contrib/test/tensor_random.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#include "main.h"

#include <Eigen/Tensor>

template <typename Scalar>
static void test_default() {
  Tensor<Scalar, 1> vec(6);

  // Fixme: we should check that the generated numbers follow a uniform
  // distribution instead.
  // For low-precision types (half, bfloat16), the RNG has limited distinct
  // values (e.g. 128 for bfloat16), so adjacent collisions are possible.
  // Retry a few times to avoid spurious failures.
  bool all_distinct = false;
  for (int attempt = 0; attempt < 10 && !all_distinct; ++attempt) {
    vec.setRandom();
    all_distinct = true;
    for (int i = 1; i < 6; ++i) {
      if (vec(i) == vec(i - 1)) {
        all_distinct = false;
        break;
      }
    }
  }
  VERIFY(all_distinct);
}

template <typename Scalar>
static void test_normal() {
  Tensor<Scalar, 1> vec(6);

  // Fixme: we should check that the generated numbers follow a gaussian
  // distribution instead.
  bool all_distinct = false;
  for (int attempt = 0; attempt < 10 && !all_distinct; ++attempt) {
    vec.template setRandom<Eigen::internal::NormalRandomGenerator<Scalar>>();
    all_distinct = true;
    for (int i = 1; i < 6; ++i) {
      if (vec(i) == vec(i - 1)) {
        all_distinct = false;
        break;
      }
    }
  }
  VERIFY(all_distinct);
}

template <typename Scalar>
static void test_normal_all_finite(Eigen::Index size) {
  // Regression test: the 16-bit uniform draw is exactly 0 with probability
  // 2^-10 (half) / 2^-7 (bfloat16). Running the ratio-of-uniforms rejection
  // in 16-bit arithmetic let log(0) = -inf poison the acceptance test and
  // returned v / 0 = +/-inf (or 0/0 = NaN) at measurable rates.
  Tensor<Scalar, 1> vec(size);
  vec.template setRandom<Eigen::internal::NormalRandomGenerator<Scalar>>();
  Eigen::Index num_not_finite = 0;
  for (Eigen::Index i = 0; i < size; ++i) {
    if (!(numext::isfinite)(vec(i))) ++num_not_finite;
  }
  VERIFY_IS_EQUAL(num_not_finite, Eigen::Index(0));
}

template <typename Scalar>
static void test_normal_zero_uniform_draw() {
  // Regression test: element 2429913123 of seed 12345 draws u == 0 (probability 2^-23 per float draw) with q between
  // 0.27597 and 0.27846, where the ratio-of-uniforms loop reached the NaN log test and returned v / 0 = -inf. The
  // element index is a uint64_t because it exceeds a 32-bit Index.
  Eigen::internal::NormalRandomGenerator<Scalar> generator(12345);
  VERIFY((numext::isfinite)(generator(numext::uint64_t(2429913123u))));
}

template <typename Scalar>
static void test_uniform_range(Eigen::Index size) {
  // All uniform draws must lie in [0, 1).
  Tensor<Scalar, 1> vec(size);
  vec.setRandom();
  Eigen::Index num_out_of_range = 0;
  for (Eigen::Index i = 0; i < size; ++i) {
    if (!(vec(i) >= Scalar(0.0f) && vec(i) < Scalar(1.0f))) ++num_out_of_range;
  }
  VERIFY_IS_EQUAL(num_out_of_range, Eigen::Index(0));
}

// Every draw is a pure function of (seed, index), which is what functor_traits reports as IsRepeatable and what
// lets the nullary evaluator serve blocks. So a materialized block has to hold exactly what the coefficient path
// produces at the same tensor-linear indices, and evaluating one expression twice has to repeat the fill.
template <typename Scalar, typename Generator, int Layout, int NumDims>
static void test_block_shape(const DSizes<Index, NumDims>& dims, const DSizes<Index, NumDims>& origin,
                             const DSizes<Index, NumDims>& sizes) {
  using TensorT = Tensor<Scalar, NumDims, Layout>;
  using Expr = TensorCwiseNullaryOp<Generator, const TensorT>;
  using Evaluator = TensorEvaluator<const Expr, DefaultDevice>;
  VERIFY(int(Evaluator::BlockAccess) == 1);

  TensorT shape(dims);
  const Expr expr = shape.template random<Generator>(Generator(1234));

  DefaultDevice device;
  Evaluator eval(expr, device);
  eval.evalSubExprsIfNeeded(nullptr);
  internal::TensorBlockScratchAllocator<DefaultDevice> scratch(device);

  const DSizes<Index, NumDims> tensor_strides = internal::strides<Layout>(dims);
  const DSizes<Index, NumDims> block_strides = internal::strides<Layout>(sizes);
  Index offset = 0;
  for (int d = 0; d < NumDims; ++d) offset += origin[d] * tensor_strides[d];

  internal::TensorBlockDescriptor<NumDims, Index> desc(offset, sizes);
  auto block = eval.block(desc, scratch);
  const Scalar* data = block.data();
  VERIFY(data != nullptr);

  DSizes<Index, NumDims> coord;
  for (int d = 0; d < NumDims; ++d) coord[d] = 0;
  for (Index i = 0; i < sizes.TotalSize(); ++i) {
    Index in_block = 0;
    Index in_tensor = 0;
    for (int d = 0; d < NumDims; ++d) {
      in_block += coord[d] * block_strides[d];
      in_tensor += (origin[d] + coord[d]) * tensor_strides[d];
    }
    VERIFY_IS_EQUAL(data[in_block], eval.coeff(in_tensor));
    for (int d = 0; d < NumDims; ++d) {
      const int dim = (Layout == ColMajor) ? d : NumDims - 1 - d;
      if (++coord[dim] < sizes[dim]) break;
      coord[dim] = 0;
    }
  }
  block.cleanup();
  eval.cleanup();

  TensorT first = expr;
  TensorT second = expr;
  for (Index i = 0; i < first.size(); ++i) VERIFY_IS_EQUAL(first(i), second(i));
}

template <typename Scalar, typename Generator>
static void test_block_materialization() {
  // Blocks strictly inside the tensor, so their runs are separated in linear-index space: 2-D in both layouts,
  // then 3-D, where the innermost dimension is a partial run either way.
  test_block_shape<Scalar, Generator, ColMajor>(DSizes<Index, 2>(17, 23), DSizes<Index, 2>(3, 5),
                                                DSizes<Index, 2>(8, 11));
  test_block_shape<Scalar, Generator, RowMajor>(DSizes<Index, 2>(17, 23), DSizes<Index, 2>(3, 5),
                                                DSizes<Index, 2>(8, 11));
  test_block_shape<Scalar, Generator, ColMajor>(DSizes<Index, 3>(9, 7, 5), DSizes<Index, 3>(2, 1, 1),
                                                DSizes<Index, 3>(5, 4, 3));
  test_block_shape<Scalar, Generator, RowMajor>(DSizes<Index, 3>(9, 7, 5), DSizes<Index, 3>(2, 1, 1),
                                                DSizes<Index, 3>(5, 4, 3));
}

template <typename Scalar>
static void test_complex_draw_order() {
  using Complex = std::complex<Scalar>;
  uint64_t scalar_state = 1234, complex_state = scalar_state;
  for (uint64_t index = 0; index < 32; ++index) {
    const Scalar real = internal::RandomToTypeUniform<Scalar>(&scalar_state, index);
    const Scalar imag = internal::RandomToTypeUniform<Scalar>(&scalar_state, index);
    VERIFY_IS_EQUAL(internal::RandomToTypeUniform<Complex>(&complex_state, index), Complex(real, imag));
    const Scalar normal_real = internal::RandomToTypeNormal<Scalar>(&scalar_state, index);
    const Scalar normal_imag = internal::RandomToTypeNormal<Scalar>(&scalar_state, index);
    VERIFY_IS_EQUAL(internal::RandomToTypeNormal<Complex>(&complex_state, index), Complex(normal_real, normal_imag));
  }
}

struct MyGenerator {
  MyGenerator() {}
  MyGenerator(const MyGenerator&) {}

  // Return a random value to be used.  "element_location" is the
  // location of the entry to set in the tensor, it can typically
  // be ignored.
  int operator()(Eigen::DenseIndex element_location, Eigen::DenseIndex /*unused*/ = 0) const {
    return static_cast<int>(3 * element_location);
  }

  // Same as above but generates several numbers at a time.
  internal::packet_traits<int>::type packetOp(Eigen::DenseIndex packet_location,
                                              Eigen::DenseIndex /*unused*/ = 0) const {
    const int packetSize = internal::packet_traits<int>::size;
    int values[packetSize];
    for (int i = 0; i < packetSize; ++i) {
      values[i] = static_cast<int>(3 * (packet_location + i));
    }
    return internal::ploadu<typename internal::packet_traits<int>::type>(values);
  }
};

static void test_custom() {
  Tensor<int, 1> vec(6);
  vec.setRandom<MyGenerator>();

  for (int i = 0; i < 6; ++i) {
    VERIFY_IS_EQUAL(vec(i), 3 * i);
  }
}

EIGEN_DECLARE_TEST(tensor_random) {
  CALL_SUBTEST((test_default<float>()));
  CALL_SUBTEST((test_normal<float>()));
  CALL_SUBTEST((test_default<double>()));
  CALL_SUBTEST((test_normal<double>()));
  CALL_SUBTEST((test_default<Eigen::half>()));
  CALL_SUBTEST((test_normal<Eigen::half>()));
  CALL_SUBTEST((test_default<Eigen::bfloat16>()));
  CALL_SUBTEST((test_normal<Eigen::bfloat16>()));
  CALL_SUBTEST((test_normal_all_finite<Eigen::half>(Eigen::Index(1) << 21)));
  CALL_SUBTEST((test_normal_all_finite<Eigen::bfloat16>(Eigen::Index(1) << 18)));
  CALL_SUBTEST(test_normal_zero_uniform_draw<float>());
  CALL_SUBTEST(test_normal_zero_uniform_draw<Eigen::half>());
  CALL_SUBTEST((test_uniform_range<Eigen::half>(Eigen::Index(1) << 16)));
  CALL_SUBTEST((test_uniform_range<Eigen::bfloat16>(Eigen::Index(1) << 16)));
  CALL_SUBTEST((test_block_materialization<float, Eigen::internal::UniformRandomGenerator<float>>()));
  CALL_SUBTEST((test_block_materialization<double, Eigen::internal::NormalRandomGenerator<double>>()));
  CALL_SUBTEST(test_custom());
  CALL_SUBTEST(test_complex_draw_order<float>());
  CALL_SUBTEST(test_complex_draw_order<double>());
}