hunk.code_window: ## Using Release Channels for Environment Variable Configuration
   Enironment variables don't exist explicitly, but you can utilize release channels to make that happen!
   Say you have a workflow of releasing builds like this:
   - `exp publish --release-channel prod-v1`
  
hunk.labels: keep keep replace keep keep keep keep
hunk.after_edit: Environment variables don't exist explicitly, but you can utilize release channels to make that happen!
  
hunk.file_path: docs/versions/v24.0.0/guides/release-channels.md
hunk.type: replace
file: // Copyright John Maddock 2006, 2007.
  // Copyright Paul A. Bristow 2007.
  
  //  Use, modification and distribution are subject to the
  //  Boost Software License, Version 1.0. (See accompanying file
  //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
  
  #ifndef BOOST_STATS_CAUCHY_HPP
  #define BOOST_STATS_CAUCHY_HPP
  
  #ifdef _MSC_VER
  #pragma warning(push)
  #pragma warning(disable : 4127) // conditional expression is constant
  #endif
  
  #include <boost/math/distributions/fwd.hpp>
  #include <boost/math/constants/constants.hpp>
  #include <boost/math/distributions/complement.hpp>
  #include <boost/math/distributions/detail/common_error_handling.hpp>
  #include <boost/config/no_tr1/cmath.hpp>
  
  #include <utility>
  
  namespace boost{ namespace math
  {
  
  template <class RealType, class Policy>
  class cauchy_distribution;
  
  namespace detail
  {
  
  template <class RealType, class Policy>
  RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement)
  {
     //
     // This calculates the cdf of the Cauchy distribution and/or its complement.
     //
     // The usual formula for the Cauchy cdf is:
     //
     // cdf = 0.5 + atan(x)/pi
     //
     // But that suffers from cancellation error as x -> -INF.
     //
     // Recall that for x < 0:
     //
     // atan(x) = -pi/2 - atan(1/x)
     //
     // Substituting into the above we get:
     //
     // CDF = -atan(1/x)  ; x < 0
     //
     // So the proceedure is to calculate the cdf for -fabs(x)
     // using the above formula, and then subtract from 1 when required
     // to get the result.
     //
     BOOST_MATH_STD_USING // for ADL of std functions
     static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)";
     RealType result = 0;
     RealType location = dist.location();
     RealType scale = dist.scale();
     if(false == detail::check_location(function, location, &result, Policy()))
     {
       return result;
     }
     if(false == detail::check_scale(function, scale, &result, Policy()))
     {
        return result;
     }
     if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
     { // cdf +infinity is unity.
       return static_cast<RealType>((complement) ? 0 : 1);
     }
     if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
     { // cdf -infinity is zero.
       return static_cast<RealType>((complement) ? 1 : 0);
     }
     if(false == detail::check_x(function, x, &result, Policy()))
     { // Catches x == NaN
        return result;
     }
     RealType mx = -fabs((x - location) / scale); // scale is > 0
     if(mx > -tools::epsilon<RealType>() / 8)
     {  // special case first: x extremely close to location.
        return 0.5;
     }
     result = -atan(1 / mx) / constants::pi<RealType>();
     return (((x > location) != complement) ? 1 - result : result);
  } // cdf
  
  template <class RealType, class Policy>
  RealType quantile_imp(
        const cauchy_distribution<RealType, Policy>& dist,
        const RealType& p,
        bool complement)
  {
     // This routine implements the quantile for the Cauchy distribution,
     // the value p may be the probability, or its complement if complement=true.
     //
     // The procedure first performs argument reduction on p to avoid error
     // when calculating the tangent, then calulates the distance from the
     // mid-point of the distribution.  This is either added or subtracted
     // from the location parameter depending on whether `complement` is true.
     //
     static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)";
     BOOST_MATH_STD_USING // for ADL of std functions
  
     RealType result = 0;
     RealType location = dist.location();
     RealType scale = dist.scale();
     if(false == detail::check_location(function, location, &result, Policy()))
     {
       return result;
     }
     if(false == detail::check_scale(function, scale, &result, Policy()))
     {
        return result;
     }
     if(false == detail::check_probability(function, p, &result, Policy()))
     {
        return result;
     }
     // Special cases:
     if(p == 1)
     {
        return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
     }
     if(p == 0)
     {
        return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy());
     }
  
     RealType P = p - floor(p);   // argument reduction of p:
     if(P > 0.5)
     {
        P = P - 1;
     }
     if(P == 0.5)   // special case:
     {
        return location;
     }
     result = -scale / tan(constants::pi<RealType>() * P);
     return complement ? RealType(location - result) : RealType(location + result);
  } // quantile
  
  } // namespace detail
  
  template <class RealType = double, class Policy = policies::policy<> >
  class cauchy_distribution
  {
  public:
     typedef RealType value_type;
     typedef Policy policy_type;
  
     cauchy_distribution(RealType l_location = 0, RealType l_scale = 1)
        : m_a(l_location), m_hg(l_scale)
     {
      static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution";
       RealType result;
       detail::check_location(function, l_location, &result, Policy());
       detail::check_scale(function, l_scale, &result, Policy());
     } // cauchy_distribution
  
     RealType location()const
     {
        return m_a;
     }
     RealType scale()const
     {
        return m_hg;
     }
  
  private:
     RealType m_a;    // The location, this is the median of the distribution.
     RealType m_hg;   // The scale )or shape), this is the half width at half height.
  };
  
  typedef cauchy_distribution<double> cauchy;
  
  template <class RealType, class Policy>
  inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&)
  { // Range of permissible values for random variable x.
    if (std::numeric_limits<RealType>::has_infinity)
    { 
       return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
    }
    else
    { // Can only use max_value.
     using boost::math::tools::max_value;
     return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.
    }
  }
  
  template <class RealType, class Policy>
  inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& )
  { // Range of supported values for random variable x.
     // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
    if (std::numeric_limits<RealType>::has_infinity)
    { 
       return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
    }
    else
    { // Can only use max_value.
       using boost::math::tools::max_value;
       return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.
    }
  }
  
  template <class RealType, class Policy>
  inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
  {  
     BOOST_MATH_STD_USING  // for ADL of std functions
  
     static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)";
     RealType result = 0;
     RealType location = dist.location();
     RealType scale = dist.scale();
     if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy()))
     {
        return result;
     }
     if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy()))
     {
        return result;
     }
     if((boost::math::isinf)(x))
     {
       return 0; // pdf + and - infinity is zero.
     }
     // These produce MSVC 4127 warnings, so the above used instead.
     //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
     //{ // pdf + and - infinity is zero.
     //  return 0;
     //}
  
     if(false == detail::check_x(function, x, &result, Policy()))
     { // Catches x = NaN
        return result;
     }
  
     RealType xs = (x - location) / scale;
     result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs));
     return result;
  } // pdf
  
  template <class RealType, class Policy>
  inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x)
  {
     return detail::cdf_imp(dist, x, false);
  } // cdf
  
  template <class RealType, class Policy>
  inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p)
  {
     return detail::quantile_imp(dist, p, false);
  } // quantile
  
  template <class RealType, class Policy>
  inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
  {
     return detail::cdf_imp(c.dist, c.param, true);
  } //  cdf complement
  
  template <class RealType, class Policy>
  inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c)
  {
     return detail::quantile_imp(c.dist, c.param, true);
  } // quantile complement
  
  template <class RealType, class Policy>
  inline RealType mean(const cauchy_distribution<RealType, Policy>&)
  {  // There is no mean:
     typedef typename Policy::assert_undefined_type assert_type;
     BOOST_STATIC_ASSERT(assert_type::value == 0);
  
     return policies::raise_domain_error<RealType>(
        "boost::math::mean(cauchy<%1%>&)",
        "The Cauchy distribution does not have a mean: "
        "the only possible return value is %1%.",
        std::numeric_limits<RealType>::quiet_NaN(), Policy());
  }
  
  template <class RealType, class Policy>
  inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/)
  {
     // There is no variance:
     typedef typename Policy::assert_undefined_type assert_type;
     BOOST_STATIC_ASSERT(assert_type::value == 0);
  
     return policies::raise_domain_error<RealType>(
        "boost::math::variance(cauchy<%1%>&)",
        "The Cauchy distribution does not have a variance: "
        "the only possible return value is %1%.",
        std::numeric_limits<RealType>::quiet_NaN(), Policy());
  }
  
  template <class RealType, class Policy>
  inline RealType mode(const cauchy_distribution<RealType, Policy>& dist)
  {
     return dist.location();
  }
  
  template <class RealType, class Policy>
  inline RealType median(const cauchy_distribution<RealType, Policy>& dist)
  {
     return dist.location();
  }
  template <class RealType, class Policy>
  inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/)
  {
     // There is no skewness:
     typedef typename Policy::assert_undefined_type assert_type;
     BOOST_STATIC_ASSERT(assert_type::value == 0);
  
     return policies::raise_domain_error<RealType>(
        "boost::math::skewness(cauchy<%1%>&)",
        "The Cauchy distribution does not have a skewness: "
        "the only possible return value is %1%.",
        std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?
  }
  
  template <class RealType, class Policy>
  inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/)
  {
     // There is no kurtosis:
     typedef typename Policy::assert_undefined_type assert_type;
     BOOST_STATIC_ASSERT(assert_type::value == 0);
  
     return policies::raise_domain_error<RealType>(
        "boost::math::kurtosis(cauchy<%1%>&)",
        "The Cauchy distribution does not have a kurtosis: "
        "the only possible return value is %1%.",
        std::numeric_limits<RealType>::quiet_NaN(), Policy());
  }
  
  template <class RealType, class Policy>
  inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/)
  {
     // There is no kurtosis excess:
     typedef typename Policy::assert_undefined_type assert_type;
     BOOST_STATIC_ASSERT(assert_type::value == 0);
  
     return policies::raise_domain_error<RealType>(
        "boost::math::kurtosis_excess(cauchy<%1%>&)",
        "The Cauchy distribution does not have a kurtosis: "
        "the only possible return value is %1%.",
        std::numeric_limits<RealType>::quiet_NaN(), Policy());
  }
  
  } // namespace math
  } // namespace boost
  
  #ifdef _MSC_VER
  #pragma warning(pop)
  #endif
  
  // This include must be at the end, *after* the accessors
  // for this distribution have been defined, in order to
  // keep compilers that support two-phase lookup happy.
  #include <boost/math/distributions/detail/derived_accessors.hpp>
  
  #endif // BOOST_STATS_CAUCHY_HPP
  