simd_sum(sumf);

    const float mean = sumf/args.ne00;

    device T * y = (device T *) (dst + i03*args.nb3 + i02*args.nb2 + i01*args.nb1);

    sumf = 0.0f;
    for (int i00 = tpitg.x; i00 < args.ne00_t; i00 += ntg.x) {
        y[i00] = x[i00] - mean;
        sumf += dot(y[i00], y[i00]);
    }
    sumf = simd_sum(sumf);

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    sumf = shmem_f32[tiisg];
    sumf = simd_sum(sumf);

    const float variance = sumf/args.ne00;

    const float scale = 1.0f/sqrt(variance + args.eps);
    for (int i00 = tpitg.x; i00 < args.ne00_t; i00 += ntg.x) {
        if (F == 1) {
            y[i00] = (y[i00]*scale);
        }
        if (F == 2) {
            y[i00] = (y[i00]*scale)*f0[i00];
        }
        if (F == 3) {
            y[i00] = (y[i00]*scale)*f0[i00] + f1[i00];
        }
    }
}

typedef decltype(kernel_norm_fuse_impl<float4, 1>) kernel_norm_fuse_t;

template [[host_name("kernel_norm_f32")]]         kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float, 1>;
template [[host_name("kernel_norm_mul_f32")]]     kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float, 2>;
template [[host_name("kernel_norm_mul_add_f32")]] kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float, 3>;

template [[host_name("kernel_norm_f32_4")]]         kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float4, 1>;
template [[host_name("kernel_norm_mul_f32_4")]]     kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float4, 2>;
template [[host_name("kernel_norm_mul_add_f32_4")]] kernel kernel_norm_fuse_t kernel_norm_fuse_impl<float4, 3>;

// F == 1 : rms_norm (no fuse)
// F == 2 : rms_norm + mul
// F == 3 : rms_norm + mul + add
template <typename T, short F>
kernel void kernel_rms_norm_fuse_impl(
        constant ggml_metal_kargs_norm & args,
        device const char * src0,
        device const char * src1_0,
        device const char * src1_1,
        device       char * dst,
        threadgroup float * shmem_f32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    if (sgitg == 0) {
        shmem_f32[tiisg] = 0.0f;
    }

    const int i01 = tgpig.x;
    const int i02 = tgpig.y;
    const int i03 = tgpig.z;

    device const T * x = (device const T *) (src0 + i03*args.nbf3[0] + i02*args.nbf2[0] + i01*args.nbf1[0]);

    device const T * f0 = (device const T *) (src1_0 + (i03%args.nef3[1])*args.nbf3[1] + (i02%args.nef2[1])*args.nbf2[1] + (i01%args.nef1[1])*args.nbf1[1]);
    device const T * f1 = (device const T *) (src1_1 + (i03%args.nef3[2])*args.nbf3[2] + (i02%args.nef2[2])*args.nbf2[2] + (i01%args.nef1[2])*args.nbf1[2]);

    float sumf = 0.0f;

    // parallel sum
    for (int i00 = tpitg.x; i00 < args.ne00_t; i00 += ntg.x) {
        sumf += dot(x[i00], x[i00]);
    }
    sumf = simd_sum(sumf);

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    sumf = shmem_f32[tiisg];
    sumf = simd_sum(sumf);

    const float mean  = sumf/args.ne00;
    const float scale = 1.0f/sqrt(mean + args.eps);

    device T * y = (device T *) (dst + i03*args.nb3 + i02*args.nb2 + i01*args.nb1);
    for (int i00 = tpitg.x; i00 < args.ne00_t; i00 += ntg.x) {
        if (F == 1) {
            y[i00] = (x[i00]*scale);
        }
        if (F == 2) {
            y[i00] = (x[i00]*scale)*f0[i00];
        }
        if (F == 3) {
            y[i00] = (x[i00]*scale)*f0[i00] + f1[i00];
        }
    }
}

typedef decltype(kernel_rms_norm_fuse_impl<float4, 1>) kernel_rms_norm_fuse_t;

template [[host_name("kernel_rms_norm_f32")]]         kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float, 1>;
template [[host_name("kernel_rms_norm_mul_f32")]]     kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float, 2>;
template [[host_name("kernel_rms_norm_mul_add_f32")]] kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float, 3>;

template [[host_name("kernel_rms_norm_f32_4")]]         kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float4, 1>;
template [[host_name("kernel_rms_norm_mul_f32_4")]]     kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float4, 2>;
template [[host_name("kernel_rms_norm_mul_add_f32_4")]] kernel kernel_rms_norm_fuse_t kernel_rms_norm_fuse_impl<float4, 3>;

kernel void kernel_l2_norm_f32(
        constant ggml_metal_kargs_l2_norm & args,
        device const char * src0,
        device       char * dst,
        threadgroup float * shmem_f32 [[threadgroup(0)]],
        uint   tgpig[[threadgroup_position_in_grid]],
        ushort tpitg[[thread_position_in_threadgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort   ntg[[threads_per_threadgroup]]) {
    if (sgitg == 0) {
        shmem_f32[tiisg] = 0.0f;
    }

    device const float4 * x = (device const float4 *) (src0 + tgpig*args.nb01);

    float sumf = 0.0f;

    // parallel sum
    for (int i00 = tpitg; i00 < args.ne00_4; i00 += ntg) {
        sumf += dot(x[i00], x[i00]);
    }
    sumf = simd_sum(sumf);

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tiisg == 0) {
        shmem_f32[sgitg] = sumf;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    sumf = shmem_f32[tiisg];
    sumf = simd_sum(sumf);

    const float scale = 1.0f/sqrt(max(sumf, args.eps));

    device float4 * y = (device float4 *) dst + tgpig*args.ne00_4;
    for (int i00 = tpitg; i00 < args.ne00_4; i00 += ntg) {
        y[i00] = x[i00] * scale;
    }
}

kernel void kernel_group_norm_f32(
        constant ggml_metal_kargs_group_norm & args,
        device const float * src0,
        device       float * dst,
        threadgroup float  * buf [[threadgroup(0)]],
        uint tgpig[[threadgroup_position_in_grid]],
        uint tpitg[[thread_position_in_threadgroup]],
        uint sgitg[[simdgroup_index_in_threadgroup]],
        uint tiisg[[thread_index_in_simdgroup]],
        uint   ntg[[threads_per_threadgroup]]) {
    const int64_t ne = args.ne00*args.ne01*args.ne02;
    const int64_t gs = args.ne00*args.ne01*((args.ne02 + args.ngrp - 1) / args.ngrp);

    int start = tgpig * gs;
    int end   = start + gs;

    start += tpitg;

    if (end >= ne) {
        end = ne;
    }

    float tmp = 0.0f; // partial sum for thread in warp

    for (int j = start; j < end; j += ntg) {
        tmp += src0[j];
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);
    tmp = simd_sum(tmp);
    if (ntg > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = 0.0f;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = tmp;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        tmp = buf[tiisg];
        tmp = simd_sum(tmp);
    }

    const float mean = tmp / gs;
    tmp = 0.0f;

    for (int j = start; j < end; j += ntg) {
        float xi = src0[j] - mean;
        dst[j] = xi;
        tmp += xi * xi;
    }

    tmp = simd_sum(tmp);
    if (ntg > N_SIMDWIDTH) {
        if (sgitg == 0) {
            buf[tiisg] = 0.0f;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (tiisg == 0) {
            buf[sgitg] = tmp;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        tmp = buf[tiisg];
        tmp = simd_sum(tmp);
    }

    const float variance = tmp / gs;
    const float scale = 1.0f/sqrt(variance + args.eps);
    for (int j = start; j < end; j += ntg) {
        dst[j] *= scale;
    }
}

// function for calculate inner product between half a q4_0 block and 16 floats (yl), sumy is SUM(yl[i])
// il indicates where the q4 quants begin (0 or QK4_0/4)
// we assume that the yl's have been multiplied with the appropriate scale factor
// that corresponds to the missing bit shifts (1, 1/16, 1/256, 1/4096)
inline float block_q_n_dot_y(device const block_q4_0 * qb_curr, float sumy, thread float * yl, int il) {
    float d = qb_curr->d;

    float acc[4] = { 0.0f, 0.0f, 0.0f, 0.0f };

    device const uint16_t * qs = ((device const uint16_t *) qb_curr + 1 + il/2);

    for (int i = 0; i < 8; i += 2) {
        acc[0] += yl[i + 0] * (qs[i / 2] & 0x000F);
        acc[1] += yl[i + 1] * (qs[i / 2] & 0x0F00);
        acc[2] += yl[i + 8] * (qs[i / 2] & 0x00F0);
        acc[3] += yl[i + 9] * (qs[i / 2] & 0xF000);
    }

    return d * (sumy * -8.f + acc[0] + acc[1] + acc[2] + acc[3]);
}

// function for calculate inner product between half a q4_1 block and 16 floats (yl), sumy is SUM(yl[i])
// il indicates where the q4 quants begin (0 or QK4_0/4)
// we assume that the yl's have been multiplied with the appropriate scale factor
// that corresponds to the missing bit shifts (1, 1/16, 1/256, 1/4096)
inline float block_q_n_dot_y(device const block_q4_1 * qb_curr, float sumy, thread float * yl, int il) {
    float d = qb_curr->d;
    float m = qb_curr->m;

    float acc[4] = { 0.0f, 0.0f, 0.0f, 0.0f };

    device const uint16_t * qs = ((device const uint16_t *) qb_curr + 2 + il/2);

    for (int i = 0; i < 8; i+=2) {
        acc[0] += yl[i + 0] * (qs[i / 2] & 0x000F);
        acc[1] += yl[i + 1] * (qs[i / 2] & 0x0F00);
        acc[2] += yl[i + 8] * (qs[i / 2] & 0x00F0);
        acc[3] += yl[i + 9] * (qs[i / 2] & 0xF000);
    }

    return d * (acc[0] + acc[1] + acc[2] + acc[3]) + sumy * m;
}

// function for calculate inner product between half a q5_0 block and 16 floats (yl), sumy is SUM(yl[i])
// il indicates where the q5 quants begin (0 or QK5_0/4)
// we assume that the yl's have been multiplied with the appropriate scale factor
// that corresponds to the missing bit shifts (1, 1/16, 1/256, 1/4096)
inline float block_q_n_dot_y(device const block_q5_0 * qb_curr, float sumy, thread float * yl, int il) {
    float d = qb_curr->d;

    float acc[4] = { 0.0f, 0.0f, 0.0f, 0.0f };

    device const uint16_t * qs =  ((device const uint16_t *)qb_curr + 3 + il/2);
           const uint32_t   qh = *((device const uint32_t *)qb_curr->qh);

    for (int i = 0; i < 8; i+=2) {
        acc[0] += yl[i + 0] * ((qs[i / 2] & 0x000F) | ((qh >> (i+0+il        ) << 4 ) & 0x00010));
        acc[1] += yl[i + 1] * ((qs[i / 2] & 0x0F00) | ((qh >> (i+1+il        ) << 12) & 0x01000));
        acc[2] += yl[i + 8] * ((qs[i / 2] & 0x00F0) | ((qh >> (i+0+il+QK5_0/2) << 8 ) & 0x00100));
        acc[3] += yl[i + 9] * ((qs[i / 2] & 0xF000) | ((qh >> (i+1+il+QK5_0/2) << 16) & 0x10000));
    }

    return d * (sumy * -16.f + acc[0] + acc[1] + acc[2] + acc[3]);
}

// function for calculate inner product between half a q5_1 block and 16 floats (yl), sumy is SUM(yl[i])
// il indicates where the q5 quants begin (0 or QK5_1/4)
// we assume that the yl's have been multiplied with the appropriate scale factor
// that corresponds to the missing bit shifts (1, 1/16, 1/256, 1/4096)
inline float block_q_n_dot_y(device const block_q5_1 * qb_curr, float sumy, thread float * yl, int il) {
    float d = qb_curr->d;
    float m = qb_curr->m;

    float acc[4] = { 0.0f, 0.0f, 0.0f, 0.0f };

    device const uint16_t * qs =  ((device const uint16_t *)qb_curr + 4 + il/2);
           const uint32_t   qh = *((device const uint32_t *)qb_curr->qh);

    for (int i = 0; i < 8; i+=2) {
        acc[0] += yl[i + 0] * ((qs[i / 2] & 0x000F) | ((qh >> (i+0+il        ) << 4 ) & 0x00010));
        acc[1] += yl[i + 1] * ((qs[i / 2] & 0x0F00) | ((qh >> (i+1+il        ) << 12) & 0x01000));
        acc[2] += yl[i + 8] * ((qs[i / 2] & 0x00F0) | ((qh >> (i+0+il+QK5_0/2) << 8 ) & 0x00100));
        acc[3] += yl[i + 9] * ((qs[i / 2] & 0xF000) | ((qh >> (i+1+il+QK5_0/2) << 16) & 0x10000));
    }

    return d * (acc[0] + acc[1] + acc[2] + acc[3]) + sumy * m;
}

template<short NR0>
static inline void helper_mv_reduce_and_write(
        device float * dst_f32,
        float sumf[NR0],
        const int r0,
        const int ne01,
        ushort tiisg,
        ushort sgitg,
        threadgroup char * shmem) {
    constexpr short NW = N_SIMDWIDTH;

    threadgroup float * shmem_f32[NR0];

    for (short row = 0; row < NR0; ++row) {
        shmem_f32[row] = (threadgroup float *) shmem + NW*row;

        if (sgitg == 0) {
            shmem_f32[row][tiisg] = 0.0f;
        }

        sumf[row] = simd_sum(sumf[row]);
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0; ++row) {
        if (tiisg == 0) {
            shmem_f32[row][sgitg] = sumf[row];
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short row = 0; row < NR0 && r0 + row < ne01; ++row) {
        float tot = simd_sum(shmem_f32[row][tiisg]);

        if (tiisg == 0 && sgitg == 0) {
            dst_f32[r0 + row] = tot;
        }
    }
}

constant short FC_mul_mv_nsg   [[function_constant(FC_MUL_MV + 0)]];
constant short FC_mul_mv_nxpsg [[function_constant(FC_MUL_MV + 1)]];

template<typename block_q_type, short NR0, typename args_t>
void mul_vec_q_n_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 16;

    const int nb = args.ne00/QK4_0;

    const int r0 = (tgpig.x*NSG + sgitg)*NR0;
  //const int r0 =  tgpig.x*NR0;
    const int r1 =  tgpig.y;
    const int im =  tgpig.z;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

  //const uint64_t offset0 = r0*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

  //device const block_q_type * x = (device const block_q_type *) (src0 + offset0);
    device const float        * y = (device const float        *) (src1 + offset1);

    // pointers to src0 rows
    device const block_q_type * ax[NR0];
    FOR_UNROLL (int row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q_type *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = {0.f};

    const short ix = (tiisg/(NW/NQ));
    const short il = (tiisg%(NW/NQ))*8;

    //const int ib0 = sgitg*NQ + ix;
    const int ib0 = ix;

    float yl[16]; // src1 vector cache

    //device const float * yb = y + ix*QK4_0 + il;
    device const float * yb = y + ib0*QK4_0 + il;

    // each thread in a SIMD group deals with half a block.
    //for (int ib = ib0; ib < nb; ib += NSG*NQ) {
    for (int ib = ib0; ib < nb; ib += NQ) {
        float sumy[2] = { 0.f, 0.f };

        FOR_UNROLL (short i = 0; i < 8; i += 2) {
            sumy[0]  += yb[i +  0] + yb[i +  1];
            yl[i + 0] = yb[i +  0];
            yl[i + 1] = yb[i +  1]/256.f;

            sumy[1]  += yb[i + 16] + yb[i + 17];
            yl[i + 8] = yb[i + 16]/16.f;
            yl[i + 9] = yb[i + 17]/4096.f;
        }

        FOR_UNROLL (short row = 0; row < NR0; row++) {
            sumf[row] += block_q_n_dot_y(ax[row] + ib, sumy[0] + sumy[1], yl, il);
        }

        yb += QK4_0 * 16;
        //yb += NSG*NQ*QK4_0;
    }

    device float * dst_f32 = (device float *) dst + im*args.ne0*args.ne1 + r1*args.ne0;

    //helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);

    for (int row = 0; row < NR0; ++row) {
        const float tot = simd_sum(sumf[row]);

        if (tiisg == 0 && r0 + row < args.ne01) {
            dst_f32[r0 + row] = tot;
        }
    }
}

kernel void kernel_mul_mv_q4_0_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    mul_vec_q_n_f32_impl<block_q4_0, N_R0_Q4_0, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

kernel void kernel_mul_mv_q4_1_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
     mul_vec_q_n_f32_impl<block_q4_1, N_R0_Q4_1, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

kernel void kernel_mul_mv_q5_0_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    mul_vec_q_n_f32_impl<block_q5_0, N_R0_Q5_0, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

kernel void kernel_mul_mv_q5_1_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    mul_vec_q_n_f32_impl<block_q5_1, N_R0_Q5_1, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<short NR0, typename args_t>
void kernel_mul_mv_q8_0_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NQ = 8;

    const int nb = args.ne00/QK8_0;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

  //const uint64_t offset0 = r0*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

  //device const block_q8_0 * x = (device const block_q8_0 *) (src0 + offset0);
    device const float      * y = (device const float      *) (src1 + offset1);

    // pointers to src0 rows
    device const block_q8_0 * ax[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const block_q8_0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NQ);
    const short il = tiisg%(NW/NQ);

    const int ib0 = sgitg*NQ + ix;

    float yl[NQ];

    device const float * yb = y + ib0*QK8_0 + il*NQ;

    // each thread in a SIMD group deals with NQ quants at a time
    for (int ib = ib0; ib < nb; ib += NSG*NQ) {
        for (short i = 0; i < NQ; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const int8_t * qs = ax[row][ib].qs + il*NQ;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NQ; ++i) {
                sumq += qs[i] * yl[i];
            }

            sumf[row] += sumq*ax[row][ib].d;
        }

        yb += NSG*NQ*QK8_0;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

[[host_name("kernel_mul_mv_q8_0_f32")]]
kernel void kernel_mul_mv_q8_0_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

// mat-vec kernel processing in chunks of float4
// chpb - chunks per quantization block
template<short r1ptg, typename q_t, short chpb, void (*deq_t4)(device const q_t *, short, thread float4 &) >
void kernel_mul_mv_ext_q4_f32_impl(
        constant ggml_metal_kargs_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 4; // chunks per thread

  //const short nxpsg = (32);
    const short nypsg = (32/nxpsg);

    const short tx = tiisg%nxpsg;
    const short ty = tiisg/nxpsg;

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = i11*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const q_t * xq = (i01 < args.ne01) ? (device const q_t *) (src0 + offset0) + tx/chpb : (device const q_t *) src0;

    device const float4 * y4[r1ptg];

    for (int ir1 = 0; ir1 < r1ptg; ++ir1) {
        y4[ir1] = (i11 + ir1 < args.ne11) ? (device const float4 *) (src1 + offset1 + ir1*args.nb11) + tx : (device const float4 *) src1;
    }

    float sumf[r1ptg] = { [ 0 ... r1ptg - 1 ] = 0.0f };

    short cch = tx%chpb; // current chunk index

    for (int ich = tx; 4*ich < args.ne00; ich += chpt*nxpsg) {
        float4 lx[chpt];

#pragma unroll(chpt)
        for (short ch = 0; ch < chpt; ++ch) {
            deq_t4(xq, cch, lx[ch]);

            cch += nxpsg;
            if (cch >= chpb) {
                xq  += cch/chpb;
                cch %= chpb;
            }
        }

#pragma unroll(chpt)
        for (short ch = 0; ch < chpt; ++ch) {
#pragma unroll(r1ptg)
            for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
                sumf[ir1] += dot(lx[ch], y4[ir1][ch*nxpsg]);
            }
        }

#pragma unroll(r1ptg)
        for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
            y4[ir1] += chpt*nxpsg;
        }
    }

    // reduce only the threads in each row
    for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
        if (nxpsg >= 32) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1], 16);
        }
        if (nxpsg >= 16) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  8);
        }
        if (nxpsg >= 8) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  4);
        }
        if (nxpsg >= 4) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  2);
        }
        if (nxpsg >= 2) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  1);
        }

        //sumf[ir1] = simd_sum(sumf[ir1]);
    }

    if (tx == 0) {
        for (short ir1 = 0; ir1 < r1ptg && i11 + ir1 < args.ne11; ++ir1) {
            device float * dst_f32 = (device float *) dst + (uint64_t)i1m*args.ne0*args.ne1 + (uint64_t)(i11 + ir1)*args.ne0;

            if (i01 < args.ne01) {
                dst_f32[i01] = sumf[ir1];
            }
        }
    }
}

// mat-vec kernel processing in chunks of float4x4
template<short r1ptg, typename q_t, short chpb, void (*deq_t4x4)(device const q_t *, short, thread float4x4 &) >
void kernel_mul_mv_ext_q4x4_f32_impl(
        constant ggml_metal_kargs_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    const short NSG   = FC_mul_mv_nsg;
    const short nxpsg = FC_mul_mv_nxpsg;

    const short chpt = 1;

  //const short nxpsg = (32);
    const short nypsg = (32/nxpsg);

    const short tx = tiisg%nxpsg;
    const short ty = tiisg/nxpsg;

    const int i01 = tgpig.x*(nypsg*NSG) + nypsg*sgitg + ty;
    const int i11 = tgpig.y*r1ptg;
    const int i1m = tgpig.z;

    const int i12 = i1m%args.ne12;
    const int i13 = i1m/args.ne12;

    const uint64_t offset0 = i01*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = i11*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const q_t * xq = (i01 < args.ne01) ? (device const q_t *) (src0 + offset0) + tx/chpb : (device const q_t *) src0;

    device const float4x4 * y4x4[r1ptg];

    for (int ir1 = 0; ir1 < r1ptg; ++ir1) {
        y4x4[ir1] = (i11 + ir1 < args.ne11) ? (device const float4x4 *) (src1 + offset1 + ir1*args.nb11) + tx : (device const float4x4 *) src1;
    }

    float sumf[r1ptg] = { [ 0 ... r1ptg - 1 ] = 0.0f };

    short cch = tx%chpb;

    for (int ich = tx; 16*ich < args.ne00; ich += chpt*nxpsg) {
        float4x4 lx[chpt];

#pragma unroll(chpt)
        for (short ch = 0; ch < chpt; ++ch) {
            deq_t4x4(xq, cch, lx[ch]);

            cch += nxpsg;
            if (cch >= chpb) {
                xq  += cch/chpb;
                cch %= chpb;
            }
        }

#pragma unroll(chpt)
        for (short ch = 0; ch < chpt; ++ch) {
#pragma unroll(r1ptg)
            for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
                sumf[ir1] +=
                    dot(lx[ch][0], y4x4[ir1][ch*nxpsg][0]) +
                    dot(lx[ch][1], y4x4[ir1][ch*nxpsg][1]) +
                    dot(lx[ch][2], y4x4[ir1][ch*nxpsg][2]) +
                    dot(lx[ch][3], y4x4[ir1][ch*nxpsg][3]);

            }
        }

#pragma unroll(r1ptg)
        for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
            y4x4[ir1] += chpt*nxpsg;
        }
    }

    for (short ir1 = 0; ir1 < r1ptg; ++ir1) {
        if (nxpsg >= 32) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1], 16);
        }
        if (nxpsg >= 16) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  8);
        }
        if (nxpsg >= 8) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  4);
        }
        if (nxpsg >= 4) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  2);
        }
        if (nxpsg >= 2) {
            sumf[ir1] += simd_shuffle_down(sumf[ir1],  1);
        }

        //sumf[ir1] = simd_sum(sumf[ir1]);
    }

    if (tx == 0) {
        for (short ir1 = 0; ir1 < r1ptg && i11 + ir1 < args.ne11; ++ir1) {
            device float * dst_f32 = (device float *) dst + (uint64_t)i1m*args.ne0*args.ne1 + (uint64_t)(i11 + ir1)*args.ne0;

            if (i01 < args.ne01) {
                dst_f32[i01] = sumf[ir1];
            }
        }
    }
}

// dispatchers needed for compile-time nxpsg
// epb - elements per quantization block
template<short r1ptg, typename q_t, short epb, void (*deq_t4)(device const q_t *, short, thread float4 &)>
kernel void kernel_mul_mv_ext_q4_f32_disp(
        constant ggml_metal_kargs_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_ext_q4_f32_impl<r1ptg, q_t, epb/4, deq_t4>(args, src0, src1, dst, tgpig, tiisg, sgitg);
}

template<short r1ptg, typename q_t, short epb, void (*deq_t4x4)(device const q_t *, short, thread float4x4 &)>
kernel void kernel_mul_mv_ext_q4x4_f32_disp(
        constant ggml_metal_kargs_mul_mv_ext & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_ext_q4x4_f32_impl<r1ptg, q_t, epb/16, deq_t4x4>(args, src0, src1, dst, tgpig, tiisg, sgitg);
}

typedef decltype(kernel_mul_mv_ext_q4_f32_disp  <2, block_q8_0, 32,  dequantize_q8_0_t4>) mul_mv_ext_q4_f32_t;
typedef decltype(kernel_mul_mv_ext_q4x4_f32_disp<2, block_q4_K, 256, dequantize_q4_K>)    mul_mv_ext_q4x4_f32_t;

template [[host_name("kernel_mul_mv_ext_f32_f32_r1_2")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, float4,       4,  dequantize_f32_t4>;
template [[host_name("kernel_mul_mv_ext_f32_f32_r1_3")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, float4,       4,  dequantize_f32_t4>;
template [[host_name("kernel_mul_mv_ext_f32_f32_r1_4")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, float4,       4,  dequantize_f32_t4>;
template [[host_name("kernel_mul_mv_ext_f32_f32_r1_5")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, float4,       4,  dequantize_f32_t4>;

template [[host_name("kernel_mul_mv_ext_f16_f32_r1_2")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, half4,        4,  dequantize_f16_t4>;
template [[host_name("kernel_mul_mv_ext_f16_f32_r1_3")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, half4,        4,  dequantize_f16_t4>;
template [[host_name("kernel_mul_mv_ext_f16_f32_r1_4")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, half4,        4,  dequantize_f16_t4>;
template [[host_name("kernel_mul_mv_ext_f16_f32_r1_5")]]    kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, half4,        4,  dequantize_f16_t4>;

template [[host_name("kernel_mul_mv_ext_q4_0_f32_r1_2")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_q4_0,   32, dequantize_q4_0_t4>;
template [[host_name("kernel_mul_mv_ext_q4_0_f32_r1_3")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_q4_0,   32, dequantize_q4_0_t4>;
template [[host_name("kernel_mul_mv_ext_q4_0_f32_r1_4")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_q4_0,   32, dequantize_q4_0_t4>;
template [[host_name("kernel_mul_mv_ext_q4_0_f32_r1_5")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_q4_0,   32, dequantize_q4_0_t4>;

template [[host_name("kernel_mul_mv_ext_q4_1_f32_r1_2")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_q4_1,   32, dequantize_q4_1_t4>;
template [[host_name("kernel_mul_mv_ext_q4_1_f32_r1_3")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_q4_1,   32, dequantize_q4_1_t4>;
template [[host_name("kernel_mul_mv_ext_q4_1_f32_r1_4")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_q4_1,   32, dequantize_q4_1_t4>;
template [[host_name("kernel_mul_mv_ext_q4_1_f32_r1_5")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_q4_1,   32, dequantize_q4_1_t4>;

template [[host_name("kernel_mul_mv_ext_q5_0_f32_r1_2")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_q5_0,   32, dequantize_q5_0_t4>;
template [[host_name("kernel_mul_mv_ext_q5_0_f32_r1_3")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_q5_0,   32, dequantize_q5_0_t4>;
template [[host_name("kernel_mul_mv_ext_q5_0_f32_r1_4")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_q5_0,   32, dequantize_q5_0_t4>;
template [[host_name("kernel_mul_mv_ext_q5_0_f32_r1_5")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_q5_0,   32, dequantize_q5_0_t4>;

template [[host_name("kernel_mul_mv_ext_q5_1_f32_r1_2")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_q5_1,   32, dequantize_q5_1_t4>;
template [[host_name("kernel_mul_mv_ext_q5_1_f32_r1_3")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_q5_1,   32, dequantize_q5_1_t4>;
template [[host_name("kernel_mul_mv_ext_q5_1_f32_r1_4")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_q5_1,   32, dequantize_q5_1_t4>;
template [[host_name("kernel_mul_mv_ext_q5_1_f32_r1_5")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_q5_1,   32, dequantize_q5_1_t4>;

template [[host_name("kernel_mul_mv_ext_q8_0_f32_r1_2")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_q8_0,   32, dequantize_q8_0_t4>;
template [[host_name("kernel_mul_mv_ext_q8_0_f32_r1_3")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_q8_0,   32, dequantize_q8_0_t4>;
template [[host_name("kernel_mul_mv_ext_q8_0_f32_r1_4")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_q8_0,   32, dequantize_q8_0_t4>;
template [[host_name("kernel_mul_mv_ext_q8_0_f32_r1_5")]]   kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_q8_0,   32, dequantize_q8_0_t4>;

template [[host_name("kernel_mul_mv_ext_mxfp4_f32_r1_2")]]  kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_mxfp4,  32, dequantize_mxfp4_t4>;
template [[host_name("kernel_mul_mv_ext_mxfp4_f32_r1_3")]]  kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_mxfp4,  32, dequantize_mxfp4_t4>;
template [[host_name("kernel_mul_mv_ext_mxfp4_f32_r1_4")]]  kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_mxfp4,  32, dequantize_mxfp4_t4>;
template [[host_name("kernel_mul_mv_ext_mxfp4_f32_r1_5")]]  kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_mxfp4,  32, dequantize_mxfp4_t4>;

template [[host_name("kernel_mul_mv_ext_iq4_nl_f32_r1_2")]] kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<2, block_iq4_nl, 32, dequantize_iq4_nl_t4>;
template [[host_name("kernel_mul_mv_ext_iq4_nl_f32_r1_3")]] kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<3, block_iq4_nl, 32, dequantize_iq4_nl_t4>;
template [[host_name("kernel_mul_mv_ext_iq4_nl_f32_r1_4")]] kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<4, block_iq4_nl, 32, dequantize_iq4_nl_t4>;
template [[host_name("kernel_mul_mv_ext_iq4_nl_f32_r1_5")]] kernel mul_mv_ext_q4_f32_t kernel_mul_mv_ext_q4_f32_disp<5, block_iq4_nl, 32, dequantize_iq4_nl_t4>;

template [[host_name("kernel_mul_mv_ext_q4_K_f32_r1_2")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<2, block_q4_K, 256, dequantize_q4_K>;
template [[host_name("kernel_mul_mv_ext_q4_K_f32_r1_3")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<3, block_q4_K, 256, dequantize_q4_K>;
template [[host_name("kernel_mul_mv_ext_q4_K_f32_r1_4")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<4, block_q4_K, 256, dequantize_q4_K>;
template [[host_name("kernel_mul_mv_ext_q4_K_f32_r1_5")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<5, block_q4_K, 256, dequantize_q4_K>;

template [[host_name("kernel_mul_mv_ext_q5_K_f32_r1_2")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<2, block_q5_K, 256, dequantize_q5_K>;
template [[host_name("kernel_mul_mv_ext_q5_K_f32_r1_3")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<3, block_q5_K, 256, dequantize_q5_K>;
template [[host_name("kernel_mul_mv_ext_q5_K_f32_r1_4")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<4, block_q5_K, 256, dequantize_q5_K>;
template [[host_name("kernel_mul_mv_ext_q5_K_f32_r1_5")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<5, block_q5_K, 256, dequantize_q5_K>;

template [[host_name("kernel_mul_mv_ext_q6_K_f32_r1_2")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<2, block_q6_K, 256, dequantize_q6_K>;
template [[host_name("kernel_mul_mv_ext_q6_K_f32_r1_3")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<3, block_q6_K, 256, dequantize_q6_K>;
template [[host_name("kernel_mul_mv_ext_q6_K_f32_r1_4")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<4, block_q6_K, 256, dequantize_q6_K>;
template [[host_name("kernel_mul_mv_ext_q6_K_f32_r1_5")]] kernel mul_mv_ext_q4x4_f32_t kernel_mul_mv_ext_q4x4_f32_disp<5, block_q6_K, 256, dequantize_q6_K>;

template<typename T0, typename T1, short NR0, typename args_t>
void kernel_mul_mv_t_t_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NB = 32;
    constexpr short NF = 8;

    const int nb = args.ne00/NB;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

  //const uint64_t offset0 = r0*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

  //device const T0 * x = (device const T0 *) (src0 + offset0);
    device const T1 * y = (device const T1 *) (src1 + offset1);

    // pointers to src0 rows
    device const T0 * ax [NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax[row] = (device const T0 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NF);
    const short il = tiisg%(NW/NF);

    const int ib0 = sgitg*NF + ix;

    T1 yl[NF];

    device const T1 * yb = y + (ib0*NB + il*NF);

    for (int ib = ib0; ib < nb; ib += NSG*NF) {
        for (short i = 0; i < NF; ++i) {
            yl[i] = yb[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const T0 * xb = ax[row] + (ib*NB + il*NF);

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NF; ++i) {
                sumq += xb[i] * yl[i];
            }

            sumf[row] += sumq;
        }

        yb += NSG*NF*NW;
    }

    for (int i = nb*NB + sgitg*NW + tiisg; i < args.ne00; i += NW*NSG) {
        for (short row = 0; row < NR0; row++) {
            sumf[row] += ax[row][i] * y[i];
        }
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

template<typename T0, typename T1, typename args_t>
void kernel_mul_mv_t_t_disp(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    switch (args.nr0) {
      //case 1: kernel_mul_mv_t_t_impl<T0, T1, 1, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
        case 2: kernel_mul_mv_t_t_impl<T0, T1, 2, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
      //case 3: kernel_mul_mv_t_t_impl<T0, T1, 3, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
      //case 4: kernel_mul_mv_t_t_impl<T0, T1, 4, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
    }
}

template<typename T0, typename T1>
kernel void kernel_mul_mv_t_t(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_t_t_disp<T0, T1, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(kernel_mul_mv_t_t<half, half>) mul_mv_t_t;

template [[host_name("kernel_mul_mv_f32_f32")]]   kernel mul_mv_t_t kernel_mul_mv_t_t<float, float>;
template [[host_name("kernel_mul_mv_f16_f32")]]   kernel mul_mv_t_t kernel_mul_mv_t_t<half,  float>;
template [[host_name("kernel_mul_mv_f16_f16")]]   kernel mul_mv_t_t kernel_mul_mv_t_t<half,  half>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mv_bf16_f32")]]  kernel mul_mv_t_t kernel_mul_mv_t_t<bfloat, float>;
template [[host_name("kernel_mul_mv_bf16_bf16")]] kernel mul_mv_t_t kernel_mul_mv_t_t<bfloat, bfloat>;
#endif

template<typename T0, typename T04, typename T1, typename T14, short NR0, typename args_t>
void kernel_mul_mv_t_t_4_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr short NW = N_SIMDWIDTH;
    constexpr short NB  = 32;
    constexpr short NF  = 16;
    constexpr short NF4 = NF/4;

    const int nb = args.ne00/NB;

    const int r0 = tgpig.x*NR0;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

  //const uint64_t offset0 = r0*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 = r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const T1  * y  = (device const T1  *) (src1 + offset1);
    device const T14 * y4 = (device const T14 *) (src1 + offset1);

    // pointers to src0 rows
    device const T0  * ax [NR0];
    device const T04 * ax4[NR0];
    FOR_UNROLL (short row = 0; row < NR0; ++row) {
        const uint64_t offset0 = (r0 + row)*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

        ax [row] = (device const T0  *) ((device char *) src0 + offset0);
        ax4[row] = (device const T04 *) ((device char *) src0 + offset0);
    }

    float sumf[NR0] = { 0.f };

    const short ix = tiisg/(NW/NF);
    const short il = tiisg%(NW/NF);

    const int ib0 = sgitg*NF + ix;

    T14 yl4[NF4];

    device const T14 * yb4 = y4 + (ib0*NB + il*NF)/4;

    for (int ib = ib0; ib < nb; ib += NSG*NF) {
        for (short i = 0; i < NF4; ++i) {
            yl4[i] = yb4[i];
        }

        for (short row = 0; row < NR0; row++) {
            device const T04 * xb4 = ax4[row] + (ib*NB + il*NF)/4;

            float sumq = 0.f;
            FOR_UNROLL (short i = 0; i < NF4; ++i) {
                sumq += dot(float4(xb4[i]), float4(yl4[i]));
            }

            sumf[row] += sumq;
        }

        yb4 += NSG*NF*NW/4;
    }

    for (int i = nb*NB + sgitg*NW + tiisg; i < args.ne00; i += NW*NSG) {
        for (short row = 0; row < NR0; row++) {
            sumf[row] += ax[row][i] * y[i];
        }
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    helper_mv_reduce_and_write<NR0>(dst_f32, sumf, r0, args.ne01, tiisg, sgitg, shmem);
}

template<typename T0, typename T04, typename T1, typename T14, typename args_t>
void kernel_mul_mv_t_t_4_disp(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    switch (args.nr0) {
      //case 1: kernel_mul_mv_t_t_4_impl<T0, T04, T1, T14, 1, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
        case 2: kernel_mul_mv_t_t_4_impl<T0, T04, T1, T14, 2, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
      //case 3: kernel_mul_mv_t_t_4_impl<T0, T04, T1, T14, 3, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
      //case 4: kernel_mul_mv_t_t_4_impl<T0, T04, T1, T14, 4, args_t>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg); break;
    };
}

template<typename T0, typename T04, typename T1, typename T14>
kernel void kernel_mul_mv_t_t_4(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_t_t_4_disp<T0, T04, T1, T14, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(kernel_mul_mv_t_t_4<half, half4, half, half4>) mul_mv_t_t_4;

template [[host_name("kernel_mul_mv_f32_f32_4")]]   kernel mul_mv_t_t_4 kernel_mul_mv_t_t_4<float, float4, float, float4>;
template [[host_name("kernel_mul_mv_f16_f32_4")]]   kernel mul_mv_t_t_4 kernel_mul_mv_t_t_4<half,  half4,  float, float4>;
template [[host_name("kernel_mul_mv_f16_f16_4")]]   kernel mul_mv_t_t_4 kernel_mul_mv_t_t_4<half,  half4,  half,  half4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mv_bf16_f32_4")]]  kernel mul_mv_t_t_4 kernel_mul_mv_t_t_4<bfloat, bfloat4, float,  float4>;
template [[host_name("kernel_mul_mv_bf16_bf16_4")]] kernel mul_mv_t_t_4 kernel_mul_mv_t_t_4<bfloat, bfloat4, bfloat, bfloat4>;
#endif

template<typename T0, typename T1, typename args_t>
void kernel_mul_mv_t_t_short_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig,
        ushort tiisg) {
    const int r0 = tgpig.x*32 + tiisg;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    if (r0 >= args.ne01) {
        return;
    }

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = r0*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;

    device const T0 * x = (device const T0 *) (src0 + offset0);

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1;

    const uint64_t offset1 = r1*args.nb11 + (i12   )*args.nb12 + (i13   )*args.nb13;

    device const T1 * y = (device const T1 *) (src1 + offset1);

    float res = 0.0f;

    for (int i = 0; i < args.ne00; ++i) {
        res += (float) x[i] * (float) y[i];
    }

    dst_f32[(uint64_t)r1*args.ne0 + r0] = res;
}

template<typename T0, typename T1>
kernel void kernel_mul_mv_t_t_short(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]]) {
    kernel_mul_mv_t_t_short_impl<T0, T1, constant ggml_metal_kargs_mul_mv &>(
        args,
        src0,
        src1,
        dst,
        tgpig,
        tiisg);
}

typedef decltype(kernel_mul_mv_t_t_short<half, half>) mul_mv_t_t_short_t;

template [[host_name("kernel_mul_mv_f32_f32_short")]]  kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<float, float>;
template [[host_name("kernel_mul_mv_f16_f32_short")]]  kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  float>;
template [[host_name("kernel_mul_mv_f16_f16_short")]]  kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<half,  half>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mv_bf16_f32_short")]]  kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<bfloat, float>;
template [[host_name("kernel_mul_mv_bf16_bf16_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<bfloat, bfloat>;
#endif

constant bool FC_rope_is_imrope [[function_constant(FC_ROPE + 0)]];

static float rope_yarn_ramp(const float low, const float high, const int i0) {
    const float y = (i0 / 2 - low) / max(0.001f, high - low);
    return 1.0f - min(1.0f, max(0.0f, y));
}

// YaRN algorithm based on LlamaYaRNScaledRotaryEmbedding.py from https://github.com/jquesnelle/yarn
// MIT licensed. Copyright (c) 2023 Jeffrey Quesnelle and Bowen Peng.
static void rope_yarn(
    float theta_extrap, float freq_scale, float corr_dims[2], int i0, float ext_factor, float mscale,
    thread float * cos_theta, thread float * sin_theta) {
    // Get n-d rotational scaling corrected for extrapolation
    float theta_interp = freq_scale * theta_extrap;
    float theta = theta_interp;
    if (ext_factor != 0.0f) {
        float ramp_mix = rope_yarn_ramp(corr_dims[0], corr_dims[1], i0) * ext_factor;
        theta = theta_interp * (1 - ramp_mix) + theta_extrap * ramp_mix;

        // Get n-d magnitude scaling corrected for interpolation
        mscale *= 1.0f + 0.1f * log(1.0f / freq_scale);
    }
    *cos_theta = cos(theta) * mscale;
    *sin_theta = sin(theta) * mscale;
}

// Apparently solving `n_rot = 2pi * x * base^((2 * max_pos_emb) / n_dims)` for x, we get
// `corr_fac(n_rot) = n_dims * log(max_pos_emb / (n_rot * 2pi)) / (2 * log(base))`
static float rope_yarn_corr_factor(int n_dims, int n_ctx_orig, float n_rot, float base) {
    return n_dims * log(n_ctx_orig / (n_rot * 2 * M_PI_F)) / (2 * log(base));
}

static void rope_yarn_corr_dims(
    int n_dims, int n_ctx_orig, float freq_base, float beta_fast, float beta_slow, float dims[2]
) {
    // start and end correction dims
    dims[0] = max(0.0f,         floor(rope_yarn_corr_factor(n_dims, n_ctx_orig, beta_fast, freq_base)));
    dims[1] = min(n_dims - 1.0f, ceil(rope_yarn_corr_factor(n_dims, n_ctx_orig, beta_slow, freq_base)));
}

template<typename T>
kernel void kernel_rope_norm(
        constant ggml_metal_kargs_rope & args,
        device const char * src0,
        device const char * src1,
        device const char * src2,
        device       char * dst,
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3 tptg [[threads_per_threadgroup]],
        uint3   tgpig[[threadgroup_position_in_grid]]) {
    const int i3 = tgpig[2];
    const int i2 = tgpig[1];
    const int i1 = tgpig[0];

    float corr_dims[2];
    rope_yarn_corr_dims(args.n_dims, args.n_ctx_orig, args.freq_base, args.beta_fast, args.beta_slow, corr_dims);

    device const int32_t * pos = (device const int32_t *) src1;

    const float theta_base = (float) pos[i2];
    const float inv_ndims = -1.f/args.n_dims;

    float cos_theta;
    float sin_theta;

    for (int i0 = 2*tiitg; i0 < args.ne0; i0 += 2*tptg.x) {
        if (i0 < args.n_dims) {
            const int ic = i0/2;

            const float theta = theta_base * pow(args.freq_base, inv_ndims*i0);

            const float freq_factor = args.src2 ? ((device const float *) src2)[ic] : 1.0f;

            rope_yarn(theta/freq_factor, args.freq_scale, corr_dims, i0, args.ext_factor, args.attn_factor, &cos_theta, &sin_theta);

            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + i0*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + i0*args.nb0);

            const float x0 = src[0];
            const float x1 = src[1];

            dst_data[0] = x0*cos_theta - x1*sin_theta;
            dst_data[1] = x0*sin_theta + x1*cos_theta;
        } else {
            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + i0*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + i0*args.nb0);

            dst_data[0] = src[0];
            dst_data[1] = src[1];
        }
    }
}

template<typename T>
kernel void kernel_rope_neox(
        constant ggml_metal_kargs_rope & args,
        device const char * src0,
        device const char * src1,
        device const char * src2,
        device       char * dst,
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3 tptg [[threads_per_threadgroup]],
        uint3   tgpig[[threadgroup_position_in_grid]]) {
    const int i3 = tgpig[2];
    const int i2 = tgpig[1];
    const int i1 = tgpig[0];

    float corr_dims[2];
    rope_yarn_corr_dims(args.n_dims, args.n_ctx_orig, args.freq_base, args.beta_fast, args.beta_slow, corr_dims);

    device const int32_t * pos = (device const int32_t *) src1;

    const float theta_base = (float) pos[i2];
    const float inv_ndims = -1.f/args.n_dims;

    float cos_theta;
    float sin_theta;

    for (int i0 = 2*tiitg; i0 < args.ne0; i0 += 2*tptg.x) {
        if (i0 < args.n_dims) {
            const int ic = i0/2;

            const float theta = theta_base * pow(args.freq_base, inv_ndims*i0);

            const float freq_factor = args.src2 ? ((device const float *) src2)[ic] : 1.0f;

            rope_yarn(theta/freq_factor, args.freq_scale, corr_dims, i0, args.ext_factor, args.attn_factor, &cos_theta, &sin_theta);

            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + ic*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + ic*args.nb0);

            const float x0 = src[0];
            const float x1 = src[args.n_dims/2];

            dst_data[0]             = x0*cos_theta - x1*sin_theta;
            dst_data[args.n_dims/2] = x0*sin_theta + x1*cos_theta;
        } else {
            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + i0*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + i0*args.nb0);

            dst_data[0] = src[0];
            dst_data[1] = src[1];
        }
    }
}

template<typename T>
kernel void kernel_rope_multi(
        constant ggml_metal_kargs_rope & args,
        device const char * src0,
        device const char * src1,
        device const char * src2,
        device       char * dst,
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3 tptg [[threads_per_threadgroup]],
        uint3   tgpig[[threadgroup_position_in_grid]]) {
    const int i3 = tgpig[2];
    const int i2 = tgpig[1];
    const int i1 = tgpig[0];

    float corr_dims[2];
    rope_yarn_corr_dims(args.n_dims, args.n_ctx_orig, args.freq_base, args.beta_fast, args.beta_slow, corr_dims);

    device const int32_t * pos = (device const int32_t *) src1;

    const float inv_ndims = -1.f/args.n_dims;

    float cos_theta;
    float sin_theta;

    for (int i0 = 2*tiitg; i0 < args.ne0; i0 += 2*tptg.x) {
        if (i0 < args.n_dims) {
            const int ic = i0/2;

            // mrope theta calculations
            // note: the rest is the same as kernel_rope_neox
            const int sect_dims = args.sect_0 + args.sect_1 + args.sect_2 + args.sect_3;
            const int sec_w01   = args.sect_0 + args.sect_1;               // end of section 1
            const int sec_w012  = args.sect_0 + args.sect_1 + args.sect_2; // end of section 2
            const int sector    = ic % sect_dims;

            float theta_base;
            if (FC_rope_is_imrope) {
                if (sector % 3 == 1 && sector < 1 + 3 * args.sect_1) { // h
                    theta_base = (float) pos[i2 + args.ne02 * 1];
                } else if (sector % 3 == 2 && sector < 2 + 3 * args.sect_2) { // w
                    theta_base = (float) pos[i2 + args.ne02 * 2];
                } else if (sector % 3 == 0 && sector < 3 * args.sect_0) { // t
                    theta_base = (float) pos[i2 + args.ne02 * 0];
                // } else { // e
                //     theta_base = (float) pos[i2 + args.ne02 * 3];
                }
            } else {
                if (sector < args.sect_0) {
                    theta_base = (float) pos[i2];
                } else if (sector < sec_w01) {
                    theta_base = (float) pos[i2 + args.ne02 * 1];
                } else if (sector < sec_w012) {
                    theta_base = (float) pos[i2 + args.ne02 * 2];
                } else {
                    theta_base = (float) pos[i2 + args.ne02 * 3];
                }
            }
            // end of mrope

            const float theta = theta_base * pow(args.freq_base, inv_ndims*i0);

            const float freq_factor = args.src2 ? ((device const float *) src2)[ic] : 1.0f;

            rope_yarn(theta/freq_factor, args.freq_scale, corr_dims, i0, args.ext_factor, args.attn_factor, &cos_theta, &sin_theta);

            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + ic*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + ic*args.nb0);

            const float x0 = src[0];
            const float x1 = src[args.n_dims/2];

            dst_data[0]             = x0*cos_theta - x1*sin_theta;
            dst_data[args.n_dims/2] = x0*sin_theta + x1*cos_theta;
        } else {
            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + i0*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + i0*args.nb0);

            dst_data[0] = src[0];
            dst_data[1] = src[1];
        }
    }
}

template<typename T>
kernel void kernel_rope_vision(
        constant ggml_metal_kargs_rope & args,
        device const char * src0,
        device const char * src1,
        device const char * src2,
        device       char * dst,
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3 tptg [[threads_per_threadgroup]],
        uint3   tgpig[[threadgroup_position_in_grid]]) {
    const int i3 = tgpig[2];
    const int i2 = tgpig[1];
    const int i1 = tgpig[0];

    float corr_dims[2];
    rope_yarn_corr_dims(args.n_dims, args.n_ctx_orig, args.freq_base, args.beta_fast, args.beta_slow, corr_dims);

    device const int32_t * pos = (device const int32_t *) src1;

    const float inv_ndims = -1.f/args.n_dims;

    float cos_theta;
    float sin_theta;

    for (int i0 = 2*tiitg; i0 < args.ne0; i0 += 2*tptg.x) {
        if (i0 < 2*args.n_dims) { // different from kernel_rope_multi
            const int ic = i0/2;

            // mrope theta calculations (only support 2 dimensions)
            const int sect_dims = args.sect_0 + args.sect_1;
            const int sector    = ic % sect_dims;

            float p;
            float theta_base;
            if (sector < args.sect_1) {
                p = (float) sector;
                theta_base = (float) pos[i2];
            } else {
                p = (float) sector - args.sect_0;
                theta_base = (float) pos[i2 + args.ne02];
            }

            const float theta = theta_base * pow(args.freq_base, 2.0f * inv_ndims * p);
            // end of mrope

            const float freq_factor = args.src2 ? ((device const float *) src2)[ic] : 1.0f;

            rope_yarn(theta/freq_factor, args.freq_scale, corr_dims, i0, args.ext_factor, args.attn_factor, &cos_theta, &sin_theta);

            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + ic*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + ic*args.nb0);

            const float x0 = src[0];
            const float x1 = src[args.n_dims]; // different from kernel_rope_multi

            dst_data[0]           = x0*cos_theta - x1*sin_theta;
            dst_data[args.n_dims] = x0*sin_theta + x1*cos_theta; // different from kernel_rope_multi
        } else {
            device const T * const src = (device T *)(src0 + i3*args.nb03 + i2*args.nb02 + i1*args.nb01 + i0*args.nb00);
            device       T * dst_data  = (device T *)( dst + i3*args.nb3  + i2*args.nb2  + i1*args.nb1  + i0*args.nb0);

            dst_data[0] = src[0];
            dst_data[1] = src[1];
        }
    }
}

typedef decltype(kernel_rope_norm<float>) kernel_rope_norm_t;
typedef decltype(kernel_rope_neox<float>) kernel_rope_neox_t;
typedef decltype(kernel_rope_multi<float>) kernel_rope_multi_t;
typedef decltype(kernel_rope_vision<float>) kernel_rope_vision_t;

template [[host_name("kernel_rope_norm_f32")]] kernel kernel_rope_norm_t kernel_rope_norm<float>;
template [[host_name("kernel_rope_norm_f16")]] kernel kernel_rope_norm_t kernel_rope_norm<half>;

template [[host_name("kernel_rope_neox_f32")]] kernel kernel_rope_neox_t kernel_rope_neox<float>;
template [[host_name("kernel_rope_neox_f16")]] kernel kernel_rope_neox_t kernel_rope_neox<half>;

template [[host_name("kernel_rope_multi_f32")]] kernel kernel_rope_multi_t kernel_rope_multi<float>;
template [[host_name("kernel_rope_multi_f16")]] kernel kernel_rope_multi_t kernel_rope_multi<half>;

template [[host_name("kernel_rope_vision_f32")]] kernel kernel_rope_vision_t kernel_rope_vision<float>;
template [[host_name("kernel_rope_vision_f16")]] kernel kernel_rope_vision_t kernel_rope_vision<half>;

typedef void (im2col_t)(
        constant ggml_metal_kargs_im2col & args,
        device const float * x,
        device        char * dst,
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3  tgpg[[threadgroups_per_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint3   ntg[[threads_per_threadgroup]]);

template <typename T>
kernel void kernel_im2col(
        constant ggml_metal_kargs_im2col & args,
        device const float * x,
        device        char * dst,
        uint3 tgpig[[threadgroup_position_in_grid]],
        uint3  tgpg[[threadgroups_per_grid]],
        uint3 tpitg[[thread_position_in_threadgroup]],
        uint3   ntg[[threads_per_threadgroup]]) {
//    const int64_t IC = tgpg[0];
    const int64_t OH = tgpg[1];
    const int64_t OW = tgpg[2];

    const int64_t KH = ntg[1];
    const int64_t KW = ntg[2];

          int64_t in  = tpitg[0];
    const int64_t ikh = tpitg[1];
    const int64_t ikw = tpitg[2];

    const int64_t iic = tgpig[0];
    const int64_t ioh = tgpig[1];
    const int64_t iow = tgpig[2];

    const int64_t iiw = iow*args.s0 + ikw*args.d0 - args.p0;
    const int64_t iih = ioh*args.s1 + ikh*args.d1 - args.p1;

    int64_t offset_dst = (in*OH*OW + ioh*OW + iow)*args.CHW + (iic*(KH*KW) + ikh*KW + ikw);

    device T * pdst = (device T *) (dst);

    if (iih < 0 || iih >= args.IH || iiw < 0 || iiw >= args.IW) {
        while (in < args.N) {
            pdst[offset_dst] = 0.0f;
            offset_dst += ntg[0]*args.CHW*OH*OW;

            in += ntg[0];
        }
    } else {
        int64_t offset_src = in*args.ofs0 + iic*args.ofs1 + iih*args.IW + iiw;

        while (in < args.N) {
            pdst[offset_dst] = x[offset_src];

            offset_dst += ntg[0]*args.CHW*OH*OW;
            offset_src += ntg[0]*args.ofs0;

            in += ntg[0];
        }
    }
}

template [[host_name("kernel_im2col_f32")]] kernel im2col_t kernel_im2col<float>;
template [[host_name("kernel_im2col_f16")]] kernel im2col_t kernel_im2col<half>;

// TODO: obolete -- remove
//typedef void (im2col_ext_t)(
//        constant ggml_metal_kargs_im2col & args,
//        device const float * x,
//        device        char * dst,
//        uint3 tgpig[[threadgroup_position_in_grid]],
//        uint3  tgpg[[threadgroups_per_grid]],
//        uint3 tpitg[[thread_position_in_threadgroup]],
//        uint3   ntg[[threads_per_threadgroup]]);
//
//template <typename T>
//kernel void kernel_im2col_ext(
//        constant ggml_metal_kargs_im2col & args,
//        device const float * x,
//        device        char * dst,
//        uint3 tgpig[[threadgroup_position_in_grid]],
//        uint3  tgpg[[threadgroups_per_grid]],      // tgpg[0] = D x IC x KH x KW, CHW = IC x KH x KW
//        uint3 tpitg[[thread_position_in_threadgroup]],
//        uint3   ntg[[threads_per_threadgroup]]) {  // [M, 1, 1]
//    const int64_t KHW = (int64_t)args.KHW;
//
//    const int64_t d   = tgpig[0] / args.CHW;
//    const int64_t chw = tgpig[0] % args.CHW;
//    const int64_t tgpig_0 = chw / KHW;  // 0 ~ (IC - 1)
//    const int64_t HW = tgpig[0] % KHW;
//
//    const int64_t tpitg_0 = (d * ntg[0]) + tpitg[0];
//    if (tpitg_0 >= args.N) {
//        return;
//    }
//
//    const int64_t tpitg_1 = HW / args.KW;
//    const int64_t tpitg_2 = HW % args.KW;
//
//    const int64_t iiw = tgpig[2] * args.s0 + tpitg_2 * args.d0 - args.p0;
//    const int64_t iih = tgpig[1] * args.s1 + tpitg_1 * args.d1 - args.p1;
//
//    const int64_t offset_dst =
//        (tpitg_0 * tgpg[1] * tgpg[2] + tgpig[1] * tgpg[2] + tgpig[2]) * args.CHW +
//        (tgpig_0 * KHW + tpitg_1 * args.KW + tpitg_2);
//
//    device T * pdst = (device T *) (dst);
//
//    if (iih < 0 || iih >= args.IH || iiw < 0 || iiw >= args.IW) {
//        pdst[offset_dst] = 0.0f;
//    } else {
//        const int64_t offset_src = tpitg_0 * args.ofs0 + tgpig_0 * args.ofs1;
//        pdst[offset_dst] = x[offset_src + iih * args.IW + iiw];
//    }
//}
//
//template [[host_name("kernel_im2col_ext_f32")]] kernel im2col_ext_t kernel_im2col_ext<float>;
//template [[host_name("kernel_im2col_ext_f16")]] kernel im2col_ext_t kernel_im2col_ext<half>;

template <typename TK>
kernel void kernel_conv_2d(
        constant ggml_metal_kargs_conv_2d & args,
        device const char * weights,
        device const char * src,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3    tgpg[[threadgroups_per_grid]],
        uint3   tpitg[[thread_position_in_threadgroup]],
        uint3     ntg[[threads_per_threadgroup]]) {

    const uint threads_per_tg = ntg.x * ntg.y * ntg.z;
    const uint tg_index = (tgpig.z * tgpg.y + tgpig.y) * tgpg.x + tgpig.x;
    const uint local_thread = tpitg.z * (ntg.x * ntg.y) + tpitg.y * ntg.x + tpitg.x;
    const uint thread_index = tg_index * threads_per_tg + local_thread;
    const uint64_t total_threads = (uint64_t) threads_per_tg * tgpg.x * tgpg.y * tgpg.z;
    const uint64_t total_outputs = (uint64_t) args.N * args.OC * args.OH * args.OW;

    for (uint64_t index = thread_index; index < total_outputs; index += total_threads) {
        uint64_t tmp = index;

        const int32_t ow = tmp % args.OW; tmp /= args.OW;
        const int32_t oh = tmp % args.OH; tmp /= args.OH;
        const int32_t oc = tmp % args.OC; tmp /= args.OC;
        const int32_t  n = tmp;

        float acc = 0.0f;

        const int32_t base_x = ow*args.s0 - args.p0;
        const int32_t base_y = oh*args.s1 - args.p1;

        int32_t ky_start = 0;
        if (base_y < 0) {
            ky_start = (-base_y + args.d1 - 1)/args.d1;
        }
        int32_t ky_end = args.KH;
        const int32_t y_max = args.IH - 1 - base_y;
        if (y_max < 0) {
            ky_end = ky_start;
        } else if (base_y + (args.KH - 1)*args.d1 >= args.IH) {
            ky_end = min(ky_end, y_max/args.d1 + 1);
        }

        int32_t kx_start = 0;
        if (base_x < 0) {
            kx_start = (-base_x + args.d0 - 1)/args.d0;
        }
        int32_t kx_end = args.KW;
        const int32_t x_max = args.IW - 1 - base_x;
        if (x_max < 0) {
            kx_end = kx_start;
        } else if (base_x + (args.KW - 1)*args.d0 >= args.IW) {
            kx_end = min(kx_end, x_max/args.d0 + 1);
        }

        if (ky_start < ky_end && kx_start < kx_end) {
            const uint64_t src_base_n = (uint64_t) n  * args.nb13;
            const uint64_t w_base_oc  = (uint64_t) oc * args.nb03;

            for (int32_t ic = 0; ic < args.IC; ++ic) {
                const uint64_t src_base_nc = src_base_n + (uint64_t) ic * args.nb12;
                const uint64_t w_base_ocic = w_base_oc  + (uint64_t) ic * args.nb02;

                for (int32_t ky = ky_start; ky < ky_end; ++ky) {
                    const int32_t iy = base_y + ky*args.d1;
                    const uint64_t src_base_row = src_base_nc + (uint64_t) iy * args.nb11;
                    const uint64_t w_base_row   = w_base_ocic + (uint64_t) ky * args.nb01;

                    for (int32_t kx = kx_start; kx < kx_end; ++kx) {
                        const int32_t ix = base_x + kx*args.d0;
                        const uint64_t src_offs = src_base_row + (uint64_t) ix * args.nb10;
                        const uint64_t w_offs   = w_base_row   + (uint64_t) kx * args.nb00;

                        const float x = *(device const float *)(src + src_offs);
                        const float w = (float) (*(device const TK *)(weights + w_offs));

                        acc += x * w;
                    }
                }
            }
        }

        const uint64_t dst_offs =
            (uint64_t) n  * args.nb3 +
            (uint64_t) oc * args.nb2 +
            (uint64_t) oh * args.nb1 +
            (uint64_t) ow * args.nb0;

        *(device float *)(dst + dst_offs) = acc;
    }
}

template [[host_name("kernel_conv_2d_f32_f32")]]
kernel void kernel_conv_2d<float>(
        constant ggml_metal_kargs_conv_2d & args,
        device const char * weights,
        device const char * src,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3    tgpg[[threadgroups_per_grid]],
        uint3   tpitg[[thread_position_in_threadgroup]],
        uint3     ntg[[threads_per_threadgroup]]);

template [[host_name("kernel_conv_2d_f16_f32")]]
kernel void kernel_conv_2d<half>(
        constant ggml_metal_kargs_conv_2d & args,
        device const char * weights,
        device const char * src,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3    tgpg[[threadgroups_per_grid]],
        uint3   tpitg[[thread_position_in_threadgroup]],
        uint3     ntg[[threads_per_threadgroup]]);

typedef void (conv_transpose_1d_t)(
        constant ggml_metal_kargs_conv_transpose_1d & args,
        device const float * src0,
        device const float * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3    tgpg[[threadgroups_per_grid]]);

template <typename T>
kernel void kernel_conv_transpose_1d(
        constant ggml_metal_kargs_conv_transpose_1d & args,
        device const     T * src0,
        device const float * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3   tgpg[[threadgroups_per_grid]]) {

    float v = 0.0f;

    for (int64_t c = 0; c < args.IC; c++) {
        const int32_t kernel_offset = c * tgpg[1] * args.K + args.K * tgpig[1];
        const int32_t input_offset = c * args.IL;

        for (int64_t i = 0; i < args.IL; i++) {
            if (tgpig[0] >= i * args.s0 && tgpig[0] < i * args.s0 + args.K) {
                v += src0[kernel_offset + tgpig[0] - i * args.s0] * src1[input_offset + i];
            }
        }
    }

    device float * dst_ptr = (device float *) (dst + tgpig[0] * args.nb0 + tgpig[1] * args.nb1);

    dst_ptr[0] = v;
}

template [[host_name("kernel_conv_transpose_1d_f32_f32")]]
kernel void kernel_conv_transpose_1d<float>(
    constant ggml_metal_kargs_conv_transpose_1d & args,
    device const float * src0,
    device const float * src1,
    device        char * dst,
    uint3   tgpig[[threadgroup_position_in_grid]],
    uint3    tgpg[[threadgroups_per_grid]]);

template [[host_name("kernel_conv_transpose_1d_f16_f32")]]
kernel void kernel_conv_transpose_1d<half>(
    constant ggml_metal_kargs_conv_transpose_1d & args,
    device const half  * src0,
    device const float * src1,
    device        char * dst,
    uint3   tgpig[[threadgroup_position_in_grid]],
    uint3    tgpg[[threadgroups_per_grid]]);


typedef void (conv_transpose_2d_t)(
        constant ggml_metal_kargs_conv_transpose_2d & args,
        device const float * src0,
        device const float * src1,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3    tgpg[[threadgroups_per_grid]]);

template <typename T>
kernel void kernel_conv_transpose_2d(
        constant ggml_metal_kargs_conv_transpose_2d & args,
        device const T * src0,
        device const float * src1,
        device        char * dst,
        threadgroup float * shared_sum [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        uint3   tpitg[[thread_position_in_threadgroup]],
        uint3     ntg[[threads_per_threadgroup]]) {

    const int64_t out_x = tgpig[0];
    const int64_t out_y = tgpig[1];
    const int64_t out_c = tgpig[2];

    const int64_t kw = tpitg[0];
    const int64_t kh = tpitg[1];

    float v = 0.0f;

    for (int64_t in_c = 0; in_c < args.IC; in_c++) {
        int64_t in_y = out_y - kh;

        if (in_y < 0 || in_y % args.s0) continue;

        in_y /= args.s0;

        if (in_y >= args.IH) continue;

        int64_t in_x = out_x - kw;

        if (in_x < 0 || in_x % args.s0) continue;

        in_x /= args.s0;

        if (in_x >= args.IW) continue;

        const int64_t input_idx = (args.IW * args.IH) * in_c + (args.IW) * in_y + in_x;
        const int64_t kernel_idx = (args.KH * args.KW * args.OC) * in_c + (args.KH * args.KW) * out_c + (args.KW) * kh + kw;

        v += (float)src0[kernel_idx] * src1[input_idx];
    }

    const uint tid = tpitg.y * ntg.x + tpitg.x;
    shared_sum[tid] = v;

    threadgroup_barrier(mem_flags::mem_threadgroup);

    if (tid == 0) {
        float total = 0.0f;
        const uint num_threads = ntg.x * ntg.y;
        for (uint i = 0; i < num_threads; i++) {
            total += shared_sum[i];
        }

        device float * dst_ptr = (device float *) (dst + out_x*args.nb0 + out_y * args.nb1 + out_c*args.nb2);
        dst_ptr[0] = total;
    }
}

template [[host_name("kernel_conv_transpose_2d_f32_f32")]]
kernel void kernel_conv_transpose_2d<float>(
    constant ggml_metal_kargs_conv_transpose_2d & args,
    device const float * src0,
    device const float * src1,
    device        char * dst,
    threadgroup float * shared_sum [[threadgroup(0)]],
    uint3   tgpig[[threadgroup_position_in_grid]],
    uint3   tpitg[[thread_position_in_threadgroup]],
    uint3     ntg[[threads_per_threadgroup]]);

template [[host_name("kernel_conv_transpose_2d_f16_f32")]]
kernel void kernel_conv_transpose_2d<half>(
    constant ggml_metal_kargs_conv_transpose_2d & args,
    device const half  * src0,
    device const float * src1,
    device        char * dst,
    threadgroup float * shared_sum [[threadgroup(0)]],
    uint3   tgpig[[threadgroup_position_in_grid]],
    uint3   tpitg[[thread_position_in_threadgroup]],
    uint3     ntg[[threads_per_threadgroup]]);

kernel void kernel_upscale_f32(
    constant ggml_metal_kargs_upscale & args,
    device  const char * src0,
    device        char * dst,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]]) {

    const int64_t i3 = tgpig.z;
    const int64_t i2 = tgpig.y;
    const int64_t i1 = tgpig.x;

    const int64_t i03 = i3/args.sf3;
    const int64_t i02 = i2/args.sf2;
    const int64_t i01 = i1/args.sf1;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        const int64_t i00 = i0/args.sf0;

        device const float * src0_ptr = (device const float *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        device       float * dst_ptr  = (device       float *) (dst  +  i3*args.nb3  +  i2*args.nb2  +  i1*args.nb1  +  i0*args.nb0);

        dst_ptr[0] = src0_ptr[0];
    }
}

kernel void kernel_pad_f32(
    constant ggml_metal_kargs_pad & args,
    device  const char * src0,
    device        char * dst,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]]) {

    const int64_t i3 = tgpig.z;
    const int64_t i2 = tgpig.y;
    const int64_t i1 = tgpig.x;

    const int64_t i03 = i3;
    const int64_t i02 = i2;
    const int64_t i01 = i1;

    device const float * src0_ptr = (device const float *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01);
    device       float * dst_ptr  = (device       float *) (dst  +  i3*args.nb3  +  i2*args.nb2  +  i1*args.nb1);

    if (i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            if (i0 < args.ne00) {
                dst_ptr[i0] = src0_ptr[i0];
            } else {
                dst_ptr[i0] = 0.0f;
            }
        }

        return;
    }

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        dst_ptr[i0] = 0.0f;
    }
}

kernel void kernel_pad_reflect_1d_f32(
    constant   ggml_metal_kargs_pad_reflect_1d & args,
    device  const char * src0,
    device        char * dst,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3  tgpg[[threadgroups_per_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]]) {

    const int64_t i3 = tgpig.z;
    const int64_t i2 = tgpig.y;
    const int64_t i1 = tgpig.x;

    const int64_t i03 = i3;
    const int64_t i02 = i2;
    const int64_t i01 = i1;

    device const float * src0_ptr = (device const float *) (src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01);
    device       float * dst_ptr  = (device       float *) (dst  +  i3*args.nb3  +  i2*args.nb2  +  i1*args.nb1);

    if (i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
        for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
            if (i0 < args.p0) {
                dst_ptr[i0] = src0_ptr[args.p0 - i0];
            } else if (i0 < args.ne0 - args.p1) {
                dst_ptr[i0] = src0_ptr[i0 - args.p0];
            } else {
                dst_ptr[i0] = src0_ptr[(args.ne0 - args.p1 - args.p0) - (args.p1 + 1 - (args.ne0 - i0)) - 1];
            }
        }
    }
}

kernel void kernel_arange_f32(
    constant   ggml_metal_kargs_arange & args,
    device        char * dst,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]]) {

    device float * dst_ptr = (device float *) dst;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        dst_ptr[i0] = args.start + args.step * i0;
    }
}

kernel void kernel_timestep_embedding_f32(
    constant  ggml_metal_kargs_timestep_embedding & args,
    device  const char * src0,
    device        char * dst,
    uint3 tgpig[[threadgroup_position_in_grid]],
    uint3 tpitg[[thread_position_in_threadgroup]],
    uint3   ntg[[threads_per_threadgroup]]) {

    int i = tgpig.x;
    device float * embed_data = (device float *)(dst + i*args.nb1);

    int half_ = args.dim / 2;
    for (int j = tpitg.x; j < half_; j += ntg.x) {
        float timestep = ((device float *)src0)[i];
        float freq = (float)exp(-log((float)args.max_period) * j / half_);
        float arg = timestep * freq;
        embed_data[j        ] = cos(arg);
        embed_data[j + half_] = sin(arg);
    }

    if (args.dim % 2 != 0 && tpitg.x == 0) {
        embed_data[2 * half_] = 0.f;
    }
}

// bitonic sort implementation following the CUDA kernels as reference
typedef void (argsort_t)(
        constant   ggml_metal_kargs_argsort & args,
        device   const char * src0,
        device      int32_t * dst,
        threadgroup int32_t * shmem_i32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]);

template<ggml_sort_order order>
kernel void kernel_argsort_f32_i32(
        constant   ggml_metal_kargs_argsort & args,
        device   const char * src0,
        device      int32_t * dst,
        threadgroup int32_t * shmem_i32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    // bitonic sort
    const int col = tpitg[0];
    const int ib  = tgpig[0] / args.ne01;

    const int i00 = ib*ntg.x;
    const int i01 = tgpig[0] % args.ne01;
    const int i02 = tgpig[1];
    const int i03 = tgpig[2];

    device const float * src0_row = (device const float *) (src0 + args.nb01*i01 + args.nb02*i02 + args.nb03*i03);

    // initialize indices
    shmem_i32[col] = i00 + col;

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (int k = 2; k <= ntg.x; k *= 2) {
        for (int j = k / 2; j > 0; j /= 2) {
            int ixj = col ^ j;
            if (ixj > col) {
                if ((col & k) == 0) {
                    if (shmem_i32[col] >= args.ne00 ||
                       (shmem_i32[ixj] <  args.ne00 && (order == GGML_SORT_ORDER_ASC ?
                            src0_row[shmem_i32[col]] > src0_row[shmem_i32[ixj]] :
                            src0_row[shmem_i32[col]] < src0_row[shmem_i32[ixj]]))
                    ) {
                        SWAP(shmem_i32[col], shmem_i32[ixj]);
                    }
                } else {
                    if (shmem_i32[ixj] >= args.ne00 ||
                       (shmem_i32[col] <  args.ne00 && (order == GGML_SORT_ORDER_ASC ?
                            src0_row[shmem_i32[col]] < src0_row[shmem_i32[ixj]] :
                            src0_row[shmem_i32[col]] > src0_row[shmem_i32[ixj]]))
                    ) {
                        SWAP(shmem_i32[col], shmem_i32[ixj]);
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);
        }
    }

    const int64_t i0 = ib*args.top_k;

    // copy the result to dst without the padding
    if (i0 + col < args.ne0 && col < args.top_k) {
        dst += i0 + args.ne0*i01 + args.ne0*args.ne1*i02 + args.ne0*args.ne1*args.ne2*i03;

        dst[col] = shmem_i32[col];
    }
}

typedef void (i32_argsort_t)(
        constant   ggml_metal_kargs_argsort & args,
        device  const int32_t * src0,
        device        int32_t * dst,
        threadgroup   int32_t * shmem_i32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]);

template<ggml_sort_order order>
kernel void kernel_argsort_i32_i32(
        constant   ggml_metal_kargs_argsort & args,
        device const int32_t * src0,
        device       int32_t * dst,
        threadgroup int32_t  * shmem_i32 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    // bitonic sort
    const int col = tpitg[0];

    const int i00 = (tgpig[0]/args.ne01)*ntg.x;
    const int i01 =  tgpig[0]%args.ne01;
    const int i02 =  tgpig[1];
    const int i03 =  tgpig[2];

    device const int32_t * src0_row = (device const int32_t *) (src0 + args.nb01*i01 + args.nb02*i02 + args.nb03*i03);

    // initialize indices
    shmem_i32[col] = i00 + col;

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (int k = 2; k <= ntg.x; k *= 2) {
        for (int j = k / 2; j > 0; j /= 2) {
            int ixj = col ^ j;
            if (ixj > col) {
                if ((col & k) == 0) {
                    if (shmem_i32[col] >= args.ne00 ||
                        (shmem_i32[ixj] <  args.ne00 && (order == GGML_SORT_ORDER_ASC ?
                            src0_row[shmem_i32[col]] > src0_row[shmem_i32[ixj]] :
                            src0_row[shmem_i32[col]] < src0_row[shmem_i32[ixj]]))
                    ) {
                        SWAP(shmem_i32[col], shmem_i32[ixj]);
                    }
                } else {
                    if (shmem_i32[ixj] >= args.ne00 ||
                        (shmem_i32[col] <  args.ne00 && (order == GGML_SORT_ORDER_ASC ?
                            src0_row[shmem_i32[col]] < src0_row[shmem_i32[ixj]] :
                            src0_row[shmem_i32[col]] > src0_row[shmem_i32[ixj]]))
                    ) {
                        SWAP(shmem_i32[col], shmem_i32[ixj]);
                    }
                }
            }
            threadgroup_barrier(mem_flags::mem_threadgroup);
        }
    }

    // copy the result to dst without the padding
    if (i00 + col < args.ne00) {
        dst += i00 + args.ne00*i01 + args.ne00*args.ne01*i02 + args.ne00*args.ne01*args.ne02*i03;

        dst[col] = shmem_i32[col];
    }
}

template [[host_name("kernel_argsort_f32_i32_asc")]]  kernel argsort_t kernel_argsort_f32_i32<GGML_SORT_ORDER_ASC>;
template [[host_name("kernel_argsort_f32_i32_desc")]] kernel argsort_t kernel_argsort_f32_i32<GGML_SORT_ORDER_DESC>;
template [[host_name("kernel_argsort_i32_i32_asc")]] kernel i32_argsort_t kernel_argsort_i32_i32<GGML_SORT_ORDER_ASC>;
template [[host_name("kernel_argsort_i32_i32_desc")]] kernel i32_argsort_t kernel_argsort_i32_i32<GGML_SORT_ORDER_DESC>;

typedef void (argsort_merge_t)(
        constant   ggml_metal_kargs_argsort_merge & args,
        device const char    * src0,
        device const int32_t * tmp,
        device       int32_t * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]);

template<ggml_sort_order order>
kernel void kernel_argsort_merge_f32_i32(
        constant   ggml_metal_kargs_argsort_merge & args,
        device const char    * src0,
        device const int32_t * tmp,
        device       int32_t * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort3 tpitg[[thread_position_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {

    const int im  = tgpig[0] / args.ne01;
    const int i01 = tgpig[0] % args.ne01;
    const int i02 = tgpig[1];
    const int i03 = tgpig[2];

    const int start = im * (2 * args.len);

    const int len0 = MIN(args.len, MAX(0, args.ne0 - (int)(start)));
    const int len1 = MIN(args.len, MAX(0, args.ne0 - (int)(start + args.len)));

    const int total = len0 + len1;

    device const int32_t * tmp0 = tmp + start
        + i01*args.ne0
        + i02*args.ne0*args.ne01
        + i03*args.ne0*args.ne01*args.ne02;

    device const int32_t * tmp1 = tmp0 + args.len;

    dst += start
        + i01*args.top_k
        + i02*args.top_k*args.ne01
        + i03*args.top_k*args.ne01*args.ne02;

    device const float * src0_row = (device const float *)(src0
        + args.nb01*i01
        + args.nb02*i02
        + args.nb03*i03);

    if (total == 0) {
        return;
    }

    const int chunk = (total + ntg.x - 1) / ntg.x;

    const int k0 = tpitg.x * chunk;
    const int k1 = MIN(MIN(k0 + chunk, total), args.top_k);

    if (k0 >= args.top_k) {
        return;
    }

    if (k0 >= total) {
        return;
    }

    int low  = k0 > len1 ? k0 - len1 : 0;
    int high = MIN(k0, len0);

    // binary-search partition (i, j) such that i + j = k
    while (low < high) {
        const int mid = (low + high) >> 1;

        const int32_t idx0 = tmp0[mid];
        const int32_t idx1 = tmp1[k0 - mid - 1];

        const float val0 = src0_row[idx0];
        const float val1 = src0_row[idx1];

        bool take_left;
        if (order == GGML_SORT_ORDER_ASC) {
            take_left = (val0 <= val1);
        } else {
            take_left = (val0 >= val1);
        }

        if (take_left) {
            low = mid + 1;
        } else {
            high = mid;
        }
    }

    int i = low;
    int j = k0 - i;

    // keep the merge fronts into registers
    int32_t idx0 = 0;
    float   val0 = 0.0f;
    if (i < len0) {
        idx0 = tmp0[i];
        val0 = src0_row[idx0];
    }

    int32_t idx1 = 0;
    float   val1 = 0.0f;
    if (j < len1) {
        idx1 = tmp1[j];
        val1 = src0_row[idx1];
    }

    for (int k = k0; k < k1; ++k) {
        int32_t out_idx;

        if (i >= len0) {
            while (k < k1) {
                dst[k++] = tmp1[j++];
            }
            break;
        } else if (j >= len1) {
            while (k < k1) {
                dst[k++] = tmp0[i++];
            }
            break;
        } else {
            bool take_left;

            if (order == GGML_SORT_ORDER_ASC) {
                take_left = (val0 <= val1);
            } else {
                take_left = (val0 >= val1);
            }

            if (take_left) {
                out_idx = idx0;
                ++i;
                if (i < len0) {
                    idx0 = tmp0[i];
                    val0 = src0_row[idx0];
                }
            } else {
                out_idx = idx1;
                ++j;
                if (j < len1) {
                    idx1 = tmp1[j];
                    val1 = src0_row[idx1];
                }
            }
        }

        dst[k] = out_idx;
    }
}

template [[host_name("kernel_argsort_merge_f32_i32_asc")]]  kernel argsort_merge_t kernel_argsort_merge_f32_i32<GGML_SORT_ORDER_ASC>;
template [[host_name("kernel_argsort_merge_f32_i32_desc")]] kernel argsort_merge_t kernel_argsort_merge_f32_i32<GGML_SORT_ORDER_DESC>;

kernel void kernel_leaky_relu_f32(
        constant     ggml_metal_kargs_leaky_relu & args,
        device const float * src0,
        device       float * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float x = src0[tpig];
    dst[tpig] = x > 0.0f ? x : x * args.slope;
}

kernel void kernel_leaky_relu_f32_4(
        constant     ggml_metal_kargs_leaky_relu & args,
        device const float4 * src0,
        device       float4 * dst,
        uint tpig[[thread_position_in_grid]]) {
    const float4 x = src0[tpig];
    dst[tpig] = float4(x > 0.0f)*x + float4(x <= 0.0f)*(x * args.slope);
}

constant bool FC_flash_attn_ext_pad_has_mask [[function_constant(FC_FLASH_ATTN_EXT_PAD + 0)]];

constant int32_t FC_flash_attn_ext_pad_ncpsg [[function_constant(FC_FLASH_ATTN_EXT_PAD + 25)]];

// pad the last chunk of C elements of k and v into a an extra pad buffer
kernel void kernel_flash_attn_ext_pad(
        constant ggml_metal_kargs_flash_attn_ext_pad & args,
        device const char * k,
        device const char * v,
        device const char * mask,
        device       char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int32_t C = FC_flash_attn_ext_pad_ncpsg;

    device char * k_pad    = dst;
    device char * v_pad    = k_pad + args.nb11*C*args.ne_12_2*args.ne_12_3;
    device char * mask_pad = v_pad + args.nb21*C*args.ne_12_2*args.ne_12_3;

    const int32_t icp = args.ne11 % C;
    const int32_t ic0 = args.ne11 - icp;

    const int32_t i1 = tgpig[0];
    const int32_t i2 = tgpig[1];
    const int32_t i3 = tgpig[2];

    if (i2 < args.ne_12_2 && i3 < args.ne_12_3) {
        device const char * k_src = k + args.nb11*(ic0 + i1) + args.nb12*i2 + args.nb13*i3;
        device const char * v_src = v + args.nb21*(ic0 + i1) + args.nb22*i2 + args.nb23*i3;

        device char * k_dst = k_pad + args.nb11*i1 + args.nb11*C*i2 + args.nb11*C*args.ne_12_2*i3;
        device char * v_dst = v_pad + args.nb21*i1 + args.nb21*C*i2 + args.nb21*C*args.ne_12_2*i3;

        if (i1 >= icp) {
            // here it is not important the exact value that will be used as we rely on masking out the scores in the attention
            for (uint64_t i = tiitg; i < args.nb11; i += ntg.x) {
                k_dst[i] = 0;
            }
            for (uint64_t i = tiitg; i < args.nb21; i += ntg.x) {
                v_dst[i] = 0;
            }
        } else {
            for (uint64_t i = tiitg; i < args.nb11; i += ntg.x) {
                k_dst[i] = k_src[i];
            }
            for (uint64_t i = tiitg; i < args.nb21; i += ntg.x) {
                v_dst[i] = v_src[i];
            }
        }
    }

    if (FC_flash_attn_ext_pad_has_mask) {
        if (i2 < args.ne32 && i3 < args.ne33) {
            for (int ib = i1; ib < args.ne31; ib += C) {
                device const half * mask_src = (device const half *)(mask      + args.nb31*ib + args.nb32*i2 + args.nb33*i3) + ic0;
                device       half * mask_dst = (device       half *)(mask_pad) + C*ib + C*args.ne31*i2 + C*args.ne31*args.ne32*i3;

                for (int i = tiitg; i < C; i += ntg.x) {
                    if (i >= icp) {
                        mask_dst[i] = -MAXHALF;
                    } else {
                        mask_dst[i] = mask_src[i];
                    }
                }
            }
        }
    }
}

constant int32_t FC_flash_attn_ext_blk_nqptg [[function_constant(FC_FLASH_ATTN_EXT_BLK + 24)]];
constant int32_t FC_flash_attn_ext_blk_ncpsg [[function_constant(FC_FLASH_ATTN_EXT_BLK + 25)]];

// scan the blocks of the mask that are not masked
// 0 -     masked (i.e. full of -INF, skip)
// 1 - not masked (i.e. at least one element of the mask is not -INF)
kernel void kernel_flash_attn_ext_blk(
        constant ggml_metal_kargs_flash_attn_ext_blk & args,
        device const char * mask,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]]) {
    // block size C x Q
    const int32_t Q = FC_flash_attn_ext_blk_nqptg;
    const int32_t C = FC_flash_attn_ext_blk_ncpsg;

    constexpr short NW  = N_SIMDWIDTH;

    const int32_t i3 = tgpig[2]/args.ne32;
    const int32_t i2 = tgpig[2]%args.ne32;
    const int32_t i1 = tgpig[1];
    const int32_t i0 = tgpig[0];

    char res = i0*C + C > args.ne30 ? 1 : 0;

    device const half * mask_src = (device const half *) (mask + (i1*Q)*args.nb31 + i2*args.nb32 + i3*args.nb33) + i0*C + tiisg;

    // fast route
    if (res == 0) {
        if (simd_max(*mask_src) > -MAXHALF/2) {
            res = 1;
        }
    }

    // detailed check of the elements of the block
    if ((C > NW || Q > 1) && res == 0) {
        half m = -MAXHALF;

        FOR_UNROLL (short j = 0; j < Q; ++j) {
            FOR_UNROLL (short ii = 0; ii < C/NW; ++ii) {
                m = max(m, mask_src[ii*NW]);
            }

            mask_src += args.nb31/2;
        }

        if (simd_max(m) > -MAXHALF/2) {
            res = 1;
        }
    }

    const int32_t nblk1 = ((args.ne01 + Q - 1)/Q);
    const int32_t nblk0 = ((args.ne30 + C - 1)/C);

    if (tiisg == 0) {
        dst[((i3*args.ne32 + i2)*nblk1 + i1)*nblk0 + i0] = res;
    }
}

constant bool FC_flash_attn_ext_has_mask  [[function_constant(FC_FLASH_ATTN_EXT + 0)]];
constant bool FC_flash_attn_ext_has_sinks [[function_constant(FC_FLASH_ATTN_EXT + 1)]];
constant bool FC_flash_attn_ext_has_bias  [[function_constant(FC_FLASH_ATTN_EXT + 2)]];
constant bool FC_flash_attn_ext_has_scap  [[function_constant(FC_FLASH_ATTN_EXT + 3)]];
constant bool FC_flash_attn_ext_has_kvpad [[function_constant(FC_FLASH_ATTN_EXT + 4)]];

constant bool FC_flash_attn_ext_bc_mask [[function_constant(FC_FLASH_ATTN_EXT + 10)]];

//constant float FC_flash_attn_ext_scale         [[function_constant(FC_FLASH_ATTN_EXT + 10)]];
//constant float FC_flash_attn_ext_max_bias      [[function_constant(FC_FLASH_ATTN_EXT + 11)]];
//constant float FC_flash_attn_ext_logit_softcap [[function_constant(FC_FLASH_ATTN_EXT + 12)]];

constant int32_t FC_flash_attn_ext_ns10 [[function_constant(FC_FLASH_ATTN_EXT + 20)]];
constant int32_t FC_flash_attn_ext_ns20 [[function_constant(FC_FLASH_ATTN_EXT + 21)]];
constant int32_t FC_flash_attn_ext_nsg  [[function_constant(FC_FLASH_ATTN_EXT + 22)]];

// ref: https://arxiv.org/pdf/2307.08691.pdf
template<
    typename q_t,     // query types in shared memory
    typename q4_t,
    typename q8x8_t,
    typename k_t,     // key types in shared memory
    typename k4x4_t,
    typename k8x8_t,
    typename v_t,     // value types in shared memory
    typename v4x4_t,
    typename v8x8_t,
    typename qk_t,    // Q*K types
    typename qk8x8_t,
    typename s_t,     // soft-max types
    typename s2_t,
    typename s8x8_t,
    typename o_t,     // attention accumulation types
    typename o4_t,
    typename o8x8_t,
    typename kd4x4_t, // key type in device memory
    short nl_k,
    void (*deq_k)(device const kd4x4_t *, short, thread k4x4_t &),
    typename vd4x4_t, // value type in device memory
    short nl_v,
    void (*deq_v)(device const vd4x4_t *, short, thread v4x4_t &),
    short DK,         // K head size
    short DV,         // V head size
    short Q,          // queries per threadgroup
    short C,          // cache items per threadgroup
    short NSG>        // number of simd groups
void kernel_flash_attn_ext_impl(
        constant ggml_metal_kargs_flash_attn_ext & args,
        device const char * q,
        device const char * k,
        device const char * v,
        device const char * mask,
        device const char * sinks,
        device const char * pad,
        device const char * blk,
        device       char * dst,
        threadgroup  half * shmem_f16,
        uint3   tgpig,
        ushort  tiisg,
        ushort  sgitg) {
    const ushort iq3 = tgpig[2];
    const ushort iq2 = tgpig[1];
    const ushort iq1 = tgpig[0]*Q;

#define NS10 (FC_flash_attn_ext_ns10)
#define NS20 (FC_flash_attn_ext_ns20)

    // note: I had some concerns that using this instead of the ugly macros above was affecting performance
    //       need to re-check carefully and if no regressions are observerd - remove the macros
    //       the concerns is that maybe using const variables requires extra registers? but not sure if the compiler
    //         is clever enough to avoid this. unfortunately, using constexpr is not possible with FC
    //const short NS10 = FC_flash_attn_ext_ns10;
    //const short NS20 = FC_flash_attn_ext_ns20;

    constexpr short KV   = 8;

    constexpr short DK4  = DK/4;
    constexpr short DK8  = DK/8;
    constexpr short DK16 = DK/16;
    constexpr short DV4  = DV/4;
  //constexpr short DV8  = DV/8;
    constexpr short DV16 = DV/16;

    constexpr short PV   = PAD2(DV, 64);
    constexpr short PV4  = PV/4;
    constexpr short PV8  = PV/8;
  //constexpr short PV16 = PV/16;

    constexpr short NW  = N_SIMDWIDTH;
    constexpr short NQ  = Q/NSG;
    constexpr short SH  = 2*C; // shared memory per simdgroup (s_t == float)

    constexpr short TS = 2*SH;
    constexpr short T  = DK + 2*PV; // shared memory size per query in (half)

    threadgroup q_t  * sq  = (threadgroup q_t  *) (shmem_f16 + 0*T); // holds the query data
    threadgroup q4_t * sq4 = (threadgroup q4_t *) (shmem_f16 + 0*T); // same as above but in q4_t
    threadgroup o_t  * so  = (threadgroup o_t  *) (shmem_f16 + 0*T + Q*DK); // the result for all queries in 8x8 matrices (the O matrix from the paper)
    threadgroup o4_t * so4 = (threadgroup o4_t *) (shmem_f16 + 0*T + Q*DK);
    threadgroup s_t  * ss  = (threadgroup s_t  *) (shmem_f16 + Q*T); // scratch buffer for attention, mask and diagonal matrix
    threadgroup s2_t * ss2 = (threadgroup s2_t *) (shmem_f16 + Q*T); // same as above but in s2_t

    threadgroup k_t    * sk    = (threadgroup k_t    *) (shmem_f16 + sgitg*(4*16*KV) + Q*T + Q*TS); // scratch buffer to load K in shared memory
    threadgroup k4x4_t * sk4x4 = (threadgroup k4x4_t *) (shmem_f16 + sgitg*(4*16*KV) + Q*T + Q*TS); // same as above but in k4x4_t

    threadgroup v_t    * sv    = (threadgroup v_t    *) (shmem_f16 + sgitg*(4*16*KV) + Q*T + Q*TS); // scratch buffer to load V in shared memory
    threadgroup v4x4_t * sv4x4 = (threadgroup v4x4_t *) (shmem_f16 + sgitg*(4*16*KV) + Q*T + Q*TS); // same as above but in v4x4_t

    // mask storage in shared mem
    threadgroup half2 * sm2 = (threadgroup half2 *) (shmem_f16 + Q*T + 2*C);

    // per-query mask pointers
    device const half2 * pm2[NQ];

    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
        const short j = jj*NSG + sgitg;

        pm2[jj] = (device const half2 *) ((device const char *) mask + (iq1 + j)*args.nb31 + (iq2%args.ne32)*args.nb32 + (iq3%args.ne33)*args.nb33);
    }

    {
        const int32_t nblk1 = ((args.ne01 + Q - 1)/Q);
        const int32_t nblk0 = ((args.ne11 + C - 1)/C);

        blk += (((iq3%args.ne33)*args.ne32 + (iq2%args.ne32))*nblk1 + iq1/Q)*nblk0;
    }

    {
        q += iq1*args.nb01 + iq2*args.nb02 + iq3*args.nb03;

        const short ikv2 = iq2/(args.ne02/args.ne_12_2);
        const short ikv3 = iq3/(args.ne03/args.ne_12_3);

        k += ikv2*args.nb12 + ikv3*args.nb13;
        v += ikv2*args.nb22 + ikv3*args.nb23;
    }

    // load heads from Q to shared memory
    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
        const short j = jj*NSG + sgitg;

        device const float4 * q4 = (device const float4 *) ((device const char *) q + j*args.nb01);

        for (short i = tiisg; i < DK4; i += NW) {
            if (iq1 + j < args.ne01) {
                sq4[j*DK4 + i] = (q4_t) q4[i];
            } else {
                sq4[j*DK4 + i] = 0;
            }
        }
    }

    // zero out
    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
        const short j = jj*NSG + sgitg;

        for (short i = tiisg; i < DV4; i += NW) {
            so4[j*PV4 + i] = 0;
        }

        for (short i = tiisg; i < SH; i += NW) {
            ss[j*SH + i] = 0.0f;
        }
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    float S[NQ] = { [0 ... NQ-1] = 0.0f };

    {
        float M[NQ] = { [0 ... NQ-1] = -FLT_MAX/2 };

        float slope = 1.0f;

        // ALiBi
        if (FC_flash_attn_ext_has_bias) {
            const short h = iq2;

            const float base = h < args.n_head_log2 ? args.m0 : args.m1;
            const short exph = h < args.n_head_log2 ? h + 1 : 2*(h - args.n_head_log2) + 1;

            slope = pow(base, exph);
        }

        // loop over the KV cache
        // each simdgroup handles blocks of Q rows and C columns
        for (int ic0 = 0; ; ++ic0) {
            int ic = ic0*C;
            if (ic >= args.ne11) {
                break;
            }

            // the last partial chunk uses the pad buffer as source
            if (FC_flash_attn_ext_has_kvpad && ic + C > args.ne11) {
                k    = pad;
                v    = k + args.nb11*C*args.ne_12_2*args.ne_12_3;
                mask = v + args.nb21*C*args.ne_12_2*args.ne_12_3;

                const short ikv2 = iq2/(args.ne02/args.ne_12_2);
                const short ikv3 = iq3/(args.ne03/args.ne_12_3);

                k += (ikv2 + ikv3*args.ne_12_2)*args.nb11*C;
                v += (ikv2 + ikv3*args.ne_12_2)*args.nb21*C;

                if (!FC_flash_attn_ext_has_mask) {
                    threadgroup half * sm = (threadgroup half *) (sm2);

                    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                        const short j = jj*NSG + sgitg;

                        for (short i = tiisg; i < C; i += NW) {
                            if (ic + i >= args.ne11) {
                                sm[2*j*SH + i] = -MAXHALF;
                            }
                        }
                    }
                } else {
                    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                        const short j = jj*NSG + sgitg;

                        pm2[jj] = (device const half2 *) ((device const half *) mask +
                                (iq1 + j)*C +
                                (iq2%args.ne32)*(C*args.ne31) +
                                (iq3%args.ne33)*(C*args.ne31*args.ne32));
                    }
                }

                ic = 0;
            }

            // read the mask into shared mem
            if (FC_flash_attn_ext_has_mask) {
                if (blk[ic0] == 0) {
                    FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                        pm2[jj] += NW;
                    }

                    continue;
                }

                FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                    const short j = jj*NSG + sgitg;

                    if (FC_flash_attn_ext_bc_mask) {
                        sm2[j*SH + tiisg] = (iq1 + j) < args.ne31 ? pm2[jj][tiisg] : half2(-MAXHALF, -MAXHALF);
                    } else {
                        sm2[j*SH + tiisg] = pm2[jj][tiisg];
                    }

                    pm2[jj] += NW;
                }

#if 0
                // note: old -INF block optimization - obsoleted by pre-computing non-masked blocks

                threadgroup_barrier(mem_flags::mem_threadgroup);

                // used to detect blocks full of -INF
                // skip only when the entire threadgroup is masked
                half2 smax2(-MAXHALF/2, -MAXHALF/2);

                FOR_UNROLL (short j = 0; j < Q; ++j) {
                    smax2 = max(smax2, sm2[j*SH + tiisg]);
                }

                smax2 = simd_max(smax2);

                if (max(smax2[0], smax2[1]) <= -MAXHALF/2) {
                    // this barrier is important
                    threadgroup_barrier(mem_flags::mem_threadgroup);

                    continue;
                }
#endif
            }

            // Q*K^T
            // this is compile-time check, so it does not have runtime overhead
            if (is_same<kd4x4_t, k4x4_t>::value) {
                // we can read directly from global memory
                device      const k_t * pk = (device const k_t *) (k + ic*args.nb11);
                threadgroup const q_t * pq = sq;
                threadgroup       s_t * ps = ss;

                pk += sgitg*(8*NS10);
                ps += sgitg*(8*1);

                static_assert((C/8) % NSG == 0, "");

                constexpr short NC = (C/8)/NSG;

                // note: do not unroll for large heads
                #pragma unroll (DK <= 64 ? NC : 1)
                for (short cc = 0; cc < NC; ++cc) {
                    qk8x8_t mqk = make_filled_simdgroup_matrix<qk_t, 8>((qk_t) 0.0f);

                    if (DK % 16 != 0) {
                        k8x8_t mk;
                        q8x8_t mq;

                        FOR_UNROLL (short i = 0; i < DK8; ++i) {
                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_load(mk, pk + 8*i, NS10, 0, true);
                            simdgroup_load(mq, pq + 8*i, DK);

                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                        }
                    } else {
                        k8x8_t mk[2];
                        q8x8_t mq[2];

                        FOR_UNROLL (short i = 0; i < DK8/2; ++i) {
                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_load(mq[0], pq + 0*8 + 16*i, DK);
                            simdgroup_load(mq[1], pq + 1*8 + 16*i, DK);

                            simdgroup_load(mk[0], pk + 0*8 + 16*i, NS10, 0, true);
                            simdgroup_load(mk[1], pk + 1*8 + 16*i, NS10, 0, true);

                            simdgroup_barrier(mem_flags::mem_none);

                            simdgroup_multiply_accumulate(mqk, mq[0], mk[0], mqk);
                            simdgroup_multiply_accumulate(mqk, mq[1], mk[1], mqk);
                        }
                    }

                    simdgroup_store(mqk, ps, SH, 0, false);

                    pk += 8*(NSG*NS10);
                    ps += 8*(NSG);
                }
            } else {
                // TODO: this is the quantized K cache branch - not optimized yet
                for (short ccc = 0; ccc < (C/8)/NSG; ++ccc) {
                    const short cc = ccc*NSG + sgitg;

                    const short tx = tiisg%4;
                    const short ty = tiisg/4;

                    qk8x8_t mqk = make_filled_simdgroup_matrix<qk_t, 8>((qk_t) 0.0f);

                    for (short ii = 0; ii < DK16; ii += 4) {
                        device const kd4x4_t * pk4x4 = (device const kd4x4_t *) (k + ((ic + 8*cc + ty)*args.nb11));

                        if (DK16%4 == 0) {
                            // the head is evenly divisible by 4*16 = 64, so no need for bound checks
                            {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            FOR_UNROLL (short k = 0; k < 4; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true); // transpose
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true); // transpose
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        } else {
                            if (ii + tx < DK16) {
                                k4x4_t tmp;
                                deq_k(pk4x4 + (ii + tx)/nl_k, (ii + tx)%nl_k, tmp);
                                sk4x4[4*ty + tx] = tmp;
                            }

                            simdgroup_barrier(mem_flags::mem_threadgroup);

                            for (short k = 0; k < 4 && ii + k < DK16; ++k) {
                                k8x8_t mk;
                                q8x8_t mq;

                                simdgroup_load(mk, sk + 16*k + 0*8, 4*16, 0, true); // transpose
                                simdgroup_load(mq, sq + (2*(ii + k) + 0)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);

                                simdgroup_load(mk, sk + 16*k + 1*8, 4*16, 0, true); // transpose
                                simdgroup_load(mq, sq + (2*(ii + k) + 1)*8, DK);
                                simdgroup_multiply_accumulate(mqk, mq, mk, mqk);
                            }
                        }
                    }

                    simdgroup_store(mqk, ss + 8*cc, SH, 0, false);
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            // online softmax
            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];

                // scale and apply the logitcap / mask
                float2 s2 = ss2[j*SH/2 + tiisg]*args.scale;

                if (FC_flash_attn_ext_has_scap) {
                    s2 = args.logit_softcap*precise::tanh(s2);
                }

                // mqk = mqk + slope*mask
                if (FC_flash_attn_ext_has_bias) {
                    s2 += s2_t(sm2[j*SH + tiisg])*slope;
                } else {
                    s2 += s2_t(sm2[j*SH + tiisg]);
                }

                M[jj] = simd_max(max(M[jj], max(s2[0], s2[1])));

                const float  ms  = exp(m  - M[jj]);
                const float2 vs2 = exp(s2 - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs2[0] + vs2[1]);

                // the P matrix from the paper (Q rows, C columns)
                ss2[j*SH/2 + tiisg] = vs2;

                if (DV4 % NW == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                        const short i = ii*NW + tiisg;

                        so4[j*PV4 + i] *= ms;
                    }
                } else {
                    for (short i = tiisg; i < DV4; i += NW) {
                        so4[j*PV4 + i] *= ms;
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);

            // O = O + (Q*K^T)*V
            {
                // we can read directly from global memory
                if (is_same<vd4x4_t, v4x4_t>::value) {
                    static_assert(PV8 % NSG == 0, "");

                    constexpr short NO = PV8/NSG;

                    o8x8_t lo[NO];

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_load(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }

                    {
                        device const v_t * pv = (device const v_t *) (v + ic*args.nb21);

                        pv += 8*sgitg;

                        if (DV <= 64) {
                            FOR_UNROLL (short cc = 0; cc < C/8; ++cc) {
                                s8x8_t vs;
                                simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[2];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs, mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs, mv[1], lo[2*ii + 1]);
                                }

                                pv  += 8*NS20;
                            }
                        } else {
                            FOR_UNROLL (short cc = 0; cc < (C/8)/2; ++cc) {
                                s8x8_t vs[2];

                                simdgroup_load(vs[0], ss + 16*cc + 0, SH, 0, false);
                                simdgroup_load(vs[1], ss + 16*cc + 8, SH, 0, false);

                                FOR_UNROLL (short ii = 0; ii < NO/2; ++ii) {
                                    v8x8_t mv[4];

                                    simdgroup_load(mv[0], pv + 0*NSG + 16*ii*NSG + 0*8*NS20, NS20, 0, false);
                                    simdgroup_load(mv[1], pv + 8*NSG + 16*ii*NSG + 0*8*NS20, NS20, 0, false);
                                    simdgroup_load(mv[2], pv + 0*NSG + 16*ii*NSG + 1*8*NS20, NS20, 0, false);
                                    simdgroup_load(mv[3], pv + 8*NSG + 16*ii*NSG + 1*8*NS20, NS20, 0, false);

                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs[0], mv[0], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs[0], mv[1], lo[2*ii + 1]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 0], vs[1], mv[2], lo[2*ii + 0]);
                                    simdgroup_multiply_accumulate(lo[2*ii + 1], vs[1], mv[3], lo[2*ii + 1]);
                                }

                                pv  += 2*8*NS20;
                            }
                        }
                    }

                    {
                        auto sot = so + 8*sgitg;

                        FOR_UNROLL (short ii = 0; ii < NO; ++ii) {
                            simdgroup_store(lo[ii], sot, PV, 0, false);

                            sot += 8*NSG;
                        }
                    }
                } else {
                    // TODO: this is the quantized V cache branch - not optimized yet

                    const short tx = tiisg%4;
                    const short ty = tiisg/4;

                    for (short cc = 0; cc < C/8; ++cc) {
                        s8x8_t vs;
                        simdgroup_load(vs, ss + 8*cc, SH, 0, false);

                        for (short ii = 4*sgitg; ii < DV16; ii += 4*NSG) {
                            device const vd4x4_t * pv4x4 = (device const vd4x4_t *) (v + ((ic + 8*cc + ty)*args.nb21));

                            if (DV16%4 == 0) {
                                // no need for bound checks
                                {
                                    v4x4_t tmp;
                                    deq_v(pv4x4 + (ii + tx)/nl_v, (ii + tx)%nl_v, tmp);
                                    sv4x4[4*ty + tx] = tmp;
                                }

                                simdgroup_barrier(mem_flags::mem_threadgroup);

                                FOR_UNROLL (short k = 0; k < 4; ++k) {
                                    v8x8_t mv[2];
                                    o8x8_t lo[2];

                                    simdgroup_load(mv[0], sv + 16*k + 0*8, 4*16, 0, false);
                                    simdgroup_load(mv[1], sv + 16*k + 1*8, 4*16, 0, false);
                                    simdgroup_load(lo[0], so + 8*(2*(ii + k) + 0), PV, 0, false);
                                    simdgroup_load(lo[1], so + 8*(2*(ii + k) + 1), PV, 0, false);

                                    simdgroup_multiply_accumulate(lo[0], vs, mv[0], lo[0]);
                                    simdgroup_multiply_accumulate(lo[1], vs, mv[1], lo[1]);

                                    simdgroup_store(lo[0], so + 8*(2*(ii + k) + 0), PV, 0, false);
                                    simdgroup_store(lo[1], so + 8*(2*(ii + k) + 1), PV, 0, false);
                                }
                            } else {
                                if (ii + tx < DV16) {
                                    v4x4_t tmp;
                                    deq_v(pv4x4 + (ii + tx)/nl_v, (ii + tx)%nl_v, tmp);
                                    sv4x4[4*ty + tx] = tmp;
                                }

                                simdgroup_barrier(mem_flags::mem_threadgroup);

                                for (short k = 0; k < 4 && ii + k < DV16; ++k) {
                                    v8x8_t mv[2];
                                    o8x8_t lo[2];

                                    simdgroup_load(mv[0], sv + 16*k + 0*8, 4*16, 0, false);
                                    simdgroup_load(mv[1], sv + 16*k + 1*8, 4*16, 0, false);
                                    simdgroup_load(lo[0], so + 8*(2*(ii + k) + 0), PV, 0, false);
                                    simdgroup_load(lo[1], so + 8*(2*(ii + k) + 1), PV, 0, false);

                                    simdgroup_multiply_accumulate(lo[0], vs, mv[0], lo[0]);
                                    simdgroup_multiply_accumulate(lo[1], vs, mv[1], lo[1]);

                                    simdgroup_store(lo[0], so + 8*(2*(ii + k) + 0), PV, 0, false);
                                    simdgroup_store(lo[1], so + 8*(2*(ii + k) + 1), PV, 0, false);
                                }
                            }
                        }
                    }
                }
            }

            threadgroup_barrier(mem_flags::mem_threadgroup);
        }

        if (FC_flash_attn_ext_has_sinks) {
            FOR_UNROLL (short jj = 0; jj < NQ; ++jj) {
                const short j = jj*NSG + sgitg;

                const float m = M[jj];
                const float s = tiisg == 0 ? ((device const float *) sinks)[iq2] : -FLT_MAX/2;

                M[jj] = simd_max(max(M[jj], s));

                const float ms = exp(m - M[jj]);
                const float vs = exp(s - M[jj]);

                S[jj] = S[jj]*ms + simd_sum(vs);

                for (short i = tiisg; i < DV4; i += NW) {
                    so4[j*PV4 + i] *= ms;
                }
            }
        }
    }

    // store to global memory
    for (short jj = 0; jj < NQ; ++jj) {
        const short j = jj*NSG + sgitg;
        if (iq1 + j >= args.ne01) {
            break;
        }

        device float4 * dst4 = (device float4 *) dst + ((uint64_t)iq3*args.ne2*args.ne1 + iq2 + (uint64_t)(iq1 + j)*args.ne1)*DV4;

        const float scale = S[jj] == 0.0 ? 0.0f : 1.0f/S[jj];

        if (DV4 % NW == 0) {
            FOR_UNROLL (short ii = 0; ii < DV4/NW; ++ii) {
                const short i = ii*NW + tiisg;

                dst4[i] = (float4) so4[j*PV4 + i]*scale;
            }
        } else {
            for (short i = tiisg; i < DV4; i += NW) {
                dst4[i] = (float4) so4[j*PV4 + i]*scale;
            }
        }
    }

#undef NS10
#undef NS20
}

template<
    typename q_t,     // query types in shared memory
    typename q4_t,
    typename q8x8_t,
    typename k_t,     // key types in shared memory
    typename k4x4_t,
    typename k8x8_t,
    typename v_t,     // value types in shared memory
    typename v4x4_t,
    typename v8x8_t,
    typename qk_t,    // Q*K types
    typename qk8x8_t,
    typename s_t,     // soft-max types
    typename s2_t,
    typename s8x8_t,
    typename o_t,     // attention accumulation types
    typename o4_t,
    typename o8x8_t,
    typename kd4x4_t, // key type in device memory
    short nl_k,
    void (*deq_k)(device const kd4x4_t *, short, thread k4x4_t &),
    typename vd4x4_t, // value type in device memory
    short nl_v,
    void (*deq_v)(device const vd4x4_t *, short, thread v4x4_t &),
    short DK,         // K head size
    short DV,         // V head size
    short Q  = OP_FLASH_ATTN_EXT_NQPTG, // queries per threadgroup
    short C  = OP_FLASH_ATTN_EXT_NCPSG> // cache items per threadgroup
kernel void kernel_flash_attn_ext(
        constant ggml_metal_kargs_flash_attn_ext & args,
        device const char * q,
        device const char * k,
        device const char * v,
        device const char * mask,
        device const char * sinks,
        device const char * pad,
        device const char * blk,
        device       char * dst,
        threadgroup  half * shmem_f16 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
#define FWD_TMPL q_t, q4_t, q8x8_t, k_t, k4x4_t, k8x8_t, v_t, v4x4_t, v8x8_t, qk_t, qk8x8_t, s_t, s2_t, s8x8_t, o_t, o4_t, o8x8_t, kd4x4_t, nl_k, deq_k, vd4x4_t, nl_v, deq_v, DK, DV, Q, C
#define FWD_ARGS args, q, k, v, mask, sinks, pad, blk, dst, shmem_f16, tgpig, tiisg, sgitg
    switch (FC_flash_attn_ext_nsg) {
      // note: disabled cases to reduce library load time
      //case 1: kernel_flash_attn_ext_impl<FWD_TMPL, 1>(FWD_ARGS); break;
      //case 2: kernel_flash_attn_ext_impl<FWD_TMPL, 2>(FWD_ARGS); break;
        case 4: kernel_flash_attn_ext_impl<FWD_TMPL, 4>(FWD_ARGS); break;
    }
#undef FWD_TMPL
#undef FWD_ARGS
}

// TODO: this is quite ugly. in the future these types will be hardcoded in the kernel, but for now keep them as
//       template to be able to explore different combinations
//
#define FA_TYPES \
    half,   half4,     simdgroup_half8x8,  \
    half,   half4x4,   simdgroup_half8x8,  \
    half,   half4x4,   simdgroup_half8x8,  \
    float,             simdgroup_float8x8, \
    float,  float2,    simdgroup_float8x8, \
    float,  float4,    simdgroup_float8x8
    //half,   half4,     simdgroup_half8x8

#define FA_TYPES_BF \
    bfloat, bfloat4,   simdgroup_bfloat8x8, \
    bfloat, bfloat4x4, simdgroup_bfloat8x8, \
    bfloat, bfloat4x4, simdgroup_bfloat8x8, \
    float,             simdgroup_float8x8,  \
    float,  float2,    simdgroup_float8x8,  \
    half,   half4,     simdgroup_half8x8
    //float,  float4,    simdgroup_float8x8

#define FA_TYPES_F32 \
    half,   half4,     simdgroup_half8x8,  \
    float,  float4x4,  simdgroup_float8x8, \
    float,  float4x4,  simdgroup_float8x8, \
    float,             simdgroup_float8x8, \
    float,  float2,    simdgroup_float8x8, \
    float,  float4,    simdgroup_float8x8
    //half,   half4,     simdgroup_half8x8

typedef decltype(kernel_flash_attn_ext<FA_TYPES, half4x4, 1, dequantize_f16, half4x4, 1, dequantize_f16, 64, 64>) flash_attn_ext_t;

template [[host_name("kernel_flash_attn_ext_f32_dk32_dv32"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  32,  32>;
template [[host_name("kernel_flash_attn_ext_f32_dk40_dv40"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  40,  40>;
template [[host_name("kernel_flash_attn_ext_f32_dk64_dv64"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  64,  64>;
template [[host_name("kernel_flash_attn_ext_f32_dk72_dv72"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  72,  72>;
template [[host_name("kernel_flash_attn_ext_f32_dk80_dv80"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  80,  80>;
template [[host_name("kernel_flash_attn_ext_f32_dk96_dv96"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  96,  96>;
template [[host_name("kernel_flash_attn_ext_f32_dk112_dv112")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  112, 112>;
template [[host_name("kernel_flash_attn_ext_f32_dk128_dv128")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  128, 128>;
template [[host_name("kernel_flash_attn_ext_f32_dk192_dv192")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  192, 192>;
template [[host_name("kernel_flash_attn_ext_f32_dk192_dv128")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  192, 128>;
template [[host_name("kernel_flash_attn_ext_f32_dk256_dv256")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  256, 256>;
template [[host_name("kernel_flash_attn_ext_f32_dk576_dv512")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  576, 512>;

template [[host_name("kernel_flash_attn_ext_f16_dk32_dv32"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  32,  32>;
template [[host_name("kernel_flash_attn_ext_f16_dk40_dv40"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  40,  40>;
template [[host_name("kernel_flash_attn_ext_f16_dk64_dv64"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  64,  64>;
template [[host_name("kernel_flash_attn_ext_f16_dk72_dv72"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  72,  72>;
template [[host_name("kernel_flash_attn_ext_f16_dk80_dv80"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  80,  80>;
template [[host_name("kernel_flash_attn_ext_f16_dk96_dv96"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  96,  96>;
template [[host_name("kernel_flash_attn_ext_f16_dk112_dv112")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  112, 112>;
template [[host_name("kernel_flash_attn_ext_f16_dk128_dv128")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  128, 128>;
template [[host_name("kernel_flash_attn_ext_f16_dk192_dv192")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  192, 192>;
template [[host_name("kernel_flash_attn_ext_f16_dk192_dv128")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  192, 128>;
template [[host_name("kernel_flash_attn_ext_f16_dk256_dv256")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  256, 256>;
template [[host_name("kernel_flash_attn_ext_f16_dk576_dv512")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  576, 512>;

#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_bf16_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 32,  32>;
template [[host_name("kernel_flash_attn_ext_bf16_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 40,  40>;
template [[host_name("kernel_flash_attn_ext_bf16_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 64,  64>;
template [[host_name("kernel_flash_attn_ext_bf16_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 72,  72>;
template [[host_name("kernel_flash_attn_ext_bf16_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 80,  80>;
template [[host_name("kernel_flash_attn_ext_bf16_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 96,  96>;
template [[host_name("kernel_flash_attn_ext_bf16_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 112, 112>;
template [[host_name("kernel_flash_attn_ext_bf16_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 128, 128>;
template [[host_name("kernel_flash_attn_ext_bf16_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 192, 192>;
template [[host_name("kernel_flash_attn_ext_bf16_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 192, 128>;
template [[host_name("kernel_flash_attn_ext_bf16_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 256, 256>;
template [[host_name("kernel_flash_attn_ext_bf16_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 576, 512>;
#endif

template [[host_name("kernel_flash_attn_ext_q4_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 32,  32>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 40,  40>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 64,  64>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 72,  72>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 80,  80>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 96,  96>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 112, 112>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 128, 128>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 192, 192>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 192, 128>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 256, 256>;
template [[host_name("kernel_flash_attn_ext_q4_0_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 576, 512>;

template [[host_name("kernel_flash_attn_ext_q4_1_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 32,  32>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 40,  40>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 64,  64>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 72,  72>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 80,  80>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 96,  96>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 112, 112>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 128, 128>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 192, 192>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 192, 128>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 256, 256>;
template [[host_name("kernel_flash_attn_ext_q4_1_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 576, 512>;

template [[host_name("kernel_flash_attn_ext_q5_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 32,  32>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 40,  40>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 64,  64>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 72,  72>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 80,  80>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 96,  96>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 112, 112>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 128, 128>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 192, 192>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 192, 128>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 256, 256>;
template [[host_name("kernel_flash_attn_ext_q5_0_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 576, 512>;

template [[host_name("kernel_flash_attn_ext_q5_1_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 32,  32>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 40,  40>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 64,  64>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 72,  72>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 80,  80>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 96,  96>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 112, 112>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 128, 128>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 192, 192>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 192, 128>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 256, 256>;
template [[host_name("kernel_flash_attn_ext_q5_1_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 576, 512>;

template [[host_name("kernel_flash_attn_ext_q8_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 32,  32>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 40,  40>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 64,  64>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 72,  72>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 80,  80>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 96,  96>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 112, 112>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk128_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 128, 128>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk192_dv192")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 192, 192>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk192_dv128")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 192, 128>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk256_dv256")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 256, 256>;
template [[host_name("kernel_flash_attn_ext_q8_0_dk576_dv512")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 576, 512>;

#undef FA_TYPES
#undef FA_TYPES_BF
#undef FA_TYPES_F32

constant bool FC_flash_attn_ext_vec_has_mask  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 0)]];
constant bool FC_flash_attn_ext_vec_has_sinks [[function_constant(FC_FLASH_ATTN_EXT_VEC + 1)]];
constant bool FC_flash_attn_ext_vec_has_bias  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 2)]];
constant bool FC_flash_attn_ext_vec_has_scap  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 3)]];
constant bool FC_flash_attn_ext_vec_has_kvpad [[function_constant(FC_FLASH_ATTN_EXT_VEC + 4)]];

//constant float FC_flash_attn_ext_vec_scale         [[function_constant(FC_FLASH_ATTN_EXT_VEC + 10)]];
//constant float FC_flash_attn_ext_vec_max_bias      [[function_constant(FC_FLASH_ATTN_EXT_VEC + 11)]];
//constant float FC_flash_attn_ext_vec_logit_softcap [[function_constant(FC_FLASH_ATTN_EXT_VEC + 12)]];

constant int32_t FC_flash_attn_ext_vec_ns10 [[function_constant(FC_FLASH_ATTN_EXT_VEC + 20)]];
constant int32_t FC_flash_attn_ext_vec_ns20 [[function_constant(FC_FLASH_ATTN_EXT_VEC + 21)]];
constant int32_t FC_flash_attn_ext_vec_nsg  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 22)]];
constant int32_t FC_flash_attn_ext_vec_nwg  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 23)]];

template<
    typename q4_t,  // query types in shared memory
    typename k4_t,  // key types in shared memory
    typename v4_t,  // value types in shared memory
    typename qk_t,  // Q*K types
    typename s_t,   // soft-max types
    typename s4_t,
    typename o4_t,  // attention accumulation types
    typename kd4_t, // key type in device memory
    short nl_k,
    void (*deq_k_t4)(device const kd4_t *, short, thread k4_t &),
    typename vd4_t, // value type in device memory
    short nl_v,
    void (*deq_v_t4)(device const vd4_t *, short, thread v4_t &),
    short DK,       // K head size
    short DV,       // V head size
    short NE,       // head elements per thread
    short Q,        // queries per threadgroup
    short C,        // cache items per threadgroup
    short NSG>      // number of simd groups
void kernel_flash_attn_ext_vec_impl(
        constant ggml_metal_kargs_flash_attn_ext_vec & args,
        device const char * q,
        device const char * k,
        device const char * v,
        device const char * mask,
        device const char * sinks,
        device const char * pad,
        device       char * dst,
        threadgroup  half * shmem_f16 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
    static_assert(DK % 32 == 0, "DK must be divisible by 32");
    static_assert(DV % 32 == 0, "DV must be divisible by 32");

#define NWG  (FC_flash_attn_ext_vec_nwg)

#define NS10 (FC_flash_attn_ext_vec_ns10)
#define NS20 (FC_flash_attn_ext_vec_ns20)

    const short iwg = tgpig[2]%NWG;

    const ushort iq3 = tgpig[2]/NWG;
    const ushort iq2 = tgpig[1];
    const ushort iq1 = tgpig[0];

    constexpr short DK4 = DK/4;
    constexpr short DV4 = DV/4;

    constexpr short PK  = PAD2(DK, 128);
    constexpr short PK4 = PK/4;

    constexpr short PV  = PAD2(DV, 128);
    constexpr short PV4 = PV/4;

    constexpr short NW  = N_SIMDWIDTH;
    constexpr short NL  = NW/NE; // note: this can be adjusted to support different head sizes and simdgroup work loads
    constexpr short SH  = 4*C;   // shared memory per simdgroup

    static_assert(DK4 % NL == 0, "DK4 must be divisible by NL");
    static_assert(DV4 % NL == 0, "DV4 must be divisible by NL");

    const short T = PK + NSG*SH; // shared memory size per query in (half)

  //threadgroup q_t   * sq  = (threadgroup q_t   *) (shmem_f16 +                    0*PK); // holds the query data
    threadgroup q4_t  * sq4 = (threadgroup q4_t  *) (shmem_f16 +                    0*PK); // same as above but in q4_t
    threadgroup s_t   * ss  = (threadgroup s_t   *) (shmem_f16 +   sgitg*SH       + Q*PK); // scratch buffer for attention
    threadgroup s4_t  * ss4 = (threadgroup s4_t  *) (shmem_f16 +   sgitg*SH       + Q*PK); // same as above but in s4_t
    threadgroup half  * sm  = (threadgroup half  *) (shmem_f16 +   sgitg*SH + 2*C + Q*PK); // scratch buffer for mask
    threadgroup o4_t  * so4 = (threadgroup o4_t  *) (shmem_f16 + 2*sgitg*PV       + Q*T);  // scratch buffer for the results

    // store the result for all queries in shared memory (the O matrix from the paper)
    so4 += tiisg;

    {
        q += iq1*args.nb01 + iq2*args.nb02 + iq3*args.nb03;

        const short ikv2 = iq2/(args.ne02/args.ne_12_2);
        const short ikv3 = iq3/(args.ne03/args.ne_12_3);

        k += ikv2*args.nb12 + ikv3*args.nb13;
        v += ikv2*args.nb22 + ikv3*args.nb23;
    }

    // load heads from Q to shared memory
    device const float4 * q4 = (device const float4 *) ((device const char *) q);

    for (short i = tiisg; i < PK4; i += NW) {
        if (iq1 < args.ne01 && i < DK4) {
            sq4[i] = (q4_t) q4[i];
        } else {
            sq4[i] = (q4_t) 0.0f;
        }
    }

    // zero out so
    for (short i = 0; i < DV4/NL; ++i) {
        so4[i*NL] = (o4_t) 0.0f;
    }

    // zero out shared memory SH
    for (short i = tiisg; i < SH/4; i += NW) {
        ss4[i] = (s4_t) 0.0f;
    }

    threadgroup_barrier(mem_flags::mem_threadgroup);

    {
        float S = 0.0f;
        float M = -FLT_MAX/2;

        // thread indices inside the simdgroup
        const short tx = tiisg%NL;
        const short ty = tiisg/NL;

        // pointer to the mask
        device const half * pm = (device const half *) (mask + iq1*args.nb31 + (iq2%args.ne32)*args.nb32 + (iq3%args.ne33)*args.nb33);

        float slope = 1.0f;

        // ALiBi
        if (FC_flash_attn_ext_vec_has_bias) {
            const short h = iq2;

            const float base = h < args.n_head_log2 ? args.m0 : args.m1;
            const short exph = h < args.n_head_log2 ? h + 1 : 2*(h - args.n_head_log2) + 1;

            slope = pow(base, exph);
        }

        // loop over the KV cache
        // each simdgroup handles blocks of Q rows and C columns
        for (int ic0 = iwg*NSG + sgitg; ; ic0 += NWG*NSG) {
            int ic = ic0*C;
            if (ic >= args.ne11) {
                break;
            }

            // the last partial chunk uses the pad buffer as source
            if (FC_flash_attn_ext_vec_has_kvpad && ic + C > args.ne11) {
                k    = pad;
                v    = k + args.nb11*C*args.ne_12_2*args.ne_12_3;
                mask = v + args.nb21*C*args.ne_12_2*args.ne_12_3;

                const short ikv2 = iq2/(args.ne02/args.ne_12_2);
                const short ikv3 = iq3/(args.ne03/args.ne_12_3);

                k += (ikv2 + ikv3*args.ne_12_2)*args.nb11*C;
                v += (ikv2 + ikv3*args.ne_12_2)*args.nb21*C;

                if (!FC_flash_attn_ext_vec_has_mask) {
                    if (ic + tiisg >= args.ne11) {
                        sm[tiisg] = -MAXHALF;
                    }
                } else {
                    pm = (device const half *) (mask) +
                        iq1*C +
                        (iq2%args.ne32)*(C*args.ne31) +
                        (iq3%args.ne33)*(C*args.ne31*args.ne32);
                }

                ic = 0;
            }

            if (FC_flash_attn_ext_vec_has_mask) {
                sm[tiisg] = pm[ic + tiisg];
            }

            // skip -INF blocks
            if (simd_max(sm[tiisg]) == -INFINITY) {
                continue;
            }

            // Q*K^T
            {
                device      const k4_t * pk4 = (device const k4_t *) (k + ic*args.nb11);
                threadgroup const q4_t * pq4 = sq4;

                pk4 += ty*NS10/4 + tx;
                pq4 += tx;

                qk_t mqk[C/NE] = { [ 0 ... C/NE - 1] = 0.0f };

                // each simdgroup processes 1 query and NE (NW/NL) cache elements
                FOR_UNROLL (short cc = 0; cc < C/NE; ++cc) {
                    if (is_same<kd4_t, k4_t>::value) {
                        FOR_UNROLL (short ii = 0; ii < DK4/NL; ++ii) {
                            mqk[cc] += dot((float4) pk4[cc*NE*NS10/4 +  ii*NL], (float4) pq4[ii*NL]);
                        }
                    } else {
                        device const kd4_t * pk = (device const kd4_t *) (k + ((ic + NE*cc + ty)*args.nb11));

                        k4_t mk;

                        FOR_UNROLL (short ii = 0; ii < DK4/NL; ++ii) {
                            const short i = ii*NL + tx;

                            deq_k_t4(pk + i/nl_k, i%nl_k, mk);

                            mqk[cc] += dot((float4) mk, (float4) sq4[i]);
                        }
                    }

                    if (NE == 1) {
                        mqk[cc] = simd_sum(mqk[cc]);
                    } else {
                        // simdgroup reduce (NE = 4)
                        // [ 0 ..  7] -> [ 0]
                        // [ 8 .. 15] -> [ 8]
                        // [16 .. 23] -> [16]
                        // [24 .. 31] -> [24]
                        if (NE <= 1) {
                            mqk[cc] += simd_shuffle_down(mqk[cc], 16);
                        }
                        if (NE <= 2) {
                            mqk[cc] += simd_shuffle_down(mqk[cc],  8);
                        }
                        if (NE <= 4) {
                            mqk[cc] += simd_shuffle_down(mqk[cc],  4);
                        }
                        if (NE <= 8) {
                            mqk[cc] += simd_shuffle_down(mqk[cc],  2);
                        }
                        if (NE <= 16) {
                            mqk[cc] += simd_shuffle_down(mqk[cc],  1);
                        }

                        // broadcast
                        mqk[cc] = simd_shuffle(mqk[cc], NL*ty);
                    }
                }

                if (FC_flash_attn_ext_vec_has_mask &&
                   !FC_flash_attn_ext_vec_has_scap &&
                   !FC_flash_attn_ext_vec_has_bias) {
                    ss[NE*tx + ty] = fma(mqk[tx], args.scale, (qk_t) sm[NE*tx + ty]);
                } else {
                    mqk[tx] *= args.scale;

                    if (FC_flash_attn_ext_vec_has_scap) {
                        mqk[tx] = args.logit_softcap*precise::tanh(mqk[tx]);
                    }

                    if (FC_flash_attn_ext_vec_has_bias) {
                        mqk[tx] += (qk_t) sm[NE*tx + ty]*slope;
                    } else {
                        mqk[tx] += (qk_t) sm[NE*tx + ty];
                    }

                    ss[NE*tx + ty] = mqk[tx];
                }
            }

            simdgroup_barrier(mem_flags::mem_threadgroup);

            // online softmax
            {
                const float m = M;
                const float s = ss[tiisg];

                M = simd_max(max(M, s));

                const float ms = exp(m - M);
                const float vs = exp(s - M);

                S = S*ms + simd_sum(vs);

                // the P matrix from the paper (Q rows, C columns)
                ss[tiisg] = vs;

                // O = diag(ms)*O
                if ((DV4/NL % NW == 0) || ty == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                        so4[ii*NL] *= ms;
                    }
                }
            }

            simdgroup_barrier(mem_flags::mem_threadgroup);

            // O = O + (Q*K^T)*V
            {
                o4_t lo[DV4/NL];
                FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                    lo[ii] = 0.0f;
                }

                if (is_same<vd4_t, v4_t>::value) {
                    device const v4_t * pv4 = (device const v4_t *) (v + ic*args.nb21);

                    pv4 += ty*NS20/4 + tx;

                    const auto sst = ss + ty;

                    FOR_UNROLL (short cc = 0; cc < C/NE; ++cc) {
                        FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                            lo[ii] += o4_t(float4(pv4[cc*NE*NS20/4 + ii*NL])*float4(sst[cc*NE]));
                        }
                    }
                } else {
                    FOR_UNROLL (short cc = 0; cc < C/NE; ++cc) {
                        device const vd4_t * pv4 = (device const vd4_t *) (v + ((ic + NE*cc + ty)*args.nb21));

                        FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                            const short i = ii*NL + tx;

                            v4_t mv;
                            deq_v_t4(pv4 + i/nl_v, i%nl_v, mv);

                            lo[ii] += o4_t(float4(mv)*float4(ss[NE*cc + ty]));
                        }
                    }
                }

                FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                    if (NE > 1) {
                        lo[ii][0] += simd_shuffle_down(lo[ii][0], 16);
                        lo[ii][1] += simd_shuffle_down(lo[ii][1], 16);
                        lo[ii][2] += simd_shuffle_down(lo[ii][2], 16);
                        lo[ii][3] += simd_shuffle_down(lo[ii][3], 16);
                    }

                    if (NE > 2) {
                        lo[ii][0] += simd_shuffle_down(lo[ii][0],  8);
                        lo[ii][1] += simd_shuffle_down(lo[ii][1],  8);
                        lo[ii][2] += simd_shuffle_down(lo[ii][2],  8);
                        lo[ii][3] += simd_shuffle_down(lo[ii][3],  8);
                    }

                    if (NE > 4) {
                        lo[ii][0] += simd_shuffle_down(lo[ii][0],  4);
                        lo[ii][1] += simd_shuffle_down(lo[ii][1],  4);
                        lo[ii][2] += simd_shuffle_down(lo[ii][2],  4);
                        lo[ii][3] += simd_shuffle_down(lo[ii][3],  4);
                    }

                    if (NE > 8) {
                        lo[ii][0] += simd_shuffle_down(lo[ii][0],  2);
                        lo[ii][1] += simd_shuffle_down(lo[ii][1],  2);
                        lo[ii][2] += simd_shuffle_down(lo[ii][2],  2);
                        lo[ii][3] += simd_shuffle_down(lo[ii][3],  2);
                    }

                    if (NE > 16) {
                        lo[ii][0] += simd_shuffle_down(lo[ii][0],  1);
                        lo[ii][1] += simd_shuffle_down(lo[ii][1],  1);
                        lo[ii][2] += simd_shuffle_down(lo[ii][2],  1);
                        lo[ii][3] += simd_shuffle_down(lo[ii][3],  1);
                    }
                }

                if ((DV4/NL % NW == 0) || ty == 0) {
                    FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                        so4[ii*NL] += lo[ii];
                    }
                }
            }
        }

        if (FC_flash_attn_ext_vec_has_sinks && sgitg == 0 && iwg == 0) {
            const float m = M;
            const float s = tiisg == 0 ? ((device const float *) sinks)[iq2] : -FLT_MAX/2;

            M = simd_max(max(M, s));

            const float ms = exp(m - M);
            const float vs = exp(s - M);

            S = S*ms + simd_sum(vs);

            if ((DV4/NL % NW == 0) || ty == 0) {
                FOR_UNROLL (short ii = 0; ii < DV4/NL; ++ii) {
                    so4[ii*NL] *= ms;
                }
            }
        }

        // these are needed for reducing the results from the simdgroups (reuse the ss buffer)
        if (tiisg == 0) {
            ss[0] = (s_t) S;
            ss[1] = (s_t) M;
        }
    }

    so4 -= tiisg;

    threadgroup_barrier(mem_flags::mem_threadgroup);

    // parallel reduce
    for (short r = NSG/2; r > 0; r >>= 1) {
        if (sgitg < r) {
            const float S0 = ss[           0];
            const float S1 = ss[r*(SH/2) + 0];

            const float M0 = ss[           1];
            const float M1 = ss[r*(SH/2) + 1];

            const float M = max(M0, M1);

            const float ms0 = exp(M0 - M);
            const float ms1 = exp(M1 - M);

            const float S = S0*ms0 + S1*ms1;

            if (tiisg == 0) {
                ss[0] = S;
                ss[1] = M;
            }

            // O_0 = diag(ms0)*O_0 + diag(ms1)*O_1
            for (short i = tiisg; i < DV4; i += NW) {
                so4[i] = so4[i]*ms0 + so4[i + r*PV4]*ms1;
            }
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    // final rescale with 1/S and store to global memory
    if (sgitg == 0) {
        const int64_t nrows = args.ne3*args.ne2*args.ne1;
        const int64_t rid   = iq3*args.ne2*args.ne1 + iq2 + iq1*args.ne1;

        device float4 * dst4 = (device float4 *) dst;
        device float  * dst1 = (device float  *) dst + nrows*DV*NWG; // the S and M are stored after the results

        const float S = NWG == 1 ? (ss[0] == 0.0f ? 0.0f : 1.0f/ss[0]) : 1.0f;

        // interleave the workgroup data
        for (short i = tiisg; i < DV4; i += NW) {
            dst4[rid*DV4*NWG + NWG*i + iwg] = (float4) so4[i]*S;
        }

        // store S and M
        if (NWG > 1) {
            if (tiisg == 0) {
                dst1[rid*(2*NWG) + 2*iwg + 0] = ss[0];
                dst1[rid*(2*NWG) + 2*iwg + 1] = ss[1];
            }
        }
    }

#undef NWG
#undef NS10
#undef NS20
}

template<
    typename q4_t,  // query types in shared memory
    typename k4_t,  // key types in shared memory
    typename v4_t,  // value types in shared memory
    typename qk_t,  // Q*K types
    typename s_t,   // soft-max types
    typename s4_t,
    typename o4_t,  // attention accumulation types
    typename kd4_t, // key type in device memory
    short nl_k,
    void (*deq_k_t4)(device const kd4_t *, short, thread k4_t &),
    typename vd4_t, // value type in device memory
    short nl_v,
    void (*deq_v_t4)(device const vd4_t *, short, thread v4_t &),
    short DK,       // K head size
    short DV,       // V head size
    short NE = 4,   // head elements per thread
    short Q  = OP_FLASH_ATTN_EXT_VEC_NQPTG,  // queries per threadgroup
    short C  = OP_FLASH_ATTN_EXT_VEC_NCPSG>  // cache items per threadgroup
kernel void kernel_flash_attn_ext_vec(
        constant ggml_metal_kargs_flash_attn_ext_vec & args,
        device const char * q,
        device const char * k,
        device const char * v,
        device const char * mask,
        device const char * sinks,
        device const char * pad,
        device       char * dst,
        threadgroup  half * shmem_f16 [[threadgroup(0)]],
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiisg[[thread_index_in_simdgroup]],
        ushort  sgitg[[simdgroup_index_in_threadgroup]]) {
#define FWD_TMPL q4_t, k4_t, v4_t, qk_t, s_t, s4_t, o4_t, kd4_t, nl_k, deq_k_t4, vd4_t, nl_v, deq_v_t4, DK, DV, NE, Q, C
#define FWD_ARGS args, q, k, v, mask, sinks, pad, dst, shmem_f16, tgpig, tiisg, sgitg
    switch (FC_flash_attn_ext_vec_nsg) {
      // note: disabled cases to reduce library load time
        case 1:  kernel_flash_attn_ext_vec_impl<FWD_TMPL,  1>(FWD_ARGS); break;
        case 2:  kernel_flash_attn_ext_vec_impl<FWD_TMPL,  2>(FWD_ARGS); break;
        case 4:  kernel_flash_attn_ext_vec_impl<FWD_TMPL,  4>(FWD_ARGS); break;
      //case 8:  kernel_flash_attn_ext_vec_impl<FWD_TMPL,  8>(FWD_ARGS); break;
      //case 16: kernel_flash_attn_ext_vec_impl<FWD_TMPL, 16>(FWD_ARGS); break;
      //case 32: kernel_flash_attn_ext_vec_impl<FWD_TMPL, 32>(FWD_ARGS); break;
    }
#undef FWD_TMPL
#undef FWD_ARGS
}

// note: I think the s_t can be half instead of float, because the Q*K scaling is done before storing to shared mem
//       in the other (non-vec) kernel, we need s_t to also be float because we scale during the soft_max
//
#define FA_TYPES \
           half4,  \
           half4,  \
           half4,  \
    float,         \
    float, float4, \
           float4

#define FA_TYPES_F32 \
           half4,  \
           float4, \
           float4, \
    float,         \
    float, float4, \
           float4

typedef decltype(kernel_flash_attn_ext_vec<FA_TYPES, half4, 1, dequantize_f16_t4, half4, 1, dequantize_f16_t4, 128, 128, 4>) flash_attn_ext_vec_t;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk32_dv32")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  32, 32, 4>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk32_dv32")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  32, 32, 4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 32, 32, 4>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 32, 32, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 32, 32, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 32, 32, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 32, 32, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk32_dv32")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 32, 32, 4>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk64_dv64")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  64, 64, 2>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk64_dv64")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  64, 64, 2>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 64, 64, 2>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 64, 64, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 64, 64, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 64, 64, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 64, 64, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk64_dv64")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 64, 64, 2>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk96_dv96")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  96, 96, 4>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk96_dv96")]]    kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  96, 96, 4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 96, 96, 4>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 96, 96, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 96, 96, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 96, 96, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 96, 96, 4>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk96_dv96")]]   kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 96, 96, 4>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk128_dv128")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  128, 128, 1>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk128_dv128")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  128, 128, 1>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 128, 128, 1>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 128, 128, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 128, 128, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 128, 128, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 128, 128, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk128_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 128, 128, 1>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk192_dv192")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  192, 192, 2>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk192_dv192")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  192, 192, 2>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 192, 192, 2>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 192, 192, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 192, 192, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 192, 192, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 192, 192, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk192_dv192")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 192, 192, 2>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk192_dv128")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  192, 128, 2>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk192_dv128")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  192, 128, 2>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 192, 128, 2>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 192, 128, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 192, 128, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 192, 128, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 192, 128, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk192_dv128")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 192, 128, 2>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk256_dv256")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  256, 256, 1>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk256_dv256")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  256, 256, 1>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 256, 256, 1>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 256, 256, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 256, 256, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 256, 256, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 256, 256, 1>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk256_dv256")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 256, 256, 1>;

template [[host_name("kernel_flash_attn_ext_vec_f32_dk576_dv512")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES_F32, float4,     1, dequantize_f32_t4,  float4,      1, dequantize_f32_t4,  576, 512, 2>;
template [[host_name("kernel_flash_attn_ext_vec_f16_dk576_dv512")]]  kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     half4,      1, dequantize_f16_t4,  half4,       1, dequantize_f16_t4,  576, 512, 2>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_flash_attn_ext_vec_bf16_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     bfloat4,    1, dequantize_bf16_t4, bfloat4,     1, dequantize_bf16_t4, 576, 512, 2>;
#endif
template [[host_name("kernel_flash_attn_ext_vec_q4_0_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_0, 8, dequantize_q4_0_t4, block_q4_0,  8, dequantize_q4_0_t4, 576, 512, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q4_1_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q4_1, 8, dequantize_q4_1_t4, block_q4_1,  8, dequantize_q4_1_t4, 576, 512, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_0_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_0, 8, dequantize_q5_0_t4, block_q5_0,  8, dequantize_q5_0_t4, 576, 512, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q5_1, 8, dequantize_q5_1_t4, block_q5_1,  8, dequantize_q5_1_t4, 576, 512, 2>;
template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 576, 512, 2>;

#undef FA_TYPES
#undef FA_TYPES_F32

constant int32_t FC_flash_attn_ext_vec_reduce_DV  [[function_constant(FC_FLASH_ATTN_EXT_VEC_REDUCE + 0)]];
constant int32_t FC_flash_attn_ext_vec_reduce_NWG [[function_constant(FC_FLASH_ATTN_EXT_VEC_REDUCE + 1)]];

kernel void kernel_flash_attn_ext_vec_reduce(
        constant ggml_metal_kargs_flash_attn_ext_vec_reduce & args,
        device  const char * htmp,
        device        char * dst,
        uint   tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
#define NWG (FC_flash_attn_ext_vec_reduce_NWG)
#define DV  (FC_flash_attn_ext_vec_reduce_DV)

    const uint64_t rid = tgpig;

    const short iwg = tiisg;

    device const float  * ss    = (device const float  *) htmp + (uint64_t)args.nrows*DV*NWG;

    float S = ss[rid*(2*NWG) + 2*iwg + 0];
    float M = ss[rid*(2*NWG) + 2*iwg + 1];

    const float m  = simd_max(M);
    const float ms = exp(M - m);

    S = simd_sum(S*ms);
    S = S == 0.0f ? 0.0f : 1.0f/S;

    const short DV4 = DV/4;

    device const float4 * htmp4 = (device const float4 *) htmp + rid*DV4*NWG;
    device       float4 * dst4  = (device       float4 *) dst  + rid*DV4;

    for (short i = sgitg; i < DV4; i += NWG) {
        const float4 v = simd_sum(htmp4[i*NWG + iwg]*ms);

        if (iwg == 0) {
            dst4[i] = v*S;
        }
    }

#undef NWG
#undef DV
}

template<typename T0, typename T1>
kernel void kernel_cpy_t_t(
        constant ggml_metal_kargs_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device T1 * dst_data = (device T1 *) (dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.ne00; ) {
        device const T0 * src = (device T0 *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + i00*args.nb00);
        dst_data[i00] = (T1) src[0];
        break;
    }
}

typedef decltype(kernel_cpy_t_t<float, float>) kernel_cpy_t;

template [[host_name("kernel_cpy_f32_f32")]]   kernel kernel_cpy_t kernel_cpy_t_t<float,   float>;
template [[host_name("kernel_cpy_f32_f16")]]   kernel kernel_cpy_t kernel_cpy_t_t<float,   half>;
template [[host_name("kernel_cpy_f32_i32")]]   kernel kernel_cpy_t kernel_cpy_t_t<float,   int32_t>;
template [[host_name("kernel_cpy_i32_f32")]]   kernel kernel_cpy_t kernel_cpy_t_t<int32_t, float>;
template [[host_name("kernel_cpy_i32_i32")]]   kernel kernel_cpy_t kernel_cpy_t_t<int32_t, int32_t>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_cpy_f32_bf16")]]  kernel kernel_cpy_t kernel_cpy_t_t<float,   bfloat>;
#endif
template [[host_name("kernel_cpy_f16_f32")]]   kernel kernel_cpy_t kernel_cpy_t_t<half,    float>;
template [[host_name("kernel_cpy_f16_f16")]]   kernel kernel_cpy_t kernel_cpy_t_t<half,    half>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_cpy_bf16_f32")]]  kernel kernel_cpy_t kernel_cpy_t_t<bfloat,  float>;
template [[host_name("kernel_cpy_bf16_bf16")]] kernel kernel_cpy_t kernel_cpy_t_t<bfloat,  bfloat>;
#endif

template<short QK,
         typename block_q,
         void (*quantize_func)(device const float *, device block_q &)>
kernel void kernel_cpy_f32_q(
        constant ggml_metal_kargs_cpy & args,
        device const char * src0,
        device char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n / (args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0) / (args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0) / args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0)/QK;

    device block_q * dst_data = (device block_q *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.nk0; ) {
        device const float * src = (device const float *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01 + (i00*QK)*args.nb00);

        quantize_func(src, dst_data[i00]);

        break;
    }
}

typedef decltype(kernel_cpy_f32_q<QK8_0,  block_q8_0,  quantize_q8_0>)  cpy_f_q_t;

template [[host_name("kernel_cpy_f32_q8_0")]]   kernel cpy_f_q_t kernel_cpy_f32_q<QK8_0,  block_q8_0,   quantize_q8_0>;
template [[host_name("kernel_cpy_f32_q4_0")]]   kernel cpy_f_q_t kernel_cpy_f32_q<QK4_0,  block_q4_0,   quantize_q4_0>;
template [[host_name("kernel_cpy_f32_q4_1")]]   kernel cpy_f_q_t kernel_cpy_f32_q<QK4_1,  block_q4_1,   quantize_q4_1>;
template [[host_name("kernel_cpy_f32_q5_0")]]   kernel cpy_f_q_t kernel_cpy_f32_q<QK5_0,  block_q5_0,   quantize_q5_0>;
template [[host_name("kernel_cpy_f32_q5_1")]]   kernel cpy_f_q_t kernel_cpy_f32_q<QK5_1,  block_q5_1,   quantize_q5_1>;
template [[host_name("kernel_cpy_f32_iq4_nl")]] kernel cpy_f_q_t kernel_cpy_f32_q<QK4_NL, block_iq4_nl, quantize_iq4_nl>;

template<typename T4x4, typename block_q, short nl, void (*dequantize_func)(device const block_q *, short, thread T4x4 &)>
kernel void kernel_cpy_q_f32(
        constant ggml_metal_kargs_cpy & args,
        device  const char * src0,
        device        char * dst,
        uint3   tgpig[[threadgroup_position_in_grid]],
        ushort  tiitg[[thread_index_in_threadgroup]],
        ushort3   ntg[[threads_per_threadgroup]]) {
    const int i03 = tgpig[2];
    const int i02 = tgpig[1];
    const int i01 = ntg[1] == 1 ? tgpig[0]%args.ne01 : tgpig[0]*ntg[1] + tiitg/ntg[0];
    const int iw0 = ntg[1] == 1 ? tgpig[0]/args.ne01 : 0;

    const int64_t n = i03*args.ne02*args.ne01*args.ne00 + i02*args.ne01*args.ne00 + i01*args.ne00;

    const int64_t i3 = n/(args.ne2*args.ne1*args.ne0);
    const int64_t i2 = (n - i3*args.ne2*args.ne1*args.ne0)/(args.ne1*args.ne0);
    const int64_t i1 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0)/args.ne0;
    const int64_t i0 = (n - i3*args.ne2*args.ne1*args.ne0 - i2*args.ne1*args.ne0 - i1*args.ne0);

    device const block_q * src_data = (device const block_q *)(src0 + i03*args.nb03 + i02*args.nb02 + i01*args.nb01);
    device       T4x4    * dst_data = (device       T4x4    *)(dst  +  i3*args.nb3  +  i2*args.nb2  +  i1*args.nb1 + i0*args.nb0);

    for (int64_t i00 = iw0*ntg[0] + tiitg%ntg[0]; i00 < args.nk0; ) {
        T4x4 temp;
        dequantize_func(src_data + i00/nl, i00%nl, temp);
        dst_data[i00] = temp;

        break;
    }
}

typedef decltype(kernel_cpy_q_f32<float4x4, block_q4_0, 2, dequantize_q4_0>) cpy_q_f_t;

template [[host_name("kernel_cpy_q4_0_f32")]] kernel cpy_q_f_t kernel_cpy_q_f32<float4x4, block_q4_0, 2, dequantize_q4_0>;
template [[host_name("kernel_cpy_q4_1_f32")]] kernel cpy_q_f_t kernel_cpy_q_f32<float4x4, block_q4_1, 2, dequantize_q4_1>;
template [[host_name("kernel_cpy_q5_0_f32")]] kernel cpy_q_f_t kernel_cpy_q_f32<float4x4, block_q5_0, 2, dequantize_q5_0>;
template [[host_name("kernel_cpy_q5_1_f32")]] kernel cpy_q_f_t kernel_cpy_q_f32<float4x4, block_q5_1, 2, dequantize_q5_1>;
template [[host_name("kernel_cpy_q8_0_f32")]] kernel cpy_q_f_t kernel_cpy_q_f32<float4x4, block_q8_0, 2, dequantize_q8_0>;

template [[host_name("kernel_cpy_q4_0_f16")]] kernel cpy_q_f_t kernel_cpy_q_f32<half4x4, block_q4_0, 2, dequantize_q4_0>;
template [[host_name("kernel_cpy_q4_1_f16")]] kernel cpy_q_f_t kernel_cpy_q_f32<half4x4, block_q4_1, 2, dequantize_q4_1>;
template [[host_name("kernel_cpy_q5_0_f16")]] kernel cpy_q_f_t kernel_cpy_q_f32<half4x4, block_q5_0, 2, dequantize_q5_0>;
template [[host_name("kernel_cpy_q5_1_f16")]] kernel cpy_q_f_t kernel_cpy_q_f32<half4x4, block_q5_1, 2, dequantize_q5_1>;
template [[host_name("kernel_cpy_q8_0_f16")]] kernel cpy_q_f_t kernel_cpy_q_f32<half4x4, block_q8_0, 2, dequantize_q8_0>;

kernel void kernel_concat(
    constant ggml_metal_kargs_concat & args,
    device  const char * src0,
    device  const char * src1,
    device        char * dst,
    uint3   tgpig[[threadgroup_position_in_grid]],
    ushort3 tpitg[[thread_position_in_threadgroup]],
    ushort3   ntg[[threads_per_threadgroup]]) {

    const int i3 = tgpig.z;
    const int i2 = tgpig.y;
    const int i1 = tgpig.x;

    int o[4] = {0, 0, 0, 0};
    o[args.dim] = args.dim == 0 ? args.ne00 : (args.dim == 1 ? args.ne01 : (args.dim == 2 ? args.ne02 : args.ne03));

    device const float * x;

    for (int i0 = tpitg.x; i0 < args.ne0; i0 += ntg.x) {
        if (i0 < args.ne00 && i1 < args.ne01 && i2 < args.ne02 && i3 < args.ne03) {
            x = (device const float *)(src0 + (i3       )*args.nb03 + (i2       )*args.nb02 + (i1       )*args.nb01 + (i0       )*args.nb00);
        } else {
            x = (device const float *)(src1 + (i3 - o[3])*args.nb13 + (i2 - o[2])*args.nb12 + (i1 - o[1])*args.nb11 + (i0 - o[0])*args.nb10);
        }

        device float * y = (device float *)(dst + i3*args.nb3 + i2*args.nb2 + i1*args.nb1 + i0*args.nb0);

        *y = *x;
    }
}

template<int nr0, typename args_t>
void kernel_mul_mv_q2_K_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_q2_K * x = (device const block_q2_K *) (src0 + offset0);
    device const float      * y = (device const float      *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const short ix = tiisg/8;  // 0...3
    const short it = tiisg%8;  // 0...7
    const short iq = it/4;     // 0 or 1
    const short ir = it%4;     // 0...3
    const short is = (8*ir)/16;// 0 or 1

    device const float * y4 = y + ix * QK_K + 128 * iq + 8 * ir;

    for (int ib = ix; ib < nb; ib += 4) {
        float4 sumy = {0.f, 0.f, 0.f, 0.f};
        for (short i = 0; i < 8; ++i) {
            yl[i+ 0] = y4[i+ 0]; sumy[0] += yl[i+ 0];
            yl[i+ 8] = y4[i+32]; sumy[1] += yl[i+ 8];
            yl[i+16] = y4[i+64]; sumy[2] += yl[i+16];
            yl[i+24] = y4[i+96]; sumy[3] += yl[i+24];
        }

        device const uint8_t  * sc = (device const uint8_t  *)x[ib].scales + 8*iq + is;
        device const uint16_t * qs = (device const uint16_t *)x[ib].qs + 16 * iq + 4 * ir;
        device const half     * dh = &x[ib].d;

        for (short row = 0; row < nr0; row++) {
            float4 acc1 = {0.f, 0.f, 0.f, 0.f};
            float4 acc2 = {0.f, 0.f, 0.f, 0.f};
            for (int i = 0; i < 8; i += 2) {
                acc1[0] += yl[i+ 0] * (qs[i/2] & 0x0003);
                acc2[0] += yl[i+ 1] * (qs[i/2] & 0x0300);
                acc1[1] += yl[i+ 8] * (qs[i/2] & 0x000c);
                acc2[1] += yl[i+ 9] * (qs[i/2] & 0x0c00);
                acc1[2] += yl[i+16] * (qs[i/2] & 0x0030);
                acc2[2] += yl[i+17] * (qs[i/2] & 0x3000);
                acc1[3] += yl[i+24] * (qs[i/2] & 0x00c0);
                acc2[3] += yl[i+25] * (qs[i/2] & 0xc000);
            }
            float dall = dh[0];
            float dmin = dh[1] * 1.f/16.f;
            sumf[row] += dall * ((acc1[0] + 1.f/256.f * acc2[0]) * (sc[0] & 0xF) * 1.f/ 1.f +
                                 (acc1[1] + 1.f/256.f * acc2[1]) * (sc[2] & 0xF) * 1.f/ 4.f +
                                 (acc1[2] + 1.f/256.f * acc2[2]) * (sc[4] & 0xF) * 1.f/16.f +
                                 (acc1[3] + 1.f/256.f * acc2[3]) * (sc[6] & 0xF) * 1.f/64.f) -
                         dmin * (sumy[0] * (sc[0] & 0xF0) + sumy[1] * (sc[2] & 0xF0) + sumy[2] * (sc[4] & 0xF0) + sumy[3] * (sc[6] & 0xF0));

            qs += args.nb01/2;
            sc += args.nb01;
            dh += args.nb01/2;
        }

        y4 += 4 * QK_K;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_q2_K_f32")]]
kernel void kernel_mul_mv_q2_K_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_q2_K_f32_impl<N_R0_Q2_K, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_q3_K_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_q3_K * x = (device const block_q3_K *) (src0 + offset0);
    device const float     * yy = (device const float      *) (src1 + offset1);

    float yl[32];

    //const uint16_t kmask1 = 0x3030;
    //const uint16_t kmask2 = 0x0f0f;

    const short tid = tiisg/4;
    const short ix  = tiisg%4;
    const short ip  = tid/4;          // 0 or 1
    const short il  = 2*((tid%4)/2);  // 0 or 2
    const short ir  = tid%2;
    const short l0  = 8*ir;

    // One would think that the Metal compiler would figure out that ip and il can only have
    // 4 possible states, and optimize accordingly. Well, no. It needs help, and we do it
    // with these two tales.
    //
    // Possible masks for the high bit
    const ushort4 mm[4] = {{0x0001, 0x0100, 0x0002, 0x0200},  // ip = 0, il = 0
                           {0x0004, 0x0400, 0x0008, 0x0800},  // ip = 0, il = 2
                           {0x0010, 0x1000, 0x0020, 0x2000},  // ip = 1, il = 0
                           {0x0040, 0x4000, 0x0080, 0x8000}}; // ip = 1, il = 2

    // Possible masks for the low 2 bits
    const int4 qm[2] = {{0x0003, 0x0300, 0x000c, 0x0c00}, {0x0030, 0x3000, 0x00c0, 0xc000}};

    const ushort4 hm = mm[2*ip + il/2];

    const short shift = 2*il;

    const float v1 = il == 0 ? 4.f : 64.f;
    const float v2 = 4.f * v1;

    const uint16_t s_shift1 = 4*ip;
    const uint16_t s_shift2 = s_shift1 + il;

    const short q_offset = 32*ip + l0;
    const short y_offset = 128*ip + 32*il + l0;

    device const float * y1 = yy + ix*QK_K + y_offset;

    uint32_t scales32, aux32;
    thread uint16_t * scales16 = (thread uint16_t *)&scales32;
    thread const int8_t * scales = (thread const int8_t *)&scales32;

    float sumf1[nr0] = {0.f};
    float sumf2[nr0] = {0.f};

    for (int i = ix; i < nb; i += 4) {
        for (short l = 0; l < 8; ++l) {
            yl[l+ 0] = y1[l+ 0];
            yl[l+ 8] = y1[l+16];
            yl[l+16] = y1[l+32];
            yl[l+24] = y1[l+48];
        }

        device const uint16_t * q = (device const uint16_t *)(x[i].qs + q_offset);
        device const uint16_t * h = (device const uint16_t *)(x[i].hmask + l0);
        device const uint16_t * a = (device const uint16_t *)(x[i].scales);
        device const half * dh = &x[i].d;

        for (short row = 0; row < nr0; ++row) {
            const float d_all = (float)dh[0];

            scales16[0] = a[4];
            scales16[1] = a[5];
            aux32 = ((scales32 >> s_shift2) << 4) & 0x30303030;
            scales16[0] = a[il+0];
            scales16[1] = a[il+1];
            scales32 = ((scales32 >> s_shift1) & 0x0f0f0f0f) | aux32;

            float s1 = 0, s2 = 0, s3 = 0, s4 = 0, s5 = 0, s6 = 0;
            for (short l = 0; l < 8; l += 2) {
                const int32_t qs = q[l/2];
                s1 += yl[l+0] * (qs & qm[il/2][0]);
                s2 += yl[l+1] * (qs & qm[il/2][1]);
                s3 += ((h[l/2] & hm[0]) ? 0.f : yl[l+0]) + ((h[l/2] & hm[1]) ? 0.f : yl[l+1]);
                s4 += yl[l+16] * (qs & qm[il/2][2]);
                s5 += yl[l+17] * (qs & qm[il/2][3]);
                s6 += ((h[l/2] & hm[2]) ? 0.f : yl[l+16]) + ((h[l/2] & hm[3]) ? 0.f : yl[l+17]);
            }
            float d1 = d_all * (s1 + 1.f/256.f * s2 - s3*v1);
            float d2 = d_all * (s4 + 1.f/256.f * s5 - s6*v2);
            sumf1[row] += d1 * (scales[0] - 32);
            sumf2[row] += d2 * (scales[2] - 32);

            s1 = s2 = s3 = s4 = s5 = s6 = 0;
            for (short l = 0; l < 8; l += 2) {
                const int32_t qs = q[l/2+8];
                s1 += yl[l+8] * (qs & qm[il/2][0]);
                s2 += yl[l+9] * (qs & qm[il/2][1]);
                s3 += ((h[l/2+8] & hm[0]) ? 0.f : yl[l+8]) + ((h[l/2+8] & hm[1]) ? 0.f : yl[l+9]);
                s4 += yl[l+24] * (qs & qm[il/2][2]);
                s5 += yl[l+25] * (qs & qm[il/2][3]);
                s6 += ((h[l/2+8] & hm[2]) ? 0.f : yl[l+24]) + ((h[l/2+8] & hm[3]) ? 0.f : yl[l+25]);
            }
            d1 = d_all * (s1 + 1.f/256.f * s2 - s3*v1);
            d2 = d_all * (s4 + 1.f/256.f * s5 - s6*v2);
            sumf1[row] += d1 * (scales[1] - 32);
            sumf2[row] += d2 * (scales[3] - 32);

            q  += args.nb01/2;
            h  += args.nb01/2;
            a  += args.nb01/2;
            dh += args.nb01/2;
        }

        y1 += 4 * QK_K;
    }

    for (int row = 0; row < nr0; ++row) {
        const float sumf = (sumf1[row] + 0.25f * sumf2[row]) / (1 << shift);
        sumf1[row] = simd_sum(sumf);
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    if (tiisg == 0) {
        for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
            dst_f32[first_row + row] = sumf1[row];
        }
    }
}

[[host_name("kernel_mul_mv_q3_K_f32")]]
kernel void kernel_mul_mv_q3_K_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_q3_K_f32_impl<N_R0_Q3_K, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_q4_K_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr uint16_t kmask1 = 0x3f3f;
    constexpr uint16_t kmask2 = 0x0f0f;
    constexpr uint16_t kmask3 = 0xc0c0;

    const short ix = tiisg/8;  // 0...3
    const short it = tiisg%8;  // 0...7
    const short iq = it/4;     // 0 or 1
    const short ir = it%4;     // 0...3

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_q4_K * x = (device const block_q4_K *) (src0 + offset0);
    device const float      * y = (device const float      *) (src1 + offset1);

    float yl[16];
    float yh[16];

    float sumf[nr0]={0.f};

    device const float * y4 = y + ix * QK_K + 64 * iq + 8 * ir;

    uint16_t sc16[4];
    thread const uint8_t * sc8 = (thread const uint8_t *)sc16;

    for (int ib = ix; ib < nb; ib += 4) {
        float4 sumy = {0.f, 0.f, 0.f, 0.f};

        for (short i = 0; i < 8; ++i) {
            yl[i+0] = y4[i+  0]; sumy[0] += yl[i+0];
            yl[i+8] = y4[i+ 32]; sumy[1] += yl[i+8];
            yh[i+0] = y4[i+128]; sumy[2] += yh[i+0];
            yh[i+8] = y4[i+160]; sumy[3] += yh[i+8];
        }

        device const uint16_t * sc = (device const uint16_t *)x[ib].scales + iq;
        device const uint16_t * q1 = (device const uint16_t *)x[ib].qs + 16 * iq + 4 * ir;
        device const half     * dh = &x[ib].d;

        for (short row = 0; row < nr0; row++) {
            sc16[0] = sc[0] & kmask1;
            sc16[1] = sc[2] & kmask1;
            sc16[2] = ((sc[4] >> 0) & kmask2) | ((sc[0] & kmask3) >> 2);
            sc16[3] = ((sc[4] >> 4) & kmask2) | ((sc[2] & kmask3) >> 2);

            device const uint16_t * q2 = q1 + 32;

            float4 acc1 = {0.f, 0.f, 0.f, 0.f};
            float4 acc2 = {0.f, 0.f, 0.f, 0.f};

            FOR_UNROLL (short i = 0; i < 4; ++i) {
                acc1[0] += yl[2*i + 0] * (q1[i] & 0x000F);
                acc1[1] += yl[2*i + 1] * (q1[i] & 0x0F00);
                acc1[2] += yl[2*i + 8] * (q1[i] & 0x00F0);
                acc1[3] += yl[2*i + 9] * (q1[i] & 0xF000);
                acc2[0] += yh[2*i + 0] * (q2[i] & 0x000F);
                acc2[1] += yh[2*i + 1] * (q2[i] & 0x0F00);
                acc2[2] += yh[2*i + 8] * (q2[i] & 0x00F0);
                acc2[3] += yh[2*i + 9] * (q2[i] & 0xF000);
            }

            sumf[row] += dh[0] * ((acc1[0] + 1.f/256.f * acc1[1]) * sc8[0] +
                                  (acc1[2] + 1.f/256.f * acc1[3]) * sc8[1] * 1.f/16.f +
                                  (acc2[0] + 1.f/256.f * acc2[1]) * sc8[4] +
                                  (acc2[2] + 1.f/256.f * acc2[3]) * sc8[5] * 1.f/16.f) -
                         dh[1] * (sumy[0] * sc8[2] + sumy[1] * sc8[3] + sumy[2] * sc8[6] + sumy[3] * sc8[7]);

            q1 += args.nb01/2;
            sc += args.nb01/2;
            dh += args.nb01/2;
        }

        y4 += 4 * QK_K;
    }

    device float * dst_f32 = (device float *) dst + (int64_t)im*args.ne0*args.ne1 + (int64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_q4_K_f32")]]
kernel void kernel_mul_mv_q4_K_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_q4_K_f32_impl<N_R0_Q4_K, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_q5_K_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_q5_K * x = (device const block_q5_K *) (src0 + offset0);
    device const float     * yy = (device const float      *) (src1 + offset1);

    float sumf[nr0]={0.f};

    float yl[16], yh[16];

    constexpr uint16_t kmask1 = 0x3f3f;
    constexpr uint16_t kmask2 = 0x0f0f;
    constexpr uint16_t kmask3 = 0xc0c0;

    const short tid = tiisg/4;
    const short ix  = tiisg%4;
    const short iq  = tid/4;
    const short ir  = tid%4;

    const short l0 = 8*ir;
    const short q_offset = 32*iq + l0;
    const short y_offset = 64*iq + l0;

    const uint8_t hm1 = 1u << (2*iq);
    const uint8_t hm2 = hm1 << 1;
    const uint8_t hm3 = hm1 << 4;
    const uint8_t hm4 = hm2 << 4;

    uint16_t sc16[4];
    thread const uint8_t * sc8 = (thread const uint8_t *)sc16;

    device const float * y1 = yy + ix*QK_K + y_offset;

    for (int i = ix; i < nb; i += 4) {
        device const uint8_t * q1 = x[i].qs + q_offset;
        device const uint8_t * qh = x[i].qh + l0;
        device const half * dh = &x[i].d;
        device const uint16_t * a = (device const uint16_t *)x[i].scales + iq;

        device const float * y2 = y1 + 128;
        float4 sumy = {0.f, 0.f, 0.f, 0.f};
        for (short l = 0; l < 8; ++l) {
            yl[l+0] = y1[l+ 0]; sumy[0] += yl[l+0];
            yl[l+8] = y1[l+32]; sumy[1] += yl[l+8];
            yh[l+0] = y2[l+ 0]; sumy[2] += yh[l+0];
            yh[l+8] = y2[l+32]; sumy[3] += yh[l+8];
        }

        for (short row = 0; row < nr0; ++row) {
            device const uint8_t * q2 = q1 + 64;

            sc16[0] = a[0] & kmask1;
            sc16[1] = a[2] & kmask1;
            sc16[2] = ((a[4] >> 0) & kmask2) | ((a[0] & kmask3) >> 2);
            sc16[3] = ((a[4] >> 4) & kmask2) | ((a[2] & kmask3) >> 2);

            float4 acc1 = {0.f};
            float4 acc2 = {0.f};
            FOR_UNROLL (short l = 0; l < 8; ++l) {
                uint8_t h = qh[l];
                acc1[0] += yl[l+0] * (q1[l] & 0x0F);
                acc1[1] += yl[l+8] * (q1[l] & 0xF0);
                acc1[2] += yh[l+0] * (q2[l] & 0x0F);
                acc1[3] += yh[l+8] * (q2[l] & 0xF0);
                acc2[0] += h & hm1 ? yl[l+0] : 0.f;
                acc2[1] += h & hm2 ? yl[l+8] : 0.f;
                acc2[2] += h & hm3 ? yh[l+0] : 0.f;
                acc2[3] += h & hm4 ? yh[l+8] : 0.f;
            }

            sumf[row] += dh[0] * (sc8[0] * (acc1[0]      + 16.f*acc2[0]) +
                                  sc8[1] * (acc1[1]/16.f + 16.f*acc2[1]) +
                                  sc8[4] * (acc1[2]      + 16.f*acc2[2]) +
                                  sc8[5] * (acc1[3]/16.f + 16.f*acc2[3])) -
                         dh[1] * (sumy[0] * sc8[2] + sumy[1] * sc8[3] + sumy[2] * sc8[6] + sumy[3] * sc8[7]);

            q1 += args.nb01;
            qh += args.nb01;
            dh += args.nb01/2;
            a  += args.nb01/2;
        }

        y1 += 4 * QK_K;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        const float tot = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = tot;
        }
    }
}

[[host_name("kernel_mul_mv_q5_K_f32")]]
kernel void kernel_mul_mv_q5_K_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_q5_K_f32_impl<N_R0_Q5_K, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_q6_K_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    constexpr uint8_t kmask1 = 0x03;
    constexpr uint8_t kmask2 = 0x0C;
    constexpr uint8_t kmask3 = 0x30;
    constexpr uint8_t kmask4 = 0xC0;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_q6_K * x = (device const block_q6_K *) (src0 + offset0);
    device const float     * yy = (device const float      *) (src1 + offset1);

    float sumf[nr0] = { 0.f };

    float yl[16];

    const short tid = tiisg/2;
    const short ix  = tiisg%2;
    const short ip  = tid/8;         // 0 or 1
    const short il  = tid%8;
    const short l0  = 4*il;
    const short is  = 8*ip + l0/16;

    const short y_offset   = 128*ip + l0;
    const short q_offset_l =  64*ip + l0;
    const short q_offset_h =  32*ip + l0;

    for (int i = ix; i < nb; i += 2) {
        device const uint8_t * q1 = x[i].ql + q_offset_l;
        device const uint8_t * q2 = q1 + 32;
        device const uint8_t * qh = x[i].qh + q_offset_h;
        device const int8_t  * sc = x[i].scales + is;
        device const half    * dh = &x[i].d;

        device const float * y = yy + i * QK_K + y_offset;

        for (short l = 0; l < 4; ++l) {
            yl[4*l + 0] = y[l +  0];
            yl[4*l + 1] = y[l + 32];
            yl[4*l + 2] = y[l + 64];
            yl[4*l + 3] = y[l + 96];
        }

        for (short row = 0; row < nr0; ++row) {
            float4 sums = {0.f, 0.f, 0.f, 0.f};

            FOR_UNROLL (short l = 0; l < 4; ++l) {
                sums[0] += yl[4*l + 0] * ((int8_t)((q1[l] & 0xF) | ((qh[l] & kmask1) << 4)) - 32);
                sums[1] += yl[4*l + 1] * ((int8_t)((q2[l] & 0xF) | ((qh[l] & kmask2) << 2)) - 32);
                sums[2] += yl[4*l + 2] * ((int8_t)((q1[l]  >> 4) | ((qh[l] & kmask3) << 0)) - 32);
                sums[3] += yl[4*l + 3] * ((int8_t)((q2[l]  >> 4) | ((qh[l] & kmask4) >> 2)) - 32);
            }

            sumf[row] += dh[0] * (sums[0] * sc[0] + sums[1] * sc[2] + sums[2] * sc[4] + sums[3] * sc[6]);

            q1 += args.nb01;
            q2 += args.nb01;
            qh += args.nb01;
            sc += args.nb01;
            dh += args.nb01/2;
        }
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_q6_K_f32")]]
kernel void kernel_mul_mv_q6_K_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_q6_K_f32_impl<N_R0_Q6_K, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

// ======================= "True" 2-bit

template<int nr0, typename args_t>
void kernel_mul_mv_iq2_xxs_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xxs * x = (device const block_iq2_xxs *) (src0 + offset0);
    device const float         * y = (device const float         *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = iq2xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xxs * xr = x + ibl;
        device const uint16_t * q2 = xr->qs + 4 * ib;
        device const half * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            const float db = dh[0];
            device const uint8_t * aux8 = (device const uint8_t *)q2;
            const uint32_t aux32 = q2[2] | (q2[3] << 16);
            const float d = db * (0.5f + (aux32 >> 28));

            float sum = 0;
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * grid = (const threadgroup uint8_t *)(svalues + aux8[l]);
                const uint8_t signs = ssigns[(aux32 >> 7*l) & 127];
                for (short j = 0; j < 8; ++j) {
                    sum += yl[8*l + j] * grid[j] * (signs & kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumf[row] += d * sum;

            dh += args.nb01/2;
            q2 += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

[[host_name("kernel_mul_mv_iq2_xxs_f32")]]
kernel void kernel_mul_mv_iq2_xxs_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    kernel_mul_mv_iq2_xxs_f32_impl<N_R0_IQ2_XXS, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq2_xs_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_xs * x = (device const block_iq2_xs *) (src0 + offset0);
    device const float        * y = (device const float        *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint64_t * svalues = (threadgroup uint64_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 512);
    {
        int nval = 8;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = iq2xs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_xs * xr = x + ibl;
        device const uint16_t * q2 = xr->qs + 4 * ib;
        device const uint8_t  * sc = xr->scales + ib;
        device const half * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            const float db = dh[0];
            const uint8_t ls1 = sc[0] & 0xf;
            const uint8_t ls2 = sc[0] >>  4;
            const float d1 = db * (0.5f + ls1);
            const float d2 = db * (0.5f + ls2);

            float sum1 = 0, sum2 = 0;
            for (short l = 0; l < 2; ++l) {
                const threadgroup uint8_t * grid = (const threadgroup uint8_t *)(svalues + (q2[l] & 511));
                const uint8_t signs = ssigns[(q2[l] >> 9)];
                for (short j = 0; j < 8; ++j) {
                    sum1 += yl[8*l + j] * grid[j] * (signs & kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            for (short l = 2; l < 4; ++l) {
                const threadgroup uint8_t * grid = (const threadgroup uint8_t *)(svalues + (q2[l] & 511));
                const uint8_t signs = ssigns[(q2[l] >> 9)];
                for (short j = 0; j < 8; ++j) {
                    sum2 += yl[8*l + j] * grid[j] * (signs & kmask_iq2xs[j] ? -1.f : 1.f);
                }
            }
            sumf[row] += d1 * sum1 + d2 * sum2;

            dh += args.nb01/2;
            q2 += args.nb01/2;
            sc += args.nb01;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

[[host_name("kernel_mul_mv_iq2_xs_f32")]]
kernel void kernel_mul_mv_iq2_xs_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq2_xs_f32_impl<N_R0_IQ2_XS, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq3_xxs_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq3_xxs * x = (device const block_iq3_xxs *) (src0 + offset0);
    device const float         * y = (device const float         *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint32_t * svalues = (threadgroup uint32_t *)(shmem);
    threadgroup uint8_t  * ssigns  = (threadgroup uint8_t  *)(svalues + 256);
    {
        int nval = 4;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = iq3xxs_grid[pos + i];
        nval = 2;
        pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) ssigns[pos+i] = ksigns_iq2xs[pos+i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq3_xxs * xr = x + ibl;
        device const uint8_t  * q3 = xr->qs + 8 * ib;
        device const uint16_t * gas = (device const uint16_t *)(xr->qs + QK_K/4) + 2 * ib;
        device const half * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            const float db = dh[0];
            const uint32_t aux32 = gas[0] | (gas[1] << 16);
            const float d = db * (0.5f + (aux32 >> 28));

            float2 sum = {0};
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint8_t * grid1 = (const threadgroup uint8_t *)(svalues + q3[2*l+0]);
                const threadgroup uint8_t * grid2 = (const threadgroup uint8_t *)(svalues + q3[2*l+1]);
                const uint8_t signs = ssigns[(aux32 >> 7*l) & 127];
                for (short j = 0; j < 4; ++j) {
                    sum[0] += yl[8*l + j + 0] * grid1[j] * (signs & kmask_iq2xs[j+0] ? -1.f : 1.f);
                    sum[1] += yl[8*l + j + 4] * grid2[j] * (signs & kmask_iq2xs[j+4] ? -1.f : 1.f);
                }
            }
            sumf[row] += d * (sum[0] + sum[1]);

            dh  += args.nb01/2;
            q3  += args.nb01;
            gas += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.5f;
        }
    }
}

[[host_name("kernel_mul_mv_iq3_xxs_f32")]]
kernel void kernel_mul_mv_iq3_xxs_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq3_xxs_f32_impl<N_R0_IQ3_XXS, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq3_s_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq3_s * x = (device const block_iq3_s *) (src0 + offset0);
    device const float       * y = (device const float       *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    threadgroup uint32_t * svalues = (threadgroup uint32_t *) shmem;
    {
        int nval = 8;
        int pos  = (32*sgitg + tiisg)*nval;
        for (int i = 0; i < nval; ++i) svalues[pos + i] = iq3s_grid[pos + i];
        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    const int ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq3_s * xr = x + ibl;
        device const uint8_t * qs = xr->qs + 8 * ib;
        device const uint8_t * qh = xr->qh + ib;
        device const uint8_t * sc = xr->scales + (ib/2);
        device const uint8_t * signs = xr->signs + 4 * ib;
        device const half * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            const float db = dh[0];
            const float d = db * (1 + 2*((sc[0] >> 4*(ib%2)) & 0xf));

            float2 sum = {0};
            for (short l = 0; l < 4; ++l) {
                const threadgroup uint32_t * table1 = qh[0] & kmask_iq2xs[2*l+0] ? svalues + 256 : svalues;
                const threadgroup uint32_t * table2 = qh[0] & kmask_iq2xs[2*l+1] ? svalues + 256 : svalues;
                const threadgroup uint8_t * grid1 = (const threadgroup uint8_t *)(table1 + qs[2*l+0]);
                const threadgroup uint8_t * grid2 = (const threadgroup uint8_t *)(table2 + qs[2*l+1]);
                for (short j = 0; j < 4; ++j) {
                    sum[0] += yl[8*l + j + 0] * grid1[j] * select(1, -1, signs[l] & kmask_iq2xs[j+0]);
                    sum[1] += yl[8*l + j + 4] * grid2[j] * select(1, -1, signs[l] & kmask_iq2xs[j+4]);
                }
            }
            sumf[row] += d * (sum[0] + sum[1]);

            dh    += args.nb01/2;
            qs    += args.nb01;
            qh    += args.nb01;
            sc    += args.nb01;
            signs += args.nb01;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_iq3_s_f32")]]
kernel void kernel_mul_mv_iq3_s_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq3_s_f32_impl<N_R0_IQ3_S, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq2_s_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq2_s * x = (device const block_iq2_s *) (src0 + offset0);
    device const float       * y = (device const float       *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    //threadgroup uint64_t * svalues = (threadgroup uint64_t *) shmem;
    //{
    //    int nval = 32;
    //    int pos  = (32*sgitg + tiisg)*nval;
    //    for (int i = 0; i < nval; ++i) svalues[pos + i] = iq2s_grid[pos + i];
    //    threadgroup_barrier(mem_flags::mem_threadgroup);
    //}

    const short ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq2_s * xr = x + ibl;
        device const uint8_t * qs = xr->qs + 4 * ib;
        device const uint8_t * qh = xr->qh + ib;
        device const uint8_t * sc = xr->scales + ib;
        device const uint8_t * signs = qs + QK_K/8;
        device const half * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            const float db = dh[0];
            const float d1 = db * (0.5f + (sc[0] & 0xf));
            const float d2 = db * (0.5f + (sc[0] >>  4));

            float2 sum = {0};
            for (short l = 0; l < 2; ++l) {
                //const threadgroup uint8_t * grid1 = (const threadgroup uint8_t *)(svalues + (qs[l+0] | ((qh[0] << (8-2*l)) & 0x300)));
                //const threadgroup uint8_t * grid2 = (const threadgroup uint8_t *)(svalues + (qs[l+2] | ((qh[0] << (4-2*l)) & 0x300)));
                constant uint8_t * grid1 = (constant uint8_t *)(iq2s_grid + (qs[l+0] | ((qh[0] << (8-2*l)) & 0x300)));
                constant uint8_t * grid2 = (constant uint8_t *)(iq2s_grid + (qs[l+2] | ((qh[0] << (4-2*l)) & 0x300)));
                for (short j = 0; j < 8; ++j) {
                    sum[0] += yl[8*l + j +  0] * grid1[j] * select(1, -1, signs[l+0] & kmask_iq2xs[j]);
                    sum[1] += yl[8*l + j + 16] * grid2[j] * select(1, -1, signs[l+2] & kmask_iq2xs[j]);
                }
            }
            sumf[row] += d1 * sum[0] + d2 * sum[1];

            dh    += args.nb01/2;
            qs    += args.nb01;
            qh    += args.nb01;
            sc    += args.nb01;
            signs += args.nb01;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all * 0.25f;
        }
    }
}

[[host_name("kernel_mul_mv_iq2_s_f32")]]
kernel void kernel_mul_mv_iq2_s_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq2_s_f32_impl<N_R0_IQ2_S, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq1_s_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq1_s * x = (device const block_iq1_s *) (src0 + offset0);
    device const float       * y = (device const float       *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    const short ix = tiisg;

    device const float * y4 = y + 32 * ix;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        float sumy = 0;
        for (short i = 0; i < 32; ++i) {
            yl[i] = y4[i];
            sumy += yl[i];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq1_s * xr = x + ibl;
        device const uint8_t  * qs = xr->qs + 4 * ib;
        device const uint16_t * qh = xr->qh + ib;
        device const half     * dh = &xr->d;

        for (short row = 0; row < nr0; row++) {
            constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | ((qh[0] << 8) & 0x700)));
            constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | ((qh[0] << 5) & 0x700)));
            constant uint8_t * grid3 = (constant uint8_t *)(iq1s_grid_gpu + (qs[2] | ((qh[0] << 2) & 0x700)));
            constant uint8_t * grid4 = (constant uint8_t *)(iq1s_grid_gpu + (qs[3] | ((qh[0] >> 1) & 0x700)));

            float sum = 0;
            for (short j = 0; j < 4; ++j) {
                sum += yl[j+ 0] * (grid1[j] & 0xf) + yl[j+ 4] * (grid1[j] >> 4)
                     + yl[j+ 8] * (grid2[j] & 0xf) + yl[j+12] * (grid2[j] >> 4)
                     + yl[j+16] * (grid3[j] & 0xf) + yl[j+20] * (grid3[j] >> 4)
                     + yl[j+24] * (grid4[j] & 0xf) + yl[j+28] * (grid4[j] >> 4);
            }
            sumf[row] += (float)dh[0] * (sum + sumy * (qh[0] & 0x8000 ? -1 - IQ1S_DELTA : -1 + IQ1S_DELTA)) * (2*((qh[0] >> 12) & 7) + 1);

            dh += args.nb01/2;
            qs += args.nb01;
            qh += args.nb01/2;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_iq1_s_f32")]]
kernel void kernel_mul_mv_iq1_s_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq1_s_f32_impl<N_R0_IQ1_S, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int nr0, typename args_t>
void kernel_mul_mv_iq1_m_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    const int nb = args.ne00/QK_K;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * nr0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq1_m * x = (device const block_iq1_m *) (src0 + offset0);
    device const float       * y = (device const float       *) (src1 + offset1);

    float yl[32];
    float sumf[nr0]={0.f};

    const int nb32 = nb * (QK_K / 32);

    const short ix = tiisg;

    device const float * y4 = y + 32 * ix;

    iq1m_scale_t scale;

    for (int ib32 = ix; ib32 < nb32; ib32 += 32) {
        float4 sumy = {0.f};
        for (short i = 0; i < 8; ++i) {
            yl[i+ 0] = y4[i+ 0]; sumy[0] += yl[i+ 0];
            yl[i+ 8] = y4[i+ 8]; sumy[1] += yl[i+ 8];
            yl[i+16] = y4[i+16]; sumy[2] += yl[i+16];
            yl[i+24] = y4[i+24]; sumy[3] += yl[i+24];
        }

        const int ibl = ib32 / (QK_K / 32);
        const int ib  = ib32 % (QK_K / 32);

        device const block_iq1_m * xr = x + ibl;
        device const uint8_t  * qs = xr->qs + 4 * ib;
        device const uint8_t  * qh = xr->qh + 2 * ib;
        device const uint16_t * sc = (device const uint16_t *)xr->scales;

        for (short row = 0; row < nr0; row++) {
            scale.u16 = (sc[0] >> 12) | ((sc[1] >> 8) & 0x00f0) | ((sc[2] >> 4) & 0x0f00) | (sc[3] & 0xf000);

            constant uint8_t * grid1 = (constant uint8_t *)(iq1s_grid_gpu + (qs[0] | ((qh[0] << 8) & 0x700)));
            constant uint8_t * grid2 = (constant uint8_t *)(iq1s_grid_gpu + (qs[1] | ((qh[0] << 4) & 0x700)));
            constant uint8_t * grid3 = (constant uint8_t *)(iq1s_grid_gpu + (qs[2] | ((qh[1] << 8) & 0x700)));
            constant uint8_t * grid4 = (constant uint8_t *)(iq1s_grid_gpu + (qs[3] | ((qh[1] << 4) & 0x700)));

            float2 sum = {0.f};
            for (short j = 0; j < 4; ++j) {
                sum[0] += yl[j+ 0] * (grid1[j] & 0xf) + yl[j+ 4] * (grid1[j] >> 4)
                        + yl[j+ 8] * (grid2[j] & 0xf) + yl[j+12] * (grid2[j] >> 4);
                sum[1] += yl[j+16] * (grid3[j] & 0xf) + yl[j+20] * (grid3[j] >> 4)
                        + yl[j+24] * (grid4[j] & 0xf) + yl[j+28] * (grid4[j] >> 4);
            }
            const float delta1 = sumy[0] * (qh[0] & 0x08 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA) + sumy[1] * (qh[0] & 0x80 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA);
            const float delta2 = sumy[2] * (qh[1] & 0x08 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA) + sumy[3] * (qh[1] & 0x80 ? -1 - IQ1M_DELTA : -1 + IQ1M_DELTA);

            sumf[row] += (float)scale.f16 * ((sum[0] + delta1) * (2*((sc[ib/2] >> (6*(ib%2)+0)) & 7) + 1) +
                                             (sum[1] + delta2) * (2*((sc[ib/2] >> (6*(ib%2)+3)) & 7) + 1));

            sc += args.nb01/2;
            qs += args.nb01;
            qh += args.nb01;
        }

        y4 += 32 * 32;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < nr0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_iq1_m_f32")]]
kernel void kernel_mul_mv_iq1_m_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq1_m_f32_impl<N_R0_IQ1_M, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, nullptr, tgpig, tiisg, sgitg);
}

template<int NR0, typename args_t>
void kernel_mul_mv_iq4_nl_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    threadgroup float * shmem_f32 = (threadgroup float *) shmem;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * NR0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq4_nl * x = (device const block_iq4_nl *) (src0 + offset0);
    device const float        * y = (device const float        *) (src1 + offset1);

    const int nb   = args.ne00/QK4_NL;
    const int ns01 = args.nb01/args.nb00;

    const short ix = tiisg/2;  // 0...15
    const short it = tiisg%2;  // 0 or 1

    shmem_f32[tiisg] = kvalues_iq4nl_f[tiisg%16];
    threadgroup_barrier(mem_flags::mem_threadgroup);

    float4 yl[4];
    float sumf[NR0]={0.f};

    device const float * yb = y + ix*QK4_NL + it*8;

    uint32_t aux32[2];
    thread const uint8_t * q8 = (thread const uint8_t *)aux32;

    float4 qf1, qf2;

    // [TAG_MUL_MV_WEIRD]
    for (int ib = ix; ib < nb && ib < ns01; ib += 16) {
        device const float4 * y4 = (device const float4 *)yb;
        yl[0] = y4[0];
        yl[1] = y4[4];
        yl[2] = y4[1];
        yl[3] = y4[5];

        for (short row = 0; row < NR0; row++) {
            device const block_iq4_nl & xb = x[row*ns01 + ib];
            device const uint16_t * q4 = (device const uint16_t *)(xb.qs + 8*it);

            float4 acc1 = {0.f}, acc2 = {0.f};

            aux32[0] = q4[0] | (q4[1] << 16);
            aux32[1] = (aux32[0] >> 4) & 0x0f0f0f0f;
            aux32[0] &= 0x0f0f0f0f;
            qf1 = {shmem_f32[q8[0]], shmem_f32[q8[1]], shmem_f32[q8[2]], shmem_f32[q8[3]]};
            qf2 = {shmem_f32[q8[4]], shmem_f32[q8[5]], shmem_f32[q8[6]], shmem_f32[q8[7]]};
            acc1 += yl[0] * qf1;
            acc2 += yl[1] * qf2;

            aux32[0] = q4[2] | (q4[3] << 16);
            aux32[1] = (aux32[0] >> 4) & 0x0f0f0f0f;
            aux32[0] &= 0x0f0f0f0f;
            qf1 = {shmem_f32[q8[0]], shmem_f32[q8[1]], shmem_f32[q8[2]], shmem_f32[q8[3]]};
            qf2 = {shmem_f32[q8[4]], shmem_f32[q8[5]], shmem_f32[q8[6]], shmem_f32[q8[7]]};
            acc1 += yl[2] * qf1;
            acc2 += yl[3] * qf2;

            acc1 += acc2;

            sumf[row] += (float)xb.d * (acc1[0] + acc1[1] + acc1[2] + acc1[3]);
        }

        yb += 16 * QK4_NL;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < NR0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_iq4_nl_f32")]]
kernel void kernel_mul_mv_iq4_nl_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq4_nl_f32_impl<N_R0_IQ4_NL, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int NR0, typename args_t>
void kernel_mul_mv_iq4_xs_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    threadgroup float * shmem_f32 = (threadgroup float *) shmem;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;
    const int first_row = (r0 * NSG + sgitg) * NR0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_iq4_xs * x = (device const block_iq4_xs *) (src0 + offset0);
    device const float        * y = (device const float        *) (src1 + offset1);

    const int nb   = args.ne00/QK_K;
    const int ns01 = args.nb01/args.nb00;

    const short ix = tiisg/16;  // 0 or 1
    const short it = tiisg%16;  // 0...15
    const short ib = it/2;
    const short il = it%2;

    shmem_f32[tiisg] = kvalues_iq4nl_f[tiisg%16];
    threadgroup_barrier(mem_flags::mem_threadgroup);

    float4 yl[4];
    float sumf[NR0]={0.f};

    device const float * yb = y + ix * QK_K + ib * 32 + il * 8;

    uint32_t aux32[2];
    thread const uint8_t * q8 = (thread const uint8_t *)aux32;

    float4 qf1, qf2;

    // [TAG_MUL_MV_WEIRD]
    for (int ibl = ix; ibl < nb && ibl < ns01; ibl += 2) {
        device const float4 * y4 = (device const float4 *)yb;
        yl[0] = y4[0];
        yl[1] = y4[4];
        yl[2] = y4[1];
        yl[3] = y4[5];

        for (short row = 0; row < NR0; ++row) {
            device const block_iq4_xs & xb = x[row*ns01 + ibl];
            device const uint32_t * q4 = (device const uint32_t *)(xb.qs + 16*ib + 8*il);

            float4 acc1 = {0.f}, acc2 = {0.f};

            aux32[0] = (q4[0]     ) & 0x0f0f0f0f;
            aux32[1] = (q4[0] >> 4) & 0x0f0f0f0f;
            qf1 = {shmem_f32[q8[0]], shmem_f32[q8[1]], shmem_f32[q8[2]], shmem_f32[q8[3]]};
            qf2 = {shmem_f32[q8[4]], shmem_f32[q8[5]], shmem_f32[q8[6]], shmem_f32[q8[7]]};
            acc1 += yl[0] * qf1;
            acc2 += yl[1] * qf2;

            aux32[0] = (q4[1]     ) & 0x0f0f0f0f;
            aux32[1] = (q4[1] >> 4) & 0x0f0f0f0f;
            qf1 = {shmem_f32[q8[0]], shmem_f32[q8[1]], shmem_f32[q8[2]], shmem_f32[q8[3]]};
            qf2 = {shmem_f32[q8[4]], shmem_f32[q8[5]], shmem_f32[q8[6]], shmem_f32[q8[7]]};
            acc1 += yl[2] * qf1;
            acc2 += yl[3] * qf2;

            acc1 += acc2;

            const int ls = (((xb.scales_l[ib/2] >> 4*(ib%2)) & 0xf) | (((xb.scales_h >> 2*ib) & 3) << 4)) - 32;
            sumf[row] += (float)xb.d * ls * (acc1[0] + acc1[1] + acc1[2] + acc1[3]);
        }

        yb += 2 * QK_K;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < NR0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_iq4_xs_f32")]]
kernel void kernel_mul_mv_iq4_xs_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_iq4_xs_f32_impl<N_R0_IQ4_XS, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<int NR0, typename args_t>
void kernel_mul_mv_mxfp4_f32_impl(
        args_t args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg) {
    const short NSG = FC_mul_mv_nsg;

    threadgroup float * shmem_f32 = (threadgroup float *) shmem;

    const int r0 = tgpig.x;
    const int r1 = tgpig.y;
    const int im = tgpig.z;

    const int first_row = (r0 * NSG + sgitg) * NR0;

    const uint i12 = im%args.ne12;
    const uint i13 = im/args.ne12;

    const uint64_t offset0 = first_row*args.nb01 + (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const uint64_t offset1 =        r1*args.nb11 + (i12        )*args.nb12 + (i13        )*args.nb13;

    device const block_mxfp4 * x = (device const block_mxfp4 *) (src0 + offset0);
    device const float       * y = (device const float       *) (src1 + offset1);

    const int nb   = args.ne00/QK_MXFP4;
    const int ns01 = args.nb01/args.nb00; // this can be larger than nb for permuted src0 tensors

    const short ix = tiisg/2;  // 0...15
    const short it = tiisg%2;  // 0 or 1

    shmem_f32[tiisg] = kvalues_mxfp4_f[tiisg%16];
    threadgroup_barrier(mem_flags::mem_threadgroup);

    float4 yl[4];
    float sumf[NR0]={0.f};

    device const float * yb = y + ix*QK_MXFP4 + it*8;

    // note: just the check `ib < nb` is enough, but adding the redundant `&& ib < ns01` check makes the kernel a bit faster
    //       no idea why that is - needs some deeper investigation [TAG_MUL_MV_WEIRD]
    for (int ib = ix; ib < nb && ib < ns01; ib += 16) {
        device const float4 * y4 = (device const float4 *) yb;

        yl[0] = y4[0];
        yl[1] = y4[4];
        yl[2] = y4[1];
        yl[3] = y4[5];

        FOR_UNROLL (short row = 0; row < NR0; row++) {
            device const block_mxfp4 & xb = x[row*ns01 + ib];
            device const uint8_t     * q2 = (device const uint8_t *)(xb.qs + 8*it);

            float4 acc1 = yl[0]*float4(shmem_f32[q2[0] &  0x0F], shmem_f32[q2[1] &  0x0F], shmem_f32[q2[2] &  0x0F], shmem_f32[q2[3] &  0x0F]);
            float4 acc2 = yl[1]*float4(shmem_f32[q2[0] >> 4   ], shmem_f32[q2[1] >> 4   ], shmem_f32[q2[2] >> 4   ], shmem_f32[q2[3] >> 4   ]);
            float4 acc3 = yl[2]*float4(shmem_f32[q2[4] &  0x0F], shmem_f32[q2[5] &  0x0F], shmem_f32[q2[6] &  0x0F], shmem_f32[q2[7] &  0x0F]);
            float4 acc4 = yl[3]*float4(shmem_f32[q2[4] >> 4   ], shmem_f32[q2[5] >> 4   ], shmem_f32[q2[6] >> 4   ], shmem_f32[q2[7] >> 4   ]);

            acc1 = (acc1 + acc3) + (acc2 + acc4);

            sumf[row] += e8m0_to_fp32(xb.e) * ((acc1[0] + acc1[1]) + (acc1[2] + acc1[3]));
        }

        yb += 16 * QK_MXFP4;
    }

    device float * dst_f32 = (device float *) dst + (uint64_t)im*args.ne0*args.ne1 + (uint64_t)r1*args.ne0;

    for (int row = 0; row < NR0 && first_row + row < args.ne0; ++row) {
        float sum_all = simd_sum(sumf[row]);
        if (tiisg == 0) {
            dst_f32[first_row + row] = sum_all;
        }
    }
}

[[host_name("kernel_mul_mv_mxfp4_f32")]]
kernel void kernel_mul_mv_mxfp4_f32(
        constant ggml_metal_kargs_mul_mv & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    kernel_mul_mv_mxfp4_f32_impl<N_R0_MXFP4, constant ggml_metal_kargs_mul_mv &>(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

template<typename block_q, short nl, void (*dequantize_func)(device const block_q *, short, thread float4x4 &)>
kernel void kernel_get_rows_q(
        constant ggml_metal_kargs_get_rows & args,
        device const void * src0,
        device const void * src1,
        device       void * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg  [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) ((const device char *) src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (device const block_q *) ((const device char *) src0 + i03*args.nb03 + i02*args.nb02 +   r*args.nb01);
    auto pdst = (device      float4x4 *) ((      device char *) dst  + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        float4x4 temp;
        dequantize_func(psrc + ind/nl, ind%nl, temp);
        pdst[ind] = temp;

        break;
    }
}

template<typename T0, typename T>
kernel void kernel_get_rows_f(
        constant ggml_metal_kargs_get_rows & args,
        device const void * src0,
        device const void * src1,
        device       void * dst,
        uint3               tgpig[[threadgroup_position_in_grid]],
        ushort              tiitg[[thread_index_in_threadgroup]],
        ushort3             ntg [[threads_per_threadgroup]]) {
    const int32_t iw0 = tgpig.x/args.ne10;
    const int32_t i10 = tgpig.x%args.ne10;
    const int32_t i11 = tgpig.y;
    const int32_t i12 = tgpig.z;

    const int32_t r = ((const device int32_t *) ((const device char *) src1 + i12*args.nb12 + i11*args.nb11 + i10*args.nb10))[0];

    const int32_t i02 = i11;
    const int32_t i03 = i12;

    auto psrc = (const device T0 *) ((const device char *) src0 + i03*args.nb03 + i02*args.nb02 +   r*args.nb01);
    auto pdst = (      device T  *) ((      device char *)  dst + i12*args.nb3  + i11*args.nb2  + i10*args.nb1);

    for (int ind = iw0*ntg.x + tiitg; ind < args.ne00t;) {
        pdst[ind] = psrc[ind];

        break;
    }
}

template<typename TI, typename block_q, void (*quantize_func)(device const float *, device block_q &)>
kernel void kernel_set_rows_q32(
        constant ggml_metal_kargs_set_rows & args,
        device const  void * src0,
        device const  void * src1,
        device       float * dst,
        uint3                tgpig[[threadgroup_position_in_grid]],
        uint                 tiitg[[thread_index_in_threadgroup]],
        uint3                tptg [[threads_per_threadgroup]]) {
    const int32_t i03 = tgpig.z;
    const int32_t i02 = tgpig.y;

    const int32_t i12 = i03%args.ne12;
    const int32_t i11 = i02%args.ne11;

    const int32_t i01 = tgpig.x*tptg.y + tiitg/tptg.x;
    if (i01 >= args.ne01) {
        return;
    }

    const int32_t i10 = i01;
    const TI      i1  = ((const device TI *) ((const device char *) src1 + i10*args.nb10 + i11*args.nb11 + i12*args.nb12))[0];

          device block_q * dst_row = (      device block_q *) ((      device char *) dst  +  i1*args.nb1  + i02*args.nb2  + i03*args.nb3);
    const device float   * src_row = (const device float   *) ((const device char *) src0 + i01*args.nb01 + i02*args.nb02 + i03*args.nb03);

    for (int ind = tiitg%tptg.x; ind < args.nk0; ind += tptg.x) {
        quantize_func(src_row + 32*ind, dst_row[ind]);
    }
}

template<typename T, typename TI>
kernel void kernel_set_rows_f(
        constant ggml_metal_kargs_set_rows & args,
        device const  void * src0,
        device const  void * src1,
        device       float * dst,
        uint3                tgpig[[threadgroup_position_in_grid]],
        uint                 tiitg[[thread_index_in_threadgroup]],
        uint3                tptg [[threads_per_threadgroup]]) {
    const int32_t i03 = tgpig.z;
    const int32_t i02 = tgpig.y;

    const int32_t i12 = i03%args.ne12;
    const int32_t i11 = i02%args.ne11;

    const int32_t i01 = tgpig.x*tptg.y + tiitg/tptg.x;
    if (i01 >= args.ne01) {
        return;
    }

    const int32_t i10 = i01;
    const TI      i1  = ((const device TI *) ((const device char *) src1 + i10*args.nb10 + i11*args.nb11 + i12*args.nb12))[0];

          device T     * dst_row = (      device T     *) ((      device char *) dst  +  i1*args.nb1  + i02*args.nb2  + i03*args.nb3);
    const device float * src_row = (const device float *) ((const device char *) src0 + i01*args.nb01 + i02*args.nb02 + i03*args.nb03);

    for (int ind = tiitg%tptg.x; ind < args.nk0; ind += tptg.x) {
        dst_row[ind] = (T) src_row[ind];
    }
}

constant bool FC_mul_mm_bc_inp [[function_constant(FC_MUL_MM + 0)]];
constant bool FC_mul_mm_bc_out [[function_constant(FC_MUL_MM + 1)]];

// each block_q contains 16*nl weights
template<typename S0, typename S0_4x4, typename S0_8x8, typename S1, typename S1_2x4, typename S1_8x8, typename block_q, short nl, void (*dequantize_func)(device const block_q *, short, thread S0_4x4 &), typename T0, typename T0_4x4, typename T1, typename T1_2x4>
kernel void kernel_mul_mm(
        constant ggml_metal_kargs_mul_mm & args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {

    threadgroup S0 * sa = (threadgroup S0 *)(shmem);
    threadgroup S1 * sb = (threadgroup S1 *)(shmem + 4096);

    threadgroup float * sc = (threadgroup float *)(shmem);

    constexpr int NR0 = 64;
    constexpr int NR1 = 32;

    constexpr int NK  = 32;
    constexpr int NL0 = NK/16;
    constexpr int NL1 = NK/8;

    const int im = tgpig.z;
    const int r0 = tgpig.y*NR0;
    const int r1 = tgpig.x*NR1;

    // if this block is of 64x32 shape or smaller
    const short nr0 = (args.ne0 - r0 < NR0) ? (args.ne0 - r0) : NR0;
    const short nr1 = (args.ne1 - r1 < NR1) ? (args.ne1 - r1) : NR1;

    // a thread shouldn't load data outside of the matrix
    const short lr0 = ((short)tiitg/NL0) < nr0 ? ((short)tiitg/NL0) : nr0 - 1; // 0 .. 63
    const short lr1 = ((short)tiitg/NL1) < nr1 ? ((short)tiitg/NL1) : nr1 - 1; // 0 .. 31

    const short il0 = (tiitg % NL0);

    short il = il0;

    const int i12 = im%args.ne12;
    const int i13 = im/args.ne12;

    const uint64_t offset0 = (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
    const short    offset1 = il0/nl;

    device const block_q * x = (device const block_q *)(src0 + args.nb01*(r0 + lr0) + offset0) + offset1;

    const short iy = 8*(tiitg % NL1);

    device const T1 * y = (device const T1 *)(src1
        + args.nb13*i13
        + args.nb12*i12
        + args.nb11*(r1 + lr1)
        + args.nb10*iy);

#ifndef GGML_METAL_HAS_TENSOR
    S0_8x8 ma[4];
    S1_8x8 mb[2];

    simdgroup_float8x8 mc[8];

    for (short i = 0; i < 8; i++){
        mc[i] = make_filled_simdgroup_matrix<float, 8>(0.f);
    }
#else
    auto tA = tensor<threadgroup S0, dextents<int32_t, 2>, tensor_inline>(sa, dextents<int32_t, 2>(NK,  NR0));
    auto tB = tensor<threadgroup S1, dextents<int32_t, 2>, tensor_inline>(sb, dextents<int32_t, 2>(NR1, NK ));

    mpp::tensor_ops::matmul2d<
        mpp::tensor_ops::matmul2d_descriptor(NR1, NR0, NK, false, true, false, mpp::tensor_ops::matmul2d_descriptor::mode::multiply_accumulate),
        execution_simdgroups<4>> mm;

    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>();
#endif

    for (int loop_k = 0; loop_k < args.ne00; loop_k += NK) {
#ifndef GGML_METAL_HAS_TENSOR
        // load data and store to threadgroup memory
        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // no need for dequantization
            for (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

              //const short lx = i%8;
              //const short ly = (tiitg/NL0)%8;
                const short lx = (tiitg/NL0)%8;
                const short ly = i%8;

                const short ib = 8*sx + sy;

                *(sa + 64*ib + 8*ly + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
            }
        } else {
            S0_4x4 temp_a;
            dequantize_func(x, il, temp_a);

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

              //const short lx = i%8;
              //const short ly = (tiitg/NL0)%8;
                const short lx = (tiitg/NL0)%8;
                const short ly = i%8;

                const short ib = 8*sx + sy;

                // NOTE: this is massively slower.. WTF?
                //sa[64*ib + 8*ly + lx] = temp_a[i/4][i%4];

                *(sa + 64*ib + 8*ly + lx) = temp_a[i/4][i%4];
            }
        }

        if (FC_mul_mm_bc_inp) {
            for (short i = 0; i < 8; ++i) {
                const short sx = (tiitg%NL1);
                const short sy = (tiitg/NL1)/8;

                const short lx = i;
                const short ly = (tiitg/NL1)%8;
              //const short lx = (tiitg/NL1)%8;
              //const short ly = i;

                const short ib = 4*sx + sy;

                *(sb + 64*ib + 8*ly + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
            }
        } else {
            const short sx = (tiitg%NL1);
            const short sy = (tiitg/NL1)/8;

            const short dx = sx;
            const short dy = sy;

            const short ly = (tiitg/NL1)%8;

            const short ib = 4*sx + sy;

            *(threadgroup S1_2x4 *)(sb + 64*ib + 8*ly) = (S1_2x4)(*((device T1_2x4 *) y));
        }
#else
        // load data and store to threadgroup memory
        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // no need for dequantization
            for (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

                const short lx = i%8;
                const short ly = (tiitg/NL0)%8;
                //const short lx = (tiitg/NL0)%8;
                //const short ly = i%8;

                *(sa + NK*(8*sy + ly) + 8*sx + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
            }
        } else {
            S0_4x4 temp_a;
            dequantize_func(x, il, temp_a);

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

                const short lx = i%8;
                const short ly = (tiitg/NL0)%8;
                //const short lx = (tiitg/NL0)%8;
                //const short ly = i%8;

                *(sa + NK*(8*sy + ly) + 8*sx + lx) = temp_a[i/4][i%4];
            }
        }

        if (FC_mul_mm_bc_inp) {
            for (short i = 0; i < 8; ++i) {
                const short sx = (tiitg%NL1);
                const short sy = (tiitg/NL1)/8;

                const short lx = i;
                const short ly = (tiitg/NL1)%8;
                //const short lx = (tiitg/NL1)%8;
                //const short ly = i;

                *(sb + NK*(8*sy + ly) + 8*sx + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
            }
        } else {
            const short sx = (tiitg%NL1);
            const short sy = (tiitg/NL1)/8;

            //const short lx = i;
            const short ly = (tiitg/NL1)%8;
            //const short lx = (tiitg/NL1)%8;
            //const short ly = i;

            *(threadgroup S1_2x4 *)(sb + NK*(8*sy + ly) + 8*sx) = (S1_2x4)(*((device T1_2x4 *) y));
        }
#endif

        il = (il + 2 < nl) ? il + 2 : il % 2;
        x  = (il < 2) ? x + (2 + nl - 1)/nl : x;

        y += NK;

        threadgroup_barrier(mem_flags::mem_threadgroup);

#ifndef GGML_METAL_HAS_TENSOR
        // load matrices from threadgroup memory and conduct outer products
        threadgroup const S0 * lsma = (sa + 4*64*(sgitg%2));
        threadgroup const S1 * lsmb = (sb + 2*64*(sgitg/2));

        FOR_UNROLL (short ik = 0; ik < NK/8; ik++) {
            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 4; i++) {
                simdgroup_load(ma[i], lsma + 64*i, 8, 0, false);
            }

            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 2; i++) {
                simdgroup_load(mb[i], lsmb + 64*i, 8, 0, false);
            }

            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 8; i++){
                simdgroup_multiply_accumulate(mc[i], mb[i/4], ma[i%4], mc[i]);
            }

            lsma += 8*64;
            lsmb += 4*64;
        }
#else
        auto sA = tA.slice(0, 0);
        auto sB = tB.slice(0, 0);

        mm.run(sB, sA, cT);
#endif
    }

    if (!FC_mul_mm_bc_out || (r0 + NR0 <= args.ne0 && r1 + NR1 <= args.ne1)) {
        // if no bounds checks on the output are needed, we can directly write to device memory
#ifdef GGML_METAL_HAS_TENSOR
        device float * C = (device float *) dst +
            r0 + \
            r1 * args.ne0 + im*args.ne1*args.ne0;

        auto tC = tensor<device float, dextents<int32_t, 2>, tensor_inline>(C, dextents<int32_t, 2>(args.ne0, NR1));
        cT.store(tC);
#else
        device float * C = (device float *) dst +
            (r0 + 32*(sgitg &  1)) + \
            (r1 + 16*(sgitg >> 1)) * args.ne0 + im*args.ne1*args.ne0;

        for (short i = 0; i < 8; i++) {
            simdgroup_store(mc[i], C + 8*(i%4) + 8*args.ne0*(i/4), args.ne0, 0, false);
        }
#endif
    } else {
        // block is smaller than 64x32, we should avoid writing data outside of the matrix
        threadgroup_barrier(mem_flags::mem_threadgroup);

        threadgroup float * temp_str = ((threadgroup float *) shmem) + 32*(sgitg&1) + (16*(sgitg >> 1))*NR0;

#ifdef GGML_METAL_HAS_TENSOR
        auto tC = tensor<threadgroup float, dextents<int32_t, 2>, tensor_inline>(sc, dextents<int32_t, 2>(NR0, NR1));
        cT.store(tC);
#else
        for (short i = 0; i < 8; i++) {
            simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*NR0*(i/4), NR0, 0, false);
        }
#endif

        threadgroup_barrier(mem_flags::mem_threadgroup);

        if (sgitg == 0) {
            for (int j = tiitg; j < nr1; j += NR1) {
                device float  * D  = (device float  *) dst + r0 + (r1 + j)*args.ne0 + im*args.ne1*args.ne0;
                device float4 * D4 = (device float4 *) D;

                threadgroup float  * C  = temp_str + (j*NR0);
                threadgroup float4 * C4 = (threadgroup float4 *) C;

                int i = 0;
                for (; i < nr0/4; i++) {
                    *(D4 + i) = *(C4 + i);
                }

                i *= 4;
                for (; i < nr0; i++) {
                    *(D + i) = *(C + i);
                }
            }
        }
    }
}

template<short ne20> // n_expert_used
kernel void kernel_mul_mm_id_map0(
        constant ggml_metal_kargs_mul_mm_id_map0 & args,
        device  const char * src2,
        device        char * htpe,
        device        char * hids,
        threadgroup   char * shmem [[threadgroup(0)]],
        ushort tpitg[[thread_position_in_threadgroup]],
        ushort   ntg[[threads_per_threadgroup]]) {
    const short ide = tpitg; // expert id

    uint32_t n_all = 0;

    device int32_t * ids_i32 = (device int32_t *) hids + ide*args.ne21;

    for (int i21 = 0; i21 < args.ne21; i21 += ntg) { // n_tokens
        if (i21 + tpitg < args.ne21) {
            device const int32_t * src2_i32 = (device const int32_t *) (src2 + (i21 + tpitg)*args.nb21);

            threadgroup uint16_t * sids = (threadgroup uint16_t *) shmem + tpitg*ne20;

            #pragma unroll(ne20)
            for (short i20 = 0; i20 < ne20; i20++) {
                sids[i20] = src2_i32[i20];
            }
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);

        for (short t = 0; t < ntg; t++) {
            if (i21 + t >= args.ne21) {
                break;
            }

            threadgroup const uint16_t * sids = (threadgroup const uint16_t *) shmem + t*ne20;

            short sel = 0;
            #pragma unroll(ne20)
            for (short i20 = 0; i20 < ne20; i20++) {
                sel += (sids[i20] == ide)*(i20 + 1);
            }

            ids_i32[n_all] = (i21 + t)*ne20 + sel - 1;

            n_all += sel > 0;
        }

        threadgroup_barrier(mem_flags::mem_threadgroup);
    }

    device uint32_t * tpe_u32 = (device uint32_t *) (htpe);
    tpe_u32[ide] = n_all;
}

typedef decltype(kernel_mul_mm_id_map0<1>) kernel_mul_mm_id_map0_t;

template [[host_name("kernel_mul_mm_id_map0_ne20_1" )]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<1>;
template [[host_name("kernel_mul_mm_id_map0_ne20_2" )]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<2>;
template [[host_name("kernel_mul_mm_id_map0_ne20_4" )]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<4>;
template [[host_name("kernel_mul_mm_id_map0_ne20_6" )]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<6>;
template [[host_name("kernel_mul_mm_id_map0_ne20_8" )]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<8>;
template [[host_name("kernel_mul_mm_id_map0_ne20_10")]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<10>;
template [[host_name("kernel_mul_mm_id_map0_ne20_16")]] kernel kernel_mul_mm_id_map0_t kernel_mul_mm_id_map0<16>;

template<typename S0, typename S0_4x4, typename S0_8x8, typename S1, typename S1_2x4, typename S1_8x8, typename block_q, short nl, void (*dequantize_func)(device const block_q *, short, thread S0_4x4 &), typename T0, typename T0_4x4, typename T1, typename T1_2x4>
kernel void kernel_mul_mm_id(
        constant ggml_metal_kargs_mul_mm_id & args,
        device const char * src0,
        device const char * src1,
        device const char * htpe,
        device const char * hids,
        device       char * dst,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    threadgroup S0 * sa = (threadgroup S0 *)(shmem);
    threadgroup S1 * sb = (threadgroup S1 *)(shmem + 4096);

    threadgroup float * sc = (threadgroup float *)(shmem);

    constexpr int NR0 = 64;
    constexpr int NR1 = 32;

    constexpr int NK  = 32;
    constexpr int NL0 = NK/16;
    constexpr int NL1 = NK/8;

    const int im = tgpig.z; // expert
    const int r0 = tgpig.y*NR0;
    const int r1 = tgpig.x*NR1;

    device const uint32_t * tpe_u32 = (device const uint32_t *) (htpe);
    device const int32_t  * ids_i32 = (device const int32_t  *) (hids);

    const int32_t neh1 = tpe_u32[im];

    if (r1 >= neh1) {
        return;
    }

    // if this block is of 64x32 shape or smaller
    const short nr0 = (args.ne0 - r0 < NR0) ? (args.ne0 - r0) : NR0;
    const short nr1 = (    neh1 - r1 < NR1) ? (    neh1 - r1) : NR1;

    // a thread shouldn't load data outside of the matrix
    const short lr0 = ((short)tiitg/NL0) < nr0 ? ((short)tiitg/NL0) : nr0 - 1; // 0 .. 63
    const short lr1 = ((short)tiitg/NL1) < nr1 ? ((short)tiitg/NL1) : nr1 - 1; // 0 .. 31

    const short il0 = (tiitg % NL0);

    short il = il0;

    const int id = ids_i32[im*args.ne21 + r1 + lr1];

    const short i11 = (id % args.ne20) % args.ne11;
    const short i12 = (id / args.ne20);
    const short i13 = 0;

    const uint64_t offset0 = im*args.nb02 + i13*args.nb03;
    const short    offset1 = il0/nl;

    device const block_q * x = (device const block_q *)(src0 + args.nb01*(r0 + lr0) + offset0) + offset1;

    const short iy = 8*(tiitg % NL1);

    device const T1 * y = (device const T1 *)(src1
        + args.nb13*i13
        + args.nb12*i12
        + args.nb11*i11
        + args.nb10*iy);

#ifndef GGML_METAL_HAS_TENSOR
    S0_8x8 ma[4];
    S1_8x8 mb[2];

    simdgroup_float8x8 mc[8];

    for (short i = 0; i < 8; i++){
        mc[i] = make_filled_simdgroup_matrix<float, 8>(0.f);
    }
#else
    auto tA = tensor<threadgroup S0, dextents<int32_t, 2>, tensor_inline>(sa, dextents<int32_t, 2>(NK,  NR0));
    auto tB = tensor<threadgroup S1, dextents<int32_t, 2>, tensor_inline>(sb, dextents<int32_t, 2>(NR1, NK ));

    mpp::tensor_ops::matmul2d<
        mpp::tensor_ops::matmul2d_descriptor(NR1, NR0, NK, false, true, false, mpp::tensor_ops::matmul2d_descriptor::mode::multiply_accumulate),
        execution_simdgroups<4>> mm;

    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>();
#endif

    for (int loop_k = 0; loop_k < args.ne00; loop_k += NK) {
#ifndef GGML_METAL_HAS_TENSOR
        // load data and store to threadgroup memory
        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // no need for dequantization
            for (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

              //const short lx = i%8;
              //const short ly = (tiitg/NL0)%8;
                const short lx = (tiitg/NL0)%8;
                const short ly = i%8;

                const short ib = 8*sx + sy;

                *(sa + 64*ib + 8*ly + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
            }
        } else {
            S0_4x4 temp_a;
            dequantize_func(x, il, temp_a);

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

              //const short lx = i%8;
              //const short ly = (tiitg/NL0)%8;
                const short lx = (tiitg/NL0)%8;
                const short ly = i%8;

                const short ib = 8*sx + sy;

                // NOTE: this is massively slower.. WTF?
                //sa[64*ib + 8*ly + lx] = temp_a[i/4][i%4];

                *(sa + 64*ib + 8*ly + lx) = temp_a[i/4][i%4];
            }
        }

        if (FC_mul_mm_bc_inp) {
            for (short i = 0; i < 8; ++i) {
                const short sx = (tiitg%NL1);
                const short sy = (tiitg/NL1)/8;

                const short lx = i;
                const short ly = (tiitg/NL1)%8;
              //const short lx = (tiitg/NL1)%8;
              //const short ly = i;

                const short ib = 4*sx + sy;

                *(sb + 64*ib + 8*ly + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
            }
        } else {
            const short sx = (tiitg%NL1);
            const short sy = (tiitg/NL1)/8;

            const short dx = sx;
            const short dy = sy;

            const short ly = (tiitg/NL1)%8;

            const short ib = 4*sx + sy;

            *(threadgroup S1_2x4 *)(sb + 64*ib + 8*ly) = (S1_2x4)(*((device T1_2x4 *) y));
        }
#else
        // load data and store to threadgroup memory
        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
            threadgroup_barrier(mem_flags::mem_threadgroup);

            // no need for dequantization
            for (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

                const short lx = i%8;
                const short ly = (tiitg/NL0)%8;
                //const short lx = (tiitg/NL0)%8;
                //const short ly = i%8;

                *(sa + NK*(8*sy + ly) + 8*sx + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
            }
        } else {
            S0_4x4 temp_a;
            dequantize_func(x, il, temp_a);

            threadgroup_barrier(mem_flags::mem_threadgroup);

            FOR_UNROLL (short i = 0; i < 16; i++) {
                const short sx = 2*il0 + i/8;
                const short sy = (tiitg/NL0)/8;

                const short lx = i%8;
                const short ly = (tiitg/NL0)%8;
                //const short lx = (tiitg/NL0)%8;
                //const short ly = i%8;

                *(sa + NK*(8*sy + ly) + 8*sx + lx) = temp_a[i/4][i%4];
            }
        }

        if (FC_mul_mm_bc_inp) {
            for (short i = 0; i < 8; ++i) {
                const short sx = (tiitg%NL1);
                const short sy = (tiitg/NL1)/8;

                const short lx = i;
                const short ly = (tiitg/NL1)%8;
                //const short lx = (tiitg/NL1)%8;
                //const short ly = i;

                *(sb + NK*(8*sy + ly) + 8*sx + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
            }
        } else {
            const short sx = (tiitg%NL1);
            const short sy = (tiitg/NL1)/8;

            //const short lx = i;
            const short ly = (tiitg/NL1)%8;
            //const short lx = (tiitg/NL1)%8;
            //const short ly = i;

            *(threadgroup S1_2x4 *)(sb + NK*(8*sy + ly) + 8*sx) = (S1_2x4)(*((device T1_2x4 *) y));
        }
#endif

        il = (il + 2 < nl) ? il + 2 : il % 2;
        x  = (il < 2) ? x + (2 + nl - 1)/nl : x;

        y += NK;

        threadgroup_barrier(mem_flags::mem_threadgroup);

#ifndef GGML_METAL_HAS_TENSOR
        // load matrices from threadgroup memory and conduct outer products
        threadgroup const S0 * lsma = (sa + 4*64*(sgitg%2));
        threadgroup const S1 * lsmb = (sb + 2*64*(sgitg/2));

        FOR_UNROLL (short ik = 0; ik < NK/8; ik++) {
            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 4; i++) {
                simdgroup_load(ma[i], lsma + 64*i, 8, 0, false);
            }

            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 2; i++) {
                simdgroup_load(mb[i], lsmb + 64*i, 8, 0, false);
            }

            simdgroup_barrier(mem_flags::mem_none);

            FOR_UNROLL (short i = 0; i < 8; i++){
                simdgroup_multiply_accumulate(mc[i], mb[i/4], ma[i%4], mc[i]);
            }

            lsma += 8*64;
            lsmb += 4*64;
        }
#else
        auto sA = tA.slice(0, 0);
        auto sB = tB.slice(0, 0);

        mm.run(sB, sA, cT);
#endif
    }

    // block is smaller than 64x32, we should avoid writing data outside of the matrix
    threadgroup_barrier(mem_flags::mem_threadgroup);

#ifdef GGML_METAL_HAS_TENSOR
    auto tC = tensor<threadgroup float, dextents<int32_t, 2>, tensor_inline>(sc, dextents<int32_t, 2>(NR0, NR1));
    cT.store(tC);
#else
    threadgroup float * temp_str = ((threadgroup float *) shmem) + 32*(sgitg&1) + (16*(sgitg >> 1))*NR0;

    for (short i = 0; i < 8; i++) {
        simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*NR0*(i/4), NR0, 0, false);
    }
#endif

    threadgroup_barrier(mem_flags::mem_threadgroup);

    for (short j = sgitg; j < nr1; j += 4) {
        const int id = ids_i32[im*args.ne21 + r1 + j];

        const short ide = id % args.ne20;
        const short idt = id / args.ne20;

        device float  * D  = (device float  *) dst + r0 + ide*args.ne0 + idt*args.ne1*args.ne0;
        device float4 * D4 = (device float4 *) D;

        threadgroup float  * C  = (threadgroup float  *) shmem + j*NR0;
        threadgroup float4 * C4 = (threadgroup float4 *) C;

        int i = tiisg;
        for (; i < nr0/4; i += 32) {
            *(D4 + i) = *(C4 + i);
        }

        i = (4*(nr0/4)) + tiisg;
        for (; i < nr0; i += 32) {
            *(D + i) = *(C + i);
        }
    }
}

#define QK_NL 16

//
// get rows
//

typedef decltype(kernel_get_rows_f<float, float>) get_rows_f_t;

template [[host_name("kernel_get_rows_f32")]]  kernel get_rows_f_t kernel_get_rows_f<float, float>;
template [[host_name("kernel_get_rows_f16")]]  kernel get_rows_f_t kernel_get_rows_f<half,  float>;
template [[host_name("kernel_get_rows_i32")]]  kernel get_rows_f_t kernel_get_rows_f<int32_t, int32_t>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_get_rows_bf16")]] kernel get_rows_f_t kernel_get_rows_f<bfloat, float>;
#endif

typedef decltype(kernel_get_rows_q<block_q4_0, 2, dequantize_q4_0>) get_rows_q_t;

template [[host_name("kernel_get_rows_q4_0")]]    kernel get_rows_q_t kernel_get_rows_q<block_q4_0,    2, dequantize_q4_0>;
template [[host_name("kernel_get_rows_q4_1")]]    kernel get_rows_q_t kernel_get_rows_q<block_q4_1,    2, dequantize_q4_1>;
template [[host_name("kernel_get_rows_q5_0")]]    kernel get_rows_q_t kernel_get_rows_q<block_q5_0,    2, dequantize_q5_0>;
template [[host_name("kernel_get_rows_q5_1")]]    kernel get_rows_q_t kernel_get_rows_q<block_q5_1,    2, dequantize_q5_1>;
template [[host_name("kernel_get_rows_q8_0")]]    kernel get_rows_q_t kernel_get_rows_q<block_q8_0,    2, dequantize_q8_0>;
template [[host_name("kernel_get_rows_mxfp4")]]   kernel get_rows_q_t kernel_get_rows_q<block_mxfp4,   2, dequantize_mxfp4>;
template [[host_name("kernel_get_rows_q2_K")]]    kernel get_rows_q_t kernel_get_rows_q<block_q2_K,    QK_NL, dequantize_q2_K>;
template [[host_name("kernel_get_rows_q3_K")]]    kernel get_rows_q_t kernel_get_rows_q<block_q3_K,    QK_NL, dequantize_q3_K>;
template [[host_name("kernel_get_rows_q4_K")]]    kernel get_rows_q_t kernel_get_rows_q<block_q4_K,    QK_NL, dequantize_q4_K>;
template [[host_name("kernel_get_rows_q5_K")]]    kernel get_rows_q_t kernel_get_rows_q<block_q5_K,    QK_NL, dequantize_q5_K>;
template [[host_name("kernel_get_rows_q6_K")]]    kernel get_rows_q_t kernel_get_rows_q<block_q6_K,    QK_NL, dequantize_q6_K>;
template [[host_name("kernel_get_rows_iq2_xxs")]] kernel get_rows_q_t kernel_get_rows_q<block_iq2_xxs, QK_NL, dequantize_iq2_xxs>;
template [[host_name("kernel_get_rows_iq2_xs")]]  kernel get_rows_q_t kernel_get_rows_q<block_iq2_xs,  QK_NL, dequantize_iq2_xs>;
template [[host_name("kernel_get_rows_iq3_xxs")]] kernel get_rows_q_t kernel_get_rows_q<block_iq3_xxs, QK_NL, dequantize_iq3_xxs>;
template [[host_name("kernel_get_rows_iq3_s")]]   kernel get_rows_q_t kernel_get_rows_q<block_iq3_s,   QK_NL, dequantize_iq3_s>;
template [[host_name("kernel_get_rows_iq2_s")]]   kernel get_rows_q_t kernel_get_rows_q<block_iq2_s,   QK_NL, dequantize_iq2_s>;
template [[host_name("kernel_get_rows_iq1_s")]]   kernel get_rows_q_t kernel_get_rows_q<block_iq1_s,   QK_NL, dequantize_iq1_s>;
template [[host_name("kernel_get_rows_iq1_m")]]   kernel get_rows_q_t kernel_get_rows_q<block_iq1_m,   QK_NL, dequantize_iq1_m>;
template [[host_name("kernel_get_rows_iq4_nl")]]  kernel get_rows_q_t kernel_get_rows_q<block_iq4_nl,  2,     dequantize_iq4_nl>;
template [[host_name("kernel_get_rows_iq4_xs")]]  kernel get_rows_q_t kernel_get_rows_q<block_iq4_xs,  QK_NL, dequantize_iq4_xs>;

//
// set rows
//

typedef decltype(kernel_set_rows_f<float, int64_t>) set_rows_f_t;

template [[host_name("kernel_set_rows_f32_i64")]]  kernel set_rows_f_t kernel_set_rows_f<float, int64_t>;
template [[host_name("kernel_set_rows_f32_i32")]]  kernel set_rows_f_t kernel_set_rows_f<float, int32_t>;
template [[host_name("kernel_set_rows_f16_i64")]]  kernel set_rows_f_t kernel_set_rows_f<half, int64_t>;
template [[host_name("kernel_set_rows_f16_i32")]]  kernel set_rows_f_t kernel_set_rows_f<half, int32_t>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_set_rows_bf16_i64")]] kernel set_rows_f_t kernel_set_rows_f<bfloat, int64_t>;
template [[host_name("kernel_set_rows_bf16_i32")]] kernel set_rows_f_t kernel_set_rows_f<bfloat, int32_t>;
#endif

typedef decltype(kernel_set_rows_q32<int64_t, block_q8_0, quantize_q8_0>) set_rows_q32_t;

template [[host_name("kernel_set_rows_q8_0_i64")]]   kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_q8_0,   quantize_q8_0>;
template [[host_name("kernel_set_rows_q8_0_i32")]]   kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_q8_0,   quantize_q8_0>;
template [[host_name("kernel_set_rows_q4_0_i64")]]   kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_q4_0,   quantize_q4_0>;
template [[host_name("kernel_set_rows_q4_0_i32")]]   kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_q4_0,   quantize_q4_0>;
template [[host_name("kernel_set_rows_q4_1_i64")]]   kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_q4_1,   quantize_q4_1>;
template [[host_name("kernel_set_rows_q4_1_i32")]]   kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_q4_1,   quantize_q4_1>;
template [[host_name("kernel_set_rows_q5_0_i64")]]   kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_q5_0,   quantize_q5_0>;
template [[host_name("kernel_set_rows_q5_0_i32")]]   kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_q5_0,   quantize_q5_0>;
template [[host_name("kernel_set_rows_q5_1_i64")]]   kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_q5_1,   quantize_q5_1>;
template [[host_name("kernel_set_rows_q5_1_i32")]]   kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_q5_1,   quantize_q5_1>;
template [[host_name("kernel_set_rows_iq4_nl_i64")]] kernel set_rows_q32_t kernel_set_rows_q32<int64_t, block_iq4_nl, quantize_iq4_nl>;
template [[host_name("kernel_set_rows_iq4_nl_i32")]] kernel set_rows_q32_t kernel_set_rows_q32<int32_t, block_iq4_nl, quantize_iq4_nl>;

//
// matrix-matrix multiplication
//

typedef decltype(kernel_mul_mm<half, half4x4, simdgroup_half8x8, half, half2x4, simdgroup_half8x8, float4x4, 1, dequantize_f32, float, float4x4, float, float2x4>) mul_mm_t;

template [[host_name("kernel_mul_mm_f32_f32")]]     kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   float4x4,      1,     dequantize_f32,     float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_f16_f32")]]     kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   half4x4,       1,     dequantize_f16,     half,   half4x4,   float, float2x4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mm_bf16_f32")]]    kernel mul_mm_t kernel_mul_mm<bfloat, bfloat4x4, simdgroup_bfloat8x8, bfloat, bfloat2x4, simdgroup_bfloat8x8, bfloat4x4,     1,     dequantize_bf16,    bfloat, bfloat4x4, float, float2x4>;
#endif
template [[host_name("kernel_mul_mm_q4_0_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_0,    2,     dequantize_q4_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q4_1_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_1,    2,     dequantize_q4_1,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q5_0_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_0,    2,     dequantize_q5_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q5_1_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_1,    2,     dequantize_q5_1,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q8_0_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q8_0,    2,     dequantize_q8_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_mxfp4_f32")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_mxfp4,   2,     dequantize_mxfp4,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q2_K_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q2_K,    QK_NL, dequantize_q2_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q3_K_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q3_K,    QK_NL, dequantize_q3_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q4_K_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_K,    QK_NL, dequantize_q4_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q5_K_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_K,    QK_NL, dequantize_q5_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_q6_K_f32")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q6_K,    QK_NL, dequantize_q6_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq2_xxs_f32")]] kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xxs, QK_NL, dequantize_iq2_xxs, float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq2_xs_f32")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xs,  QK_NL, dequantize_iq2_xs,  float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq3_xxs_f32")]] kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_xxs, QK_NL, dequantize_iq3_xxs, float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq3_s_f32")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_s,   QK_NL, dequantize_iq3_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq2_s_f32")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_s,   QK_NL, dequantize_iq2_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq1_s_f32")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_s,   QK_NL, dequantize_iq1_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq1_m_f32")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_m,   QK_NL, dequantize_iq1_m,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq4_nl_f32")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_nl,  2,     dequantize_iq4_nl,  float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_iq4_xs_f32")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_xs,  QK_NL, dequantize_iq4_xs,  float,  float4x4,  float, float2x4>;

template [[host_name("kernel_mul_mm_f32_f16")]]     kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   float4x4,      1,     dequantize_f32,     float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_f16_f16")]]     kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   half4x4,       1,     dequantize_f16,     half,   half4x4,   half, half2x4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mm_bf16_f16")]]    kernel mul_mm_t kernel_mul_mm<bfloat, bfloat4x4, simdgroup_bfloat8x8, half,   half2x4,   simdgroup_half8x8,   bfloat4x4,     1,     dequantize_bf16,    bfloat, bfloat4x4, half, half2x4>;
#endif
template [[host_name("kernel_mul_mm_q4_0_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_0,    2,     dequantize_q4_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q4_1_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_1,    2,     dequantize_q4_1,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q5_0_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_0,    2,     dequantize_q5_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q5_1_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_1,    2,     dequantize_q5_1,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q8_0_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q8_0,    2,     dequantize_q8_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_mxfp4_f16")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_mxfp4,   2,     dequantize_mxfp4,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q2_K_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q2_K,    QK_NL, dequantize_q2_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q3_K_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q3_K,    QK_NL, dequantize_q3_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q4_K_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_K,    QK_NL, dequantize_q4_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q5_K_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_K,    QK_NL, dequantize_q5_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_q6_K_f16")]]    kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q6_K,    QK_NL, dequantize_q6_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq2_xxs_f16")]] kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xxs, QK_NL, dequantize_iq2_xxs, float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq2_xs_f16")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xs,  QK_NL, dequantize_iq2_xs,  float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq3_xxs_f16")]] kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_xxs, QK_NL, dequantize_iq3_xxs, float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq3_s_f16")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_s,   QK_NL, dequantize_iq3_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq2_s_f16")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_s,   QK_NL, dequantize_iq2_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq1_s_f16")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_s,   QK_NL, dequantize_iq1_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq1_m_f16")]]   kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_m,   QK_NL, dequantize_iq1_m,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq4_nl_f16")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_nl,  2,     dequantize_iq4_nl,  float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_iq4_xs_f16")]]  kernel mul_mm_t kernel_mul_mm<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_xs,  QK_NL, dequantize_iq4_xs,  float,  float4x4,  half, half2x4>;

//
// indirect matrix-matrix multiplication
//

typedef decltype(kernel_mul_mm_id<half, half4x4, simdgroup_half8x8, half, half2x4, simdgroup_half8x8, float4x4, 1, dequantize_f32, float, float4x4, float, float2x4>) mul_mm_id;

template [[host_name("kernel_mul_mm_id_f32_f32")]]     kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   float4x4,      1,     dequantize_f32,     float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_f16_f32")]]     kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   half4x4,       1,     dequantize_f16,     half,   half4x4,   float, float2x4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mm_id_bf16_f32")]]    kernel mul_mm_id kernel_mul_mm_id<bfloat, bfloat4x4, simdgroup_bfloat8x8, bfloat, bfloat2x4, simdgroup_bfloat8x8, bfloat4x4,     1,     dequantize_bf16,    bfloat, bfloat4x4, float, float2x4>;
#endif
template [[host_name("kernel_mul_mm_id_q4_0_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_0,    2,     dequantize_q4_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q4_1_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_1,    2,     dequantize_q4_1,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q5_0_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_0,    2,     dequantize_q5_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q5_1_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_1,    2,     dequantize_q5_1,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q8_0_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q8_0,    2,     dequantize_q8_0,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_mxfp4_f32")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_mxfp4,   2,     dequantize_mxfp4,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q2_K_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q2_K,    QK_NL, dequantize_q2_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q3_K_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q3_K,    QK_NL, dequantize_q3_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q4_K_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_K,    QK_NL, dequantize_q4_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q5_K_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_K,    QK_NL, dequantize_q5_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_q6_K_f32")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q6_K,    QK_NL, dequantize_q6_K,    float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq2_xxs_f32")]] kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xxs, QK_NL, dequantize_iq2_xxs, float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq2_xs_f32")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xs,  QK_NL, dequantize_iq2_xs,  float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq3_xxs_f32")]] kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_xxs, QK_NL, dequantize_iq3_xxs, float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq3_s_f32")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_s,   QK_NL, dequantize_iq3_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq2_s_f32")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_s,   QK_NL, dequantize_iq2_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq1_s_f32")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_s,   QK_NL, dequantize_iq1_s,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq1_m_f32")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_m,   QK_NL, dequantize_iq1_m,   float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq4_nl_f32")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_nl,  2,     dequantize_iq4_nl,  float,  float4x4,  float, float2x4>;
template [[host_name("kernel_mul_mm_id_iq4_xs_f32")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_xs,  QK_NL, dequantize_iq4_xs,  float,  float4x4,  float, float2x4>;

template [[host_name("kernel_mul_mm_id_f32_f16")]]     kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   float4x4,      1,     dequantize_f32,     float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_f16_f16")]]     kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   half4x4,       1,     dequantize_f16,     half,   half4x4,   half, half2x4>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mm_id_bf16_f16")]]    kernel mul_mm_id kernel_mul_mm_id<bfloat, bfloat4x4, simdgroup_bfloat8x8, half,   half2x4,   simdgroup_half8x8,   bfloat4x4,     1,     dequantize_bf16,    bfloat, bfloat4x4, half, half2x4>;
#endif
template [[host_name("kernel_mul_mm_id_q4_0_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_0,    2,     dequantize_q4_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q4_1_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_1,    2,     dequantize_q4_1,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q5_0_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_0,    2,     dequantize_q5_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q5_1_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_1,    2,     dequantize_q5_1,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q8_0_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q8_0,    2,     dequantize_q8_0,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_mxfp4_f16")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_mxfp4,   2,     dequantize_mxfp4,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q2_K_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q2_K,    QK_NL, dequantize_q2_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q3_K_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q3_K,    QK_NL, dequantize_q3_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q4_K_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q4_K,    QK_NL, dequantize_q4_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q5_K_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q5_K,    QK_NL, dequantize_q5_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_q6_K_f16")]]    kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_q6_K,    QK_NL, dequantize_q6_K,    float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq2_xxs_f16")]] kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xxs, QK_NL, dequantize_iq2_xxs, float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq2_xs_f16")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_xs,  QK_NL, dequantize_iq2_xs,  float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq3_xxs_f16")]] kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_xxs, QK_NL, dequantize_iq3_xxs, float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq3_s_f16")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq3_s,   QK_NL, dequantize_iq3_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq2_s_f16")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq2_s,   QK_NL, dequantize_iq2_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq1_s_f16")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_s,   QK_NL, dequantize_iq1_s,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq1_m_f16")]]   kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq1_m,   QK_NL, dequantize_iq1_m,   float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq4_nl_f16")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_nl,  2,     dequantize_iq4_nl,  float,  float4x4,  half, half2x4>;
template [[host_name("kernel_mul_mm_id_iq4_xs_f16")]]  kernel mul_mm_id kernel_mul_mm_id<half,   half4x4,   simdgroup_half8x8,   half,   half2x4,   simdgroup_half8x8,   block_iq4_xs,  QK_NL, dequantize_iq4_xs,  float,  float4x4,  half, half2x4>;

//
// matrix-vector multiplication
//

typedef void (kernel_mul_mv_disp_t)(
        ggml_metal_kargs_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        uint3  tgpig,
        ushort tiisg);

typedef void (kernel_mul_mv2_disp_t)(
        ggml_metal_kargs_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiisg,
        ushort sgitg);

template<kernel_mul_mv_disp_t disp_fn>
void mmv_fn(
        ggml_metal_kargs_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, tgpig, tiisg);
}

template<kernel_mul_mv2_disp_t disp_fn>
void mmv_fn(
        ggml_metal_kargs_mul_mv args,
        device const char * src0,
        device const char * src1,
        device       char * dst,
        threadgroup  char * shmem,
        uint3  tgpig,
        ushort tiitg,
        ushort tiisg,
        ushort sgitg) {
    disp_fn(args, src0, src1, dst, shmem, tgpig, tiisg, sgitg);
}

typedef decltype(mmv_fn<kernel_mul_mv_t_t_disp<half, half, ggml_metal_kargs_mul_mv>>) mul_mv_disp_fn_t;

template<mul_mv_disp_fn_t disp_fn>
kernel void kernel_mul_mv_id(
        constant ggml_metal_kargs_mul_mv_id & args,
        device const char * src0s,
        device const char * src1,
        device       char * dst,
        device const char * ids,
        threadgroup  char * shmem [[threadgroup(0)]],
        uint3  tgpig[[threadgroup_position_in_grid]],
        ushort tiitg[[thread_index_in_threadgroup]],
        ushort tiisg[[thread_index_in_simdgroup]],
        ushort sgitg[[simdgroup_index_in_threadgroup]]) {
    const int iid1 = tgpig.z/args.nei0;
    const int idx  = tgpig.z%args.nei0;

    tgpig.z = 0;

    const int32_t i02 = ((device const int32_t *) (ids + iid1*args.nbi1))[idx];

    const int64_t i11 = idx % args.ne11;
    const int64_t i12 = iid1;

    const int64_t i1 = idx;
    const int64_t i2 = i12;

    device const char * src0_cur = src0s + i02*args.nb02;
    device const char * src1_cur = src1  + i11*args.nb11 + i12*args.nb12;

    device char * dst_cur = dst + (i1*args.ne0 + i2*args.ne1*args.ne0)*sizeof(float);

    ggml_metal_kargs_mul_mv args0 = {
        /*.ne00 =*/ args.ne00,
        /*.ne01 =*/ args.ne01,
        /*.ne02 =*/ 1, // args.ne02,
        /*.nb00 =*/ args.nb00,
        /*.nb01 =*/ args.nb01,
        /*.nb02 =*/ args.nb02,
        /*.nb03 =*/ args.nb02, // args.ne02 == 1
        /*.ne10 =*/ args.ne10,
        /*.ne11 =*/ 1, // args.ne11,
        /*.ne12 =*/ 1, // args.ne12,
        /*.nb10 =*/ args.nb10,
        /*.nb11 =*/ args.nb11,
        /*.nb12 =*/ args.nb12,
        /*.nb13 =*/ args.nb12, // ne12 == 1
        /*.ne0  =*/ args.ne0,
        /*.ne1  =*/ 1, // args.ne1,
        /*.nr0  =*/ args.nr0,
        /*.r2   =*/ 1,
        /*.r3   =*/ 1,
    };

    disp_fn(
        args0,
        /* src0 */ src0_cur,
        /* src1 */ src1_cur,
        /* dst  */ dst_cur,
        shmem,
        tgpig,
        tiitg,
        tiisg,
        sgitg);
}

typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_disp<float, float>>>) kernel_mul_mv_id_t;

typedef decltype(kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_4_disp<float, float4, float, float4>>>) kernel_mul_mv_id_4_t;

template [[host_name("kernel_mul_mv_id_f32_f32")]]     kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_disp<float, float>>>;
template [[host_name("kernel_mul_mv_id_f16_f32")]]     kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_disp<half,  float>>>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mv_id_bf16_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_disp<bfloat, float>>>;
#endif
template [[host_name("kernel_mul_mv_id_f32_f32_4")]]   kernel kernel_mul_mv_id_4_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_4_disp<float, float4, float, float4>>>;
template [[host_name("kernel_mul_mv_id_f16_f32_4")]]   kernel kernel_mul_mv_id_4_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_4_disp<half,  half4,  float, float4>>>;
#if defined(GGML_METAL_HAS_BF16)
template [[host_name("kernel_mul_mv_id_bf16_f32_4")]]  kernel kernel_mul_mv_id_4_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_t_t_4_disp<bfloat, bfloat4, float, float4>>>;
#endif

template [[host_name("kernel_mul_mv_id_q8_0_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q8_0_f32_impl<N_R0_Q8_0>>>;

template [[host_name("kernel_mul_mv_id_q4_0_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<mul_vec_q_n_f32_impl<block_q4_0, N_R0_Q4_0>>>;
template [[host_name("kernel_mul_mv_id_q4_1_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<mul_vec_q_n_f32_impl<block_q4_1, N_R0_Q4_1>>>;
template [[host_name("kernel_mul_mv_id_q5_0_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<mul_vec_q_n_f32_impl<block_q5_0, N_R0_Q5_0>>>;
template [[host_name("kernel_mul_mv_id_q5_1_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<mul_vec_q_n_f32_impl<block_q5_1, N_R0_Q5_1>>>;

template [[host_name("kernel_mul_mv_id_mxfp4_f32")]]   kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_mxfp4_f32_impl<N_R0_MXFP4>>>;

template [[host_name("kernel_mul_mv_id_q2_K_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q2_K_f32_impl   <N_R0_Q2_K>>>;
template [[host_name("kernel_mul_mv_id_q3_K_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q3_K_f32_impl   <N_R0_Q3_K>>>;
template [[host_name("kernel_mul_mv_id_q4_K_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q4_K_f32_impl   <N_R0_Q4_K>>>;
template [[host_name("kernel_mul_mv_id_q5_K_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q5_K_f32_impl   <N_R0_Q5_K>>>;
template [[host_name("kernel_mul_mv_id_q6_K_f32")]]    kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_q6_K_f32_impl   <N_R0_Q6_K>>>;
template [[host_name("kernel_mul_mv_id_iq1_s_f32")]]   kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq1_s_f32_impl  <N_R0_IQ1_S>>>;
template [[host_name("kernel_mul_mv_id_iq1_m_f32")]]   kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq1_m_f32_impl  <N_R0_IQ1_M>>>;
template [[host_name("kernel_mul_mv_id_iq2_xxs_f32")]] kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq2_xxs_f32_impl<N_R0_IQ2_XXS>>>;
template [[host_name("kernel_mul_mv_id_iq2_xs_f32")]]  kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq2_xs_f32_impl <N_R0_IQ2_XS>>>;
template [[host_name("kernel_mul_mv_id_iq3_xxs_f32")]] kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq3_xxs_f32_impl<N_R0_IQ3_XXS>>>;
template [[host_name("kernel_mul_mv_id_iq3_s_f32")]]   kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq3_s_f32_impl  <N_R0_IQ3_S>>>;
template [[host_name("kernel_mul_mv_id_iq2_s_f32")]]   kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq2_s_f32_impl  <N_R0_IQ2_S>>>;
template [[host_name("kernel_mul_mv_id_iq4_nl_f32")]]  kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq4_nl_f32_impl <N_R0_IQ4_NL>>>;
template [[host_name("kernel_mul_mv_id_iq4_xs_f32")]]  kernel kernel_mul_mv_id_t kernel_mul_mv_id<mmv_fn<kernel_mul_mv_iq4_xs_f32_impl <N_R0_IQ4_XS>>>;

kernel void kernel_pool_2d_max_f32(
        constant    ggml_metal_kargs_pool_2d & args,
        device  const float * src0,
        device        float * dst,
        uint        gid[[thread_position_in_grid]]) {

    if (gid >= args.np) {
        return;
    }

    const int idx = gid;
    const int I_HW = args.IH * args.IW;
    const int O_HW = args.OH * args.OW;
    const int nc = idx / O_HW;
    const int cur_oh = idx % O_HW / args.OW;
    const int cur_ow = idx % O_HW % args.OW;

    device const float * i_ptr = src0 + nc * I_HW;
    device       float * o_ptr = dst  + nc * O_HW;

    const int start_h = cur_oh * args.s1 - args.p1;
    const int bh = MAX(0,  start_h);
    const int eh = MIN(args.IH, start_h + args.k1);
    const int start_w = cur_ow * args.s0 - args.p0;
    const int bw = MAX(0,  start_w);
    const int ew = MIN(args.IW, start_w + args.k0);

    float res = -INFINITY;

    for (int i = bh; i < eh; i += 1) {
        for (int j = bw; j < ew; j += 1) {
            res = MAX(res, i_ptr[i * args.IW + j]);
        }
    }

    o_ptr[cur_oh * args.OW + cur_ow] = res;
}

kernel void kernel_pool_2d_avg_f32(
        constant    ggml_metal_kargs_pool_2d & args,
        device  const float * src0,
        device        float * dst,
        uint        gid[[thread_position_in_grid]]) {

    if (gid >= args.np) {
        return;
    }

    const int idx = gid;
    const int I_HW = args.IH * args.IW;
    const int O_HW = args.OH * args.OW;
    const int nc = idx / O_HW;
    const int cur_oh = idx % O_HW / args.OW;
    const int cur_ow = idx % O_HW % args.OW;

    device const float * i_ptr = src0 + nc * I_HW;
    device       float * o_ptr = dst  + nc * O_HW;

    const int start_h = cur_oh * args.s1 - args.p1;
    const int bh = MAX(0,  start_h);
    const int eh = MIN(args.IH, start_h + args.k1);
    const int start_w = cur_ow * args.s0 - args.p0;
    const int bw = MAX(0,  start_w);
    const int ew = MIN(args.IW, start_w + args.k0);
    // const float scale = 1. / ((eh - bh) * (ew - bw));
    const float scale = 1. / (args.k0 * args.k1);

    float res = 0;

    for (int i = bh; i < eh; i += 1) {
        for (int j = bw; j < ew; j += 1) {
            float cur = i_ptr[i * args.IW + j];
            res += cur * scale;
        }
    }

    o_ptr[cur_oh * args.OW + cur_ow] = res;
}

kernel void kernel_opt_step_adamw_f32(
        constant    ggml_metal_kargs_opt_step_adamw & args,
        device       float * x,
        device const float * g,
        device       float * g_m,
        device       float * g_v,
        device const float * pars,
        uint        gid[[thread_position_in_grid]]) {

    if (gid >= args.np) {
        return;
    }

    const float alpha  = pars[0];
    const float beta1  = pars[1];
    const float beta2  = pars[2];
    const float eps    = pars[3];
    const float wd     = pars[4];
    const float beta1h = pars[5];
    const float beta2h = pars[6];

    const float gi = g[gid];
    const float gmi = g_m[gid] * beta1 +      gi * (1.0f - beta1);
    const float gvi = g_v[gid] * beta2 + gi * gi * (1.0f - beta2);

    g_m[gid] = gmi;
    g_v[gid] = gvi;

    const float mh =      gmi * beta1h;
    const float vh = sqrt(gvi * beta2h) + eps;

    x[gid] = x[gid] * (1.0f - alpha * wd) - alpha * mh / vh;
}

kernel void kernel_opt_step_sgd_f32(
        constant    ggml_metal_kargs_opt_step_sgd & args,
        device       float * x,
        device const float * g,
        device const float * pars,
        uint        gid[[thread_position_in_grid]]) {

    if (gid >= args.np) {
        return;
    }

    x[gid] = x[gid] * (1.0f - pars[0] * pars[1]) - pars[0] * g[gid];
}
