codac2_ceil.h

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#pragma once
 
#include "codac2_Interval.h"
#include "codac2_AnalyticType.h"
#include "codac2_AnalyticExprWrapper.h"
 
namespace codac2
{
  struct CeilOp
  {
    template<typename X1>
    static std::string str(const X1& x1)
    {
      return "⌈" + x1->str() + "⌉";
    }
 
    template<typename X1>
    static std::pair<Index,Index> output_shape([[maybe_unused]] const X1& s1)
    {
      return {1,1};
    }
 
    static Interval fwd(const Interval& x1);
    static ScalarType fwd_natural(const ScalarType& x1);
    static ScalarType fwd_centered(const ScalarType& x1);
    static void bwd(const Interval& y, Interval& x1);
  };
 
  // Analytic operator
  // The following function can be used to build analytic expressions.
 
  inline ScalarExpr
  ceil(const ScalarExpr& x1)
  {
    return { std::make_shared<AnalyticOperationExpr<CeilOp,ScalarType,ScalarType>>(x1) };
  }
 
  // Inline functions
 
  inline Interval CeilOp::fwd(const Interval& x1)
  {
    return ceil(x1);
  }
 
  inline ScalarType CeilOp::fwd_natural(const ScalarType& x1)
  {
    return {
      fwd(x1.a),
      x1.def_domain
    };
  }
 
  inline ScalarType CeilOp::fwd_centered(const ScalarType& x1)
  {
    return {
      fwd(x1.m),
      fwd(x1.a),
      IntervalMatrix(0,0), // not supported yet for auto diff
      x1.def_domain
    };
  }
 
  inline void CeilOp::bwd(const Interval& y, Interval& x1)
  {
    // The content of this function comes from the IBEX library.
    // See ibex::Interval (IBEX lib, main author: Gilles Chabert)
    //   https://ibex-lib.readthedocs.io
 
    if(y.is_empty())
      x1.set_empty();
 
    else
    {
      double r = std::floor(y.ub());
      double l = std::ceil(y.lb());
 
      if(r < l)
        x1.set_empty();
 
      else
        x1 &= Interval(l,r) + Interval(-1,0);
    }
  }
}