caffe2/perfkernels/batch_box_cox_avx2.cc

#include <immintrin.h>
#ifdef CAFFE2_PERF_USE_MKL
#include <c10/util/irange.h>
#include <caffe2/perfkernels/common.h>
#include <folly/SingletonThreadLocal.h>

#include "vectorizer.h"

// Enable compiler vectorized version only if numerical consistency is not
// required between dev and opt versions - disabled for now
#ifndef FAST_VECTORIZED_KERNEL
#define CPU_CAPABILITY_AVX2
#include <ATen/cpu/vec/vec.h>

namespace at::vec {

// Implements the vectorized version of std::max() operation,
// which DOESNOT propagates NaN for second argument
template <typename scalar_t>
Vectorized<scalar_t> max(const Vectorized<scalar_t>& a, const Vectorized<scalar_t>& b);

template <>
Vectorized<double> max(const Vectorized<double>& a, const Vectorized<double>& b) {
  // std::max(NaN, nonNan) -> NaN
  return _mm256_max_pd(b, a);
}

template <>
Vectorized<float> max(const Vectorized<float>& a, const Vectorized<float>& b) {
  // std::max(NaN, nonNan) -> NaN
  return _mm256_max_ps(b, a);
}

// Implements recieprocal method based on newton-rapson method
// 1. user RCP approximiation
// 2. update with RCP = RCP * (2 - X * RCP)
template <typename scalar_t>
Vectorized<scalar_t> fast_recieprocal(const Vectorized<scalar_t>& b);
template <typename scalar_t>
scalar_t fast_recieprocal(scalar_t b);

template<>
Vectorized<float> fast_recieprocal(const Vectorized<float>& b) {
  auto minus2 = _mm256_set1_ps(-2.f);
  auto rcp = _mm256_rcp_ps(b);
  rcp = _mm256_mul_ps(rcp,  _mm256_fnmsub_ps(rcp, b, minus2));
  rcp = _mm256_mul_ps(rcp,  _mm256_fnmsub_ps(rcp, b, minus2));
  return rcp;
}

template <>
float fast_recieprocal(float b) {
  auto minus2 = _mm_set_ss(-2.f);
  auto b_reg = _mm_set_ss(b);
  auto rcp = _mm_rcp_ss(b_reg);
  rcp = _mm_mul_ss(rcp,  _mm_fnmsub_ss(rcp, b_reg, minus2));
  rcp = _mm_mul_ss(rcp,  _mm_fnmsub_ss(rcp, b_reg, minus2));
  return _mm_cvtss_f32(rcp);
}

template<>
Vectorized<double> fast_recieprocal(const Vectorized<double>& b) {
  return b.reciprocal();
}

template <>
double fast_recieprocal(double b) {
  return 1./b;
}

}
#endif

#include <cstdint>
#include <cmath>
#include <vector>

#include <mkl.h>

namespace caffe2::details {

// MKL VML function templates.
template <typename T>
void PackV(const int N, const T* a, const int* ia, T* y);
template <typename T>
void UnpackV(const int N, const T* a, T* y, const int* iy);

#define DELEGATE_PACKV_FUNCTION(T, OriginalFunc)                \
  template <>                                                   \
  void PackV<T>(const int N, const T* a, const int* ia, T* y) { \
    OriginalFunc(N, a, ia, y);                                  \
  }
DELEGATE_PACKV_FUNCTION(float, vsPackV)
DELEGATE_PACKV_FUNCTION(double, vdPackV)
#undef DELEGATE_PACKV_FUNCTION

#define DELEGATE_UNPACKV_FUNCTION(T, OriginalFunc)                \
  template <>                                                     \
  void UnpackV<T>(const int N, const T* a, T* y, const int* iy) { \
    OriginalFunc(N, a, y, iy);                                    \
  }
DELEGATE_UNPACKV_FUNCTION(float, vsUnpackV)
DELEGATE_UNPACKV_FUNCTION(double, vdUnpackV)
#undef DELEGATE_UNPACKV_FUNCTION

#ifndef FAST_VECTORIZED_KERNEL
template <typename T>
void box_cox_zero_lambda(
    size_t D,
    const T* const self_data,
    const T* const lambda2_data,
    T k_eps,
    T* const output_data) {
  int j = 0;
  using Vec = at::vec::Vectorized<T>;
  constexpr int64_t VLEN = Vec::size();
  auto k_eps_vec = Vec(k_eps);
  for(; j + VLEN < D; j += VLEN) {
    auto data = Vec::loadu(self_data + j);
    auto lambda2 = Vec::loadu(lambda2_data + j);
    auto sum = data + lambda2;
    auto max = at::vec::max(sum, k_eps_vec);
    auto res = max.log();
    res.store(output_data + j);
  }
  for ( ;j < D; ++j) {
    auto sum = self_data[j] + lambda2_data[j];
    auto max = std::max(sum, k_eps);
    output_data[j] = std::log(max);
  }
}

template <typename T>
void box_cox_nonzero_lambda(
    int64_t D,
    const T* data_ptr,
    const T* lambda1_ptr,
    const T* lambda2_ptr,
    T k_eps,
    T* out) {

  int j = 0;
  using Vec = at::vec::Vectorized<T>;
  constexpr int64_t VLEN = Vec::size();
  auto k_eps_vec = Vec(k_eps);
  for(; j + VLEN < D; j += VLEN) {
    auto data = Vec::loadu(data_ptr + j);
    auto lambda2 = Vec::loadu(lambda2_ptr + j);
    auto sum = data + lambda2;
    auto max = at::vec::max(sum, k_eps_vec);
    auto lambda1 = Vec::loadu(lambda1_ptr + j);
    auto lambda_over_1 = at::vec::fast_recieprocal(lambda1);
    auto pow = max.pow(lambda1);
    auto res = at::vec::fmsub(pow, lambda_over_1, lambda_over_1);
    res.store(out + j);
  }
  for ( ;j < D; ++j) {
    auto sum = data_ptr[j] + lambda2_ptr[j];
    auto max = std::max(sum, k_eps);
    auto lambda_over_1 = at::vec::fast_recieprocal(lambda1_ptr[j]);
    auto pow = std::pow(max, lambda1_ptr[j]);
    out[j] = pow * lambda_over_1 - lambda_over_1;
  }
}
#else
template <typename T>
void box_cox_zero_lambda(
    size_t D,
    const T* const self_data,
    const T* const lambda2_data,
    T k_eps,
    T* const output_data) {
  VECTOR_LOOP for (auto j=0 ;j < D; ++j) {
    auto sum = self_data[j] + lambda2_data[j];
    auto max = std::max(sum, k_eps);
    output_data[j] = std::log(max);
  }
}

template <typename T>
void box_cox_nonzero_lambda(
    int64_t D,
    const T* data_ptr,
    const T* lambda1_ptr,
    const T* lambda2_ptr,
    T k_eps,
    T* out) {

  VECTOR_LOOP for (auto j=0 ;j < D; ++j) {
    FAST_MATH
    auto sum = data_ptr[j] + lambda2_ptr[j];
    auto max = std::max(sum, k_eps);
    auto lamda1 = lambda1_ptr[j];
    auto lambda_over_1 = 1 / lamda1;
    if constexpr (std::is_same<T, float>::value) {
      lambda_over_1 = lambda_over_1 * (T{2} - lambda_over_1 * lamda1);
      lambda_over_1 = lambda_over_1 * (T{2} - lambda_over_1 * lamda1);
    }
    auto pow = std::pow(max, lamda1);
    out[j] = pow * lambda_over_1 - lambda_over_1;
  }
}
#endif

template <typename T>
void box_cox_mixed_lambda(
    const T* const self_data,
    const std::vector<int>& nonzeros,
    const std::vector<int>& zeros,
    const T* const lambda1,
    const T* const lambda2,
    const T* const lambda2_z_,
    T k_eps,
    T* const buffer,
    T* const output_data) {
  PackV(nonzeros.size(), self_data, nonzeros.data(), buffer);
  box_cox_nonzero_lambda<T>(
      nonzeros.size(), buffer, lambda1, lambda2, k_eps, buffer);
  UnpackV(nonzeros.size(), buffer, output_data, nonzeros.data());

  PackV(zeros.size(), self_data, zeros.data(), buffer);
  box_cox_zero_lambda<T>(
      zeros.size(), buffer, lambda2_z_, k_eps, buffer);
  UnpackV(zeros.size(), buffer, output_data, zeros.data());
}

template <typename T>
void TileArrayIntoVector(
    const T* const a,
    const size_t D,
    const int K,
    std::vector<T>& b) {
  b.resize(K * D);
  for (const auto k : c10::irange(K)) {
    std::copy(a, a + D, b.begin() + k * D);
  }
}

void TileIndicesInPlace(std::vector<int>& v, const std::size_t D, const std::size_t K) {
  auto n = v.size();
  v.resize(K * n);
  for (const auto k : c10::irange(1, K)) {
    for (const auto j : c10::irange(n)) {
      v[k * n + j] = v[j] + k * D;
    }
  }
}

template <typename T>
void compute_batch_box_cox__avx2_fma(
    std::size_t N,
    std::size_t D,
    std::size_t block_size,
    const T* self_data,
    const T* __restrict lambda1_data,
    const T* __restrict lambda2_data,
    T* output_data) {
  constexpr T k_eps = static_cast<T>(1e-6);

  FOLLY_DECLARE_REUSED(zeros, std::vector<int>);
  FOLLY_DECLARE_REUSED(nonzeros, std::vector<int>);
  // Don't bother calling reserve; calls after the first will get a
  // correctly-sized allocation anyway.
  for (const auto j : c10::irange(D)) {
    if (lambda1_data[j] == 0) {
      zeros.push_back(j);
    } else {
      nonzeros.push_back(j);
    }
  }

  // Process K rows at a time for effective vectorization with small rows.
  const auto K = std::min(N, (block_size + D - 1) / D);

  FOLLY_DECLARE_REUSED(lambda1_, std::vector<T>);
  FOLLY_DECLARE_REUSED(lambda2_, std::vector<T>);
  FOLLY_DECLARE_REUSED(lambda2_z_, std::vector<T>);

  if (nonzeros.size() == D) {
    // ((x + lambda2)^lambda1 - 1)/lambda1, if lambda1 != 0
    size_t i = 0;
    if (K > 1) {
      TileArrayIntoVector(lambda1_data, D, K, lambda1_);
      TileArrayIntoVector(lambda2_data, D, K, lambda2_);
      DCHECK_EQ(K * D, lambda1_.size());
      DCHECK_EQ(K * D, lambda2_.size());
      for (; i < N - K + 1; i += K, self_data += K * D, output_data += K * D) {
        box_cox_nonzero_lambda<T>(
            K * D,
            self_data,
            lambda1_.data(),
            lambda2_.data(),
            k_eps,
            output_data);
      }
    }
    for (; i < N; i++, self_data += D, output_data += D) {
      box_cox_nonzero_lambda<T>(
          D, self_data, lambda1_data, lambda2_data, k_eps, output_data);
    }
  } else if (zeros.size() == D) {
    // ln(x + lambda2), if lambda1 == 0
    size_t i = 0;
    if (K > 1) {
      TileArrayIntoVector(lambda2_data, D, K, lambda2_z_);
      DCHECK_EQ(K * D, lambda2_z_.size());
      for (; i < N - K + 1; i += K, self_data += K * D, output_data += K * D) {
        box_cox_zero_lambda<T>(
            K * D, self_data, lambda2_z_.data(), k_eps, output_data);
      }
    }
    for (; i < N; i++, self_data += D, output_data += D) {
      box_cox_zero_lambda<T>(
          D, self_data, lambda2_data, k_eps, output_data);
    }
  } else {
    // mix zeros and nonzeros
    const size_t n = nonzeros.size();
    if (K > 1) {
      TileIndicesInPlace(nonzeros, 0, K);
      TileIndicesInPlace(zeros, 0, K);
    }

    FOLLY_DECLARE_REUSED(buffer, std::vector<T>);

    buffer.resize(std::max(nonzeros.size(), zeros.size()));
    lambda1_.resize(nonzeros.size());
    lambda2_.resize(nonzeros.size());
    lambda2_z_.resize(zeros.size());
    PackV(nonzeros.size(), lambda1_data, nonzeros.data(), lambda1_.data());
    PackV(nonzeros.size(), lambda2_data, nonzeros.data(), lambda2_.data());
    PackV(zeros.size(), lambda2_data, zeros.data(), lambda2_z_.data());

    size_t i = 0;
    if (K > 1) {
      // Truncate to original size, and re-tile with offsets this time.
      nonzeros.resize(n);
      DCHECK_GT(D, n);
      zeros.resize(D - n);
      TileIndicesInPlace(nonzeros, D, K);
      TileIndicesInPlace(zeros, D, K);
      DCHECK_EQ(nonzeros.size(), lambda1_.size());
      DCHECK_EQ(nonzeros.size(), lambda2_.size());
      DCHECK_EQ(zeros.size(), lambda2_z_.size());

      for (; i < N - K + 1; i += K, self_data += K * D, output_data += K * D) {
        box_cox_mixed_lambda<T>(
            self_data,
            nonzeros,
            zeros,
            lambda1_.data(),
            lambda2_.data(),
            lambda2_z_.data(),
            k_eps,
            buffer.data(),
            output_data);
      }
      // Truncate to original size.
      nonzeros.resize(n);
      zeros.resize(D - n);
    }
    for (; i < N; i++, self_data += D, output_data += D) {
      box_cox_mixed_lambda<T>(
          self_data,
          nonzeros,
          zeros,
          lambda1_.data(),
          lambda2_.data(),
          lambda2_z_.data(),
          k_eps,
          buffer.data(),
          output_data);
    }
  }
};


template
void compute_batch_box_cox__avx2_fma<float>(
  std::size_t N,
  std::size_t D,
  std::size_t block_size,
  const float* self_data,
  const float* __restrict lambda1_data,
  const float* __restrict lambda2_data,
  float* output_data);

template
void compute_batch_box_cox__avx2_fma<double>(
  std::size_t N,
  std::size_t D,
  std::size_t block_size,
  const double* self_data,
  const double* __restrict lambda1_data,
  const double* __restrict lambda2_data,
  double* output_data);

} // namespace caffe2::detail
#endif