test/rand.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

#include <cstdlib>
#include "main.h"
#include "SafeScalar.h"

// SafeScalar<T> is used to simulate custom Scalar types, which use a more generalized approach to generate random
// numbers

// For GCC-6, if this function is inlined then there is an optimization
// bug that triggers a failure.  This failure goes away if you access `r` in
// in any way, and for any other compiler.
template <typename Scalar>
EIGEN_DONT_INLINE Scalar check_in_range(Scalar x, Scalar y) {
  Scalar r = internal::random<Scalar>(x, y);
  VERIFY(r >= x);
  if (y >= x) {
    VERIFY(r <= y);
  }
  return r;
}

template <typename Scalar>
void check_all_in_range(Scalar x, Scalar y) {
  constexpr int repeats = 32;
  Index count = static_cast<Index>(y) - static_cast<Index>(x) + 1;
  ArrayX<bool> mask(count);
  mask.setConstant(false);
  for (Index k = 0; k < count; k++)
    for (int repeat = 0; repeat < repeats; repeat++) {
      Scalar r = check_in_range(x, y);
      Index i = static_cast<Index>(r) - static_cast<Index>(x);
      mask(i) = true;
    }
  for (Index i = 0; i < mask.size(); ++i)
    if (mask(i) == false) std::cout << "WARNING: value " << x + i << " not reached." << std::endl;
  VERIFY(mask.cwiseEqual(true).all());
}

template <typename Scalar>
void check_all_in_range() {
  const Scalar x = NumTraits<Scalar>::lowest();
  const Scalar y = NumTraits<Scalar>::highest();
  check_all_in_range(x, y);
}

template <typename Scalar, typename EnableIf = void>
class HistogramHelper {
 public:
  HistogramHelper(int nbins) : HistogramHelper(Scalar(-1), Scalar(1), nbins) {}
  HistogramHelper(Scalar lower, Scalar upper, int nbins) {
    lower_ = static_cast<double>(lower);
    upper_ = static_cast<double>(upper);
    num_bins_ = nbins;
    bin_width_ = (upper_ - lower_) / static_cast<double>(nbins);
  }
  int bin(Scalar v) {
    double result = (static_cast<double>(v) - lower_) / bin_width_;
    return std::min<int>(static_cast<int>(result), num_bins_ - 1);
  }

  double uniform_bin_probability(int bin) {
    double range = upper_ - lower_;
    if (bin < num_bins_ - 1) {
      return bin_width_ / range;
    }
    return (upper_ - (lower_ + double(bin) * bin_width_)) / range;
  }

 private:
  double lower_;
  double upper_;
  int num_bins_;
  double bin_width_;
};

// helper class to avoid extending std:: namespace
template <typename T>
struct get_range_type {
  using type = std::conditional_t<(sizeof(T) < sizeof(int)), unsigned int, std::make_unsigned_t<T>>;
};
template <typename T>
struct get_range_type<SafeScalar<T>> : internal::make_unsigned<T> {};

template <typename Scalar>
class HistogramHelper<Scalar, std::enable_if_t<Eigen::NumTraits<Scalar>::IsInteger>> {
 public:
  using RangeType = typename get_range_type<Scalar>::type;
  HistogramHelper(int nbins)
      : HistogramHelper(Eigen::NumTraits<Scalar>::lowest(), Eigen::NumTraits<Scalar>::highest(), nbins) {}
  HistogramHelper(Scalar lower, Scalar upper, int nbins)
      : lower_{lower}, upper_{upper}, num_bins_{nbins}, bin_width_{bin_width(lower, upper, nbins)} {}

  int bin(Scalar v) { return static_cast<int>(RangeType(RangeType(v) - RangeType(lower_)) / bin_width_); }

  double uniform_bin_probability(int bin) {
    // The full range upper - lower + 1 might overflow the RangeType by one.
    // So instead, we know we have (nbins - 1) bins of width bin_width_,
    // and the last bin of width:
    RangeType last_bin_width =
        RangeType(upper_) - (RangeType(lower_) + RangeType(num_bins_ - 1) * bin_width_) + RangeType(1);
    double last_bin_ratio = static_cast<double>(last_bin_width) / static_cast<double>(bin_width_);
    // Total probability = (nbins - 1) * p + last_bin_ratio * p = 1.0
    // p = 1.0 / (nbins - 1 + last_bin_ratio)
    double p = 1.0 / (last_bin_ratio + num_bins_ - 1);
    if (bin < num_bins_ - 1) {
      return p;
    }
    return last_bin_ratio * p;
  }

 private:
  static constexpr RangeType bin_width(Scalar lower, Scalar upper, int nbins) {
    // Avoid overflow in computing the full range.
    // floor( (upper - lower + 1) / nbins) )
    //    = floor( (upper- nbins - lower + 1 + nbins) / nbins) )
    return RangeType(RangeType(upper - nbins) - RangeType(lower) + 1) / nbins + 1;
  }

  Scalar lower_;
  Scalar upper_;
  int num_bins_;
  RangeType bin_width_;
};

template <typename Scalar>
void check_histogram(Scalar x, Scalar y, int bins) {
  constexpr int repeats = 10000;
  double count = double(bins) * double(repeats);
  Eigen::VectorXd hist = Eigen::VectorXd::Zero(bins);
  HistogramHelper<Scalar> hist_helper(x, y, bins);
  for (int k = 0; k < bins; k++)
    for (int repeat = 0; repeat < repeats; repeat++) {
      Scalar r = check_in_range(x, y);
      int bin = hist_helper.bin(r);
      hist(bin)++;
    }
  //  Normalize bins by probability.
  hist /= count;
  for (int i = 0; i < bins; ++i) {
    hist(i) = hist(i) / hist_helper.uniform_bin_probability(i);
  }
  VERIFY(((hist.array() - 1.0).abs() < 0.05).all());
}

template <typename Scalar>
void check_histogram(int bins) {
  constexpr int repeats = 10000;
  double count = double(bins) * double(repeats);
  Eigen::VectorXd hist = Eigen::VectorXd::Zero(bins);
  HistogramHelper<Scalar> hist_helper(bins);
  for (int k = 0; k < bins; k++)
    for (int repeat = 0; repeat < repeats; repeat++) {
      Scalar r = Eigen::internal::random<Scalar>();
      int bin = hist_helper.bin(r);
      hist(bin)++;
    }
  //  Normalize bins by probability.
  hist /= count;
  for (int i = 0; i < bins; ++i) {
    hist(i) = hist(i) / hist_helper.uniform_bin_probability(i);
  }
  VERIFY(((hist.array() - 1.0).abs() < 0.05).all());
}

template <>
void check_histogram<bool>(int) {
  constexpr int bins = 2;
  constexpr int repeats = 10000;
  double count = double(bins) * double(repeats);
  double true_count = 0.0;
  for (int k = 0; k < bins; k++)
    for (int repeat = 0; repeat < repeats; repeat++) {
      bool r = Eigen::internal::random<bool>();
      if (r) true_count += 1.0;
    }
  double p = true_count / count;
  VERIFY(numext::abs(p - 0.5) < 0.05);
}

EIGEN_DECLARE_TEST(rand) {
  int64_t int64_ref = NumTraits<int64_t>::highest() / 10;
  // the minimum guarantees that these conversions are safe
  int8_t int8t_offset = static_cast<int8_t>((std::min)(g_repeat, 64));
  int16_t int16t_offset = static_cast<int16_t>((std::min)(g_repeat, 8000));
  EIGEN_UNUSED_VARIABLE(int64_ref);
  EIGEN_UNUSED_VARIABLE(int8t_offset);
  EIGEN_UNUSED_VARIABLE(int16t_offset);

  for (int i = 0; i < g_repeat * 10000; i++) {
    CALL_SUBTEST_1(check_in_range<float>(10.0f, 11.0f));
    CALL_SUBTEST_1(check_in_range<float>(1.24234523f, 1.24234523f));
    CALL_SUBTEST_1(check_in_range<float>(-1.0f, 1.0f));
    CALL_SUBTEST_1(check_in_range<float>(-1432.2352f, -1432.2352f));

    CALL_SUBTEST_2(check_in_range<double>(10.0, 11.0));
    CALL_SUBTEST_2(check_in_range<double>(1.24234523, 1.24234523));
    CALL_SUBTEST_2(check_in_range<double>(-1.0, 1.0));
    CALL_SUBTEST_2(check_in_range<double>(-1432.2352, -1432.2352));

    CALL_SUBTEST_3(check_in_range<long double>(10.0L, 11.0L));
    CALL_SUBTEST_3(check_in_range<long double>(1.24234523L, 1.24234523L));
    CALL_SUBTEST_3(check_in_range<long double>(-1.0L, 1.0L));
    CALL_SUBTEST_3(check_in_range<long double>(-1432.2352L, -1432.2352L));

    CALL_SUBTEST_4(check_in_range<half>(half(10.0f), half(11.0f)));
    CALL_SUBTEST_4(check_in_range<half>(half(1.24234523f), half(1.24234523f)));
    CALL_SUBTEST_4(check_in_range<half>(half(-1.0f), half(1.0f)));
    CALL_SUBTEST_4(check_in_range<half>(half(-1432.2352f), half(-1432.2352f)));

    CALL_SUBTEST_5(check_in_range<bfloat16>(bfloat16(10.0f), bfloat16(11.0f)));
    CALL_SUBTEST_5(check_in_range<bfloat16>(bfloat16(1.24234523f), bfloat16(1.24234523f)));
    CALL_SUBTEST_5(check_in_range<bfloat16>(bfloat16(-1.0f), bfloat16(1.0f)));
    CALL_SUBTEST_5(check_in_range<bfloat16>(bfloat16(-1432.2352f), bfloat16(-1432.2352f)));

    CALL_SUBTEST_6(check_in_range<int32_t>(0, -1));
    CALL_SUBTEST_6(check_in_range<int16_t>(0, -1));
    CALL_SUBTEST_6(check_in_range<int64_t>(0, -1));
    CALL_SUBTEST_6(check_in_range<int32_t>(-673456, 673456));
    CALL_SUBTEST_6(check_in_range<int32_t>(-RAND_MAX + 10, RAND_MAX - 10));
    CALL_SUBTEST_6(check_in_range<int16_t>(-24345, 24345));
    CALL_SUBTEST_6(check_in_range<int64_t>(-int64_ref, int64_ref));
  }

  CALL_SUBTEST_7(check_all_in_range<int8_t>(11, 11));
  CALL_SUBTEST_7(check_all_in_range<int8_t>(11, 11 + int8t_offset));
  CALL_SUBTEST_7(check_all_in_range<int8_t>(-5, 5));
  CALL_SUBTEST_7(check_all_in_range<int8_t>(-11 - int8t_offset, -11));
  CALL_SUBTEST_7(check_all_in_range<int8_t>(-126, -126 + int8t_offset));
  CALL_SUBTEST_7(check_all_in_range<int8_t>(126 - int8t_offset, 126));
  CALL_SUBTEST_7(check_all_in_range<int8_t>());
  CALL_SUBTEST_7(check_all_in_range<uint8_t>());

  CALL_SUBTEST_8(check_all_in_range<int16_t>(11, 11));
  CALL_SUBTEST_8(check_all_in_range<int16_t>(11, 11 + int16t_offset));
  CALL_SUBTEST_8(check_all_in_range<int16_t>(-5, 5));
  CALL_SUBTEST_8(check_all_in_range<int16_t>(-11 - int16t_offset, -11));
  CALL_SUBTEST_8(check_all_in_range<int16_t>(-24345, -24345 + int16t_offset));
  CALL_SUBTEST_8(check_all_in_range<int16_t>());
  CALL_SUBTEST_8(check_all_in_range<uint16_t>());

  CALL_SUBTEST_9(check_all_in_range<int32_t>(11, 11));
  CALL_SUBTEST_9(check_all_in_range<int32_t>(11, 11 + g_repeat));
  CALL_SUBTEST_9(check_all_in_range<int32_t>(-5, 5));
  CALL_SUBTEST_9(check_all_in_range<int32_t>(-11 - g_repeat, -11));
  CALL_SUBTEST_9(check_all_in_range<int32_t>(-673456, -673456 + g_repeat));
  CALL_SUBTEST_9(check_all_in_range<int32_t>(673456, 673456 + g_repeat));

  CALL_SUBTEST_10(check_all_in_range<int64_t>(11, 11));
  CALL_SUBTEST_10(check_all_in_range<int64_t>(11, 11 + g_repeat));
  CALL_SUBTEST_10(check_all_in_range<int64_t>(-5, 5));
  CALL_SUBTEST_10(check_all_in_range<int64_t>(-11 - g_repeat, -11));
  CALL_SUBTEST_10(check_all_in_range<int64_t>(-int64_ref, -int64_ref + g_repeat));
  CALL_SUBTEST_10(check_all_in_range<int64_t>(int64_ref, int64_ref + g_repeat));

  CALL_SUBTEST_11(check_histogram<int32_t>(-5, 5, 11));
  int bins = 100;
  EIGEN_UNUSED_VARIABLE(bins)
  CALL_SUBTEST_11(check_histogram<int32_t>(-3333, -3333 + bins * (3333 / bins) - 1, bins));
  bins = 1000;
  CALL_SUBTEST_11(check_histogram<int32_t>(-RAND_MAX + 10, -RAND_MAX + 10 + bins * (RAND_MAX / bins) - 1, bins));
  CALL_SUBTEST_11(check_histogram<int32_t>(-RAND_MAX + 10,
                                           -int64_t(RAND_MAX) + 10 + bins * (2 * int64_t(RAND_MAX) / bins) - 1, bins));

  CALL_SUBTEST_12(check_histogram<bool>(/*bins=*/2));
  CALL_SUBTEST_12(check_histogram<uint8_t>(/*bins=*/16));
  CALL_SUBTEST_12(check_histogram<uint16_t>(/*bins=*/1024));
  CALL_SUBTEST_12(check_histogram<uint32_t>(/*bins=*/1024));
  CALL_SUBTEST_12(check_histogram<uint64_t>(/*bins=*/1024));

  CALL_SUBTEST_13(check_histogram<int8_t>(/*bins=*/16));
  CALL_SUBTEST_13(check_histogram<int16_t>(/*bins=*/1024));
  CALL_SUBTEST_13(check_histogram<int32_t>(/*bins=*/1024));
  CALL_SUBTEST_13(check_histogram<int64_t>(/*bins=*/1024));

  CALL_SUBTEST_14(check_histogram<float>(-10.0f, 10.0f, /*bins=*/1024));
  CALL_SUBTEST_14(check_histogram<double>(-10.0, 10.0, /*bins=*/1024));
  CALL_SUBTEST_14(check_histogram<long double>(-10.0L, 10.0L, /*bins=*/1024));
  CALL_SUBTEST_14(check_histogram<half>(half(-10.0f), half(10.0f), /*bins=*/512));
  CALL_SUBTEST_14(check_histogram<bfloat16>(bfloat16(-10.0f), bfloat16(10.0f), /*bins=*/64));
  CALL_SUBTEST_14(check_histogram<SafeScalar<float>>(-10.0f, 10.0f, /*bins=*/1024));
  CALL_SUBTEST_14(check_histogram<SafeScalar<half>>(half(-10.0f), half(10.0f), /*bins=*/512));
  CALL_SUBTEST_14(check_histogram<SafeScalar<bfloat16>>(bfloat16(-10.0f), bfloat16(10.0f), /*bins=*/64));

  CALL_SUBTEST_15(check_histogram<float>(/*bins=*/1024));
  CALL_SUBTEST_15(check_histogram<double>(/*bins=*/1024));
  CALL_SUBTEST_15(check_histogram<long double>(/*bins=*/1024));
  CALL_SUBTEST_15(check_histogram<half>(/*bins=*/512));
  CALL_SUBTEST_15(check_histogram<bfloat16>(/*bins=*/64));
  CALL_SUBTEST_15(check_histogram<SafeScalar<float>>(/*bins=*/1024));
  CALL_SUBTEST_15(check_histogram<SafeScalar<half>>(/*bins=*/512));
  CALL_SUBTEST_15(check_histogram<SafeScalar<bfloat16>>(/*bins=*/64));
}