math.h

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#ifndef XGBOOST_COMMON_MATH_H_
#define XGBOOST_COMMON_MATH_H_
 
#include <xgboost/base.h>  // for XGBOOST_DEVICE
 
#include <algorithm>    // for max
#include <cmath>        // for exp, abs, log, lgamma
#include <limits>       // for numeric_limits
#include <type_traits>  // for is_floating_point, conditional, is_signed, is_same, declval, enable_if
#include <utility>      // for pair
 
namespace xgboost {
namespace common {
 
template <typename T> XGBOOST_DEVICE T Sqr(T const &w) { return w * w; }
 
XGBOOST_DEVICE inline float Sigmoid(float x) {
  float constexpr kEps = 1e-16;  // avoid 0 div
  x = std::min(-x, 88.7f);       // avoid exp overflow
  auto denom = expf(x) + 1.0f + kEps;
  auto y = 1.0f / denom;
  return y;
}
 
XGBOOST_DEVICE inline double Sigmoid(double x) {
  auto denom = std::exp(-x) + 1.0;
  auto y = 1.0 / denom;
  return y;
}
template <typename T, typename U>
XGBOOST_DEVICE constexpr bool CloseTo(T a, U b) {
  using Casted =
      typename std::conditional<
        std::is_floating_point<T>::value || std::is_floating_point<U>::value,
          double,
          typename std::conditional<
            std::is_signed<T>::value || std::is_signed<U>::value,
            int64_t,
            uint64_t>::type>::type;
  return std::is_floating_point<Casted>::value ?
      std::abs(static_cast<Casted>(a) -static_cast<Casted>(b)) < 1e-6 : a == b;
}
 
template <typename Iterator>
XGBOOST_DEVICE inline void Softmax(Iterator start, Iterator end) {
  static_assert(std::is_same<bst_float,
                typename std::remove_reference<
                  decltype(std::declval<Iterator>().operator*())>::type
                >::value,
                "Values should be of type bst_float");
  bst_float wmax = *start;
  for (Iterator i = start+1; i != end; ++i) {
    wmax = fmaxf(*i, wmax);
  }
  double wsum = 0.0f;
  for (Iterator i = start; i != end; ++i) {
    *i = expf(*i - wmax);
    wsum += *i;
  }
  for (Iterator i = start; i != end; ++i) {
    *i /= static_cast<float>(wsum);
  }
}
 
template<typename Iterator>
XGBOOST_DEVICE inline Iterator FindMaxIndex(Iterator begin, Iterator end) {
  Iterator maxit = begin;
  for (Iterator it = begin; it != end; ++it) {
    if (*it > *maxit) maxit = it;
  }
  return maxit;
}
 
inline float LogSum(float x, float y) {
  if (x < y) {
    return y + std::log(std::exp(x - y) + 1.0f);
  } else {
    return x + std::log(std::exp(y - x) + 1.0f);
  }
}
 
template<typename Iterator>
inline float LogSum(Iterator begin, Iterator end) {
  float mx = *begin;
  for (Iterator it = begin; it != end; ++it) {
    mx = std::max(mx, *it);
  }
  float sum = 0.0f;
  for (Iterator it = begin; it != end; ++it) {
    sum += std::exp(*it - mx);
  }
  return mx + std::log(sum);
}
 
// Redefined here to workaround a VC bug that doesn't support overloading for integer
// types.
template <typename T>
XGBOOST_DEVICE typename std::enable_if<
  std::numeric_limits<T>::is_integer, bool>::type
CheckNAN(T) {
  return false;
}
 
#if XGBOOST_STRICT_R_MODE && !defined(__CUDA_ARCH__)
 
bool CheckNAN(double v);
 
#else
 
XGBOOST_DEVICE bool inline CheckNAN(float x) {
#if defined(__CUDA_ARCH__)
  return isnan(x);
#else
  return std::isnan(x);
#endif  // defined(__CUDA_ARCH__)
}
 
XGBOOST_DEVICE bool inline CheckNAN(double x) {
#if defined(__CUDA_ARCH__)
  return isnan(x);
#else
  return std::isnan(x);
#endif  // defined(__CUDA_ARCH__)
}
 
#endif  // XGBOOST_STRICT_R_MODE && !defined(__CUDA_ARCH__)
// GPU version is not uploaded in CRAN anyway.
// Specialize only when using R with CPU.
#if XGBOOST_STRICT_R_MODE && !defined(XGBOOST_USE_CUDA)
double LogGamma(double v);
 
#else  // Not R or R with GPU.
 
template<typename T>
XGBOOST_DEVICE inline T LogGamma(T v) {
#ifdef _MSC_VER
 
#if _MSC_VER >= 1800
  return lgamma(v);
#else
#pragma message("Warning: lgamma function was not available until VS2013"\
                ", poisson regression will be disabled")
  utils::Error("lgamma function was not available until VS2013");
  return static_cast<T>(1.0);
#endif  // _MSC_VER >= 1800
 
#else
  return lgamma(v);
#endif  // _MSC_VER
}
 
#endif  // XGBOOST_STRICT_R_MODE && !defined(XGBOOST_USE_CUDA)
 
}  // namespace common
}  // namespace xgboost
#endif  // XGBOOST_COMMON_MATH_H_