truncated_gaussian_random_op.cc

/* Copyright (c) 2018 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. */

#include <limits>
#include <random>
#include "paddle/fluid/framework/op_registry.h"

namespace paddle {
namespace operators {

// reference: https://gist.github.com/lakshayg/d80172fe5ae3c5d2c2aedb53c250320e
template <typename T>
T Erfinv(T x) {
  if (x < -1 || x > 1) {
    return std::numeric_limits<T>::quiet_NaN();
  } else if (x == 1.0) {
    return std::numeric_limits<T>::infinity();
  } else if (x == -1.0) {
    return -std::numeric_limits<T>::infinity();
  }

  const T LN2 = 6.931471805599453094172321214581e-1;

  const T A0 = 1.1975323115670912564578e0;
  const T A1 = 4.7072688112383978012285e1;
  const T A2 = 6.9706266534389598238465e2;
  const T A3 = 4.8548868893843886794648e3;
  const T A4 = 1.6235862515167575384252e4;
  const T A5 = 2.3782041382114385731252e4;
  const T A6 = 1.1819493347062294404278e4;
  const T A7 = 8.8709406962545514830200e2;

  const T B0 = 1.0000000000000000000e0;
  const T B1 = 4.2313330701600911252e1;
  const T B2 = 6.8718700749205790830e2;
  const T B3 = 5.3941960214247511077e3;
  const T B4 = 2.1213794301586595867e4;
  const T B5 = 3.9307895800092710610e4;
  const T B6 = 2.8729085735721942674e4;
  const T B7 = 5.2264952788528545610e3;

  const T C0 = 1.42343711074968357734e0;
  const T C1 = 4.63033784615654529590e0;
  const T C2 = 5.76949722146069140550e0;
  const T C3 = 3.64784832476320460504e0;
  const T C4 = 1.27045825245236838258e0;
  const T C5 = 2.41780725177450611770e-1;
  const T C6 = 2.27238449892691845833e-2;
  const T C7 = 7.74545014278341407640e-4;

  const T D0 = 1.4142135623730950488016887e0;
  const T D1 = 2.9036514445419946173133295e0;
  const T D2 = 2.3707661626024532365971225e0;
  const T D3 = 9.7547832001787427186894837e-1;
  const T D4 = 2.0945065210512749128288442e-1;
  const T D5 = 2.1494160384252876777097297e-2;
  const T D6 = 7.7441459065157709165577218e-4;
  const T D7 = 1.4859850019840355905497876e-9;

  const T E0 = 6.65790464350110377720e0;
  const T E1 = 5.46378491116411436990e0;
  const T E2 = 1.78482653991729133580e0;
  const T E3 = 2.96560571828504891230e-1;
  const T E4 = 2.65321895265761230930e-2;
  const T E5 = 1.24266094738807843860e-3;
  const T E6 = 2.71155556874348757815e-5;
  const T E7 = 2.01033439929228813265e-7;

  const T F0 = 1.414213562373095048801689e0;
  const T F1 = 8.482908416595164588112026e-1;
  const T F2 = 1.936480946950659106176712e-1;
  const T F3 = 2.103693768272068968719679e-2;
  const T F4 = 1.112800997078859844711555e-3;
  const T F5 = 2.611088405080593625138020e-5;
  const T F6 = 2.010321207683943062279931e-7;
  const T F7 = 2.891024605872965461538222e-15;

  T abs_x = abs(x);

  if (abs_x <= 0.85) {
    T r = 0.180625 - 0.25 * x * x;
    T num =
        (((((((A7 * r + A6) * r + A5) * r + A4) * r + A3) * r + A2) * r + A1) *
             r +
         A0);
    T den =
        (((((((B7 * r + B6) * r + B5) * r + B4) * r + B3) * r + B2) * r + B1) *
             r +
         B0);
    return x * num / den;
  }

  T r = sqrt(LN2 - log(1.0 - abs_x));

  T num, den;
  if (r <= 5.0) {
    r = r - 1.6;
    num =
        (((((((C7 * r + C6) * r + C5) * r + C4) * r + C3) * r + C2) * r + C1) *
             r +
         C0);
    den =
        (((((((D7 * r + D6) * r + D5) * r + D4) * r + D3) * r + D2) * r + D1) *
             r +
         D0);
  } else {
    r = r - 5.0;
    num =
        (((((((E7 * r + E6) * r + E5) * r + E4) * r + E3) * r + E2) * r + E1) *
             r +
         E0);
    den =
        (((((((F7 * r + F6) * r + F5) * r + F4) * r + F3) * r + F2) * r + F1) *
             r +
         F0);
  }

  if (x < 0) {
    return -num / den;
  } else {
    return num / den;
  }
}

template <typename T>
struct TruncatedNormal {
  T mean, std;
  T a_normal_cdf;
  T b_normal_cdf;
  TruncatedNormal(T mean, T std) : mean(mean), std(std) {
    auto normal_cdf = [](T x) {
      return (1.0 + std::erf(x / std::sqrt(2.0))) / 2.0;
    };
    a_normal_cdf = normal_cdf(-2.0);
    b_normal_cdf = normal_cdf(2.0);
  }

  T operator()(T value) const {
    auto p = a_normal_cdf + (b_normal_cdf - a_normal_cdf) * value;
    return std::sqrt(2.0) * Erfinv(2 * p - 1) * std + mean;
  }
};

template <typename T>
class CPUTruncatedGaussianRandomKernel : public framework::OpKernel<T> {
 public:
  void Compute(const framework::ExecutionContext& context) const override {
    float mean = context.Attr<float>("mean");
    float std = context.Attr<float>("std");
    auto* tensor = context.Output<framework::Tensor>("Out");
    T* data = tensor->mutable_data<T>(context.GetPlace());

    unsigned int seed = static_cast<unsigned int>(context.Attr<int>("seed"));
    std::minstd_rand engine;
    if (seed == 0) {
      seed = std::random_device()();
    }
    engine.seed(seed);
    std::uniform_real_distribution<T> dist(std::numeric_limits<float>::min(),
                                           1.0);
    TruncatedNormal<T> truncated_normal(mean, std);
    int64_t size = tensor->numel();
    for (int64_t i = 0; i < size; ++i) {
      data[i] = truncated_normal(dist(engine));
    }
  }
};

class TruncatedGaussianRandomOp : public framework::OperatorWithKernel {
 public:
  using framework::OperatorWithKernel::OperatorWithKernel;

  void InferShape(framework::InferShapeContext* ctx) const override {
    PADDLE_ENFORCE(
        ctx->HasOutput("Out"),
        "Output(Out) of TruncatedGaussianRandomOp should not be null.");
    auto shape = ctx->Attrs().Get<std::vector<int>>("shape");
    std::vector<int64_t> out_dim;
    out_dim.reserve(shape.size());
    for (auto dim : shape) {
      out_dim.push_back(static_cast<int64_t>(dim));
    }
    PADDLE_ENFORCE(shape.size() > 0UL,
                   "shape can be one int or array. shape must be set.");
    ctx->SetOutputDim("Out", framework::make_ddim(out_dim));
  }

 protected:
  framework::OpKernelType GetExpectedKernelType(
      const framework::ExecutionContext& ctx) const override {
    framework::LibraryType library{framework::LibraryType::kPlain};
    framework::DataLayout layout{framework::DataLayout::kAnyLayout};
    return framework::OpKernelType(
        static_cast<framework::proto::VarType::Type>(ctx.Attr<int>("dtype")),
        ctx.device_context(), layout, library);
  }
};

class TruncatedGaussianRandomOpMaker
    : public framework::OpProtoAndCheckerMaker {
 public:
  void Make() override {
    AddOutput("Out", "Output tensor of truncated gaussian random op.");

    AddAttr<std::vector<int>>("shape",
                              "(vector<int>) "
                              "The dimension of random tensor.");
    AddAttr<float>("mean",
                   "(float, default 0.0) "
                   "mean of random tensor.")
        .SetDefault(.0f);
    AddAttr<float>("std",
                   "(float, default 1.0) "
                   "std of random tensor.")
        .SetDefault(1.0f);
    AddAttr<int>("seed",
                 "(int, default 0) "
                 "Random seed of generator."
                 "0 means use system wide seed."
                 "Note that if seed is not 0, this operator will always "
                 "generate the same random numbers every time.")
        .SetDefault(0);
    AddAttr<int>("dtype",
                 "(int, default 5(FP32)) "
                 "Output data type.")
        .SetDefault(framework::proto::VarType::FP32);
    AddComment(R"DOC(
TruncatedGaussianRandom Operator.

Used to initialize tensors with truncated gaussian random generator.

)DOC");
  }
};

}  // namespace operators
}  // namespace paddle

namespace ops = paddle::operators;
REGISTER_OP_WITHOUT_GRADIENT(truncated_gaussian_random,
                             ops::TruncatedGaussianRandomOp,
                             ops::TruncatedGaussianRandomOpMaker);
REGISTER_OP_CPU_KERNEL(truncated_gaussian_random,
                       ops::CPUTruncatedGaussianRandomKernel<float>);