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 //------------------------------- -*- C++ -*- -------------------------------//
 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details
 // SPDX-License-Identifier: (Apache-2.0 OR MIT)
 //---------------------------------------------------------------------------//
 //! \file celeritas/em/msc/detail/MscStepFromGeo.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include <cmath>
 
 #include "corecel/math/Algorithms.hh"
 #include "celeritas/Types.hh"
 #include "celeritas/em/data/UrbanMscData.hh"
 #include "celeritas/phys/Interaction.hh"
 
 namespace celeritas
 {
 namespace detail
 {
 //---------------------------------------------------------------------------//
 /*!
  * Convert the "geometrical" path traveled to the true path with MSC.
  *
  * The "true" step length is the physical path length taken along the
  * geometrical path length (which is straight without magnetic fields or curved
  * with them), accounting for the extra distance taken between
  * along-step elastic collisions.
  *
  * The transformation can be written as
  * \f[
  *     t(z) = \langle t \rangle = -\lambda_{1} \log(1 - \frac{z}{\lambda_{1}})
  * \f]
  * or \f$ t(z) = \frac{1}{\alpha} [ 1 - (1-\alpha w z)^{1/w}] \f$ if the
  * geom path is small, where \f$ w = 1 + \frac{1}{\alpha \lambda_{10}}\f$.
  *
  * \param true_path the proposed step before transportation.
  * \param gstep the proposed step after transportation.
  * \param alpha variable from UrbanMscStepLimit.
  */
 class MscStepFromGeo
 {
   public:
     //!@{
     //! \name Type aliases
     using MscParameters = UrbanMscParameters;
     //!@}
 
   public:
     // Construct with path length data
     inline CELER_FUNCTION MscStepFromGeo(MscParameters const& params_,
                                          MscStep const& step,
                                          real_type range,
                                          real_type lambda);
 
     // Calculate the true path
     inline CELER_FUNCTION real_type operator()(real_type gstep) const;
 
   private:
     // Urban MSC parameters
     MscParameters const& params_;
     //! Physical path length limited and transformed by MSC
     real_type true_step_;
     //! Scaled slope of the MFP
     real_type alpha_;
     //! Range for checking edge cases
     real_type range_;
     //! MFP at the start of step
     real_type lambda_;
 };
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct from MSC data.
  */
 CELER_FUNCTION MscStepFromGeo::MscStepFromGeo(MscParameters const& params,
                                               MscStep const& step,
                                               real_type range,
                                               real_type lambda)
     : params_(params)
     , true_step_(step.true_path)
     , alpha_(step.alpha)
     , range_(range)
     , lambda_(lambda)
 {
     CELER_EXPECT(lambda_ > 0);
     CELER_EXPECT(true_step_ <= range_);
     // TODO: expect that the "skip sampling" conditions are false.
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate and return the true path from the input "geometrical" step.
  *
  * This should only be applied if the step was geometry-limited. Otherwise, the
  * original interaction length is correct.
  */
 CELER_FUNCTION real_type MscStepFromGeo::operator()(real_type gstep) const
 {
     CELER_EXPECT(gstep >= 0 && gstep <= true_step_);
 
     if (gstep < params_.min_step_transform)
     {
         // Geometrical path length is true path length for a very small step
         return gstep;
     }
 
     real_type tstep = [&] {
         if (alpha_ == MscStep::small_step_alpha())
         {
             // Cross section was assumed to be constant over the step:
             // z = lambda * (1 - exp(-g / lambda))
             // => g = -lambda * log(1 - g / lambda)
             real_type tstep = -lambda_ * std::log1p(-gstep / lambda_);
             if (tstep < params_.min_step_transform)
             {
                 // Very small step: did not transform path length
                 return gstep;
             }
             return tstep;
         }
 
         real_type w = 1 + 1 / (alpha_ * lambda_);
         real_type x = alpha_ * w * gstep;  // = (1 - (1 - alpha * true)^w)
         // Range-limited step results in x = 1, which gives the correct
         // result in the inverted equation below for alpha = 1/range.
         // x >= 1 corresponds to the stopping MFP being <= 0: x=1 meaning
         // ending MFP of zero is correct when the step is the range. Precision
         // loss means this conversion also may result in x > 1, which we guard
         // against.
         x = min(x, real_type(1));
         // Near x=1, (1 - (1-x)^(1/w)) suffers from numerical precision loss;
         // the maximum value of the expression should be range_.
         // TODO: we should use the action ID to avoid applying this
         // transformation if not range-limited.
         real_type temp = 1 - fastpow(1 - x, 1 / w);
         real_type result = temp / alpha_;
         return min(result, range_);
     }();
 
     // The result can be no less than the geometry path (effectively no
     // scattering took place) and no more than the original calculated true
     // path (if the step is path-limited).
     // The result can be slightly outside the bounds due to numerical
     // imprecision and edge cases:
     // - a few ULP due to inexactness of log1p/expm1
     // - small travel distance results in roundoff error inside (1 -
     //   alpha/true)^w
     // - gstep is just above min_step_transform so that the updated
     // recalculation of
     //   tstep is just below min_step_transform
     return clamp(tstep, gstep, true_step_);
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace detail
 }  // namespace celeritas

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