极智AI | 量化实现分享一：详解 min-max 对称量化算法实现

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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。

文章目录

1、量化使用
2、min-max 量化
- 2.1 激活值量化
- 2.2 权值 & 偏置量化
- - 2.2.1 创建 graph
  - 2.2.2 优化激活值量化 scale
  - 2.2.3 权值 & 偏置量化

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);}
}

2.2 权值 & 偏置量化

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;}

2.2.2 优化激活值量化 scale

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;}}}
}

2.2.3 权值 & 偏置量化

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){// TODOfor (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 charweight_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;elseint32_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 intbias_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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