/*******************************************************************************
* Copyright 2017-2022 Intel Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*     http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/

#include "utils/parallel.hpp"

#include "deconv/ref_deconv.hpp"

// Copy paste from conv/ref_wino.cpp.
// TODO: remove the duplication.

namespace deconv {

template <typename Telem, size_t Tdims>
struct array_offset_calculator_t {
    template <typename... Targs>
    array_offset_calculator_t(Telem *base, Targs... Fargs) : _dims {Fargs...} {
        _base_ptr = base;
    }
    template <typename... Targs>
    inline Telem &operator()(Targs... Fargs) {
        return *(_base_ptr + _offset(1, Fargs...));
    }

private:
    template <typename... Targs>
    inline size_t _offset(size_t const dimension, size_t element) {
        return element;
    }

    template <typename... Targs>
    inline size_t _offset(
            size_t const dimension, size_t theta, size_t element) {
        return element + (_dims[dimension] * theta);
    }

    template <typename... Targs>
    inline size_t _offset(size_t const dimension, size_t theta, size_t element,
            Targs... Fargs) {
        size_t t_prime = element + (_dims[dimension] * theta);
        return _offset(dimension + 1, t_prime, Fargs...);
    }

    Telem *_base_ptr;
    const int64_t _dims[Tdims];
};

void trans_I_4x4_3x3(float Iw[6][6], float I[6][6]) {
    float T[6][6];
    float t0;
    float t1;
    float t2;
    float t3;
    float t4;
    float t5;

    for (int i = 0; i < 6; i++) {
        t0 = I[2][i] * -2.25f + I[4][i];
        t1 = I[1][i] * -2.25f + I[3][i];
        t2 = I[2][i] * -0.390625f + I[4][i];
        t3 = I[1][i] * -0.390625f + I[3][i];
        t4 = I[0][i] * 0.87890625f + I[4][i];
        t5 = I[1][i] * 0.87890625f + I[5][i];

        T[0][i] = I[2][i] * -2.640625f + t4;
        T[1][i] = t1 * 0.625f + t0;
        T[2][i] = t1 * -0.625f + t0;
        T[3][i] = t3 * 1.5f + t2;
        T[4][i] = t3 * -1.5f + t2;
        T[5][i] = I[3][i] * -2.640625f + t5;
    }

    for (int i = 0; i < 6; i++) {
        t0 = T[i][2] * -2.25f + T[i][4];
        t1 = T[i][1] * -2.25f + T[i][3];
        t2 = T[i][2] * -0.390625f + T[i][4];
        t3 = T[i][1] * -0.390625f + T[i][3];
        t4 = T[i][0] * 0.87890625f + T[i][4];
        t5 = T[i][1] * 0.87890625f + T[i][5];

        Iw[i][0] = T[i][2] * -2.640625f + t4;
        Iw[i][1] = t1 * 0.625f + t0;
        Iw[i][2] = t1 * -0.625f + t0;
        Iw[i][3] = t3 * 1.5f + t2;
        Iw[i][4] = t3 * -1.5f + t2;
        Iw[i][5] = T[i][3] * -2.640625f + t5;
    }
}

void trans_W_4x4_3x3(float Fw_[6][6], float F[3][3]) {
    float Fw[6];
    float T[6][3];
    float t0;
    float t1;
    float t2;

    for (int i = 0; i < 3; i++) {
        t0 = 0.26890756302521f * F[2][i];
        t1 = -t0 - 0.688403361344538f * F[0][i];
        t2 = t0 + 0.119514472455649f * F[0][i];

        T[0][i] = 1.13777777777778f * F[0][i];
        T[1][i] = t1 - 0.430252100840336f * F[1][i];
        T[2][i] = t1 + 0.430252100840336f * F[1][i];
        T[3][i] = t2 + 0.179271708683473f * F[1][i];
        T[4][i] = t2 - 0.179271708683473f * F[1][i];
        T[5][i] = F[2][i];
    }

    for (int i = 0; i < 6; i++) {
        t0 = 0.26890756302521f * T[i][2];
        t1 = -t0 - 0.688403361344538f * T[i][0];
        t2 = t0 + 0.119514472455649f * T[i][0];

        Fw[0] = 1.13777777777778f * T[i][0];
        Fw[1] = t1 - 0.430252100840336f * T[i][1];
        Fw[2] = t1 + 0.430252100840336f * T[i][1];
        Fw[3] = t2 + 0.179271708683473f * T[i][1];
        Fw[4] = t2 - 0.179271708683473f * T[i][1];
        Fw[5] = T[i][2];
        for (int l = 0; l < 6; l++) {
            Fw_[i][l] = Fw[l];
        }
    }
}

void trans_O_4x4_3x3(float Mw[6][6], float O[4][4]) {
    float T[4][6];
    float t0;
    float t1;
    float t2;
    float t3;

    for (int i = 0; i < 6; i++) {
        t0 = Mw[1][i] + Mw[2][i];
        t1 = Mw[3][i] + Mw[4][i];
        t2 = Mw[1][i] - Mw[2][i];
        t3 = Mw[3][i] - Mw[4][i];

        T[0][i] = t0 + t1 + Mw[0][i];
        T[1][i] = t2 * 0.625f + t3 * 1.5f;
        T[2][i] = t0 * 0.390625f + t1 * 2.25f;
        T[3][i] = t2 * 0.244140625f + t3 * 3.375f + Mw[5][i];
    }

    for (int i = 0; i < 4; i++) {
        t0 = T[i][1] + T[i][2];
        t1 = T[i][3] + T[i][4];
        t2 = T[i][1] - T[i][2];
        t3 = T[i][3] - T[i][4];

        O[i][0] = t0 + t1 + T[i][0];
        O[i][1] = t2 * 0.625f + t3 * 1.5f;
        O[i][2] = t0 * 0.390625f + t1 * 2.25f;
        O[i][3] = t2 * 0.244140625f + t3 * 3.375f + T[i][5];
    }
}

void trans_W_3x3_4x4_wu(float Fw[6][6], float F[4][6]) {
    float T[6][4];
    float t0;
    float t1;
    float t2;
    float t3;
    float t4;

    for (int i = 0; i < 4; i++) {
        t0 = F[2][i] * 0.26890756302521f;
        t1 = F[0][i] * -0.688403361344538f - t0;
        t2 = F[0][i] * 0.119514472455649f + t0;
        t3 = F[1][i] * 0.430252100840336f + F[3][i] * 0.168067226890756f;
        t4 = F[1][i] * 0.179271708683473f + F[3][i] * 0.403361344537815f;

        T[0][i] = F[0][i] * 1.13777777777778f;
        T[1][i] = t1 - t3;
        T[2][i] = t1 + t3;
        T[3][i] = t2 + t4;
        T[4][i] = t2 - t4;
        T[5][i] = F[3][i];
    }

    for (int i = 0; i < 6; i++) {
        t0 = T[i][2] * 0.26890756302521f;
        t1 = T[i][0] * -0.688403361344538f - t0;
        t2 = T[i][0] * 0.119514472455649f + t0;
        t3 = T[i][1] * 0.430252100840336f + T[i][3] * 0.168067226890756f;
        t4 = T[i][1] * 0.179271708683473f + T[i][3] * 0.403361344537815f;

        Fw[i][0] = T[i][0] * 1.13777777777778f;
        Fw[i][1] = t1 - t3;
        Fw[i][2] = t1 + t3;
        Fw[i][3] = t2 + t4;
        Fw[i][4] = t2 - t4;
        Fw[i][5] = T[i][3];
    }
}

void trans_O_3x3_4x4_wu(float Mw[6][6], float M[3][3]) {
    float T[3][6];
    float t0;
    float t1;
    float t2;
    float M_[3];

    for (int i = 0; i < 6; i++) {
        t0 = Mw[1][i] + Mw[2][i];
        t1 = Mw[3][i] + Mw[4][i];
        t2 = t1 * 2.25f + Mw[5][i];

        T[0][i] = Mw[0][i] + t0 + t1;
        T[1][i] = 0.625f * (Mw[1][i] - Mw[2][i]) + 1.5f * (Mw[3][i] - Mw[4][i]);
        T[2][i] = t0 * 0.390625f + t2;
    }
    for (int i = 0; i < 3; i++) {
        t0 = T[i][1] + T[i][2];
        t1 = T[i][3] + T[i][4];
        t2 = t1 * 2.25f + T[i][5];

        M_[0] = T[i][0] + t0 + t1;
        M_[1] = 0.625f * (T[i][1] - T[i][2]) + 1.5f * (T[i][3] - T[i][4]);
        M_[2] = t0 * 0.390625f + t2;

        for (int k = 0; k < 3; k++) {
            M[i][k] = M_[k];
        }
    }
}

struct scratchpad_t {
    float *_u_ptr;
    float *_m_ptr;
    float *_v_ptr;

    int64_t h_tiles;
    int64_t w_tiles;

    const int64_t alpha = 6;
    const int64_t out_dim = 4;
};

int init_scratchpad(const prb_t *prb, scratchpad_t &sp) {
    if (sp.out_dim != 4 || sp.alpha != 6) return FAIL;

    sp.h_tiles = prb->dir == FLAG_FWD ? div_up(prb->oh, sp.out_dim)
                                      : div_up(prb->ih, sp.out_dim);
    sp.w_tiles = prb->dir == FLAG_FWD ? div_up(prb->ow, sp.out_dim)
                                      : div_up(prb->iw, sp.out_dim);

    sp._u_ptr = (float *)zmalloc(
            sizeof(float) * sp.alpha * sp.alpha * prb->oc * prb->ic, 64);
    sp._v_ptr = (float *)zmalloc(sizeof(float) * sp.alpha * sp.alpha * prb->ic
                    * prb->mb * sp.h_tiles * sp.w_tiles,
            64);
    sp._m_ptr = (float *)zmalloc(sizeof(float) * sp.alpha * sp.alpha * prb->oc
                    * prb->mb * sp.h_tiles * sp.w_tiles,
            64);

    if (sp._u_ptr == nullptr || sp._v_ptr == nullptr || sp._m_ptr == nullptr)
        return dnnl_out_of_memory;

    array_set((char *)sp._u_ptr,
            sizeof(float) * sp.alpha * sp.alpha * prb->oc * prb->ic);
    array_set((char *)sp._v_ptr,
            sizeof(float) * sp.alpha * sp.alpha * prb->ic * prb->mb * sp.h_tiles
                    * sp.w_tiles);
    array_set((char *)sp._m_ptr,
            sizeof(float) * sp.alpha * sp.alpha * prb->oc * prb->mb * sp.h_tiles
                    * sp.w_tiles);

    return OK;
}

void free_scratchpad(scratchpad_t *sp) {
    if (sp->_u_ptr != nullptr) zfree(sp->_u_ptr);
    if (sp->_v_ptr != nullptr) zfree(sp->_v_ptr);
    if (sp->_m_ptr != nullptr) zfree(sp->_m_ptr);
}

void compute_wino_ref_fwd(const prb_t *prb, const args_t &args) {
    const dnn_mem_t &src_m = args.find(DNNL_ARG_SRC);
    const dnn_mem_t &wei_m = args.find(DNNL_ARG_WEIGHTS);
    const dnn_mem_t &bia_m = args.find(DNNL_ARG_BIAS);
    const dnn_mem_t &dst_m = args.find(DNNL_ARG_DST);
    scratchpad_t sp {};
    SAFE_V(init_scratchpad(prb, sp));

    array_offset_calculator_t<float, 4> U(
            sp._u_ptr, sp.alpha, sp.alpha, prb->oc, prb->ic);
    array_offset_calculator_t<float, 6> V(sp._v_ptr, sp.alpha, sp.alpha,
            prb->ic, prb->mb, sp.h_tiles, sp.w_tiles);
    array_offset_calculator_t<float, 6> M(sp._m_ptr, sp.alpha, sp.alpha,
            prb->oc, prb->mb, sp.h_tiles, sp.w_tiles);

    SAFE_V(prb->kh == 3 ? OK : FAIL);
    SAFE_V(prb->kw == 3 ? OK : FAIL);

    bool with_bias = prb->dir & FLAG_BIA;
    const int64_t t_pad = prb->ph;
    const int64_t l_pad = prb->pw;
    const int64_t wp_max = prb->iw + l_pad;
    const int64_t hp_max = prb->ih + t_pad;
    const int64_t p_dim = prb->mb * sp.h_tiles * sp.w_tiles;

    benchdnn_parallel_nd(prb->mb, prb->ic, sp.h_tiles, sp.w_tiles,
            [&](int64_t img, int64_t c, int64_t hfm, int64_t wfm) {
                float I[6][6] = {};
                float _v[6][6] = {};
                /* src_transform v <- B_t * d * B */
                for (int64_t j = 0; j < sp.alpha; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if ((t_pad <= ydim) && (ydim < hp_max)) {
                        for (int64_t k = 0; k < sp.alpha; k++) {
                            int64_t xdim = wfm * sp.out_dim + k;
                            if ((l_pad <= xdim) && (xdim < wp_max)) {
                                size_t src_off = src_off_f(prb, img, 0, c, 0,
                                        ydim - t_pad, xdim - l_pad);
                                I[j][k] = ((float *)src_m)[src_off];
                            }
                        }
                    }
                }
                trans_I_4x4_3x3(_v, I);

                /* scatter v:V */
                for (int64_t j = 0; j < sp.alpha; j++) {
                    for (int64_t k = 0; k < sp.alpha; k++) {
                        V(j, k, c, img, hfm, wfm) = _v[j][k];
                    }
                }
            });

    benchdnn_parallel_nd(prb->oc, prb->ic, [&](int64_t oc, int64_t ic) {
        float F[3][3] = {};
        float _u[6][6] = {};
        /* wei_transform u <- G * g * G_t */
        for_(int64_t j = 0; j < prb->kh; j++)
        for (int64_t i = 0; i < prb->kw; i++) {
            size_t wei_off = wei_off_f(prb, 0, oc, ic, 0, j, i);
            F[j][i] = ((float *)wei_m)[wei_off];
        }
        trans_W_4x4_3x3(_u, F);

        /* scatter u:U */
        for_(int64_t j = 0; j < sp.alpha; j++)
        for (int64_t k = 0; k < sp.alpha; k++) {
            U(j, k, oc, ic) = _u[j][k];
        }
    });

    benchdnn_parallel_nd(sp.alpha, sp.alpha, [&](int64_t j, int64_t k) {
        /* M = U * V */
        gemm("C", "N", "N", prb->oc, p_dim, prb->ic, 1.0,
                (float *)&(U(j, k, 0, 0)), prb->ic,
                (float *)&(V(j, k, 0, 0, 0, 0)), p_dim, 1.0,
                (float *)&(M(j, k, 0, 0, 0, 0)), p_dim);
    });

    auto v_po_masks = prb->attr.post_ops.get_po_masks();
    benchdnn_parallel_nd(prb->oc, prb->mb, sp.h_tiles, sp.w_tiles,
            [&](int64_t oc, int64_t img, int64_t hfm, int64_t wfm) {
                float O[4][4] = {};
                float _m[6][6] = {};
                /* Y = A_t *m * A */
                for_(int64_t j = 0; j < sp.alpha; j++)
                for (int64_t k = 0; k < sp.alpha; k++) {
                    _m[j][k] = M(j, k, oc, img, hfm, wfm);
                }
                trans_O_4x4_3x3(_m, O);

                for (int64_t j = 0; j < sp.out_dim; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if (ydim >= prb->oh) continue;

                    for (int64_t k = 0; k < sp.out_dim; k++) {
                        float conv_res = O[j][k];
                        int64_t xdim = wfm * sp.out_dim + k;
                        if (xdim >= prb->ow) continue;

                        const size_t dst_off
                                = dst_off_f(prb, img, 0, oc, 0, ydim, xdim);
                        float &dst = ((float *)dst_m)[dst_off];

                        const size_t bia_off = bia_off_f(prb, 0, oc);
                        conv_res += with_bias ? ((float *)bia_m)[bia_off] : 0.f;

                        const auto v_po_vals = prepare_po_vals(
                                dst_m, args, v_po_masks, dst_off);

                        maybe_post_ops(prb->attr, conv_res, dst, v_po_vals);

                        dst = conv_res;
                    }
                }
            });
    free_scratchpad(&sp);
}

void compute_wino_ref_bwd_d(const prb_t *prb, const args_t &args) {
    const dnn_mem_t &diff_src_m = args.find(DNNL_ARG_DIFF_SRC);
    const dnn_mem_t &wei_m = args.find(DNNL_ARG_WEIGHTS);
    const dnn_mem_t &bia_m = args.find(DNNL_ARG_BIAS);
    const dnn_mem_t &diff_dst_m = args.find(DNNL_ARG_DIFF_DST);
    scratchpad_t sp {};
    SAFE_V(init_scratchpad(prb, sp));

    array_offset_calculator_t<float, 4> U(
            sp._u_ptr, sp.alpha, sp.alpha, prb->ic, prb->oc);
    array_offset_calculator_t<float, 6> V(sp._m_ptr, sp.alpha, sp.alpha,
            prb->oc, prb->mb, sp.h_tiles, sp.w_tiles);
    array_offset_calculator_t<float, 6> M(sp._v_ptr, sp.alpha, sp.alpha,
            prb->ic, prb->mb, sp.h_tiles, sp.w_tiles);

    SAFE_V(prb->kh == 3 ? OK : FAIL);
    SAFE_V(prb->kw == 3 ? OK : FAIL);

    const int64_t r_pad = MAX2(0, prb->ow - 1 + prb->kw - prb->iw - prb->pw);
    const int64_t l_pad = prb->iw + r_pad - prb->ow;
    const int64_t t_pad = prb->ih + prb->ph - prb->oh;
    const int64_t wp_max = prb->ow + l_pad;
    const int64_t hp_max = prb->oh + t_pad;
    const int64_t p_dim = prb->mb * sp.h_tiles * sp.w_tiles;

    bool with_bias = prb->dir & FLAG_BIA;

    benchdnn_parallel_nd(prb->mb, prb->oc, sp.h_tiles, sp.w_tiles,
            [&](int64_t img, int64_t c, int64_t hfm, int64_t wfm) {
                float I[6][6] = {};
                float _v[6][6] = {};
                /* diff_src transform v <- B_t * d * B */
                for (int64_t j = 0; j < sp.alpha; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if ((t_pad <= ydim) && (ydim < hp_max)) {
                        for (int64_t k = 0; k < sp.alpha; k++) {
                            int64_t xdim = wfm * sp.out_dim + k;
                            if ((l_pad <= xdim) && (xdim < wp_max)) {
                                size_t dst_off = dst_off_f(prb, img, 0, c, 0,
                                        ydim - t_pad, xdim - l_pad);
                                I[j][k] = ((float *)diff_dst_m)[dst_off];
                            }
                        }
                    }
                    trans_I_4x4_3x3(_v, I);

                    /* scatter v:V */
                    for_(int64_t j = 0; j < sp.alpha; j++)
                    for (int64_t k = 0; k < sp.alpha; k++) {
                        V(j, k, c, img, hfm, wfm) = _v[j][k];
                    }
                }
            });

    benchdnn_parallel_nd(prb->ic, prb->oc, [&](int64_t ic, int64_t oc) {
        float F[3][3] = {};
        float _u[6][6] = {};
        /* wei_transform u <- G * g * G_t */
        for_(int64_t j = 0; j < prb->kh; j++)
        for (int64_t i = 0; i < prb->kw; i++) {
            size_t wei_off = wei_off_f(
                    prb, 0, oc, ic, 0, prb->kh - j - 1, prb->kw - i - 1);
            F[j][i] = ((float *)wei_m)[wei_off];
        }
        trans_W_4x4_3x3(_u, F);

        /* scatter u:U */
        for_(int64_t j = 0; j < sp.alpha; j++)
        for (int64_t k = 0; k < sp.alpha; k++) {
            U(j, k, ic, oc) = _u[j][k];
        }
    });

    benchdnn_parallel_nd(sp.alpha, sp.alpha, [&](int64_t j, int64_t k) {
        /* M = U * V */
        gemm("C", "N", "N", prb->ic, p_dim, prb->oc, 1.0,
                (float *)&(U(j, k, 0, 0)), prb->oc,
                (float *)&(V(j, k, 0, 0, 0, 0)), p_dim, 1.0,
                (float *)&(M(j, k, 0, 0, 0, 0)), p_dim);
    });

    benchdnn_parallel_nd(prb->ic, prb->mb, sp.h_tiles, sp.w_tiles,
            [&](int64_t c, int64_t img, int64_t hfm, int64_t wfm) {
                float O[4][4] = {};
                float _m[6][6] = {};
                /* diff_dst: Y = A_t *m * A */
                for_(int64_t j = 0; j < sp.alpha; j++)
                for (int64_t k = 0; k < sp.alpha; k++) {
                    _m[j][k] = M(j, k, c, img, hfm, wfm);
                }
                trans_O_4x4_3x3(_m, O);

                float bia = with_bias ? ((float *)bia_m)[c] : 0.f;

                for (int64_t j = 0; j < sp.out_dim; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if (ydim < prb->ih) {
                        for (int64_t k = 0; k < sp.out_dim; k++) {
                            int64_t xdim = wfm * sp.out_dim + k;
                            if (xdim < prb->iw) {
                                size_t src_off = src_off_f(
                                        prb, img, 0, c, 0, ydim, xdim);
                                ((float *)diff_src_m)[src_off] = O[j][k] + bia;
                            }
                        }
                    }
                }
            });

    free_scratchpad(&sp);
}

void compute_wino_ref_bwd_w(const prb_t *prb, const args_t &args) {
    const dnn_mem_t &src_m = args.find(DNNL_ARG_SRC);
    const dnn_mem_t &diff_wei_m = args.find(DNNL_ARG_DIFF_WEIGHTS);
    const dnn_mem_t &diff_dst_m = args.find(DNNL_ARG_DIFF_DST);
    scratchpad_t sp {};
    SAFE_V(init_scratchpad(prb, sp));

    array_offset_calculator_t<float, 4> U(
            sp._u_ptr, sp.alpha, sp.alpha, prb->oc, prb->ic);
    array_offset_calculator_t<float, 6> V(sp._v_ptr, sp.alpha, sp.alpha,
            prb->mb, sp.h_tiles, sp.w_tiles, prb->ic);
    array_offset_calculator_t<float, 6> M(sp._m_ptr, sp.alpha, sp.alpha,
            prb->oc, prb->mb, sp.h_tiles, sp.w_tiles);

    SAFE_V(prb->kh == 3 ? OK : FAIL);
    SAFE_V(prb->kw == 3 ? OK : FAIL);

    const int64_t t_pad = prb->ph;
    const int64_t l_pad = prb->pw;
    const int64_t wp_max = prb->iw + l_pad;
    const int64_t hp_max = prb->ih + t_pad;
    const int64_t p_dim = prb->mb * sp.h_tiles * sp.w_tiles;

    benchdnn_parallel_nd(prb->mb, sp.h_tiles, sp.w_tiles, prb->ic,
            [&](int64_t img, int64_t hfm, int64_t wfm, int64_t ic) {
                float I[6][6] = {};
                float _v[6][6] = {};
                /* src transform v <- B_t * d * B */
                for (int64_t j = 0; j < sp.alpha; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if ((t_pad <= ydim) && (ydim < hp_max)) {
                        for (int64_t k = 0; k < sp.alpha; k++) {
                            int64_t xdim = wfm * sp.out_dim + k;
                            if ((l_pad <= xdim) && (xdim < wp_max)) {
                                size_t src_off = src_off_f(prb, img, 0, ic, 0,
                                        ydim - t_pad, xdim - l_pad);
                                I[j][k] = ((float *)src_m)[src_off];
                            }
                        }
                    }
                }
                trans_I_4x4_3x3(_v, I);

                /* scatter v:V */
                for_(int64_t j = 0; j < sp.alpha; j++)
                for (int64_t k = 0; k < sp.alpha; k++) {
                    V(j, k, img, hfm, wfm, ic) = _v[j][k];
                }
            });

    benchdnn_parallel_nd(prb->oc, prb->mb, sp.h_tiles, sp.w_tiles,
            [&](int64_t oc, int64_t img, int64_t hfm, int64_t wfm) {
                float O[6][6] = {};
                float _m[6][6] = {};
                /* diff_dst transform */
                for (int64_t j = 0; j < sp.alpha; j++) {
                    int64_t ydim = hfm * sp.out_dim + j;
                    if (ydim < prb->oh) {
                        for (int64_t k = 0; k < sp.alpha; k++) {
                            int64_t xdim = wfm * sp.out_dim + k;
                            if (xdim < prb->ow) {
                                size_t dst_off = dst_off_f(
                                        prb, img, 0, oc, 0, ydim, xdim);
                                O[j][k] = ((float *)diff_dst_m)[dst_off];
                            }
                        }
                    }
                }
                trans_W_3x3_4x4_wu(_m, O);
                /* scatter v:V */
                for_(int64_t j = 0; j < sp.alpha; j++)
                for (int64_t k = 0; k < sp.alpha; k++) {
                    M(j, k, oc, img, hfm, wfm) = _m[j][k];
                }
            });

    benchdnn_parallel_nd(sp.alpha, sp.alpha, [&](int64_t j, int64_t k) {
        /* GeMM U = M * V */
        gemm("C", "N", "N", prb->oc, prb->ic, p_dim, 1.0,
                (float *)&(M(j, k, 0, 0, 0, 0)), p_dim,
                (float *)&(V(j, k, 0, 0, 0, 0)), prb->ic, 1.0,
                (float *)&(U(j, k, 0, 0)), prb->ic);
    });

    benchdnn_parallel_nd(prb->oc, prb->ic, [&](int64_t oc, int64_t ic) {
        float F[6][6] = {};
        float _u[3][3] = {};
        for_(int64_t j = 0; j < sp.alpha; j++)
        for (int64_t k = 0; k < sp.alpha; k++) {
            F[j][k] = U(j, k, oc, ic);
        }
        trans_O_3x3_4x4_wu(F, _u);

        /* scatter u:U */
        for_(int64_t kh = 0; kh < prb->kh; kh++)
        for (int64_t kw = 0; kw < prb->kw; kw++) {
            size_t wei_off = wei_off_f(prb, 0, oc, ic, 0, kh, kw);
            ((float *)diff_wei_m)[wei_off] = _u[kh][kw];
        }
    });

    free_scratchpad(&sp);

    if (prb->dir & FLAG_BIA) compute_ref_bwd_bias(prb, args);
}

} // namespace deconv
