einsum_impl.h

// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
//
// 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.
#pragma once

#include <set>
#include "paddle/phi/core/dense_tensor.h"
#include "paddle/phi/kernels/matmul_kernel.h"
#include "paddle/phi/kernels/reduce_sum_kernel.h"
#include "paddle/phi/kernels/transpose_kernel.h"
#include "paddle/utils/string/string_helper.h"

namespace phi {

// check the validation of the Einsum equation.
// 1. the label must between 'a' - 'z'.
// 2. the dim of the same label must be same.
// 3. the broad cast dims in two operands is broadcastable.
// 4. there must exist '->' and the default output is complete in python.
// may be we can skip validation check in C++ and just put it in python.
inline static void ValidationCheck(const std::string& equation) {
  auto n_part = paddle::string::split_string(equation, "->").size();
  PADDLE_ENFORCE_EQ(n_part,
                    2,
                    phi::errors::InvalidArgument(
                        "Required at least one `->` in equation of EinsumOp."));
  size_t pos;
  auto trimed_equ = equation;
  if ((pos = trimed_equ.find("->", 0)) != std::string::npos) {
    trimed_equ.replace(pos, 2, ".");
  }
  auto is_valid_char = [](char c) {
    if (c >= 'a' && c <= 'z') return true;
    if (c == '.' || c == ',') return true;
    return false;
  };
  for (auto c : trimed_equ) {
    if (!is_valid_char(c))
      PADDLE_THROW(phi::errors::InvalidArgument(
          "Found invalid char in equation. Einsum only accept `a`-`z` and `...`"
          "but get:`%c`",
          c));
  }
}

enum LabelType {
  ALL_TYPE = 0,
  Batch = 1,    // ABO
  AO,           // AO --  free label
  BO,           // BO --  free label
  Contraction,  // AB
  Reduction,    // A, B
};

// map a label('a' - 'z') -> int, O(1) speed.
class LabelMap {
  constexpr static int N =
      26 + 1;  // 'a' - 'z' + '.', '.' is for broadcast dims
  int default_value;
  int map[N];

 public:
  explicit LabelMap(int default_value = 0) {
    this->default_value = default_value;
    for (int i = 0; i < N; ++i) map[i] = default_value;
  }
  int& operator[](int label) {
    int i = label - 'a';
    if (label == '.') i = N - 1;
    return map[i];
  }
  int operator[](int label) const {
    int i = label - 'a';
    if (label == '.') i = N - 1;
    return map[i];
  }
  // non-exist is present by is_default
  bool is_default(char label) {
    return (*this)[static_cast<int>(label)] == default_value;
  }
};

inline std::string label_to_string(const std::vector<char>& all_labels,
                                   const LabelMap& label2type) {
  std::string str;
  for (int a : all_labels) {
    std::stringstream ss;
    ss << label2type[a];
    str += ss.str();
  }
  return str;
}

inline static void ReplaceEllipsis(std::string& s) {  // NOLINT
  size_t pos;
  if ((pos = s.find("...", 0)) != std::string::npos) {
    s.replace(pos, 3, ".");
  }
  // remove all the space in the expression
  while ((pos = s.find(" ", 0)) != std::string::npos) {
    s.replace(pos, 1, "");
  }
}

inline std::vector<char> union_labels(const std::vector<char>& a,
                                      const std::vector<char>& b) {
  LabelMap counter(0);
  std::vector<char> res;
  auto f = [&](char c) {
    if (counter[static_cast<int>(c)] == 0) {
      res.push_back(c);
    }
    counter[static_cast<int>(c)] += 1;
  };
  std::for_each(a.begin(), a.end(), f);
  std::for_each(b.begin(), b.end(), f);
  return res;
}

// Apply transforms to all_labels and get another all_labels
inline std::vector<char> TransformLabelsOrder(
    const std::vector<char>& all_labels,
    const LabelMap& type,
    std::vector<LabelType> new_order) {
  std::vector<char> ret;
  for (auto cnt_type : new_order) {
    std::vector<char> tmp;
    for (int c : all_labels) {
      if (type[c] == cnt_type) tmp.push_back(c);
    }
    ret.insert(ret.end(), tmp.begin(), tmp.end());
  }
  return ret;
}

inline static void GlobalInfo(const std::vector<std::string>& op_labels,
                              const std::string& right,
                              LabelMap* label2type,
                              std::vector<char>* sorted_labels) {
  std::vector<char> all;
  LabelMap counter(0);
  for (auto& ch : right) {  // char
    int c = ch;
    (*label2type)[c] = LabelType::BO;
  }

  for (auto& op : op_labels) {
    for (auto& ch : op) {  // char
      int c = ch;
      if (counter.is_default(c)) {
        all.push_back(ch);
      }
      counter[c] += 1;
      if ((*label2type)[c] != LabelType::BO && counter[c] == 2)
        (*label2type)[c] = LabelType::Contraction;
      else if (counter[c] == 2)
        (*label2type)[c] = LabelType::Batch;
    }
  }

  // BO is represent Free, so we need find the AO.
  for (int c : op_labels[0]) {
    if ((*label2type)[c] == LabelType::BO) (*label2type)[c] = LabelType::AO;
  }

  (*label2type)['.'] = LabelType::Batch;

  if (sorted_labels->size()) {
    std::set<char> exist(all.begin(), all.end());
    all.clear();
    std::for_each(
        sorted_labels->begin(), sorted_labels->end(), [&exist, &all](char c) {
          if (exist.count(c)) all.push_back(c);
        });
  }

  *sorted_labels = TransformLabelsOrder(all,
                                        *label2type,
                                        {LabelType::Batch,
                                         LabelType::AO,
                                         LabelType::BO,
                                         LabelType::Contraction,
                                         LabelType::Reduction});

  if (counter[static_cast<int>('.')] > 0) {
    std::vector<char> tmp;
    tmp.push_back('.');
    // push '.' in the front
    *sorted_labels = union_labels(tmp, *sorted_labels);
  }
  VLOG(5) << "GlobalInfo: sorted_labels after: "
          << paddle::string::join_strings(*sorted_labels, ",");
}

inline static void InferLabelShape(const std::vector<std::string>& op_labels,
                                   const std::vector<DDim>& inputs,
                                   LabelMap* labelshape,
                                   std::vector<std::vector<int>>* ellipsis_dims,
                                   std::vector<int>* broadcast_dims) {
  VLOG(5) << "Start InferLabelShape";
  int n_broadcast_dims = 0;
  for (size_t i = 0; i < op_labels.size(); ++i) {
    VLOG(5) << "oplabels: " << op_labels[i];
    int valid_indices = std::count_if(op_labels[i].begin(),
                                      op_labels[i].end(),
                                      [](char c) { return c != '.'; });
    int n_ellipsis = inputs[i].size() - valid_indices;
    VLOG(5) << "valid indices and n_ellipsis: " << valid_indices << " "
            << n_ellipsis;
    ellipsis_dims->at(i).resize(n_ellipsis);
    n_broadcast_dims = std::max(n_broadcast_dims, n_ellipsis);
  }
  VLOG(5) << "InferLabelShape: Broadcast ndims:" << n_broadcast_dims;
  *broadcast_dims = std::vector<int>(n_broadcast_dims, 1);

  for (size_t i = 0; i < op_labels.size(); ++i) {
    auto& op_str = op_labels[i];
    auto& op_dim = inputs[i];
    int dim_ptr = 0;
    for (int c : op_str) {
      if (c == '.') {
        for (auto& v : ellipsis_dims->at(i)) {
          v = op_dim[dim_ptr];
          dim_ptr++;
        }
      } else if (labelshape->is_default(c) || (*labelshape)[c] == -1) {
        (*labelshape)[c] = op_dim[dim_ptr];
        dim_ptr++;
      } else {
        PADDLE_ENFORCE_EQ(
            (*labelshape)[c],
            op_dim[dim_ptr],
            phi::errors::InvalidArgument(
                "Same label have different shapes for label: `%c`", c));
        dim_ptr++;
      }
    }
  }
  for (size_t i = 0; i < op_labels.size(); ++i) {
    VLOG(5) << "InferLabelShape: Ellipsis ndims:"
            << paddle::string::join_strings(ellipsis_dims->at(i), ",");
    int idx = n_broadcast_dims - ellipsis_dims->at(i).size();
    for (auto v : ellipsis_dims->at(i)) {
      PADDLE_ENFORCE_EQ(
          v == 1 || broadcast_dims->at(idx) == 1 ||
              broadcast_dims->at(idx) == v,
          true,
          phi::errors::InvalidArgument(
              "Ellipsis dims can't broadcasts. Please Check you operands."));
      broadcast_dims->at(idx) = std::max(v, broadcast_dims->at(idx));
      idx += 1;
    }
  }
  VLOG(5) << "InferLabelShape: Broadcast dims:"
          << paddle::string::join_strings(*broadcast_dims, ",");
}

inline static void InferLabelPerm(const std::string& op,
                                  int n_broadcast,
                                  LabelMap* label2perm) {
  int cur = 0;
  for (int c : op) {
    (*label2perm)[c] = cur;
    if (c == '.') {
      cur += n_broadcast;
    } else {
      cur += 1;
    }
  }
}

inline static void InferOutputDims(const std::string& right,
                                   const std::vector<int>& broadcast_dims,
                                   const LabelMap& labelshape,
                                   std::vector<int>* output_dims) {
  for (int c : right) {
    if (c == '.') {
      output_dims->insert(
          output_dims->end(), broadcast_dims.begin(), broadcast_dims.end());
    } else {
      output_dims->push_back(labelshape[c]);
    }
  }
}
//
inline static void ParseEinsumEquation(
    const std::string& equation,
    const std::vector<DDim>& inputs,
    LabelMap* labelshape,
    LabelMap* labeltype,
    std::vector<char>* all_labels,
    std::vector<LabelMap>* label2perms,
    std::vector<std::vector<int>>* ellipsis_dims,
    std::vector<int>* broadcast_dims,
    std::vector<int>* output_dims,
    std::string* right) {
  auto results = paddle::string::split_string(equation, "->");
  auto left = results[0];
  ReplaceEllipsis(left);
  *right = results[1].substr(1);
  ReplaceEllipsis(*right);
  auto op_labels = paddle::string::split_string(left, ",");
  // split_string("i,") -> ["i"], we expect 2 op_labels.
  if (left[left.size() - 1] == ',') op_labels.push_back("");
  std::for_each(op_labels.begin(), op_labels.end(), ReplaceEllipsis);
  GlobalInfo(op_labels, *right, labeltype, all_labels);
  InferLabelShape(op_labels, inputs, labelshape, ellipsis_dims, broadcast_dims);
  VLOG(5) << "Einsum Infershape: right:" << *right;
  VLOG(5) << "Einsum Infershape: left :"
          << paddle::string::join_strings(op_labels, '\n');
  InferOutputDims(*right, *broadcast_dims, *labelshape, output_dims);
  for (size_t i = 0; i < inputs.size(); ++i) {
    InferLabelPerm(
        op_labels[i], ellipsis_dims->at(i).size(), &((*label2perms)[i]));
  }
  VLOG(5) << "Einsum Infershape: end";
}

template <typename T>
std::vector<T> GetLabelIndexByType(const std::vector<char>& all_labels,
                                   const LabelMap& type,
                                   const LabelMap& perm,
                                   const std::vector<int>& ellipsis,
                                   LabelType filter) {
  std::vector<T> res;
  for (T c : all_labels) {
    if ((filter == LabelType::ALL_TYPE || type[c] == filter) && perm[c] != -1) {
      if (c == '.') {
        for (size_t i = 0; i < ellipsis.size(); ++i) res.push_back(perm[c] + i);
      } else {
        res.push_back(perm[c]);
      }
    }
  }
  return res;
}

template <typename T>
std::vector<T> GetShapeByType(const std::vector<char>& all_labels,
                              const LabelMap& type,
                              const LabelMap& perm,
                              const LabelMap& label2shape,
                              const std::vector<int>& ellipsis,
                              std::set<LabelType> filter) {
  std::vector<T> res;
  for (T c : all_labels) {
    if ((filter.count(LabelType::ALL_TYPE) ||
         filter.count(LabelType(type[c]))) &&
        perm[c] != -1) {
      if (c == '.')
        res.insert(res.end(), ellipsis.begin(), ellipsis.end());
      else
        res.push_back(label2shape[c]);
    }
  }
  return res;
}

template <typename T, typename Context>
DenseTensor PerformReduction(const Context& dev_ctx,
                             const DenseTensor& tensor,
                             const LabelMap& label2perm,
                             const std::vector<char>& all_labels,
                             const std::vector<int>& ellipsis,
                             const LabelMap& label2type) {
  auto indices = GetLabelIndexByType<int64_t>(
      all_labels, label2type, label2perm, ellipsis, LabelType::Reduction);
  VLOG(5) << "call PerformReduction: with axis: "
          << paddle::string::join_strings(indices, ",");
  if (indices.size() == 0) return tensor;
  return Sum<T, Context>(dev_ctx, tensor, indices, tensor.dtype(), true);
}

inline bool is_no_need_transpose(const std::vector<int>& axis) {
  for (size_t i = 0; i < axis.size(); ++i) {
    if (i != static_cast<size_t>(axis[i])) return false;
  }
  return true;
}

template <typename T, typename Context>
DenseTensor PerformTranspose(const Context& dev_ctx,
                             const DenseTensor& tensor,
                             const LabelMap& label2perm,
                             const std::vector<char>& all_labels,
                             const std::vector<int>& ellipsis,
                             const LabelMap& label2type) {
  auto axis = GetLabelIndexByType<int>(
      all_labels, label2type, label2perm, ellipsis, LabelType::ALL_TYPE);
  VLOG(5) << "PerformTranspose: " << paddle::string::join_strings(axis, ",");
  if (is_no_need_transpose(axis)) {
    return tensor;
  }
  auto ret = Transpose<T, Context>(dev_ctx, tensor, axis);
  VLOG(5) << "PerformTranspose: do_transpose()";
  return ret;
}

template <typename T, typename Context>
DenseTensor PerformContraction(
    const Context& dev_ctx,
    const DenseTensor& A,
    const DenseTensor& B,
    const std::vector<LabelMap>& label2perm,
    const std::vector<char>& all_labels,
    const LabelMap& label2type,
    const LabelMap& label2shape,
    const std::vector<std::vector<int>>& ellipsis_dims,
    const std::vector<int>& broadcast_dims,
    std::vector<DenseTensor*> cache,
    bool use_cache) {
  // Get All the Batches, so perm is
  auto all_valid = LabelMap(1);
  auto recover_dim = GetShapeByType<int>(all_labels,
                                         label2type,
                                         all_valid,
                                         label2shape,
                                         broadcast_dims,
                                         {LabelType::Batch});
  auto preprocess = [&](const DenseTensor& t,
                        const LabelMap& perm,
                        const std::vector<int>& ellipsis,
                        int operand_idx) -> DenseTensor {
    // reshape
    auto frees = GetShapeByType<int>(all_labels,
                                     label2type,
                                     perm,
                                     label2shape,
                                     ellipsis,
                                     {LabelType::AO, LabelType::BO});
    auto conts = GetShapeByType<int>(all_labels,
                                     label2type,
                                     perm,
                                     label2shape,
                                     ellipsis,
                                     {LabelType::Contraction});
    std::vector<char> reordered_all_labels = all_labels;
    if (operand_idx == 1) {
      reordered_all_labels = TransformLabelsOrder(all_labels,
                                                  label2type,
                                                  {LabelType::Batch,
                                                   LabelType::Contraction,
                                                   LabelType::AO,
                                                   LabelType::BO,
                                                   LabelType::Reduction});
    }
    // reduction
    DenseTensor trans_t;
    if (use_cache && cache[operand_idx] != nullptr &&
        cache[operand_idx]->IsInitialized()) {
      trans_t.ShareBufferWith(*(cache[operand_idx]));
      VLOG(5) << "Cache Used!";
    } else {
      auto reduct_t = PerformReduction<T, Context>(
          dev_ctx, t, perm, all_labels, ellipsis, label2type);
      trans_t = PerformTranspose<T, Context>(
          dev_ctx, reduct_t, perm, reordered_all_labels, ellipsis, label2type);
      if (cache[operand_idx] != nullptr)
        cache[operand_idx]->ShareBufferWith(trans_t);
    }
    auto mul_dims = GetShapeByType<int>(all_labels,
                                        label2type,
                                        perm,
                                        label2shape,
                                        ellipsis,
                                        {LabelType::Batch});
    recover_dim.insert(recover_dim.end(), frees.begin(), frees.end());
    if (operand_idx == 0) {
      mul_dims.push_back(std::accumulate(
          frees.begin(), frees.end(), 1, std::multiplies<int>()));
      mul_dims.push_back(std::accumulate(
          conts.begin(), conts.end(), 1, std::multiplies<int>()));
    } else {
      mul_dims.push_back(std::accumulate(
          conts.begin(), conts.end(), 1, std::multiplies<int>()));
      mul_dims.push_back(std::accumulate(
          frees.begin(), frees.end(), 1, std::multiplies<int>()));
    }
    VLOG(5) << "PerformContraction: mul_dims: "
            << paddle::string::join_strings(mul_dims, ",");
    trans_t.Resize(make_ddim(mul_dims));
    return trans_t;
  };

  // Reduction, Reshape and Matmul
  auto trans_a = preprocess(A, label2perm[0], ellipsis_dims[0], 0);
  auto trans_b = preprocess(B, label2perm[1], ellipsis_dims[1], 1);
  auto after_contraction =
      Matmul<T, Context>(dev_ctx, trans_a, trans_b, false, false);
  VLOG(5) << "PerformContraction: recover_dim: "
          << paddle::string::join_strings(recover_dim, ",");
  after_contraction.Resize(make_ddim(recover_dim));
  return after_contraction;
}

template <typename T, typename Context>
void TransposeToOutput(const Context& dev_ctx,
                       const DenseTensor& to_trans,
                       const std::string& right,
                       const std::vector<char>& all_labels,
                       int n_broadcast_dims,
                       DenseTensor* output) {
  std::vector<int> axis;
  int offset = 0;
  if (std::find(all_labels.begin(), all_labels.end(), '.') !=
      all_labels.end()) {
    offset = n_broadcast_dims - 1;
  }
  for (char c : right) {
    if (c == '.') {
      for (int i = 0; i < n_broadcast_dims; ++i) axis.push_back(i);
    } else {
      auto it = std::find(all_labels.begin(), all_labels.end(), c);
      PADDLE_ENFORCE_NE(it,
                        all_labels.end(),
                        phi::errors::InvalidArgument("Must in all_labels."));
      axis.push_back(it - all_labels.begin() + offset);
    }
  }
  if (is_no_need_transpose(axis)) {
    output->ShareBufferWith(to_trans);
    return;
  }
  VLOG(5) << "call TransposeToOutput: with axis: "
          << paddle::string::join_strings(axis, ",");
  TransposeKernel<T, Context>(dev_ctx, to_trans, axis, output);
}

template <typename T, typename Context>
void EinsumKernelImpl(const Context& dev_ctx,
                      const std::vector<char>& forward_all_labels,
                      const std::vector<const DenseTensor*>& inputs,
                      const std::string& equation,
                      DenseTensor* out,
                      std::vector<DenseTensor*> cache,
                      bool is_forward = true) {
  ValidationCheck(equation);
  // collect the following informations to prepare einsum.
  LabelMap labelshape(0);
  LabelMap labeltype(LabelType::Reduction);
  std::vector<LabelMap> label2perms(inputs.size(), LabelMap(-1));
  std::vector<char> all_labels;  // order: ABO, AO, BO, AB, Reduce
  std::vector<std::vector<int>> ellipsis_dims(2);
  std::vector<int> broadcast_dims;
  std::vector<int> output_dims;

  std::vector<DDim> input_dims;
  for (auto& i : inputs) {
    input_dims.push_back(i->dims());
  }
  std::string right;
  if (!is_forward) {
    all_labels = forward_all_labels;
  }
  ParseEinsumEquation(equation,
                      input_dims,
                      &labelshape,
                      &labeltype,
                      &all_labels,
                      &label2perms,
                      &ellipsis_dims,
                      &broadcast_dims,
                      &output_dims,
                      &right);
  out->Resize(make_ddim(output_dims));
  if (inputs.size() == 2) {
    auto& A = inputs[0];
    auto& B = inputs[1];
    // Reduction and Contract Procedure
    auto after_contraction = PerformContraction<T, Context>(dev_ctx,
                                                            *A,
                                                            *B,
                                                            label2perms,
                                                            all_labels,
                                                            labeltype,
                                                            labelshape,
                                                            ellipsis_dims,
                                                            broadcast_dims,
                                                            cache,
                                                            !is_forward);
    TransposeToOutput<T, Context>(dev_ctx,
                                  after_contraction,
                                  right,
                                  all_labels,
                                  broadcast_dims.size(),
                                  out);
    // Reshape Procedure
  } else if (inputs.size() == 1) {
    auto reduce_A = PerformReduction<T, Context>(dev_ctx,
                                                 *inputs[0],
                                                 label2perms[0],
                                                 all_labels,
                                                 ellipsis_dims[0],
                                                 labeltype);
    std::vector<char> right_labels;
    for (auto c : right) right_labels.push_back(c);
    right_labels = union_labels(right_labels, all_labels);
    *out = PerformTranspose<T, Context>(dev_ctx,
                                        reduce_A,
                                        label2perms[0],
                                        right_labels,
                                        broadcast_dims,
                                        labeltype);
    out->Resize(make_ddim(output_dims));
  } else {
    PADDLE_THROW(phi::errors::InvalidArgument(
        "EinsumOp kernel only support len(operands) between (0, 2]. Use "
        "opt_einsum first to convert multi-variable to binary-variable."));
  }
}

template <typename T, typename Context>
void EinsumKernelRaw(const Context& dev_ctx,
                     const std::vector<const DenseTensor*>& inputs,
                     const std::string& equation,
                     DenseTensor* out,
                     std::vector<DenseTensor*> cache) {
  std::vector<char> tmp;
  // for the sake of compatibility, we may load and run v2.3 EinsumOp. Output
  // may have nullptr and the cache.size() is not equal to inputs.size(). refer
  // to BuildPhiKernelContext for details.
  int diff = inputs.size() - cache.size();
  for (int i = 0; i < diff; ++i) {
    cache.push_back(nullptr);
  }
  EinsumKernelImpl<T, Context>(
      dev_ctx, tmp, inputs, equation, out, cache, /*forward=*/true);
}

template <typename T, typename Context>
void EinsumKernel(const Context& dev_ctx,
                  const std::vector<const DenseTensor*>& inputs,
                  const std::string& equation,
                  DenseTensor* out) {
  std::vector<char> place_holder;
  std::vector<DenseTensor*> cache_tensor(
      inputs.size());  // set empty; TA, TB, TdC
  for (size_t i = 0; i < inputs.size(); ++i) {
    cache_tensor[i] = nullptr;
  }
  EinsumKernelImpl<T, Context>(
      dev_ctx, place_holder, inputs, equation, out, cache_tensor, true);
}

}  // namespace phi