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  大家好，我是极智视界，本文剖析一下 min-max 对称量化算法实现，以 Tengine 的实现为例。

  Tengine 是 OpenAILab 开源的优秀端侧深度学习推理框架，其核心主要由 C 语言实现，包裹的功能代码嵌套了 C++。量化是推理加速必不可少的优化环节，成熟的推理框架一般会把量化模块剥离出来形成独立的一套工具，如 Tengine、NCNN、昇腾、寒武纪都这么做，这主要是因为量化过程和硬件非强相关，解耦开来能干更多的事。

  min-max 和 kl 量化算法是硬件厂商适配推理引擎的基础和标配， 其中 kl 量化深受用户喜爱，如英伟达的 TensorRT 也正是采用了 kl 量化策略；而这里要介绍的 min-max 的特点是逻辑简单、效果良好，作为量化实现分享系列的开篇比较合适，这里带大家一起研究一下 Tengine 中 minx-max 量化策略的具体实现。

1、量化使用

  量化主要分为激活值（动态）量化、权值&偏置（静态）量化，而权值&偏置的量化是对精度影响比较大的，激活值的量化对整体影响较小，但也需要量化，才有可能协同达到整体满意的效果。对于一般量化来说，权值&偏置的量化会采用逐通道 perChannel 的方式，而激活值的量化一般是逐层 perLayer 的方式。解释一下为啥会这样，对于量化来说，卷积肯定是大头，对于卷积来说，若激活值量化采用逐通道方式，这和卷积核参数共享是相悖的，所以一般激活值就用逐层量化，以契合卷积参数共享。

  这里主要看一下 Tengine 量化需要的传参：

Input model：传入的 fp32 tmfile 模型文件；Output model：生成的 int8 tmfile 模型文件；Calib images：传入的激活值量化校准图片；Scale file：生成的校准表文件；Agorithm：量化算法，可选 MIN-MAX、KL、ACIQ、DFQ、EQ；Dims：输入校准图的 shape，这里传三维 c h w，n 在代码中写死 n = 1；Mean：图像预处理均值；Scale：图像预处理缩放尺度；BGR2RGB：通道转换；Center crop：图像预处理，裁剪；Letter box：图像预处理，保持横纵比的前提下对图像做 resize；YOLOv5 focus：类似 yolov5 的预处理注意力机制；Thread num：量化多线程设置；2、min-max 量化

  min-max 是最简单的量化算法，主要逻辑如下：

  在 Tengine 中实现 min-max 方法的主要代码如下：

case ALGORITHM_MIN_MAX:{    if (quant_tool.scale_file.empty()){        quant_tool.scale_file = "table_minmax.scale";        quant_tool.activation_quant_tool();    }    save_graph_i8_perchannel(quant_tool.model_file.c_str(), quant_tool.scale_file.c_str(), quant_tool.output_file, quant_tool.inplace, false);    /* Evaluate quantitative losses */    if (quant_tool.evaluate){        fprintf(stderr, "[Quant Tools Info]: Step Evaluate, evaluate quantitative losses\n");        quant_tool.assess_quant_loss(0);    }    break;}

  其中最主要的量化搜索策略接口是 quant_tool.activation_quant_tool() 和 save_graph_i8_perchannel，对于 min-max 来说这两个接口分别做了两件事：

  (1) 激活值量化，生成 table_minmax.scale；

  (2) 权值&偏置量化，生成 scale_weight.txt 和 scale_bias.txt；

2.1 激活值量化

  看 Tengine 源码一定要抓住 struct graph* ir_graph，graph 这个结构体是精髓。

  激活值量化是个动态的过程，需要动态的获取每层的数据分布，这也就是为啥需要你喂一定数量校准图片的原因。

  先说一下预处理模块，这个其他量化算法是通用的：

// 将 input_tensor 和 input_data 地址绑定，而 input_tensor=>ir_graph->tensor_list。注意：这一步一定要看到，不然后续代码很难看懂tensor_t input_tensor = get_graph_input_tensor(ir_graph, 0, 0);if (set_tensor_shape(input_tensor, dims, 4) < 0){    fprintf(stderr, "Set input tensor shape failed\n");    return -1;}if (set_tensor_buffer(input_tensor, input_data.data(), img_size * sizeof(float)) < 0){    fprintf(stderr, "Set input tensor buffer failed\n");    return -1;}// prerun graph，做一些初始化配置if (prerun_graph_multithread(ir_graph, this->opt) < 0){    fprintf(stderr, "Prerun multithread graph failed.\n");    return -1;}// 图像预处理，传出 input_data，这个和前面的 input_tensor & ir_graph->tensor_list[0] 输入参 绑定，修改了 input_data 即修改了 ir_graph.tensor_list，这样就能看懂get_input_data_cv(imgs_list[nums].c_str(), input_data.data(), img_c, img_h, img_w, mean, scale, sw_RGB, center_crop, letterbox_rows, letterbox_cols, focus);

  然后 run 一下，把中间激活值记录到 ir_graph->tensor_list[i] 里：

if (run_graph(ir_graph, 1) < 0){    fprintf(stderr, "Run graph failed\n");    return -1;}

  激活激活值的 min、max 值：

/* get the min/max value of activation tensor */for (int i = 0; i < ir_graph->tensor_num; i++){    struct tensor* act_tensor = ir_graph->tensor_list[i];    if (act_tensor->tensor_type == TENSOR_TYPE_VAR || act_tensor->tensor_type == TENSOR_TYPE_INPUT){        float* start_addr = (float*)act_tensor->data;        float* end_addr = (float*)act_tensor->data + act_tensor->elem_num;        max_activation[i] = std::max(max_activation[i], *std::max_element(start_addr, end_addr));        min_activation[i] = std::min(min_activation[i], *std::min_element(start_addr, end_addr));}}

  计算激活值量化尺度，对于 softmax 层 scale 默认为 1 / 127.f：

/* save the calibration file with min-max algorithm */FILE* fp_minmax = fopen("table_minmax.scale", "wb");for (int i = 0; i < ir_graph->tensor_num; i++){    struct tensor* t = ir_graph->tensor_list[i];    if (t->tensor_type == TENSOR_TYPE_VAR || t->tensor_type == TENSOR_TYPE_INPUT){        float act_scale = 1.f;        int act_zero_point = 0;        act_scale = std::max(std::abs(max_activation[i]), std::abs(min_activation[i])) / 127.f;        /* the scale of softmax is always scale = 1 / 127.f */        for (int j = 0; j < ir_graph->node_num; j++){            struct node* noden = ir_graph->node_list[j];            struct tensor* tensor_tmp = get_ir_graph_tensor(ir_graph, noden->output_tensors[0]);            if (!(tensor_tmp->tensor_type == TENSOR_TYPE_INPUT || tensor_tmp->tensor_type == TENSOR_TYPE_VAR))                continue;            std::string tmp_op_name = get_op_name_from_type(noden->op.type);            std::string cur_name = t->name;            std::string tmp_name = tensor_tmp->name;            if ((cur_name == tmp_name) && tmp_op_name == "Softmax"){                act_scale = 1 / 127.f;                break;}        }        fprintf(fp_minmax, "%s %f %d\n", ir_graph->tensor_list[i]->name, act_scale, act_zero_point);}}

  权值 & 偏置量化和激活值量化不太一样，激活值量化需要校准图片推理以获得输入数据的动态分布，而权值 & 偏置是静态的，单纯的量化过程不需执行前向推理。

2.2.1 创建 graph

  加载 tmfile，构建 graph：

struct graph* ir_graph = (struct graph*)create_graph(nullptr, "tengine", model_file);if (nullptr == ir_graph){fprintf(stderr, "Create graph failed.\n");return -1;}

  这里主要做一个 quant.inplace 的优化，这是针对非卷积算子的量化处理策略。

if (inplace == 0){    for (int i = 0; i < ir_graph->tensor_num; i++){        struct tensor* ir_tensor = ir_graph->tensor_list[i];        if (ir_tensor->tensor_type == TENSOR_TYPE_VAR || ir_tensor->tensor_type == TENSOR_TYPE_INPUT){            ir_tensor->scale = layer_scale[ir_tensor->name];            ir_tensor->zero_point = layer_zeropoint[ir_tensor->name];}}    }    else{        std::tr1::unordered_map<std::string, bool> layer_pass;        for (int i = ir_graph->tensor_num - 1; i >= 0; i--){            struct tensor* ir_tensor = ir_graph->tensor_list[i];            if (ir_tensor->tensor_type == TENSOR_TYPE_VAR || ir_tensor->tensor_type == TENSOR_TYPE_INPUT){                if (layer_pass[ir_tensor->name] == false){                    uint32_t ir_node_idx = ir_tensor->producer;                    struct node* t_node = ir_graph->node_list[ir_node_idx];                    std::string op_name = get_op_name_from_type(t_node->op.type);                    bool poolTrue = false;                    bool reluTrue = false;                    if (op_name == "Pooling"){                        struct pool_param* pool_param = (struct pool_param*)t_node->op.param_mem;                        if (pool_param->pool_method == 0)                            poolTrue = true;                    }                    else if (op_name == "ReLU"){                        struct relu_param* relu_param = (struct relu_param*)t_node->op.param_mem;                        if (relu_param->negative_slope == 0.f)                            reluTrue = true;                    }                    if (op_name == "Flatten" || op_name == "Reshape" || op_name == "Squeeze" || op_name == "Clip" || op_name == "Slice" || poolTrue || reluTrue){                        struct tensor* t_in_tensor = ir_graph->tensor_list[t_node->input_tensors[0]];                        if (layer_scale[ir_tensor->name] != 0){                            ir_tensor->scale = layer_scale[ir_tensor->name];                            ir_tensor->zero_point = layer_zeropoint[ir_tensor->name];                            if (t_in_tensor->tensor_type == TENSOR_TYPE_VAR || t_in_tensor->tensor_type == TENSOR_TYPE_INPUT){                                recursion_pass_through(ir_graph, ir_tensor->name, t_in_tensor, layer_used, layer_scale, layer_zeropoint, layer_pass);}}                    }                    else{                        ir_tensor->scale = layer_scale[ir_tensor->name];                        ir_tensor->zero_point = layer_zeropoint[ir_tensor->name];                    }                    layer_pass[ir_tensor->name] = true;}}}}

  量化的整个过程和激活值量化类似，即先搜索 min、max 值，后做截断缩放处理。这里不仅需要计算 scale，而且还要做截断缩放处理的原因是需要生成 int8 tmfile 量化模型文件。这里还有一点需要注意的是权值量化精度为 int8，偏置量化精度为 int32，因为权值做完矩阵乘后值很有可能就会溢出 int8，所以需要权值矩阵乘后的值用 int32 存储，然后与 int32 的偏置做加法。

  除了以上这些，和激活值量化还有个区别是，激活值量化是 perLayer 的，而权值 & 偏置量化是 perChannel 的。

  权值 int8 量化：

/* quantize the weight data from fp32 to int8 */if (op_name == "Convolution" || op_name == "FullyConnected" || op_name == "Deconvolution"){    struct tensor* weight_tensor = ir_graph->tensor_list[noden->input_tensors[1]];    int channel_num = weight_tensor->dims[0];    int cstep = int(weight_tensor->elem_num / channel_num);    float* weight_data = (float*)weight_tensor->data;    int8_t* i8_weight_data = (int8_t*)sys_malloc(weight_tensor->elem_num * sizeof(int8_t));    float* weight_scale_list = (float*)sys_malloc(channel_num * sizeof(float));    int* weight_zp_list = (int*)sys_malloc(channel_num * sizeof(int));    fprintf(fp_weight, "%s ", weight_tensor->name);    /* calculate the quant scale value of weight perchannel, scale = abs(min, max) / 127 */    if (internal){        // TODO        for (int ch = 0; ch < channel_num; ch++){            weight_scale_list[ch] = weight_tensor->scale_list[ch];            weight_zp_list[ch] = 0;}    }    else{        for (int ch = 0; ch < channel_num; ch++){            float* weight_data_ch_start = weight_data + ch * cstep;            float* weight_data_ch_end = weight_data + (ch + 1) * cstep;            float weight_max = *std::max_element(weight_data_ch_start, weight_data_ch_end);            float weight_min = *std::min_element(weight_data_ch_start, weight_data_ch_end);            weight_scale_list[ch] = std::max(std::abs(weight_max), std::abs(weight_min)) / 127.f;            weight_zp_list[ch] = 0;            fprintf(fp_weight, "%8.8f ", weight_scale_list[ch]);        }        fprintf(fp_weight, "\n");    }    /* quantize the value of weight from Float32 to Int8, value_i8 = (value_fp32 / scale).round().clip(-127, 127) */    for (int ch = 0; ch < channel_num; ch++){        for (int j = 0; j < cstep; j++){            if (weight_data[ch * cstep + j] == 0 || weight_scale_list[ch] == 0)                i8_weight_data[ch * cstep + j] = 0;            else{                float int8_data = round(weight_data[ch * cstep + j] / weight_scale_list[ch]);                int8_data = int8_data > 127.f ? 127.f : int8_data;                int8_data = int8_data < -127.f ? -127.f : int8_data;                i8_weight_data[ch * cstep + j] = int8_t(int8_data);}}    }    weight_tensor->scale_list = weight_scale_list;    weight_tensor->zp_list = weight_zp_list;    weight_tensor->data_type = TENGINE_DT_INT8;    weight_tensor->elem_size = sizeof(int8_t); // int8, signed char    weight_tensor->data = i8_weight_data;    weight_tensor->quant_param_num = channel_num;}

  偏置 int32 量化：

/* quantize the weight data from fp32 to int32 */if (noden->input_num > 2){    struct tensor* input_tensor = ir_graph->tensor_list[noden->input_tensors[0]];    struct tensor* bias_tensor = ir_graph->tensor_list[noden->input_tensors[2]];    float* bias_scale_list = (float*)sys_malloc(bias_tensor->dims[0] * sizeof(float));    int* bias_zp_list = (int*)sys_malloc(bias_tensor->dims[0] * sizeof(int32_t));    float* bias_data = (float*)bias_tensor->data;    int* int32_bias_data = (int*)sys_malloc(bias_tensor->elem_num * sizeof(int32_t));    int bstep = int(bias_tensor->elem_num / channel_num);    fprintf(fp_bias, "%s ", bias_tensor->name);    /* calculate the quant scale value of bias perchannel, scale = scale_weight * scale_in */    for (int ch = 0; ch < channel_num; ch++){        bias_scale_list[ch] = weight_scale_list[ch] * input_tensor->scale;        bias_zp_list[ch] = 0;        fprintf(fp_bias, "%8.8f ", bias_scale_list[ch]);    }    fprintf(fp_bias, "\n");    /* quantize the value of bias from Float32 to Int32, value_i32 = (value_fp32 / scale).round() */    for (int ch = 0; ch < channel_num; ch++){        for (int bi = 0; bi < bstep; bi++){            if (bias_data[ch * bstep + bi] == 0 || bias_scale_list[ch] == 0)                int32_bias_data[ch * bstep + bi] = 0;            else                int32_bias_data[ch * bstep + bi] = int(round(bias_data[ch * bstep + bi] / bias_scale_list[ch]));}    }    bias_tensor->scale_list = bias_scale_list;    bias_tensor->zp_list = bias_zp_list;    bias_tensor->data_type = TENGINE_DT_INT32;    bias_tensor->elem_size = sizeof(int32_t); // int32, signed int    bias_tensor->data = int32_bias_data;    bias_tensor->quant_param_num = channel_num;}

  到这里权值 & 偏置的量化就介绍的差不多咯。

  以上详细介绍了 min-max 量化算法的实现，主要以 Tengine 为例进行代码说明，希望我的分享能对你的学习有一点帮助。

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《【模型推理】量化实现分享一：详解 min-max 对称量化算法实现》