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 //------------------------------- -*- C++ -*- -------------------------------//
 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details
 // SPDX-License-Identifier: (Apache-2.0 OR MIT)
 //---------------------------------------------------------------------------//
 //! \file corecel/math/SoftEqual.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include <cmath>
 
 #include "corecel/Assert.hh"
 #include "corecel/Macros.hh"
 #include "corecel/Types.hh"
 
 #include "detail/SoftEqualTraits.hh"
 
 namespace celeritas
 {
 //---------------------------------------------------------------------------//
 /*!
  * Square root of the soft equivalence tolerance for Celeritas.
  *
  * This tolerance is needed for operations where the accuracy is limited by the
  * square root of machine precision.
  *
  * \todo Move orange tolerance and related operations into corecel/math
  * alongside this, revisit ArrayUtils soft comparisons.
  */
 CELER_CONSTEXPR_FUNCTION real_type sqrt_tol()
 {
     return detail::SoftEqualTraits<real_type>::sqrt_prec();
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Functor for noninfinite floating point equality.
  *
  * This function-like class considers an \em absolute tolerance for values near
  * zero, and a \em relative tolerance for values far from zero. It correctly
  * returns "false" if either value being compared is NaN.  The call operator is
  * \em commutative: \c eq(a,b) should always give the same as \c eq(b,a).
  *
  * The actual comparison is: \f[
  |a - b| < \max(\epsilon_r \max(|a|, |b|), \epsilon_a)
  \f]
  *
  * \note The edge case where both values are infinite (with the same sign)
  * returns \em false for equality, which could be considered reasonable because
  * relative error is meaningless. To explicitly allow infinities to compare
  * equal, you must test separately, e.g., `a == b || soft_eq(a, b)` using \c
  * celeritas::EqualOr.
  */
 template<class RealType = ::celeritas::real_type>
 class SoftEqual
 {
   public:
     //!@{
     //! \name Type aliases
     using value_type = RealType;
     //!@}
 
   public:
     // Construct with default relative/absolute precision
     CELER_CONSTEXPR_FUNCTION SoftEqual();
 
     // Construct with default absolute precision
     explicit CELER_FUNCTION SoftEqual(value_type rel);
 
     // Construct with both relative and absolute precision
     CELER_FUNCTION SoftEqual(value_type rel, value_type abs);
 
     //// COMPARISON ////
 
     // Compare two values (implicitly casting arguments)
     bool CELER_FUNCTION operator()(value_type a, value_type b) const;
 
     //// ACCESSORS ////
 
     //! Relative allowable error
     CELER_CONSTEXPR_FUNCTION value_type rel() const { return rel_; }
 
     //! Absolute tolerance
     CELER_CONSTEXPR_FUNCTION value_type abs() const { return abs_; }
 
   private:
     value_type rel_;
     value_type abs_;
 
     using SETraits = detail::SoftEqualTraits<value_type>;
 };
 
 //---------------------------------------------------------------------------//
 /*!
  * Compare for equality before checking with the given functor.
  *
  * This CRTP class allows \c SoftEqual to work for infinities.
  */
 template<class F>
 class EqualOr : public F
 {
   public:
     //! Forward arguments to parent class
     template<class... C>
     CELER_FUNCTION EqualOr(C&&... args) : F{std::forward<C>(args)...}
     {
     }
 
     //! Forward arguments to comparison operator after comparing
     template<class T, class U>
     bool CELER_FUNCTION operator()(T a, U b) const
     {
         return a == b || static_cast<F const&>(*this)(a, b);
     }
 };
 
 //---------------------------------------------------------------------------//
 /*!
  * Functor for comparing values with an absolute precision.
  */
 template<class RealType = ::celeritas::real_type>
 class SoftClose
 {
   public:
     //!@{
     //! \name Type aliases
     using value_type = RealType;
     //!@}
 
   public:
     // Construct with default absolute precision
     CELER_CONSTEXPR_FUNCTION SoftClose();
 
     // Construct with absolute precision
     CELER_FUNCTION SoftClose(value_type abs);
 
     //// COMPARISON ////
 
     // Compare two values (implicitly casting arguments)
     bool CELER_FUNCTION operator()(value_type a, value_type b) const;
 
     //// ACCESSORS ////
 
     //! Absolute tolerance
     CELER_CONSTEXPR_FUNCTION value_type abs() const { return abs_; }
 
   private:
     value_type abs_;
 
     using SETraits = detail::SoftEqualTraits<value_type>;
 };
 
 //---------------------------------------------------------------------------//
 /*!
  * Functor for comparing values to zero with an absolute precision.
  */
 template<class RealType = ::celeritas::real_type>
 class SoftZero
 {
   public:
     //!@{
     //! \name Type aliases
     using argument_type = RealType;
     using value_type = RealType;
     //!@}
 
   public:
     // Construct with default absolute precision
     CELER_CONSTEXPR_FUNCTION SoftZero();
 
     // Construct with absolute precision
     explicit CELER_FUNCTION SoftZero(value_type abs);
 
     //// COMPARISON ////
 
     // Compare the given value to zero
     inline CELER_FUNCTION bool operator()(value_type actual) const;
 
     //// ACCESSORS ////
 
     //! Absolute tolerance
     CELER_CONSTEXPR_FUNCTION value_type abs() const { return abs_; }
 
   private:
     value_type abs_;
 
     using SETraits = detail::SoftEqualTraits<value_type>;
 };
 
 //---------------------------------------------------------------------------//
 // TEMPLATE DEDUCTION GUIDES
 //---------------------------------------------------------------------------//
 template<class T>
 CELER_FUNCTION SoftEqual(T) -> SoftEqual<T>;
 template<class T>
 CELER_FUNCTION SoftEqual(T, T) -> SoftEqual<T>;
 template<class F>
 CELER_FUNCTION EqualOr(F&&) -> EqualOr<F>;
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct with default relative/absolute precision.
  */
 template<class RealType>
 CELER_CONSTEXPR_FUNCTION SoftEqual<RealType>::SoftEqual()
     : rel_{SETraits::rel_prec()}, abs_{SETraits::abs_thresh()}
 {
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with scaled absolute precision.
  */
 template<class RealType>
 CELER_FUNCTION SoftEqual<RealType>::SoftEqual(value_type rel)
     : SoftEqual(rel, rel * (SETraits::abs_thresh() / SETraits::rel_prec()))
 {
     CELER_EXPECT(rel > 0);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with both relative and absolute precision.
  *
  * \param rel tolerance of relative error (default 1.0e-12 for doubles)
  *
  * \param abs threshold for absolute error when comparing small quantities
  *           (default 1.0e-14 for doubles)
  */
 template<class RealType>
 CELER_FUNCTION SoftEqual<RealType>::SoftEqual(value_type rel, value_type abs)
     : rel_{rel}, abs_{abs}
 {
     CELER_EXPECT(rel > 0);
     CELER_EXPECT(abs > 0);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Compare two values, implicitly casting arguments.
  */
 template<class RealType>
 CELER_FUNCTION bool
 SoftEqual<RealType>::operator()(value_type a, value_type b) const
 {
     real_type rel = rel_ * std::fmax(std::fabs(a), std::fabs(b));
     return std::fabs(a - b) < std::fmax(abs_, rel);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with default absolute precision.
  */
 template<class RealType>
 CELER_CONSTEXPR_FUNCTION SoftClose<RealType>::SoftClose()
     : abs_(SETraits::abs_thresh())
 {
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with absolute precision.
  *
  * \param abs threshold for absolute error (default 1.0e-14 for doubles)
  */
 template<class RealType>
 CELER_FUNCTION SoftClose<RealType>::SoftClose(value_type abs) : abs_(abs)
 {
     CELER_EXPECT(abs > 0);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Compare two values (implicitly casting arguments)
  */
 template<class RealType>
 CELER_FUNCTION bool
 SoftClose<RealType>::operator()(value_type a, value_type b) const
 {
     return std::fabs(a - b) < abs_;
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with default absolute precision.
  */
 template<class RealType>
 CELER_CONSTEXPR_FUNCTION SoftZero<RealType>::SoftZero()
     : abs_(SETraits::abs_thresh())
 {
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Construct with absolute precision.
  *
  * \param abs threshold for absolute error (default 1.0e-14 for doubles)
  */
 template<class RealType>
 CELER_FUNCTION SoftZero<RealType>::SoftZero(value_type abs) : abs_(abs)
 {
     CELER_EXPECT(abs > 0);
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * See if the value is within absolute tolerance of zero.
  *
  * \param actual scalar floating point value
  */
 template<class RealType>
 CELER_FUNCTION bool SoftZero<RealType>::operator()(value_type actual) const
 {
     return std::fabs(actual) < abs_;
 }
 
 //---------------------------------------------------------------------------//
 //! Soft equivalence with default tolerance
 template<class RealType>
 inline CELER_FUNCTION bool soft_equal(RealType expected, RealType actual)
 {
     return SoftEqual<RealType>()(expected, actual);
 }
 
 //---------------------------------------------------------------------------//
 //! Soft equivalence with relative error
 template<class RealType>
 inline CELER_FUNCTION bool
 soft_near(RealType expected, RealType actual, RealType rel_error)
 {
     return SoftEqual<RealType>(rel_error)(expected, actual);
 }
 
 //---------------------------------------------------------------------------//
 //! Soft equivalence to zero, with default tolerance
 template<class RealType>
 inline CELER_FUNCTION bool soft_zero(RealType actual)
 {
     return SoftZero<RealType>()(actual);
 }
 
 //---------------------------------------------------------------------------//
 //! Soft modulo operator
 template<class RealType>
 inline CELER_FUNCTION bool soft_mod(RealType dividend, RealType divisor)
 {
     auto remainder = std::fmod(dividend, divisor);
 
     SoftEqual<RealType> seq(detail::SoftEqualTraits<RealType>::rel_prec());
 
     return seq(0, remainder) || seq(divisor, remainder);
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace celeritas

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