R134a.mo

within Modelica.Media;
package R134a "R134a: Medium model for R134a"
  extends Modelica.Icons.VariantsPackage;
  package Common
    extends Modelica.Icons.Package;

    record PhaseBoundaryProperties
      "Thermodynamic base properties on the phase boundary"
      extends Modelica.Icons.Record;

      SI.Density d "Density";
      SI.SpecificEnthalpy h "Enthalpy";
      SI.SpecificEnergy u "Inner energy";
      SI.SpecificEntropy s "Entropy";
      SI.SpecificHeatCapacity cp
        "Heat capacity at constant pressure";
      SI.SpecificHeatCapacity cv
        "Heat capacity at constant volume";
      SI.IsothermalCompressibility kappa "Isentropic exponent";
      SI.Velocity a "Velocity of sound";
      Modelica.Media.Interfaces.Types.IsobaricExpansionCoefficient beta
        "Isobaric expansion coefficient";
      SI.IsentropicExponent gamma "Isentropic exponent";
      SI.DerPressureByTemperature pt
        "Derivative of pressure w.r.t. temperature";
      SI.DerPressureByDensity pd
        "Derivative of pressure w.r.t. density";

    end PhaseBoundaryProperties;

    record InverseDerivatives_rhoT
      "Derivatives required for inversion of density and temperature functions w.r.t. pressure and enthalpy states"
      extends Modelica.Icons.Record;

      Integer phase "Number of phases";
      SI.Pressure p "Pressure";
      SI.Temperature T "Kelvin-temperature";
      SI.Density rho "Density";
      SI.SpecificEnthalpy h "Specific enthalpy";
      SI.SpecificHeatCapacity cv
        "Specific heat capacity at constant volume";
      Real pt "Derivative of pressure w.r.t. temperature";
      Real pd "Derivative of pressure w.r.t. density";
      Real dpT "dp/dT derivative of saturation curve";

    end InverseDerivatives_rhoT;

    record EOSIdealCoeff
      "Record for coefficients of ideal term of Helmholtz equation of state"
      extends Modelica.Icons.Record;

      parameter Integer nc=5 "No. of coefficients in a";
      parameter Real[nc] a
        "Coefficients of ideal term of Helmholtz equation of state";

    end EOSIdealCoeff;

    record EOSResidualCoeff
      "Record for coefficients of residual term of Helmholtz equation of state"
      extends Modelica.Icons.Record;

      parameter Integer nc=20 "No. of coefficients in c, d, t, n";
      parameter Integer ns1 "No. of zero coefficients in c";
      parameter Real[nc] c
        "Coefficients of residual term of Helmholtz equation of state";
      parameter Real[nc] d
        "Coefficients of residual term of Helmholtz equation of state";
      parameter Real[nc] t
        "Coefficients of residual term of Helmholtz equation of state";
      parameter Real[nc] n
        "Coefficients of residual term of Helmholtz equation of state";

    end EOSResidualCoeff;

    function CubicSplineDerEval "Derivative of cubic spline"
      extends Modelica.Icons.Function;

      input Real x "Input";
      input Real[4] coefs "Spline coefficients";
      output Real yder "Spline derivative";
    algorithm
      yder := coefs[3] + x*(2.0*coefs[2] + x*3.0*coefs[1]);

    end CubicSplineDerEval;

    function CubicSplineEval "Cubic spline"
      extends Modelica.Icons.Function;

      input Real x "Input";
      input Real[4] coefs "Spline coefficients";
      output Real y "Output";
    algorithm
      y := coefs[4] + x*(coefs[3] + x*(coefs[2] + x*coefs[1]));

    end CubicSplineEval;

    function cv2Phase
      "Compute isochoric specific heat capacity inside the two-phase region"
      extends Modelica.Icons.Function;

      input PhaseBoundaryProperties liq "Properties on the boiling curve";
      input PhaseBoundaryProperties vap "Properties on the condensation curve";
      input SI.MassFraction x "Vapour mass fraction";
      input SI.Temperature T "Temperature";
      input SI.Pressure p "Pressure";
      output SI.SpecificHeatCapacity cv "Isochoric specific heat capacity";
      output Real dpT "Derivative of pressure w.r.t. temperature";
    protected
      Real dxv "Derivative of vapour mass fraction w.r.t. specific volume";
      Real dvTl "Derivative of liquid specific volume w.r.t. temperature";
      Real dvTv "Derivative of vapour specific volume w.r.t. temperature";
      Real duTl "Derivative of liquid specific inner energy w.r.t. temperature";
      Real duTv "Derivative of vapour specific inner energy w.r.t. temperature";
      Real dxt "Derivative of vapour mass fraction w.r.t. temperature";
    algorithm
      dxv := if (liq.d <> vap.d) then liq.d*vap.d/(liq.d - vap.d) else 0.0;
      dpT := (vap.s - liq.s)*dxv;
      // wrong at critical point
      dvTl := (liq.pt - dpT)/liq.pd/liq.d/liq.d;
      dvTv := (vap.pt - dpT)/vap.pd/vap.d/vap.d;
      dxt := -dxv*(dvTl + x*(dvTv - dvTl));
      duTl := liq.cv + (T*liq.pt - p)*dvTl;
      duTv := vap.cv + (T*vap.pt - p)*dvTv;
      cv := duTl + x*(duTv - duTl) + dxt*(vap.u - liq.u);

    end cv2Phase;

    function FindInterval "Half-interval search algorithm"
      extends Modelica.Icons.Function;

      input Real x "Input";
      input Real[:] breaks "Grid points defining the intervals";
      output Integer i "Found interval number";
      output Integer error=0 "1=did not find interval";
    protected
      Integer n=scalar(size(breaks)) - 1 "Max value";
      Integer ix=1 "Min value";
      Integer m=n "New interval";
    algorithm
      i := 1;
      if ((x < breaks[1]) or (x >= breaks[n])) then
        error := 1;
      end if;
      if ((x < breaks[1]) or (x >= breaks[2])) then
        while m <> ix loop
          if (x < breaks[m]) then
            n := m;
          else
            ix := m;
          end if;
          m := integer(div(ix + n, 2));
        end while;
        i := ix;
      end if;

    end FindInterval;

    function helmholtzToBoundaryProps
      "Calculate phase boundary property record from dimensionless Helmholtz function"

      extends Modelica.Icons.Function;

      input Modelica.Media.Common.HelmholtzDerivs f
        "Dimensionless derivatives of Helmholtz function";
      output PhaseBoundaryProperties sat "Phase boundary property record";
    protected
      SI.Pressure p "Pressure";
    algorithm
      p := f.R_s*f.d*f.T*f.delta*f.fdelta;
      sat.d := f.d;
      sat.h := f.R_s*f.T*(f.tau*f.ftau + f.delta*f.fdelta);
      sat.s := f.R_s*(f.tau*f.ftau - f.f);
      sat.u := f.R_s*f.T*f.tau*f.ftau;
      sat.cp := f.R_s*(-f.tau*f.tau*f.ftautau + (f.delta*f.fdelta - f.delta*f.tau
        *f.fdeltatau)^2/(2*f.delta*f.fdelta + f.delta*f.delta*f.fdeltadelta));
      sat.cv := f.R_s*(-f.tau*f.tau*f.ftautau);
      sat.pt := f.R_s*f.d*(f.delta*(f.fdelta - f.tau*f.fdeltatau));
      sat.pd := f.R_s*f.T*(f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta));
      sat.a := abs(f.R_s*f.T*(2*f.delta*f.fdelta + f.delta*f.delta*f.fdeltadelta
         - ((f.delta*f.fdelta - f.delta*f.tau*f.fdeltatau)*(f.delta*f.fdelta -
        f.delta*f.tau*f.fdeltatau))/(f.tau*f.tau*f.ftautau)))^0.5;
      sat.kappa := 1/(f.d*f.R_s*f.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta));
      sat.beta := f.R_s*f.d*f.delta*(f.fdelta - f.tau*f.fdeltatau)*sat.kappa;
      sat.gamma := sat.a^2/f.R_s/f.T;

    end helmholtzToBoundaryProps;
  end Common;

  package R134a_ph "Medium model for R134a and p,h as states"

    extends Modelica.Media.Interfaces.PartialTwoPhaseMedium(
      ThermoStates=Modelica.Media.Interfaces.Choices.IndependentVariables.ph,
      mediumName="R134a_ph",
      substanceNames={"tetrafluoroethane"},
      singleState=false,
      SpecificEnthalpy(start=h_default, nominal=5.0e5),
      Density(start=4, nominal=500),
      AbsolutePressure(start=p_default, nominal=10e5),
      Temperature(start=T_default, nominal=350),
      smoothModel=false,
      onePhase=false,
      fluidConstants=r134aConstants,
      h_default=420e3);

    constant Boolean ph_explicit=true;
    constant Boolean dT_explicit=false;
    constant Modelica.Media.Interfaces.Types.FluidLimits[1] r134aLimits(
      each TMIN=169.85,
      each TMAX=455,
      each DMIN=0,
      each DMAX=1591.7,
      each PMIN=389.563789,
      each PMAX=7e7,
      each HMIN=0,
      each HMAX=0,
      each SMIN=0,
      each SMAX=0);

    constant Modelica.Media.Interfaces.Types.TwoPhase.FluidConstants[1]
      r134aConstants(
      each chemicalFormula="CF3CH2F",
      each structureFormula="1,1,1,2-tetrafluoroethane",
      each iupacName="tetrafluoroethane",
      each casRegistryNumber="811-97-2",
      each molarMass=R134aData.data.MM,
      each criticalMolarVolume=R134aData.data.MM/R134aData.data.DCRIT,
      each criticalTemperature=R134aData.data.TCRIT,
      each criticalPressure=R134aData.data.PCRIT,
      each triplePointTemperature=R134aData.data.TTRIPLE,
      each triplePointPressure=R134aData.data.PTRIPLE,
      each meltingPoint=172.15,
      each normalBoilingPoint=247.076,
      each acentricFactor=0.32684,
      each dipoleMoment=1.99,
      each hasCriticalData=true);

    redeclare record extends SaturationProperties
    end SaturationProperties;

    redeclare record extends ThermodynamicState "Thermodynamic state"
      SpecificEnthalpy h "Specific enthalpy";
      Density d "Density";
      Temperature T "Temperature";
      AbsolutePressure p "Pressure";

    end ThermodynamicState;

    redeclare replaceable model extends BaseProperties(
      h(stateSelect=StateSelect.prefer),
      d(stateSelect=StateSelect.default),
      T(stateSelect=StateSelect.default),
      p(stateSelect=StateSelect.prefer),
      sat(Tsat(start=273.0), psat(start=3.0e5))) "Base properties of R134a"
      Integer phase(
        min=0,
        max=2,
        start=1,
        fixed=false) "2 for two-phase, 1 for one-phase, 0 if not known";
      MassFraction quality "Quality of vapour";

    equation
      MM = R134aData.data.MM;
      phase = 0;

      T = temperature_ph(p, h);
      d = density_ph(p, h);
      sat.Tsat = saturationTemperature(p=p);
      sat.psat = p;
      quality = vapourQuality(state);

      u = h - p/d;
      R_s = R134aData.data.R_s;
      h = state.h;
      p = state.p;
      T = state.T;
      d = state.d;
      phase = state.phase;
    end BaseProperties;

    redeclare function extends setState_phX
      "Set state for pressure and specific enthalpy (X not used since single substance)"
    algorithm
      state := ThermodynamicState(phase=getPhase_ph(p, h), p=p, h=h, d=density_ph(p, h), T=temperature_ph(p, h));
      annotation (Documentation(info="<html>
<p>This function should be used by default in order to calculate the thermodynamic state record used as input by many functions.</p>
<p>
Example:
</p>
<blockquote><pre>
parameter Medium.AbsolutePressure p = 3e5;
parameter Medium.SpecificEnthalpy h = 4.2e5;

Medium.Density rho;

<strong>equation</strong>

rho = Medium.density(setState_phX(p, h, fill(0, Medium.nX)));
</pre></blockquote>
</html>",     revisions="<html>
<p>2020-01-20 Stefan Wischhusen: Converted into single line assignment for state record.</p>
</html>"));
    end setState_phX;

    redeclare function extends setState_dTX
      "Set state for density and temperature (X not used since single substance)"
    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      SI.SpecificHeatCapacity R_s "Specific gas constant";
      SaturationProperties sat "Saturation temperature and pressure";
      SI.Density dl "Liquid density";
      SI.Density dv "Vapor density";

    algorithm
      R_s := R134aData.data.R_s;
      sat := setSat_T(T);
      dl := bubbleDensity(sat);
      dv := dewDensity(sat);
      if d < dl and d > dv and T < R134aData.data.FTCRIT then
        f := Modelica.Media.Common.HelmholtzDerivs(
          d=d, T=T, R_s=R_s, delta=0, tau=0, f=0, fdelta=0,
          fdeltadelta=0, ftau=0, ftautau=0, fdeltatau=0);
        state.p := saturationPressure_sat(sat);
        state.h := (dl*dv/d*(dewEnthalpy(sat) - bubbleEnthalpy(sat))
                  - dv*dewEnthalpy(sat) + dl*bubbleEnthalpy(sat))/(dl - dv);
        state.phase := 2;
      else
        f := f_R134a(d=d, T=T);
        state.p := d*R_s*T*f.delta*f.fdelta;
        state.h := R_s*T*(f.tau*f.ftau + f.delta*f.fdelta);
        state.phase := 1;
      end if;
      state.T := T;
      state.d := d;
      annotation (Documentation(revisions="<html>
<p>2019-12-20  Francesco Casella and Stefan Wischhusen: Two-phase calculation corrected.</p>
<p>2012-08-01  Stefan Wischhusen: Corrected passing-error of inputs.</p>
</html>", info="<html>
<p>Although the medium package is explicit for pressure and specific enthalpy, this function may be used in order to calculate the thermodynamic state record used as input by many functions. It will calculate the missing states:</p>
<ul>
<li>pressure</li>
<li>specific enthalpy</li>
</ul>
<p>
Example:
</p>
<blockquote><pre>
parameter Medium.Density d = 4;
parameter Medium.Temperature T = 298;

Medium.SpecificEntropy s;

<strong>equation</strong>

s = Medium.specificEntropy(setState_dTX(d, T, fill(0, Medium.nX)));
</pre></blockquote>

</html>"));
    end setState_dTX;

    redeclare function extends setState_psX
      "Set state for pressure and specific entropy (X not used since single substance)"

    protected
      SI.Pressure delp=1e-2 "Iteration accuracy for pressure";
      SI.SpecificEntropy dels=1e-1
        "Iteration accuracy for entropy";
      Integer error "If newton iteration fails (too many calls)";
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      SaturationProperties sat "Saturation temperature and pressure";
    algorithm
      state.p := p;
      state.phase := getPhase_ps(p, s);
      if state.phase == 1 then
        (state.d, state.T, error) := dtofpsOnePhase(
              p=p,
              s=s,
              delp=delp,
              dels=dels);
        f := f_R134a(d=state.d, T=state.T);
        state.h := R134aData.R_s*state.T*(f.tau*f.ftau + f.delta*f.fdelta);
      else
        state.h := hofpsTwoPhase(p, s);
        (state.d, state.T) := dt_ph(p, state.h);
      end if;

      annotation (Documentation(info="<html>
<p>This function may be used in order to calculate the thermodynamic state record used as input by many functions. It will calculate the missing states:</p>
<ul>
<li>density</li>
<li>pressure</li>
<li>specific enthalpy</li>
</ul>
<p>
Example:
</p>
<blockquote><pre>
parameter Medium.AbsolutePressure p = 3e5;
parameter Medium.SpecificEntropy s = 1.7e3;

Medium.SpecificEnthalpy h;

<strong>equation</strong>

h = Medium.specificEnthalpy(setState_psX(p, s, fill(0, Medium.nX)));
</pre></blockquote>
</html>", revisions="<html>
<p>2020-02-05 Stefan Wischhusen: Added missing property calculation for d and T.</p>
</html>"));
    end setState_psX;

    redeclare function extends setState_pTX
      "Set state for pressure and temperature (X not used since single substance)"

    protected
        SI.Pressure delp=1.0e-2
        "Relative error in p in iteration";

    algorithm
      Modelica.Media.R134a.R134a_ph.phaseBoundaryAssert(p, T);

      state := ThermodynamicState(
              d=dofpT(p, T, delp),
              T=T,
              h=hofpT(p, T, delp),
              p=p,
              phase=1);
      annotation (Inline=true, Documentation(info="<html>
<p>This function should be used by default in order to calculate the thermodynamic state record used as input by many functions.</p>
<p>
Example:
</p>
<blockquote><pre>
parameter Medium.AbsolutePressure p = 3e5;
parameter Medium.Temperature T = 290;

Medium.Density rho;

<strong>equation</strong>

rho = Medium.density(setState_pTX(p, T, fill(0, Medium.nX)));
</pre></blockquote>
<p>
Please note, that in contrast to setState_phX, setState_dTX and setState_psX this function can not calculate properties in the two-phase region since pressure and temperature are dependent variables. A guard function will be called if the temperature difference to the phase boundary is lower than 1K or the pressure difference to the critical pressure is lower than 1000 Pa.
</p>
</html>"));
    end setState_pTX;

    redeclare function extends setBubbleState
      "Return the thermodynamic state on the bubble line"
    algorithm
      if sat.psat < Modelica.Media.R134a.R134aData.data.FPCRIT then
        state.p := sat.psat;
        state.T := saturationTemperature(sat.psat);
        state.d := bubbleDensity(sat);
        state.h := bubbleEnthalpy(sat);
      else
        assert(sat.psat < Modelica.Media.R134a.R134aData.data.FPCRIT,
          "Function setBubbleState is only valid in two-phase regime");
      end if;
      annotation (Documentation(info="<html>
<p>This function shall be used in order to calculate the thermodynamic state record for the liquid phase boundary. It requires the saturation record as input which can be determined by both functions setSat_p and setSat_T:
</p>
<p>
Example:
</p>
<blockquote><pre>
Medium.AbsolutePressure p=3e5;
// Viscosity on the liquid phase boundary
SI.DynamicViscosity eta_liq;

equation

eta_liq = Medium.DynamicViscosity(Medium.setBubbleState(Medium.setSat_p(p)));
</pre></blockquote>

<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end setBubbleState;

    redeclare function extends setDewState
      "Return the thermodynamic state on the dew line"
    algorithm
      if sat.psat < Modelica.Media.R134a.R134aData.data.FPCRIT then
        state.p := sat.psat;
        state.T := saturationTemperature(sat.psat);
        state.d := dewDensity(sat);
        state.h := dewEnthalpy(sat);
      else
        assert(sat.psat < Modelica.Media.R134a.R134aData.data.FPCRIT,
          "Function setDewState is only valid in two-phase regime");
      end if;
      annotation (Documentation(info="<html>
<p>This function shall be used in order to calculate the thermodynamic state record for the vapor phase boundary. It requires the saturation record as input which can be determined by both functions setSat_p and setSat_T:
</p>
<p>
Example:
</p>
<blockquote><pre>
Medium.AbsolutePressure p=3e5;
// Viscosity on the vapor phase boundary
SI.DynamicViscosity eta_vap;

equation

eta_vap = Medium.DynamicViscosity(Medium.setBubbleState(Medium.setSat_p(p)));
</pre></blockquote>

<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end setDewState;

    redeclare function density_ph
      "Density as function of pressure and specific enthalpy"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Integer phase=0 "2 for two-phase, 1 for one-phase, 0 if not known";
      output Density d "Density";

    algorithm
      d := rho_props_ph(
            p,
            h,
            derivsOf_ph(
              p,
              h,
              getPhase_ph(p, h)));

      annotation (Inline=true, Documentation(info="<html>
<p>This function calculates the density of R134a from the state variables p (absolute pressure) and h (specific enthalpy). The density is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>

<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)d-Diagram-R134a.png\"/></p>

</html>"));
    end density_ph;

    redeclare function extends density
      "Density as function of pressure and specific enthalpy | use setState_phX function for input"

    algorithm
      d := state.d;

      annotation (Inline=true, Documentation(info="<html>
<p>
This function calculates the density of R134a from the state record
(e.g., use setState_phX function for input). The density is modelled
by the fundamental equation of state of Tillner-Roth and Baehr (1994).
</p>

<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)d-Diagram-R134a.png\"/></p>
</html>"));
    end density;

    redeclare function temperature_ph
      "Temperature as function of pressure and specific enthalpy"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Integer phase=0 "2 for two-phase, 1 for one-phase, 0 if not known";
      output Temperature T "Temperature";

    algorithm
      T := T_props_ph(
            p,
            h,
            derivsOf_ph(
              p,
              h,
              getPhase_ph(p, h)));

      annotation (Inline=true, Documentation(info="<html>
<p>This function calculates the Kelvin temperature of R134a from the state variables p (absolute pressure) and h (specific enthalpy). The temperature is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>

<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)h-Diagram-R134a.png\"/></p>

</html>"));
    end temperature_ph;

    redeclare function extends temperature
      "Temperature as function of pressure and specific enthalpy | use setState_phX function for input"

    algorithm
      T := state.T;

      annotation (Inline=true, Documentation(info="<html>
<p>This function calculates the Kelvin temperature of R134a from the state record (e.g., use setState_phX function for input). The temperature is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)h-Diagram-R134a.png\"/></p>
</html>"));
    end temperature;

    redeclare function extends pressure "Pressure w.r.t. thermodynamic state"
    algorithm
      p := state.p;
      annotation (Inline=true, Documentation(info="<html>
<p>This function is included for the sake of completeness.</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)h-Diagram-R134a.png\"/></p>
</html>"));
    end pressure;

    redeclare function extends specificInternalEnergy
      "Specific internal energy w.r.t. thermodynamic state"
    algorithm
      u := specificEnthalpy(state) - pressure(state)/density(state);

      annotation (Inline=true, Documentation(info="<html>
<p>This function calculates the specific internal energy of R134a from the state record (e.g., use setState_phX function for input). The specific internal energy is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)u-Diagram-R134a.png\"/></p>

</html>"));
    end specificInternalEnergy;

    redeclare function extends specificEnthalpy
      "Specific enthalpy w.r.t. thermodynamic state | use setState_phX function for input"

    algorithm
      h := state.h;

      annotation (Inline=true, Documentation(info="<html>
<p>This function is included for the sake of completeness.</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)h-Diagram-R134a.png\"/></p>
</html>"));
    end specificEnthalpy;

    redeclare function extends specificEntropy
      "Specific entropy w.r.t. thermodynamic state | use setState_phX function for input if necessary"

    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      Common.PhaseBoundaryProperties liq "Properties on liquid phase boundary";
      SaturationProperties sat "Saturation temperature and pressure";
      Common.PhaseBoundaryProperties vap "Properties on vapor phase boundary";

      SI.MassFraction x "Vapor quality";

    algorithm
      if getPhase_ph(state.p, state.h) == 2 then
        sat.psat := state.p;
        sat.Tsat := saturationTemperature(state.p);
        liq := R134a_liqofdT(T=state.T);
        vap := R134a_vapofdT(T=state.T);
        x := if liq.h <> vap.h then (state.h - liq.h)/(vap.h - liq.h) else if
          state.h >= vap.h then 1 else 0;
        s := liq.s + x*(vap.s - liq.s);
      else
        f := f_R134a(state.d, state.T);
        s := R134aData.R_s*(f.tau*f.ftau - f.f);
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the specific entropy of R134a from the state record (e.g., use setState_phX function for input). The specific entropy is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)s-Diagram-R134a.png\"/></p>
</html>"));
    end specificEntropy;

    redeclare function extends saturationTemperature
      "Saturation temperature in two-phase region"

    protected
      constant Real T_coef[:, :]=R134aData.Tcoef
        "Coefficients of cubic spline for Tsat(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      T := Common.CubicSplineEval(localx, T_coef[int, :]);

      // annotation(smoothOrder=5);
      annotation (derivative=saturationTemperature_der_p, Documentation(info="<html>
<p>This function calculates the saturation temperature of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)Tsat-Diagram-R134a.png\"/></p>
</html>"));
    end saturationTemperature;

    redeclare function extends saturationTemperature_derp
      "Derivative of saturation temperature in two-phase region"

    protected
      constant Real T_coef[:, :]=R134aData.Tcoef
        "Coefficients of cubic spline for Tsat(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dTp := Common.CubicSplineDerEval(localx, T_coef[int, :])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of saturation temperature of R134a with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.saturationTemperature\"> saturatuionTemperature</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end saturationTemperature_derp;

    function saturationTemperature_der_p
      "Time derivative of saturation temperature in two-phase region"
      extends Modelica.Icons.Function;

      input SI.AbsolutePressure p "Pressure";
      input Real der_p "Time derivative of pressure";
      output Real der_Tsat "Time derivative of saturation temperature";
    protected
      constant Real T_coef[:, :]=R134aData.Tcoef
        "Coefficients of cubic spline for Tsat(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_Tsat := Common.CubicSplineDerEval(localx, T_coef[int, :])/R134aData.data.FPCRIT
        *der_p;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of saturation temperature of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.saturationTemperature\"> saturatuionTemperature</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end saturationTemperature_der_p;

    redeclare function extends bubbleDensity
      "Density of liquid phase w.r.t. saturation pressure | use setSat_p function for input"

    protected
      constant Real dl_coef[:, :]=R134aData.dlcoef
        "Coefficients of cubic spline for d_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dl := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dl_coef[int, 1
        :4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dBubbleDensity_dPressure_der_sat, Documentation(
            info="<html>
<p>This function calculates the liquid phase density of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end bubbleDensity;

    redeclare function extends dBubbleDensity_dPressure
      "Derivative of liquid density in two-phase region w.r.t. pressure"

    protected
      constant Real dl_coef[:, :]=R134aData.dlcoef
        "Coefficients of cubic spline for d_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      ddldp := R134aData.data.FDCRIT*Common.CubicSplineDerEval(localx, dl_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of liquid density of R134a in the two-phase region with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleDensity\"> bubbleDensity</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleDensity_dPressure;

    function dBubbleDensity_dPressure_der_sat
      "Time derivative of liquid density in two-phase region w.r.t. pressure"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_ddldp
        "Time derivative of liquid density in two-phase region w.r.t. pressure";
    protected
      constant Real dl_coef[:, :]=R134aData.dlcoef
        "Coefficients of cubic spline for d_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_ddldp := R134aData.data.FDCRIT*Common.CubicSplineDerEval(localx,
        dl_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of liquid density of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleDensity\"> bubbleDensity</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleDensity_dPressure_der_sat;

    redeclare function extends dewDensity
      "Density of vapor phase w.r.t. saturation pressure | use setSat_p function for input"

    protected
      constant Real dv_coef[:, :]=R134aData.dvcoef
        "Coefficients of cubic spline for d_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dv := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dv_coef[int, 1
        :4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dDewDensity_dPressure_der_sat, Documentation(info="<html>
<p>This function calculates the vapor phase density of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dewDensity;

    redeclare function extends dDewDensity_dPressure
      "Derivative of vapor density in two-phase region w.r.t. pressure"

    protected
      constant Real dv_coef[:, :]=R134aData.dvcoef
        "Coefficients of cubic spline for d_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      ddvdp := R134aData.data.FDCRIT*Common.CubicSplineDerEval(localx, dv_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of vapor density of R134a in two-phase region with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewDensity\"> dewDensity</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewDensity_dPressure;

    function dDewDensity_dPressure_der_sat
      "Time derivative of vapor density in two-phase region w.r.t. pressure"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_ddvdp
        "Time derivative of vapor density in two-phase region w.r.t. pressure";
    protected
      constant Real dv_coef[:, :]=R134aData.dvcoef
        "Coefficients of cubic spline for d_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_ddvdp := R134aData.data.FDCRIT*Common.CubicSplineDerEval(localx,
        dv_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of vapor density of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewDensity\"> dewDensity</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewDensity_dPressure_der_sat;

    redeclare function extends bubbleEnthalpy
      "Specific enthalpy of liquid phase w.r.t. saturation pressure | use setSat_p function for input"

    protected
      constant Real hl_coef[:, :]=R134aData.hlcoef
        "Coefficients of cubic spline for h_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      hl := R134aData.data.HCRIT*Common.CubicSplineEval(localx, hl_coef[int, 1:
        4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dBubbleEnthalpy_dPressure_der_sat, Documentation(
            info="<html>
<p>This function calculates the liquid phase enthalpy of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end bubbleEnthalpy;

    redeclare function extends dBubbleEnthalpy_dPressure
      "Derivative of liquid specific enthalpy in two-phase region w.r.t. pressure"

    protected
      constant Real hl_coef[:, :]=R134aData.hlcoef
        "Coefficients of cubic spline for h_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dhldp := R134aData.data.HCRIT*Common.CubicSplineDerEval(localx, hl_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of liquid enthalpy of R134a with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleEnthalpy\"> bubbleEnthalpy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleEnthalpy_dPressure;

    function dBubbleEnthalpy_dPressure_der_sat
      "Time derivative of liquid specific enthalpy in two-phase region w.r.t. pressure"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_dhldp
        "Time derivative of liquid specific enthalpy in two-phase region w.r.t. pressure";
    protected
      constant Real hl_coef[:, :]=R134aData.hlcoef
        "Coefficients of cubic spline for h_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_dhldp := R134aData.data.HCRIT*Common.CubicSplineDerEval(localx,
        hl_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of liquid specific enthalpy of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleEnthalpy\"> bubbleEnthalpy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleEnthalpy_dPressure_der_sat;

    redeclare function extends dewEnthalpy
      "Specific enthalpy of vapor phase w.r.t. saturation pressure | use setSat_p function for input"

    protected
      constant Real hv_coef[:, :]=R134aData.hvcoef
        "Coefficients of cubic spline for h_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      hv := R134aData.data.HCRIT*Common.CubicSplineEval(localx, hv_coef[int, 1:
        4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dDewEnthalpy_dPressure_der_sat, Documentation(info=
             "<html>
<p>This function calculates the vapor phase enthalpy of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dewEnthalpy;

    redeclare function extends dDewEnthalpy_dPressure
      "Derivative of vapor specific enthalpy in two-phase region w.r.t. pressure"

    protected
      constant Real hv_coef[:, :]=R134aData.hvcoef
        "Coefficients of cubic spline for h_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dhvdp := R134aData.data.HCRIT*Common.CubicSplineDerEval(localx, hv_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of vapor enthalpy of R134a in the two-phase region with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewEnthalpy\"> dewEnthalpy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewEnthalpy_dPressure;

    function dDewEnthalpy_dPressure_der_sat
      "Time derivative of vapor specific enthalpy in two-phase region w.r.t. pressure"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_dhvdp
        "Derivative of vapor specific enthalpy in two-phase region w.r.t. pressure";
    protected
      constant Real hv_coef[:, :]=R134aData.hvcoef
        "Coefficients of cubic spline for h_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_dhvdp := R134aData.data.HCRIT*Common.CubicSplineDerEval(localx,
        hv_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of vapor enthalpy of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewEnthalpy\"> dewEnthalpy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewEnthalpy_dPressure_der_sat;

    redeclare function extends dewEntropy
      "Specific entropy of vapor phase w.r.t. saturation pressure | use setSat_p function for input"

    protected
      constant Real sv_coef[:, :]=R134aData.svcoef
        "Coefficients of cubic spline for s_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      sv := R134aData.data.SCRIT*Common.CubicSplineEval(localx, sv_coef[int, 1:
        4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dDewEntropy_dPressure_der_sat, Documentation(info="<html>
<p>This function calculates the vapor phase entropy of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dewEntropy;

    function dDewEntropy_dPressure
      "Derivative of vapor specific entropy in two-phase region w.r.t. pressure | use setState_phX function for input"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      output Real dsvdp
        "Derivative of vapor specific entropy in two-phase region w.r.t. pressure";
    protected
      constant Real sv_coef[:, :]=R134aData.svcoef
        "Coefficients of cubic spline for s_vap(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dsvdp := R134aData.data.SCRIT*Common.CubicSplineDerEval(localx, sv_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of vapor entropy of R134a with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewEntropy\"> dewEntropy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewEntropy_dPressure;

    function dDewEntropy_dPressure_der_sat
      "Time derivative of vapor specific entropy in two-phase region w.r.t. pressure | use setState_phX function for input"
      extends Modelica.Icons.Function;

      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_dsvdp
        "Derivative of vapor specific entropy in two-phase region w.r.t. pressure";
    protected
      constant Real sv_coef[:, :]=R134aData.svcoef
        "Coefficients of cubic spline for s_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_dsvdp := R134aData.data.SCRIT*Common.CubicSplineDerEval(localx,
        sv_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of vapor specific entropy of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.dewEntropy\"> dewEntropy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dDewEntropy_dPressure_der_sat;

    redeclare function extends bubbleEntropy
      "Specific entropy of liquid phase w.r.t. saturation pressure | use setSat_p function for input"
    protected
      constant Real sl_coef[:, :]=R134aData.slcoef
        "Coefficients of cubic spline for s_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      sl := R134aData.data.SCRIT*Common.CubicSplineEval(localx, sl_coef[int, 1:
        4]);

      // annotation(smoothOrder=5);
      annotation (derivative=dBubbleEntropy_dPressure_der_sat, Documentation(
            info="<html>
<p>This function calculates the liquid phase entropy of R134a from the state variable p (absolute pressure). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from
the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end bubbleEntropy;

    function dBubbleEntropy_dPressure
      "Derivative of liquid specific entropy in two-phase region w.r.t. pressure | use setState_phX function for input"
      extends Modelica.Icons.Function;
      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      output Real dsldp
        "Derivative of liquid specific entropy in two-phase region w.r.t. pressure";
    protected
      constant Real sl_coef[:, :]=R134aData.slcoef
        "Coefficients of cubic spline for s_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      dsldp := R134aData.data.SCRIT*Common.CubicSplineDerEval(localx, sl_coef[
        int, 1:4])/R134aData.data.FPCRIT;

      annotation (Documentation(info="<html>
<p>This function calculates the derivative of liquid entropy of R134a with regard to the state variable p (absolute pressure). The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleEntropy\"> bubbleEntropy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleEntropy_dPressure;

    function dBubbleEntropy_dPressure_der_sat
      "Time derivative of liquid specific entropy in two-phase region w.r.t. pressure | use setState_phX function for input"
      extends Modelica.Icons.Function;
      input SaturationProperties sat
        "Saturation properties | pressure is used for interpolation";
      input SaturationProperties der_sat "Derivative of saturation properties";
      output Real der_dsldp
        "Derivative of liquid specific entropy in two-phase region w.r.t. pressure";
    protected
      constant Real sl_coef[:, :]=R134aData.slcoef
        "Coefficients of cubic spline for s_liq(p)";
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      pred := min(sat.psat/R134aData.data.FPCRIT, 1.0);
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      der_dsldp := R134aData.data.SCRIT*Common.CubicSplineDerEval(localx,
        sl_coef[int, 1:4])/R134aData.data.FPCRIT*der_sat.psat;

      annotation (Documentation(info="<html>
<p>This function calculates the time derivative of liquid specific entropy of R134a with regard to the time derivative of p. The non-derivative function is <a href=\"modelica://Modelica.Media.R134a.R134a_ph.bubbleEntropy\"> bubbleEntropy</a>.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
</html>"));
    end dBubbleEntropy_dPressure_der_sat;

    redeclare function extends saturationPressure
      "Saturation pressure w.r.t. temperature"

    protected
      constant Real pt_coef[:, :]=R134aData.ptcoef
        "Coefficients of cubic spline for psat(T)";
      constant Real T_breaks[:]=R134aData.Tbreaks
        "Grid points of reduced pressure";
      Real Tred "Reduced temperature";
      Integer int "Interval number";
      Integer error "Interval for spline interpolation not found";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
    algorithm
      Tred := T/R134aData.data.FTCRIT;
      (int,error) := Common.FindInterval(Tred, T_breaks);
      localx := Tred - T_breaks[int];
      p := R134aData.data.FPCRIT*Common.CubicSplineEval(localx, pt_coef[int, :]);

      annotation (smoothOrder=5, Documentation(info="<html>
<p>This function calculates the saturation pressure of R134a from the state variable T (temperature). It is modelled by cubic splines which are fitted with non-equidistant grid points derived from the fundamental equation of state of Tillner-Roth and Baehr (1994) and the Maxwell criteria.
</p>
<h4> Restrictions</h4>
<p>It is only valid in the two-phase region (i.e., p<sub>triple</sub> &le; p &le; p<sub>crit</sub> ).
</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)Tsat-Diagram-R134a.png\"/></p>
</html>"));
    end saturationPressure;

    redeclare function extends specificHeatCapacityCp
      "Specific heat capacity at constant pressure | turns infinite in two-phase region! | use setState_phX function for input"

    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";

    algorithm
      f := f_R134a(state.d, state.T);
      cp := if getPhase_ph(state.p, state.h) == 2 then 0 else R134aData.R_s*(-f.tau
        *f.tau*f.ftautau + (f.delta*f.fdelta - f.delta*f.tau*f.fdeltatau)^2/(2*
        f.delta*f.fdelta + f.delta*f.delta*f.fdeltadelta));

      annotation (Documentation(info="<html>
<p>This function calculates the specific heat capacity of R134a at <strong>constant pressure</strong> from the state record (e.g., use setState_phX function for input). The specific heat capacity is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)cp-Diagram-R134a.png\"/></p>
</html>"));
    end specificHeatCapacityCp;

    redeclare function extends specificHeatCapacityCv
      "Specific heat capacity at constant volume | use setState_phX function for input"

    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      Common.PhaseBoundaryProperties liq "Properties on liquid phase boundary";
      SaturationProperties sat "Saturation temperature and pressure";
      Common.PhaseBoundaryProperties vap "Properties on vapor phase boundary";

      SI.MassFraction x "Vapor quality";

    algorithm
      if getPhase_ph(state.p, state.h) == 2 then
        sat.psat := state.p;
        sat.Tsat := saturationTemperature(state.p);
        liq := R134a_liqofdT(T=state.T);
        vap := R134a_vapofdT(T=state.T);
        x := if liq.h <> vap.h then (state.h - liq.h)/(vap.h - liq.h) else if
          state.h >= vap.h then 1 else 0;
        cv := Common.cv2Phase(
              liq=liq,
              vap=vap,
              x=x,
              T=state.T,
              p=state.p);
      else
        f := f_R134a(state.d, state.T);
        cv := R134aData.R_s*(-f.tau*f.tau*f.ftautau);
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the specific heat capacity of R134a at <strong>constant volume</strong> from the state record (e.g., use setState_phX function for input). The specific heat capacity is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<p>
Please note, that the function can also be called in the two-phase region, but the output is not continuous for a phase transition (see Tillner-Roth and Baehr, 1994). Values in two-phase region are considerably higher than in one-phase domain. The following figure just shows one-phase properties.
</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)cv-Diagram-R134a.png\"/></p>
</html>"));
    end specificHeatCapacityCv;

    redeclare function extends dynamicViscosity
      "Dynamic viscosity w.r.t. temperature and density | use setState_phX function for input"

    protected
      Real omega_log "Log of collision integral";
      Real omega "Collision integral";

      constant Real K=0.021357 "Constant for low density term eta_star";
      constant SI.Length sigma=0.50647e-09 "Hard-sphere diameter";
      constant SI.Temperature epsilon_k=288.82 "Empirical factor";
      constant Real a[5]={2.218816e-01,-5.079322e-01,1.285776e-01,-8.328165e-02,
          -2.713173e-02} "Coefficients for term of collision integral";
      constant Real b[13]={-1.7999496,4.6692621e+01,-5.3460794e+02,
          3.3604074e+03,-1.3019164e+04,3.3414230e+04,-5.8711743e+04,
          7.1426686e+04,-5.9834012e+04,3.3652741e+04,-1.2027350e+04,
          2.4348205e+03,-2.0807957e+02}
        "Coefficients for term of 2nd viscosity virial coefficient";
      constant Real c[6]={-0.331249e-01,-0.468509e-03,0.156983,3.073830,-0.306398,
          0.215221} "Coefficients for term of residual viscosity";
      constant Real DCRIT_mol=4.9788 "Critical density in mol/l";
      Real d_red "Reduced density";
      Real B_eta "2nd viscosity virial coeff.";
      Real E "Temperature contribution to residual viscosity";
      Real eta_res "Residual part";
      Real eta_star "Dilute part";

    algorithm
      omega_log := 0;
      for i in 1:5 loop
        omega_log := omega_log + a[i]*(Modelica.Math.log(state.T/epsilon_k))^(i
           - 1);
      end for;
      omega := Modelica.Math.exp(omega_log);
      eta_star := (K*sqrt(R134aData.data.MM*1000))/((sigma*1e+09)^2*omega)*sqrt(
        state.T);

      d_red := state.d/R134aData.data.DCRIT;
      E := 1 + c[3]*state.T/R134aData.data.TCRIT;
      B_eta := 0;
      for i in 1:13 loop
        B_eta := B_eta + b[i]*(sqrt(state.T/epsilon_k))^(i - 1);
      end for;
      B_eta := B_eta*602.2137*(sigma)^3*DCRIT_mol;

      eta_res := (c[1] + B_eta*eta_star)*d_red + c[2]*d_red^2 + (c[5] + c[6]*
        d_red)/(c[4]*E - d_red) - c[5]/(c[4]*E);

      eta := (eta_star + eta_res*1e3)*1e-06;

      annotation (Documentation(info="<html>
<p>This function calculates the dynamic viscosity of R134a from the state record (e.g., use setState_phX function for input). The dynamic viscosity is modelled by the corresponding states method of Klein, McLinden and Laesecke (1997).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
<h4>References</h4>
<dl><dt>Klein, McLinden and Laesecke: </dt>
<dd><strong>An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures</strong>.
Int. J. Refrig., Vol. 20, No.3, pp. 208-217, 1997.</dd>
</dl>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)eta-Diagram-R134a.png\"/></p>
</html>"));
    end dynamicViscosity;

    redeclare function extends thermalConductivity
      "Thermal conductivity w.r.t. thermodynamic state | use setState_phX function for input"

    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      Modelica.Media.Common.HelmholtzDerivs f_ref
        "Helmholtz derivatives for reference state";
      SI.ThermalConductivity lambda_dg
        "Dilute gas contribution to lambda";
      R134aData.CoeffsThermalConductivity coeff
        "Coefficients of thermal conductivity model";
      SI.ThermalConductivity lambda_reduced "Reduced lambda";
      SI.ThermalConductivity lambda_crit
        "Enhancement of lambda in the critical region";
      SI.ThermalConductivity chi_star "Correlation length";
      SI.ThermalConductivity chi_star_ref "Correlation length";
      SI.ThermalConductivity delta_chi "Chi_star - chi_star_ref";
      Real rho_molar "Molar density [mol/l]";
      Real dddp "Derivative of density w.r.t. pressure";
      Real dddp_ref "Derivative of density w.r.t. pressure for reference state";
      SI.Length xi "Correlation length";
      SI.SpecificHeatCapacity cp
        "Specific heat capacity at constant pressure";
      SI.SpecificHeatCapacity cv
        "Specific heat capacity at constant volume";
      SI.DynamicViscosity eta "Dynamic viscosity";
      SI.ThermalConductivity omega "Crossover function";
      SI.ThermalConductivity omega_0 "Crossover function";

    algorithm
      f := f_R134a(state.d, state.T);
      f_ref := f_R134a(state.d, coeff.T_ref);

      // dilute gas contribution
      lambda_dg := coeff.a_0 + coeff.a_1*state.T;

      // reduced lambda
      rho_molar := state.d/(R134aData.data.MM*1000);
      // [mol/L]
      lambda_reduced := 0;
      for i in 1:4 loop
        lambda_reduced := lambda_reduced + coeff.b[i]*(rho_molar/coeff.rho_crit)
          ^i;
      end for;
      lambda_reduced := lambda_reduced*coeff.lambda_reducing;

      // critical lambda
      dddp := 1/(f.R_s*f.T*f.delta*(2.0*f.fdelta + f.delta*f.fdeltadelta));
      chi_star := state.d*coeff.p_crit*1e3/((coeff.rho_crit*R134aData.data.MM*
        1000)^2)*dddp;
      dddp_ref := 1/(f_ref.R_s*f_ref.T*f_ref.delta*(2.0*f_ref.fdelta + f_ref.delta
        *f_ref.fdeltadelta));
      chi_star_ref := state.d*coeff.p_crit*1e3/((coeff.rho_crit*R134aData.data.MM
        *1000)^2)*dddp_ref;
      delta_chi := max(1e-10, (chi_star - chi_star_ref));
      xi := coeff.xi_0*(1/coeff.GAMMA*(delta_chi))^(coeff.nu/coeff.gamma);
      cp := R134aData.data.R_s*(-f.tau*f.tau*f.ftautau + (f.delta*f.fdelta - f.delta
        *f.tau*f.fdeltatau)^2/(2*f.delta*f.fdelta + f.delta*f.delta*f.fdeltadelta));
      eta := dynamicViscosity(state=state);
      cv := specificHeatCapacityCv(state=state);
      omega := 2/Modelica.Constants.pi*(((cp - cv)/cp)*Modelica.Math.atan(coeff.q_d
        *xi) + cv/cp*coeff.q_d*xi);
      omega_0 := 2/Modelica.Constants.pi*(1 - Modelica.Math.exp(-1/((coeff.q_d*
        xi)^(-1) + 1/3*(coeff.q_d*xi*coeff.rho_crit/(state.d/(R134aData.data.MM
        *1000)))^2)));
      lambda_crit := state.d*cp*(1.03*Modelica.Constants.k*state.T)/(6*Modelica.Constants.pi
        *eta*xi)*(omega - omega_0);

      // conclusion
      lambda := max(lambda_dg + lambda_reduced + lambda_crit, 1e-8);

      annotation (Documentation(info="<html>
<p>This function calculates the thermal conductivity of R134a from the state record (e.g., use setState_phX function for input). The thermal conductivity is modelled by the corresponding states model of McLinden, Klein. and Perkins (2000).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
<h4>References</h4>
<dl><dt>McLinden, Klein. and Perkins: </dt>
<dd><strong>An extended corresponding states model for the thermal conductivity
of refrigerants and refrigerant mixtures</strong>.
Int. J. Refrig., 23 (2000) 43-63.</dd>
</dl>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)lambda-Diagram-R134a.png\"/></p>
</html>"));
    end thermalConductivity;

    redeclare function extends surfaceTension
      "Surface tension as a function of temperature (below critical point)"

    protected
      Real tau "Reduced temperature";
      R134aData.CoeffsSurfaceTension coeff "Polynomial coefficients";
      SI.Temperature Tc=374.21 "Critical temperature";

    algorithm
      if sat.Tsat > Tc then
        tau := 0.0;
        sigma := 0.0;
      else
        tau := 1.0 - sat.Tsat/Tc;
        sigma := 0.0;
        for i in 1:coeff.nterm loop
          sigma := sigma + coeff.sigmak[i]*tau^coeff.sigexp[i];
        end for;
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the surface tension of R134a from the saturation record (e.g., use setSat_T function for input). The property is modelled by an approach of Okada and Higashi (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in two-phase region.
</p>
<h4>References</h4>
<dl><dt>Okada and Higashi: </dt>
<dd><strong>Surface tension correlation of HFC-134a and HCFC-123</strong>.
Proceedings of the Joint Meeting of IIR Commissions B1, B2, E1, and E2, Padua, Italy, pp. 541-548, 1994.</dd>
</dl>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/Tsigma-Diagram-R134a.png\"/></p>
</html>"));
    end surfaceTension;

    redeclare function extends velocityOfSound
      "Velocity of sound w.r.t. thermodynamic state (only valid for one-phase)"
    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    algorithm

      if getPhase_ph(state.p, state.h) == 2 then
        a := 0;
        // assert(getPhase_ph(state.p, state.h)==1, "Function for velocity of sound is only valid for one-phase regime!");
      else
        f := f_R134a(state.d, state.T);
        a := abs(R134aData.data.R_s*state.T*(2*f.delta*f.fdelta + f.delta*f.delta
          *f.fdeltadelta - ((f.delta*f.fdelta - f.delta*f.tau*f.fdeltatau)*(f.delta
          *f.fdelta - f.delta*f.tau*f.fdeltatau))/(f.tau*f.tau*f.ftautau)))^0.5;
      end if;
      annotation (Documentation(info="<html>
<p>This function calculates the velocity of sound of R134a from the state record (e.g., use setState_phX function for input). The velocity of sound is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
<p><img src=\"modelica://Modelica/Resources/Images/Media/R134a/log(p)a-Diagram-R134a.png\"/></p>
</html>"));
    end velocityOfSound;

    redeclare function extends isothermalCompressibility
      "Isothermal compressibility w.r.t. thermodynamic state (only valid for one-phase)"
    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    algorithm
      if getPhase_ph(state.p, state.h) == 2 then
        kappa := 0;
        // assert(getPhase_ph(state.p, state.h)==1, "Function for isothermal compressibility is only valid for one-phase regime!");
      else
        f := f_R134a(state.d, state.T);
        kappa := 1/(state.d*R134aData.data.R_s*state.T*f.delta*(2.0*f.fdelta + f.delta
          *f.fdeltadelta));
      end if;
      annotation (Documentation(info="<html>
<p>This function calculates the isothermal compressibility of R134a from the state record (e.g., use setState_phX function for input). The isothermal compressibility is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
</html>"));
    end isothermalCompressibility;

    redeclare function extends isobaricExpansionCoefficient
      "Isobaric expansion coefficient w.r.t. thermodynamic state (only valid for one-phase)"
    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    algorithm
      if getPhase_ph(state.p, state.h) == 2 then
        beta := 0;
        // assert(getPhase_ph(state.p, state.h)==1, "Function for isobaric expansion coefficient is only valid for one-phase regime!");
      else
        f := f_R134a(state.d, state.T);
        beta := R134aData.data.R_s*state.d*f.delta*(f.fdelta - f.tau*f.fdeltatau)
          *isothermalCompressibility(state);
      end if;
      annotation (Documentation(info="<html>
<p>This function calculates the isobaric expansion coefficient of R134a from the state record (e.g., use setState_phX function for input). The isobaric expansion coefficient is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
</html>"));
    end isobaricExpansionCoefficient;

    redeclare function extends isentropicExponent
      "Isentropic exponent gamma w.r.t. thermodynamic state | not defined in two-phase region | use setState_phX function for input"

    algorithm
      gamma := density(state)/(if pressure(state) > 1e-6 then pressure(state)
         else 1e-6)*velocityOfSound(state)^2;

      annotation (Inline=true, Documentation(info="<html>
<p>This function calculates the isentropic exponent of R134a from the state record (e.g., use setState_phX function for input). The isentropic exponent is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).</p>
<h4> Restrictions</h4>
<p>This property is only defined in one-phase region.
</p>
</html>"));
    end isentropicExponent;

    redeclare function extends specificGibbsEnergy
      "Specific gibbs energy w.r.t. thermodynamic state"
    algorithm
      g := state.h - state.T*specificEntropy(state);
      annotation (Documentation(info="<html>
<p>This function calculates the specific Gibbs energy of R134a from the state record (e.g., use setState_phX function for input). The isentropic exponent is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).
</p>
</html>"));
    end specificGibbsEnergy;

    redeclare function extends specificHelmholtzEnergy
      "Helmholtz energy w.r.t. thermodynamic state"
    algorithm
      f := state.h - state.p/state.d - state.T*specificEntropy(state);
      annotation (Documentation(info="<html>
<p>This function calculates the specific Helmholtz energy of R134a from the state record (e.g., use setState_phX function for input). The Helmholtz energy is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994).
</p>
</html>"));
    end specificHelmholtzEnergy;

    redeclare function extends density_derh_p
      "Density derivative by specific enthalpy | use setState_phX function for input"

    protected
      Common.InverseDerivatives_rhoT derivs
        "Inverse derivatives for density and temperature";

    algorithm
      derivs := derivsOf_ph(
            state.p,
            state.h,
            getPhase_ph(p=state.p, h=state.h));
      ddhp := if getPhase_ph(p=state.p, h=state.h) == 2 then -state.d*state.d/(
        derivs.dpT*state.T) else -state.d*state.d*derivs.pt/(state.d*state.d*
        derivs.pd*derivs.cv + state.T*derivs.pt^2);

      annotation (Documentation(info="<html>
<p>This function calculates the density derivative w.r.t. specific enthalpy at constant pressure of R134a (e.g., use setState_phX function for input). The derivative is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994). It can be used for manual state transformations (e.g. from density to specific enthalpy).
</p>
</html>"));
    end density_derh_p;

    redeclare function extends density_derp_h
      "Density derivative by pressure | use setState_phX function for input"

    protected
      Common.InverseDerivatives_rhoT derivs
        "Inverse derivatives for density and temperature";

    algorithm
      derivs := derivsOf_ph(
            state.p,
            state.h,
            getPhase_ph(p=state.p, h=state.h));
      ddph := if getPhase_ph(p=state.p, h=state.h) == 2 then state.d*(state.d*
        derivs.cv/derivs.dpT + 1)/(derivs.dpT*state.T) else (state.d*(derivs.cv
        *state.d + derivs.pt))/(state.d*state.d*derivs.pd*derivs.cv + state.T*
        derivs.pt^2);

      annotation (Documentation(info="<html>
<p>This function calculates the density derivative w.r.t. absolute pressure at constant specific enthalpy of R134a (e.g., use setState_phX function for input). The derivative is modelled by the fundamental equation of state of Tillner-Roth and Baehr (1994). It can be used for manual state transformations (e.g. from density to pressure).
</p>
</html>"));
    end density_derp_h;

    redeclare function extends isentropicEnthalpy
      "Isentropic enthalpy of downstream pressure and upstream thermodynamic state (specific entropy)"
    algorithm
      h_is := specificEnthalpy_psX(
            p_downstream,
            specificEntropy(refState),
            reference_X);
      annotation (Documentation(info="<html>
<p>
This function calculates the specific enthalpy of R134a for an isentropic pressure change
from refState.p to p_downstream (e.g., use setState_phX function for input of refState).
</p>

<p>
The function can be used for instance to calculate an isentropic efficiency
of a compressor or calculate the power consumption (obtained from the isentropic enthalpy)
for a given efficiency.
</p>

<p>
Example:
</p>
<blockquote><pre>
  Medium.AbsolutePressure p_downstream=10e5;
  Medium.SpecificEnthalpy h_downstream=4.1e5;
  Medium.AbsolutePressure p_upstream=3e5;
  Medium.SpecificEnthalpy h_upstream=4.0e5;

  // Isentropic efficiency of a compressor:
  Real eta_is;

equation

  h_is = isentropicEnthalpy(p_downstream, Medium.setState_phX(p_upstream, h_upstream));

  eta_is = (h_is-h_upstream)/(h_downstream - h_upstream);
</pre></blockquote>

<h4>Restrictions</h4>
<p>
The isentropic efficiency function should not be applied in liquid region.
</p>
</html>"));
    end isentropicEnthalpy;

    function derivsOf_ph
      "Derivatives required for inversion of temperature and density functions"

      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Integer phase "Number of phases";
      output Common.InverseDerivatives_rhoT derivs
        "Inverse derivatives for density and temperature";

    protected
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      SaturationProperties sat "Saturation temperature and pressure";
      Common.PhaseBoundaryProperties liq "Properties on liquid phase boundary";
      Common.PhaseBoundaryProperties vap "Properties on vapor phase boundary";
      Modelica.Media.Common.NewtonDerivatives_ph newder "Newton derivatives";
      Real x "Vapor quality";
      Real dxv "1/(v_vap - v_liq)";
    algorithm
      derivs.p := p;
      derivs.h := h;
      derivs.phase := getPhase_ph(p, h);

      sat.psat := p;
      sat.Tsat := saturationTemperature(p);

      (derivs.rho,derivs.T) := dt_ph(p=p, h=h);

      if derivs.phase == 2 then
        liq := R134a_liqofdT(T=derivs.T);
        vap := R134a_vapofdT(T=derivs.T);
        x := if liq.h <> vap.h then (h - liq.h)/(vap.h - liq.h) else if h >=
          vap.h then 1 else 0;
        derivs.cv := Common.cv2Phase(
              liq=liq,
              vap=vap,
              x=x,
              p=p,
              T=derivs.T);
        dxv := if (liq.d <> vap.d) then liq.d*vap.d/(liq.d - vap.d) else 0.0;
        derivs.dpT := (vap.s - liq.s)*dxv;
      else
        f := f_R134a(d=derivs.rho, T=derivs.T);
        f.d := derivs.rho;
        f.T := derivs.T;
        f.R_s := R134aData.R_s;
        newder := Modelica.Media.Common.Helmholtz_ph(f=f);
        derivs.cv := -f.R_s*(f.tau*f.tau*f.ftautau);
        derivs.pd := newder.pd;
        derivs.pt := newder.pt;
        //derivs.dpT := 0;
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the derivatives required for an inversion of temperature and density function.
</p>
</html>"));
    end derivsOf_ph;

    function dt_ph
      "Density and temperature w.r.t. pressure and specific enthalpy"

      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      output Density d "Density";
      output Temperature T "Temperature";
    protected
      SaturationProperties sat(psat=p, Tsat=0)
        "Saturation temperature and pressure";
      SI.Pressure delp=1.0e-2 "Relative error in p in iteration";
      SI.SpecificEnthalpy delh=1.0e-2
        "Relative error in h in iteration";
      SI.SpecificEnthalpy hvapor=dewEnthalpy(sat=sat)
        "Vapor enthalpy";
      SI.SpecificEnthalpy hliquid=bubbleEnthalpy(sat=sat)
        "Liquid enthalpy";
      Integer error "Iteration error";
      Real x "Vapor quality";
      Real vvap "Specific volume vapor";
      Real vliq "Specific volume liquid";
    algorithm
      if ((h < hliquid) or (h > hvapor) or (p > R134aData.data.FPCRIT)) then
        (d,T,error) := Modelica.Media.R134a.R134a_ph.dtofphOnePhase(
              p,
              h,
              delp,
              delh);
      else
        vvap := 1/dewDensity(sat=sat);
        vliq := 1/bubbleDensity(sat=sat);
        x := (h - hliquid)/(hvapor - hliquid);
        error := 0;
        T := saturationTemperature(p);
        d := 1/(vliq + x*(vvap - vliq));
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the density and temperature of R134a from absolute pressure and specific enthalpy. In one-phase region the function calls the fundamental Helmholtz equation of Tillner-Roth (1994). In two-phase the density and temperature is computed from cubic splines for saturated pressure, liquid and vapor density.
</p>
<h4>Restrictions</h4>
The function cannot be inverted in a numerical way. Please use functions <a href=\"modelica://Modelica.Media.R134a.R134a_ph.rho_props_ph\">rho_props_ph</a> and <a href=\"modelica://Modelica.Media.R134a.R134a_ph.T_props_ph\">T_props_ph</a> for this purpose.
</html>"));
    end dt_ph;

    function dtofphOnePhase
      "Density and temperature w.r.t. pressure and specific enthalpy in one-phase region"

      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Enthalpy";
      input AbsolutePressure delp "Absolute error in p in iteration";
      input SpecificEnthalpy delh "Absolute error in h in iteration";

      output Density d "Density";
      output Temperature T "Temperature";
      output Integer error "1 if did not converged";

    protected
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      constant Real hl_coef[:, 4]=R134aData.hlcoef
        "Coefficients of cubic spline for h_liq(p)";
      constant Real dl_coef[:, 4]=R134aData.dlcoef
        "Coefficients of cubic spline for rho_liq(p)";
      constant Real T_coef[:, 4]=R134aData.Tcoef
        "Coefficients of cubic spline for Tsat(p)";
      constant Real dv_coef[:, 4]=R134aData.dvcoef
        "Coefficients of cubic spline for rho_vap(p)";

      SI.SpecificEnthalpy hl "Liquid enthalpy";
      Boolean liquid "Is liquid";
      Boolean supercritical "Is supercritical";
      Integer int "Interval number";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
      Integer i "Newton iteration number";
      Real dh "Difference in h";
      Real dp "Difference in p";
      Real damping "Damping constant";
      Real det "Determinant";
      Real deld "Density change";
      Real delt "Temperature change";
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
      Modelica.Media.Common.NewtonDerivatives_ph nDerivs "Newton derivatives";
      Boolean found "Iteration converged";
    algorithm
      i := 0;
      error := 0;
      found := false;
      damping := 1.0;
      //by default no damping
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      // set decent initial guesses for d and T
      supercritical := p > R134aData.data.FPCRIT;
      if supercritical then
        // iteration seems to work better if coming from high densities
        d := R134aData.data.FDCRIT*3.0;
        //      dTR.T := data.TCRIT + 10.0;
        // linear approximation that can be made generic
        T := 270.0 + 120.0*(h/R134aData.data.HCRIT);
      else
        liquid := h < 1.01*R134aData.data.HCRIT*Common.CubicSplineEval(localx,
          hl_coef[int, 1:4]);
        if liquid then
          damping := 0.3;
          //damping on the liquid side
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dl_coef[int,
            1:4])*1.02;
          T := Common.CubicSplineEval(localx, T_coef[int, 1:4]);
        else
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dv_coef[int,
            1:4])*0.95;
          T := Common.CubicSplineEval(localx, T_coef[int, 1:4]);
        end if;
      end if;

      // the Newton iteration
      while ((i < 50) and not found) loop
        f := f_R134a(d, T);
        // nDerivs are the symbolic derivatives needed in the iteration
        // for given d and T
        nDerivs := Modelica.Media.Common.Helmholtz_ph(f);
        dh := nDerivs.h - h;
        dp := nDerivs.p - p;
        if ((abs(dh) <= delh) and (abs(dp) <= delp)) then
          found := true;
          error := if not found then 1 else 0;
        end if;
        det := nDerivs.ht*nDerivs.pd - nDerivs.pt*nDerivs.hd;
        if abs(det) < 1e-10 then
          det := sign(det)*1e-10;
        end if;
        delt := (nDerivs.pd*dh - nDerivs.hd*dp)/det;
        deld := (nDerivs.ht*dp - nDerivs.pt*dh)/det;
        T := T - damping*delt;
        d := d - damping*deld;
        // Check for limit of state variables
        if T < R134aData.triple.TTRIPLE then
          T := R134aData.triple.TTRIPLE + 0.1;
        end if;
        if d <= 0.0 then
          d := R134aData.triple.DVTRIPLE;
        elseif d > 1.5*R134aData.triple.DLTRIPLE then
          d := R134aData.triple.DLTRIPLE;
        end if;
        i := i + 1;
      end while;

      annotation (Documentation(info="<html>
<p>This function calculates the density and temperature of R134a from absolute pressure and specific enthalpy in one-phase region. The function calls the fundamental Helmholtz equation of Tillner-Roth (1994) which is requiring density and temperature for input. Thus, a newton iteration is performed to determine density and temperature. The newton iteration stops if the inputs for pressure difference delp and specific enthalpy difference delh are larger than the actual differences derived from the newton iteration.
</p>
<h4>Restrictions</h4>
The function shall only be used for one-phase inputs since the fundamental equation is not valid for two-phase states.
</html>"));
    end dtofphOnePhase;

    function dtofpsOnePhase
      "Inverse iteration in one phase region (d,T) = f(p,s)"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEntropy s "Specific entropy";
      input AbsolutePressure delp "Absolute iteration accuracy";
      input SpecificEntropy dels "Absolute iteration accuracy";
      output Density d "Density";
      output Temperature T "Temperature";
      output Integer error "Error flag: trouble if different from 0";

    protected
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      constant Real dl_coef[:, 4]=R134aData.dlcoef
        "Coefficients of cubic spline for rho_liq(p)";
      constant Real dv_coef[:, 4]=R134aData.dvcoef
        "Coefficients of cubic spline for rho_vap(p)";
      constant Real sl_coef[:, 4]=R134aData.slcoef
        "Coefficients of cubic spline for s_liq(p)";
      constant Real sv_coef[:, 4]=R134aData.svcoef
        "Coefficients of cubic spline for s_vap(p)";
      constant Real T_coef[:, 4]=R134aData.Tcoef
        "Coefficients of cubic spline for Tsat(p)";
      Integer i "Newton iteration number";
      Real ds "Difference in s";
      Real dp "Difference in p";
      Real det "Determinant";
      Real deld "Density change";
      Real delt "Temperature change";
      Modelica.Media.Common.HelmholtzDerivs f
        "Dimensionless Helmholtz function and derivatives w.r.t. dimensionless d and T";
      Modelica.Media.Common.NewtonDerivatives_ps nDerivs "Newton derivatives";
      Boolean liquid "Is liquid";
      Boolean supercritical "Is supercritical";
      Boolean found "Iteration converged";
      Integer int "Interval number";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
      Real sl "Liquid entropy";
      Real sv "Vapor entropy";
    algorithm
      i := 0;
      error := 0;
      found := false;
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      // set decent initial guesses for d and T
      supercritical := p > R134aData.data.FPCRIT;
      if supercritical then
        d := R134aData.data.FDCRIT + 500.0;
        T := R134aData.data.FTCRIT + 10.0;
      else
        sl := R134aData.data.SCRIT*Common.CubicSplineEval(localx, sl_coef[int,
          1:4]);
        sv := R134aData.data.SCRIT*Common.CubicSplineEval(localx, sv_coef[int,
          1:4]);
        liquid := s < sl;
        if liquid then
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dl_coef[int,
            1:4])*1.1;
          //1.05
          T := Common.CubicSplineEval(localx, T_coef[int, 1:4])*0.9;
          //0.95
        else
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dv_coef[int,
            1:4])*0.8;
          //0.9
          T := Common.CubicSplineEval(localx, T_coef[int, 1:4])*1.1 + 0.5*(s -
            sv);
        end if;
      end if;

      while ((i < 100) and not found) loop
        f := f_R134a(d=d, T=T);
        nDerivs := Modelica.Media.Common.Helmholtz_ps(f);
        ds := nDerivs.s - s;
        dp := nDerivs.p - p;
        if ((abs(ds/s) <= dels) and (abs(dp/p) <= delp)) then
          found := true;
        end if;
        det := nDerivs.st*nDerivs.pd - nDerivs.pt*nDerivs.sd;
        delt := (nDerivs.pd*ds - nDerivs.sd*dp)/det;
        deld := (nDerivs.st*dp - nDerivs.pt*ds)/det;
        T := T - delt;
        d := d - deld;
        i := i + 1;
      end while;
      if not found then
        error := 1;
      end if;

      annotation (Documentation(info="<html>
<p>This function calculates the density and temperature of R134a from absolute pressure and specific entropy in one-phase region. The function calls the fundamental helmholtz equation of Tillner-Roth (1994) which is requiring density and temperature for input. Thus, a newton iteration is performed to determine density and temperature. The newton iteration stops if the inputs for pressure difference delp and specific entropy difference dels are larger than the actual differences derived from the newton iteration.
</p>
<h4>Restrictions</h4>
The function shall only be used for one-phase inputs since the fundamental equation is not valid for two-phase states. The iteration could fail for liquid states with high pressures.
</html>"));
    end dtofpsOnePhase;

    function f_R134a
      "Calculation of helmholtz derivatives by density and temperature"
      extends Modelica.Icons.Function;

      input Density d "Density";
      input Temperature T "Temperature";
      output Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    protected
      Real delta "Reduced density";
      Real tau "Reduced temperature";
      Modelica.Media.Common.HelmholtzDerivs fid "Helmholtz derivstives";

    algorithm
      delta := d/R134aData.data.DCRIT;
      tau := R134aData.data.TCRIT/T;
      fid := fid_R134a(delta=delta, tau=tau);
      f := fres_R134a(delta=delta, tau=tau);
      f.f := f.f + fid.f;
      f.fdelta := f.fdelta + fid.fdelta;
      f.fdeltadelta := f.fdeltadelta + fid.fdeltadelta;
      f.ftau := f.ftau + fid.ftau;
      f.ftautau := f.ftautau + fid.ftautau;
      f.d := d;
      f.T := T;
      f.R_s := R134aData.R_s;

      annotation (Documentation(info="<html>
This function adds the ideal gas contribution of the fundamental equation to the residual contribution and computes the helmholtz derivatives w.r.t. temperature and density.
</html>"));
    end f_R134a;

    function fid_R134a "Helmholtz coefficients of ideal part"
      extends Modelica.Icons.Function;

      input Real delta "Reduced density (delta=d/dcrit)";
      input Real tau "Reduced temperature (tau=Tcrit/T)";
      output Modelica.Media.Common.HelmholtzDerivs fid
        "Helmholtz derivatives of ideal part";
    protected
      Modelica.Media.R134a.R134aData.Ideal id "Ideal coefficients";
      Real atau=abs(tau) "|tau|";
      Real adelta=abs(delta) "|delta|";
    algorithm
      fid.delta := delta;
      fid.tau := tau;
      fid.f := Modelica.Math.log(adelta) + id.a[1] + id.a[2]*atau + id.a[3]*
        Modelica.Math.log(atau) + id.a[4]*atau^(-0.5) + id.a[5]*atau^(-0.75);
      fid.fdelta := 1.0/adelta;
      fid.fdeltadelta := -1.0/(adelta*adelta);
      fid.ftau := id.a[2] + id.a[3]/atau - 0.5*id.a[4]*atau^(-1.5) - 0.75*id.a[
        5]*atau^(-1.75);
      fid.ftautau := -id.a[3]/(atau*atau) + 0.75*id.a[4]*atau^(-2.5) + 1.3125*
        id.a[5]*atau^(-2.75);
      fid.fdeltatau := 0.0;
      fid.d := fid.delta*R134aData.data.DCRIT;
      fid.T := R134aData.data.TCRIT/fid.tau;
      fid.R_s := R134aData.R_s;

      annotation (Documentation(info="<html>
This function computes the ideal gas helmholtz derivatives of the fundamental equation of Tillner-Roth and Baehr for R134a (1994) w.r.t. to reduced temperature (tau=T_crit/T) and reduced density (delta=rho/rho_crit).
</html>"));
    end fid_R134a;

    function fres_R134a "Calculation of helmholtz derivatives"
      extends Modelica.Icons.Function;

      input Real delta "Reduced density (delta=d/dcrit)";
      input Real tau "Reduced temperature (tau=Tcrit/T)";
      output Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    protected
      Modelica.Media.R134a.R134aData.Residual res "Residual coefficient";
      Real k "Helping var";
      Real dc "Helping var";
      Real cdc "Helping var";
    algorithm
      f.tau := abs(tau);
      f.delta := abs(delta);
      f.f := 0.0;
      f.ftau := 0.0;
      f.fdelta := 0.0;
      f.ftautau := 0.0;
      f.fdeltadelta := 0.0;
      f.fdeltatau := 0.0;
      for i in 1:res.ns1 loop
        k := res.n[i]*f.delta^res.d[i]*f.tau^res.t[i];
        f.f := f.f + k;
        f.fdelta := f.fdelta + k*res.d[i];
        f.fdeltadelta := f.fdeltadelta + k*res.d[i]*(res.d[i] - 1.0);
        f.ftau := f.ftau + k*res.t[i];
        f.ftautau := f.ftautau + k*res.t[i]*(res.t[i] - 1.0);
        f.fdeltatau := f.fdeltatau + k*res.t[i]*res.d[i];
      end for;
      for i in res.ns1 + 1:21 loop
        dc := f.delta^res.c[i];
        cdc := res.c[i]*dc;
        k := Modelica.Math.exp(-dc)*res.n[i]*delta^res.d[i]*f.tau^res.t[i];
        f.f := f.f + k;
        f.fdelta := f.fdelta + k*(res.d[i] - cdc);
        f.fdeltadelta := f.fdeltadelta + k*((res.d[i] - cdc)*(res.d[i] - 1.0 -
          cdc) - res.c[i]*cdc);
        f.ftau := f.ftau + k*res.t[i];
        f.ftautau := f.ftautau + k*res.t[i]*(res.t[i] - 1.0);
        f.fdeltatau := f.fdeltatau + k*res.t[i]*(res.d[i] - cdc);
      end for;
      f.fdelta := f.fdelta/delta;
      f.fdeltadelta := f.fdeltadelta/(delta*delta);
      f.ftau := f.ftau/tau;
      f.ftautau := f.ftautau/(tau*tau);
      f.fdeltatau := f.fdeltatau/(delta*tau);
      f.d := f.delta*R134aData.data.DCRIT;
      f.T := R134aData.data.TCRIT/f.tau;
      f.R_s := R134aData.R_s;

      annotation (Documentation(info="<html>
This function computes the residual helmholtz derivatives of the fundamental equation of Tillner-Roth and Baehr for R134a (1994) w.r.t. to reduced temperature (tau=T_crit/T) and reduced density (delta=rho/rho_crit). The function can be used for special properties depending just on the residual derivative parts.
</html>"));
    end fres_R134a;

    function getPhase_ph "Number of phases by pressure and specific enthalpy"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";

      output Integer phase "Number of phases";

    protected
      SaturationProperties sat(psat=p, Tsat=0)
        "Saturation temperature and pressure";
      SI.SpecificEnthalpy hl=bubbleEnthalpy(sat)
        "Liquid enthalpy";
      SI.SpecificEnthalpy hv=dewEnthalpy(sat) "Vapor enthalpy";

    algorithm
      phase := if ((h < hl) or (h > hv) or (p > R134aData.data.FPCRIT)) then 1
         else 2;

      annotation (Documentation(info="<html>
This function computes the number of phases for R134a depending on the inputs for absolute pressure and specific enthalpy. It makes use of cubic spline functions for liquid and vapor specific enthalpy.
</html>"));
    end getPhase_ph;

    function getPhase_ps "Number of phases by pressure and entropy"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEntropy s "Specific entropy";
      output Integer phase "Number of phases";

    protected
      SaturationProperties sat(psat=p, Tsat=0)
        "Saturation temperature and pressure";
      SI.SpecificEntropy sl=bubbleEntropy(sat) "Liquid entropy";
      SI.SpecificEntropy sv=dewEntropy(sat) "Vapor entropy";

    algorithm
      phase := if ((s < sl) or (s > sv) or (p > R134aData.data.FPCRIT)) then 1
         else 2;

      annotation (Documentation(info="<html>
This function computes the number of phases for R134a depending on the inputs for absolute pressure and specific entropy. It makes use of cubic spline functions for liquid and vapor specific entropy.
</html>"));
    end getPhase_ps;

    function hofpsTwoPhase
      "Isentropic specific enthalpy in two phase region h(p,s)"
      extends Modelica.Icons.Function;
      input AbsolutePressure p "Pressure";
      input SpecificEntropy s "Specific entropy";
      output SpecificEnthalpy h "Specific enthalpy";

    protected
      SaturationProperties sat "Saturation temperature and pressure";
      SI.MassFraction x "Vapor quality";
      SI.SpecificEntropy sl "Liquid entropy";
      SI.SpecificEntropy sv "Vapor entropy";
      SI.SpecificEnthalpy hl "Liquid enthalpy";
      SI.SpecificEnthalpy hv "Vapor enthalpy";
    algorithm
      sat.psat := p;
      // dummy
      sat.Tsat := 0;
      hl := bubbleEnthalpy(sat=sat);
      hv := dewEnthalpy(sat=sat);
      sl := bubbleEntropy(sat=sat);
      sv := dewEntropy(sat=sat);
      x := (s - sl)/(sv - sl);
      h := hl + x*(hv - hl);

      annotation (Documentation(info="<html>
This function computes the specific enthalpy in two-phase for R134a depending on the inputs for absolute pressure and specific entropy. It makes use of cubic spline functions for liquid and vapor specific enthalpy as well as specific entropy.
</html>"));
    end hofpsTwoPhase;

    function R134a_liqofdT "Properties on liquid boundary phase"

      extends Modelica.Icons.Function;

      input Temperature T "Temperature";

      output Common.PhaseBoundaryProperties liq
        "Properties on liquid boundary phase";
    protected
      SI.Temperature T_liq "Liquid temperature";
      SI.Density d_liq "Liquid density";
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    algorithm
      if T < R134aData.data.TCRIT then
        d_liq := bubbleDensity(setSat_T(T));
        T_liq := T;
      else
        d_liq := R134aData.data.DCRIT;
        T_liq := R134aData.data.TCRIT;
      end if;
      f := f_R134a(d_liq, T_liq);
      liq := Common.helmholtzToBoundaryProps(f);

    end R134a_liqofdT;

    function R134a_vapofdT "Properties on vapor boundary phase"

      extends Modelica.Icons.Function;

      input Temperature T "Temperature";

      output Common.PhaseBoundaryProperties vap
        "Properties on vapor boundary phase";
    protected
      SI.Temperature T_vap "Vapor temperature";
      SI.Density d_vap "Vapor density";
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";
    algorithm
      if T < R134aData.data.TCRIT then
        d_vap := dewDensity(setSat_T(T));
        T_vap := T;
      else
        d_vap := R134aData.data.DCRIT;
        T_vap := R134aData.data.TCRIT;
      end if;
      f := f_R134a(d_vap, T_vap);
      vap := Common.helmholtzToBoundaryProps(f);

    end R134a_vapofdT;

    function rho_ph_der "Time derivative function of density_ph"
      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Common.InverseDerivatives_rhoT derivs "Record for derivatives";
      input Real p_der "Derivative of pressure";
      input Real h_der "Derivative of specific enthalpy";
      output Real d_der "Derivative of density";
    algorithm
      if (derivs.phase == 2) then
        d_der := (derivs.rho*(derivs.rho*derivs.cv/derivs.dpT + 1.0)/(derivs.dpT
          *derivs.T))*p_der + (-derivs.rho*derivs.rho/(derivs.dpT*derivs.T))*
          h_der;
      else
        d_der := ((derivs.rho*(derivs.cv*derivs.rho + derivs.pt))/(derivs.rho*
          derivs.rho*derivs.pd*derivs.cv + derivs.T*derivs.pt*derivs.pt))*p_der
           + (-derivs.rho*derivs.rho*derivs.pt/(derivs.rho*derivs.rho*derivs.pd
          *derivs.cv + derivs.T*derivs.pt*derivs.pt))*h_der;
      end if;

      annotation (Documentation(info="<html>
This function calculates the derivative of density w.r.t. time. It is used as derivative function for <a href=\"modelica://Modelica.Media.R134a.R134a_ph.rho_props_ph\"> rho_props_ph</a>.
</html>"));
    end rho_ph_der;

    function rho_props_ph
      "Density as function of pressure and specific enthalpy"
      extends Modelica.Icons.Function;

      input SI.Pressure p "Pressure";
      input SI.SpecificEnthalpy h "Specific enthalpy";
      input Common.InverseDerivatives_rhoT derivs
        "Record for the calculation of rho_ph_der";
      output SI.Density d "Density";
    algorithm
      d := derivs.rho;

      annotation (
        derivative(noDerivative=derivs) = rho_ph_der,
        Inline=false,
        LateInline=true,
        Documentation(info="<html>
This function integrates the derivative of density w.r.t. time in order to allow a numerical inversion for the complex fundamental equation of state.
</html>"));
    end rho_props_ph;

    function T_ph_der "Time derivative function of T_ph"
      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Common.InverseDerivatives_rhoT derivs "Auxiliary record";
      input Real p_der "Derivative of pressure";
      input Real h_der "Derivative of specific enthalpy";
      output Real T_der "Derivative of temperature";
    algorithm
      if (derivs.phase == 2) then
        T_der := 1/derivs.dpT*p_der;
      else
        T_der := ((-derivs.rho*derivs.pd + derivs.T*derivs.pt)/(derivs.rho*
          derivs.rho*derivs.pd*derivs.cv + derivs.T*derivs.pt*derivs.pt))*p_der
           + ((derivs.rho*derivs.rho*derivs.pd)/(derivs.rho*derivs.rho*derivs.pd
          *derivs.cv + derivs.T*derivs.pt*derivs.pt))*h_der;
      end if;

      annotation (Documentation(info="<html>
This function calculates the derivative of temperature w.r.t. time. It is used as derivative function for <a href=\"modelica://Modelica.Media.R134a.R134a_ph.T_props_ph\"> T_props_ph</a>.
</html>"));
    end T_ph_der;

    function T_props_ph
      "Temperature as function of pressure and specific enthalpy"
      extends Modelica.Icons.Function;

      input AbsolutePressure p "Pressure";
      input SpecificEnthalpy h "Specific enthalpy";
      input Common.InverseDerivatives_rhoT derivs
        "Record for the calculation of T_ph_der";
      output Temperature T "Temperature";
    algorithm
      T := derivs.T;

      annotation (
        derivative(noDerivative=derivs) = T_ph_der,
        Inline=false,
        LateInline=true,
        Documentation(info="<html>
This function integrates the derivative of temperature w.r.t. time in order to allow a numerical inversion for the complex fundamental equation of state.
</html>"));
    end T_props_ph;

    redeclare function extends setSmoothState
      "Smooth transition function between state_a and state_b"
      import Modelica.Media.Common.smoothStep;
    algorithm
      state := ThermodynamicState(
        p=smoothStep(
          x,
          state_a.p,
          state_b.p,
          x_small),
        h=smoothStep(
          x,
          state_a.h,
          state_b.h,
          x_small),
        T=temperature_ph(smoothStep(
          x,
          state_a.p,
          state_b.p,
          x_small), smoothStep(
          x,
          state_a.h,
          state_b.h,
          x_small)),
        d=density_ph(smoothStep(
          x,
          state_a.p,
          state_b.p,
          x_small), smoothStep(
          x,
          state_a.h,
          state_b.h,
          x_small)),
        phase=0);
      annotation (Inline=true);
    end setSmoothState;

    function dofpT "Compute d for given p and T"
      extends Modelica.Icons.Function;
      input SI.Pressure p "Pressure";
      input SI.Temperature T "Temperature";
      input SI.Pressure delp "Iteration converged if (p-pre(p) < delp)";
      output SI.Density d "Density";

    protected
      constant Real p_breaks[:]=R134aData.pbreaks
        "Grid points of reduced pressure";
      constant Real dl_coef[:, 4]=R134aData.dlcoef
        "Coefficients of cubic spline for rho_liq(p)";
      constant Real dv_coef[:, 4]=R134aData.dvcoef
        "Coefficients of cubic spline for rho_vap(p)";

      Boolean liquid "Is liquid";
      Boolean supercritical "Is supercritcal";
      Integer int "Interval number";
      Real pred "Reduced pressure";
      Real localx "Abscissa of local spline";
      Integer i "Newton iteration number";
      Real dp "Pressure difference";
      SI.Density deld "Density step";
      Modelica.Media.Common.HelmholtzDerivs f
        "Dimensionless Helmholtz function and derivatives w.r.t. delta and tau";
      Modelica.Media.Common.NewtonDerivatives_pT nDerivs
        "Derivatives needed in Newton iteration";
      Boolean found "Flag for iteration success";
      Integer error "1 if did not converged";

    algorithm
      Modelica.Media.R134a.R134a_ph.phaseBoundaryAssert(p, T);
      i := 0;
      error := 0;
      found := false;
      pred := p/R134aData.data.FPCRIT;
      (int,error) := Common.FindInterval(pred, p_breaks);
      localx := pred - p_breaks[int];
      // set decent initial guesses for d and T
      supercritical := p > R134aData.data.FPCRIT;
      if supercritical then
        // iteration seems to work better if coming from high densities
        d := R134aData.data.FDCRIT*3.0;
      else
        liquid := T <= Modelica.Media.R134a.R134a_ph.saturationTemperature(p);
        if liquid then
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dl_coef[int,
            1:4])*1.02;
        else
          d := R134aData.data.FDCRIT*Common.CubicSplineEval(localx, dv_coef[int,
            1:4])*0.95;
        end if;
      end if;

      while ((i < 100) and not found) loop
        f := Modelica.Media.R134a.R134a_ph.f_R134a(d, T);
        nDerivs := Modelica.Media.Common.Helmholtz_pT(f);
        dp := nDerivs.p - p;
        if (abs(dp) <= delp) then
          found := true;
        end if;
        deld := dp/nDerivs.pd;
        d := d - deld;
        i := i + 1;
      end while;

      annotation (Documentation(info="<html>
<p>This function calculates the density of R134a from absolute pressure and temperature. The function can only be executed in one-phase region. The safety margin to the phase boundary is 1[K] and 1000[Pa].
</p>
<h4>Restrictions</h4>
The function cannot be inverted in a numerical way. Please use functions <a href=\"modelica://Modelica.Media.R134a.R134a_ph.rho_props_ph\">rho_props_ph</a> and <a href=\"modelica://Modelica.Media.R134a.R134a_ph.T_props_ph\">T_props_ph</a> for this purpose.
</html>"));
    end dofpT;

    function hofpT "Compute h for given p and T"
      extends Modelica.Icons.Function;
      input SI.Pressure p "Pressure";
      input SI.Temperature T "Temperature";
      input SI.Pressure delp
        "Iteration converged if (p-pre(p) < delp)";
      output SI.SpecificEnthalpy h "Specific Enthalpy";

    protected
      SI.Density d "Density";
      Modelica.Media.Common.HelmholtzDerivs f "Helmholtz derivatives";

    algorithm
      Modelica.Media.R134a.R134a_ph.phaseBoundaryAssert(p, T);
      d := dofpT(p, T, delp);
      f := f_R134a(d, T);
      h := R134aData.data.R_s*T*(f.tau*f.ftau + f.delta*f.fdelta);

      annotation (Documentation(info="<html>
<p>This function calculates the specific enthalpy of R134a from absolute pressure and temperature. The function can only be executed in one-phase region. The safety margin to the phase boundary is 1[K] and 1000[Pa].
</p>
</html>"));
    end hofpT;

    function phaseBoundaryAssert
      "Assert function for checking threshold to phase boundary"
      extends Modelica.Icons.Function;
      input SI.Pressure p "Refrigerant pressure";
      input SI.Temperature T "Refrigerant temperature";

    protected
      SI.Temperature T_lim_gas "Upper temperature limit";
      SI.Temperature T_lim_liq "Lower temperature limit";
      SI.Temperature T_sat "Saturation temperature";

    algorithm
      T_sat := Modelica.Media.R134a.R134a_ph.saturationTemperature(p);
      T_lim_gas := T_sat + 1;
      T_lim_liq := T_sat - 1;

      assert(p>R134aData.data.PCRIT+1000 or not
                                          (T<T_lim_gas and T>T_lim_liq), "Fluid state is too close to the two-phase region (p="+String(p)+"[Pa], T="+String(T)+"[K]. Pressure and temperature can not be used to determine properties in two-phase region.");

      annotation (Documentation(info="<html>
This function is used as a guard for property functions using pTX as an input. Property functions for two-phase media using pressure and temperature as inputs shall not be used close to the phase boundary in order to avoid errors and high deviations for just small deviations in the input arguments. The refrigerant state can not be determined in the two-phase region using pressure and temperature.
</html>"));
    end phaseBoundaryAssert;
    annotation (Documentation(info="<html>
<p>
Calculation of fluid properties for Tetrafluoroethane (R134a) in the fluid region of 0.0039 bar (Triple pressure) to 700 bar and 169.85 Kelvin (Triple temperature) to 455 Kelvin.
</p>
<h4>Restriction</h4>
<p>
The functions provided by this package shall be used inside of the restricted limits according to the referenced literature.
</p>
<ul>
 <li>
      <strong> 0.0039 bar &le; p &le; 700 bar </strong>
 </li>
 <li>
      <strong> 169.85 Kelvin &le; T &le; 455 Kelvin  </strong>
 </li>
 <li>
      <strong> explicit for pressure and specific enthalpy </strong>
 </li>
</ul>

<p><strong>References</strong></p>
<dl><dt>Baehr, H.D. and Tillner-Roth, R.: </dt>
<dd><strong>Thermodynamic Properties of Environmentally Acceptable Refrigerants -
Equations of State and Tables for Ammonia, R22, R134a, R152a, and R123</strong>. Springer-Verlag, Berlin (Germany), 1994.</dd>
</dl>
<dl><dt>Klein, McLinden and Laesecke: </dt>
<dd><strong>An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures</strong>.
Int. J. Refrig., Vol. 20, No.3, pp. 208-217, 1997.</dd>
</dl>
<dl><dt>McLinden, Klein. and Perkins: </dt>
<dd><strong>An extended corresponding states model for the thermal conductivity
of refrigerants and refrigerant mixtures</strong>.
Int. J. Refrig., 23 (2000) 43-63.</dd>
</dl>
<dl><dt>Okada and Higashi: </dt>
<dd><strong>Surface tension correlation of HFC-134a and HCFC-123</strong>.
Proceedings of the Joint Meeting of IIR Commissions B1, B2, E1, and E2, Padua, Italy, pp. 541-548, 1994.</dd>
</dl>
</html>"));
  end R134a_ph;

  package R134aData "R134a data required by package R134a_ph"

    extends Modelica.Icons.Package;
    constant SI.SpecificHeatCapacity R_s=data.R_s;
    constant Integer Npoints=478;
    constant Integer Ninterval=Npoints - 1;
    constant Real[Npoints] pbreaks={9.597762848258994e-005,
        9.869357747732370e-005,1.010264375639950e-004,1.065169584583328e-004,
        1.123059413359126e-004,1.184094248412308e-004,1.248446933924201e-004,
        1.316297064467259e-004,1.387835295300911e-004,1.463261079761978e-004,
        1.542786111807819e-004,1.626631846135783e-004,1.715035062398977e-004,
        1.808243694992149e-004,1.906517107583061e-004,2.010132485287069e-004,
        2.119377912202213e-004,2.234561174702443e-004,2.356004528862385e-004,
        2.484047512716141e-004,2.616284653191377e-004,2.747881183685521e-004,
        2.885158790807569e-004,3.028318826616158e-004,3.177568016040576e-004,
        3.333118542894548e-004,3.495188133266056e-004,3.664000141427236e-004,
        3.839783631625294e-004,4.022773464529003e-004,4.213210377579724e-004,
        4.411341070924892e-004,4.617418287585031e-004,4.831700895846934e-004,
        5.054453973240350e-004,5.285948883287491e-004,5.526463359992557e-004,
        5.776281585116855e-004,6.035694268866237e-004,6.304998727332601e-004,
        6.584498962084673e-004,6.874505733153568e-004,7.175336642444060e-004,
        7.487316202293097e-004,7.810775914127821e-004,8.146054342502127e-004,
        8.493497185583605e-004,8.853457349505343e-004,9.226295020377572e-004,
        9.612377731634476e-004,1.001208043569667e-003,1.042578557225471e-003,
        1.085388313487843e-003,1.129677073668393e-003,1.175485367705820e-003,
        1.222854500460934e-003,1.271826558129384e-003,1.322444414376414e-003,
        1.374751736326610e-003,1.428792990668195e-003,1.484613449495073e-003,
        1.542259195759381e-003,1.601777129328165e-003,1.663214972080042e-003,
        1.726621273310258e-003,1.792045415319891e-003,1.859537618008464e-003,
        1.929148944128722e-003,2.000931304128618e-003,2.074937460870742e-003,
        2.151221034049469e-003,2.229836504887513e-003,2.310839220352569e-003,
        2.394285397224690e-003,2.480232126358037e-003,2.568737376543922e-003,
        2.659859998183566e-003,2.753659727089886e-003,2.850197187960054e-003,
        2.949533897578886e-003,3.051732268501956e-003,3.156855611648015e-003,
        3.264968139624009e-003,3.376134969543659e-003,3.490422125512034e-003,
        3.607896541474759e-003,3.728626063414313e-003,3.852679451797347e-003,
        3.980126383732962e-003,4.111037454976533e-003,4.245484181734639e-003,
        4.383539002791262e-003,4.525275280559336e-003,4.670767303162268e-003,
        4.820090285488170e-003,4.973320370546478e-003,5.130534630480654e-003,
        5.291811067763014e-003,5.457228615833621e-003,5.626867140010384e-003,
        5.800807438004561e-003,5.979131240454509e-003,6.161921211248477e-003,
        6.349260947941199e-003,6.541234981608406e-003,6.737928777105548e-003,
        6.939428732811780e-003,7.145822180530093e-003,7.357197385013741e-003,
        7.573643543593235e-003,7.795250785685322e-003,8.022110172037484e-003,
        8.254313693933356e-003,8.491954272338212e-003,8.735125756982369e-003,
        8.983922925176295e-003,9.238441480673905e-003,9.498778052406051e-003,
        9.765030192907764e-003,1.003729637709093e-002,1.031567600057533e-002,
        1.060026937790312e-002,1.089117774088576e-002,1.118850323681089e-002,
        1.149234892629966e-002,1.180281878149178e-002,1.212001768378737e-002,
        1.244405142182634e-002,1.277502668901607e-002,1.311305108132637e-002,
        1.345823309485172e-002,1.381068212326552e-002,1.417050845529529e-002,
        1.453782327208102e-002,1.491273864445383e-002,1.529536753016332e-002,
        1.568582377114743e-002,1.608422209040166e-002,1.649067808931178e-002,
        1.690530824446280e-002,1.732822990453687e-002,1.775956128744187e-002,
        1.819942147677864e-002,1.864793041887473e-002,1.910520891956503e-002,
        1.957137864057372e-002,2.004656209644468e-002,2.053088265103482e-002,
        2.102446451411387e-002,2.152743273774831e-002,2.203991321298626e-002,
        2.256203266622321e-002,2.309391865555178e-002,2.363569956736602e-002,
        2.418750461246241e-002,2.474946382258750e-002,2.532170804665175e-002,
        2.590436894709933e-002,2.649757899613318e-002,2.710147147198215e-002,
        2.771618045516845e-002,2.834184082475825e-002,2.897858825451354e-002,
        2.962655920917527e-002,3.028589094062469e-002,3.095672148415131e-002,
        3.163918965453092e-002,3.233343504239619e-002,3.303959801019879e-002,
        3.375781968861326e-002,3.448824197265431e-002,3.523100751788461e-002,
        3.598625973665024e-002,3.675414279428406e-002,3.753480160540696e-002,
        3.832838183003045e-002,3.913502986997648e-002,3.995489286516166e-002,
        4.078811868980567e-002,4.163485594877166e-002,4.249525397402870e-002,
        4.336946282080187e-002,4.425763326428060e-002,4.515991679581355e-002,
        4.607646561937220e-002,4.700743264819789e-002,4.795297150115203e-002,
        4.891323649938621e-002,4.988838266300229e-002,5.087856570747507e-002,
        5.188394204050219e-002,5.290466875872184e-002,5.394090364435762e-002,
        5.499280516221097e-002,5.606053245635714e-002,5.714424534717350e-002,
        5.824410432822266e-002,5.936027056331945e-002,6.049290588356860e-002,
        6.164217278454836e-002,6.280823442343543e-002,6.399125461636106e-002,
        6.519139783552948e-002,6.640882920680599e-002,6.764371450704471e-002,
        6.889622016163087e-002,7.016651324207315e-002,7.145476146359577e-002,
        7.276113318295722e-002,7.408579739616779e-002,7.542892373645665e-002,
        7.679068247215846e-002,7.817124450477091e-002,7.957078136711258e-002,
        8.098946522143942e-002,8.242746885787376e-002,8.388496569268521e-002,
        8.536212976679605e-002,8.685913574431177e-002,8.837615891128831e-002,
        8.991337517436447e-002,9.147096105967481e-002,9.304909371182504e-002,
        9.464795089290083e-002,9.626771098168203e-002,9.790855297290042e-002,
        9.957065647660095e-002,1.012542017176483e-001,1.029593695353304e-001,
        1.046863413830815e-001,1.064352993283296e-001,1.082064260525101e-001,
        1.099999048510082e-001,1.118159196335355e-001,1.136546549243387e-001,
        1.155162958627491e-001,1.174010282037917e-001,1.193090383188843e-001,
        1.212405131966888e-001,1.231956404442420e-001,1.251746082880320e-001,
        1.271776055753336e-001,1.292048217756560e-001,1.312564469824424e-001,
        1.333326719147161e-001,1.354336879191573e-001,1.375596869720684e-001,
        1.397108616817379e-001,1.418874052908662e-001,1.440895116791160e-001,
        1.463173753659727e-001,1.485711915136508e-001,1.508511559303043e-001,
        1.531574650734013e-001,1.554903160532023e-001,1.578499066364259e-001,
        1.602364352504390e-001,1.626501009871427e-001,1.650911036075191e-001,
        1.675596435460891e-001,1.700559219157807e-001,1.725801405130011e-001,
        1.751325018227866e-001,1.777132090243812e-001,1.803224659969848e-001,
        1.829604773257499e-001,1.856274483079854e-001,1.883235849597385e-001,
        1.910490940225762e-001,1.938041829705809e-001,1.965890600178195e-001,
        1.994039341258457e-001,2.022490150118090e-001,2.051245131564867e-001,
        2.080306398131010e-001,2.109676070159534e-001,2.139356275898521e-001,
        2.169349151595292e-001,2.199656841596673e-001,2.230281498451127e-001,
        2.261225283015071e-001,2.292490364564299e-001,2.324078920906696e-001,
        2.355993138502352e-001,2.388235212584440e-001,2.420807347286962e-001,
        2.453711755776573e-001,2.486950660387031e-001,2.520526292761376e-001,
        2.554440893996220e-001,2.588696714792741e-001,2.623296015612792e-001,
        2.658241066839430e-001,2.693534148944132e-001,2.729177552658184e-001,
        2.765173579152221e-001,2.801524540219758e-001,2.838232758468616e-001,
        2.875300567517182e-001,2.912730312199488e-001,2.950524348775986e-001,
        2.988685045151655e-001,3.027214781102109e-001,3.066115948507304e-001,
        3.105390951593055e-001,3.145042207181398e-001,3.185072144949388e-001,
        3.225483207696795e-001,3.266277851623652e-001,3.307458546616600e-001,
        3.349027776546629e-001,3.390988039576249e-001,3.433341848477569e-001,
        3.476091730962973e-001,3.519240230025824e-001,3.562789904294610e-001,
        3.606743328399952e-001,3.651103093353738e-001,3.695871806943437e-001,
        3.741052094140343e-001,3.786646597522729e-001,3.832657977714583e-001,
        3.879088913841363e-001,3.925942104002511e-001,3.973220265761317e-001,
        4.020926136654290e-001,4.069062474719831e-001,4.117632059046955e-001,
        4.166637690345744e-001,4.216082191539507e-001,4.265968408381747e-001,
        4.316299210096456e-001,4.367077490044181e-001,4.418306166415828e-001,
        4.469988182954611e-001,4.522126509707460e-001,4.574724143807979e-001,
        4.627784110292650e-001,4.681309462951913e-001,4.735303285216456e-001,
        4.789768691084685e-001,4.844708826088187e-001,4.900126868302581e-001,
        4.956026029402373e-001,5.012409555764841e-001,5.069280729624649e-001,
        5.126642870282773e-001,5.184499335373062e-001,5.242853522190180e-001,
        5.302680522792256e-001,5.362148870570488e-001,5.421125034763555e-001,
        5.479604123151721e-001,5.537581634208009e-001,5.595053445140967e-001,
        5.652015800117042e-001,5.708465298673534e-001,5.764398884324107e-001,
        5.819813833363990e-001,5.874707743877503e-001,5.929078524952066e-001,
        5.982924386100538e-001,6.036243826896056e-001,6.089035626818212e-001,
        6.141298835313674e-001,6.193032762071714e-001,6.244236967514051e-001,
        6.294911253499476e-001,6.345055654242815e-001,6.394670427446655e-001,
        6.443756045645810e-001,6.492313187762216e-001,6.540342730869820e-001,
        6.587845742164332e-001,6.634823471141452e-001,6.681277341974906e-001,
        6.727208946097391e-001,6.772620034977512e-001,6.817512513092869e-001,
        6.861888431095735e-001,6.905749979167365e-001,6.949099480559251e-001,
        6.991939385318118e-001,7.034272264190118e-001,7.076100802703395e-001,
        7.117427795423493e-001,7.158256140379710e-001,7.198588833658458e-001,
        7.238428964161435e-001,7.277779708523336e-001,7.316644326187892e-001,
        7.355026154637049e-001,7.392928604808265e-001,7.430355156427725e-001,
        7.467309354101930e-001,7.503794802847638e-001,7.539815165033564e-001,
        7.575374158563575e-001,7.610475525042479e-001,7.645123095847116e-001,
        7.679320711405823e-001,7.713072258757592e-001,7.746381659738916e-001,
        7.779252867810481e-001,7.811689864996086e-001,7.843696658934009e-001,
        7.875277280034720e-001,7.906435778747776e-001,7.937176222932615e-001,
        7.967502695335140e-001,8.000199630662463e-001,8.033009258512434e-001,
        8.065932139849678e-001,8.098968847000179e-001,8.132119945147386e-001,
        8.165386053633329e-001,8.198767769333629e-001,8.232265712101035e-001,
        8.265880515436206e-001,8.299612827168834e-001,8.333463310190913e-001,
        8.367432643245871e-001,8.401521521779828e-001,8.435730658861569e-001,
        8.470060786178580e-001,8.504512655117438e-001,8.539087037939039e-001,
        8.573784729060409e-001,8.608606546457506e-001,8.643553333207711e-001,
        8.678625959196853e-001,8.713825323024099e-001,8.749152354154032e-001,
        8.784608015388341e-001,8.820193305769569e-001,8.855909230615221e-001,
        8.891756908959754e-001,8.927737444522241e-001,8.963852006600686e-001,
        9.000101817311734e-001,9.036488156539342e-001,9.073012367571003e-001,
        9.109675863549037e-001,9.146480134897557e-001,9.183426757925104e-001,
        9.220517404865118e-001,9.257753855697142e-001,9.295138012239329e-001,
        9.332671915249889e-001,9.370357765779688e-001,9.408197916132383e-001,
        9.446194993887446e-001,9.484351827283455e-001,9.522671554710838e-001,
        9.561157672135285e-001,9.599814113076552e-001,9.638645356406839e-001,
        9.677656576771091e-001,9.716853843570205e-001,9.756244470156604e-001,
        9.795837477900006e-001,9.825671883209557e-001,9.855632858038894e-001,
        9.886965153922347e-001,9.917147058660856e-001,9.939889544462242e-001,
        9.955107773467575e-001,9.966554757188424e-001,9.976501440012482e-001,
        9.985707411825207e-001,9.989551169812724e-001,9.991090113187927e-001,
        9.993400213037331e-001,9.995459937617709e-001,9.997521475624808e-001,
        9.998552980391523e-001,9.999068928446231e-001,1.0};
    constant Real[Npoints] Tbreaks={0.453892958213191,0.454558816062682,
        0.455118075727735,0.456391027473952,0.457672503868159,0.458962558356426,
        0.460261324553926,0.461568882629760,0.462885339476068,0.464210775261953,
        0.465545296879551,0.466888984497968,0.468241971732374,0.469604365474908,
        0.470976245894674,0.472357746606843,0.473748947780518,0.475149983030873,
        0.476560959250045,0.477981983330171,0.479384515070455,0.480720666793156,
        0.482056818515856,0.483392970238556,0.484729121961257,0.486065273683957,
        0.487401425406658,0.488737577129358,0.490073728852059,0.491409880574759,
        0.492746032297459,0.494082184020160,0.495418335742860,0.496754487465561,
        0.498090639188261,0.499426790910961,0.500762942633662,0.502099094356362,
        0.503435246079063,0.504771397801763,0.506107549524464,0.507443701247164,
        0.508779852969864,0.510116004692565,0.511452156415265,0.512788308137966,
        0.514124459860666,0.515460611583366,0.516796763306067,0.518132915028767,
        0.519469066751468,0.520805218474168,0.522141370196869,0.523477521919569,
        0.524813673642269,0.526149825364970,0.527485977087670,0.528822128810371,
        0.530158280533071,0.531494432255771,0.532830583978472,0.534166735701172,
        0.535502887423873,0.536839039146573,0.538175190869274,0.539511342591974,
        0.540847494314674,0.542183646037375,0.543519797760075,0.544855949482776,
        0.546192101205476,0.547528252928176,0.548864404650877,0.550200556373577,
        0.551536708096278,0.552872859818978,0.554209011541679,0.555545163264379,
        0.556881314987079,0.558217466709780,0.559553618432480,0.560889770155181,
        0.562225921877881,0.563562073600581,0.564898225323282,0.566234377045982,
        0.567570528768683,0.568906680491383,0.570242832214084,0.571578983936784,
        0.572915135659484,0.574251287382185,0.575587439104885,0.576923590827586,
        0.578259742550286,0.579595894272986,0.580932045995687,0.582268197718387,
        0.583604349441088,0.584940501163788,0.586276652886489,0.587612804609189,
        0.588948956331889,0.590285108054590,0.591621259777290,0.592957411499991,
        0.594293563222691,0.595629714945391,0.596965866668092,0.598302018390792,
        0.599638170113493,0.600974321836193,0.602310473558894,0.603646625281594,
        0.604982777004294,0.606318928726995,0.607655080449695,0.608991232172396,
        0.610327383895096,0.611663535617796,0.612999687340497,0.614335839063197,
        0.615671990785898,0.617008142508598,0.618344294231299,0.619680445953999,
        0.621016597676699,0.622352749399400,0.623688901122100,0.625025052844801,
        0.626361204567501,0.627697356290201,0.629033508012902,0.630369659735602,
        0.631705811458303,0.633041963181003,0.634378114903704,0.635714266626404,
        0.637050418349104,0.638386570071805,0.639722721794505,0.641058873517206,
        0.642395025239906,0.643731176962606,0.645067328685307,0.646403480408007,
        0.647739632130708,0.649075783853408,0.650411935576109,0.651748087298809,
        0.653084239021509,0.654420390744210,0.655756542466910,0.657092694189611,
        0.658428845912311,0.659764997635011,0.661101149357712,0.662437301080412,
        0.663773452803113,0.665109604525813,0.666445756248514,0.667781907971214,
        0.669118059693914,0.670454211416615,0.671790363139315,0.673126514862016,
        0.674462666584716,0.675798818307416,0.677134970030117,0.678471121752817,
        0.679807273475518,0.681143425198218,0.682479576920918,0.683815728643619,
        0.685151880366319,0.686488032089020,0.687824183811720,0.689160335534421,
        0.690496487257121,0.691832638979821,0.693168790702522,0.694504942425222,
        0.695841094147923,0.697177245870623,0.698513397593323,0.699849549316024,
        0.701185701038724,0.702521852761425,0.703858004484125,0.705194156206826,
        0.706530307929526,0.707866459652226,0.709202611374927,0.710538763097627,
        0.711874914820328,0.713211066543028,0.714547218265728,0.715883369988429,
        0.717219521711129,0.718555673433830,0.719891825156530,0.721227976879231,
        0.722564128601931,0.723900280324631,0.725236432047332,0.726572583770032,
        0.727908735492733,0.729244887215433,0.730581038938133,0.731917190660834,
        0.733253342383534,0.734589494106235,0.735925645828935,0.737261797551636,
        0.738597949274336,0.739934100997036,0.741270252719737,0.742606404442437,
        0.743942556165138,0.745278707887838,0.746614859610538,0.747951011333239,
        0.749287163055939,0.750623314778640,0.751959466501340,0.753295618224041,
        0.754631769946741,0.755967921669441,0.757304073392142,0.758640225114842,
        0.759976376837543,0.761312528560243,0.762648680282943,0.763984832005644,
        0.765320983728344,0.766657135451045,0.767993287173745,0.769329438896446,
        0.770665590619146,0.772001742341846,0.773337894064547,0.774674045787247,
        0.776010197509948,0.777346349232648,0.778682500955348,0.780018652678049,
        0.781354804400749,0.782690956123450,0.784027107846150,0.785363259568851,
        0.786699411291551,0.788035563014251,0.789371714736952,0.790707866459652,
        0.792044018182353,0.793380169905053,0.794716321627753,0.796052473350454,
        0.797388625073154,0.798724776795855,0.800060928518555,0.801397080241256,
        0.802733231963956,0.804069383686656,0.805405535409357,0.806741687132057,
        0.808077838854758,0.809413990577458,0.810750142300158,0.812086294022859,
        0.813422445745559,0.814758597468260,0.816094749190960,0.817430900913661,
        0.818767052636361,0.820103204359061,0.821439356081762,0.822775507804462,
        0.824111659527163,0.825447811249863,0.826783962972563,0.828120114695264,
        0.829456266417964,0.830792418140665,0.832128569863365,0.833464721586066,
        0.834800873308766,0.836137025031466,0.837473176754167,0.838809328476867,
        0.840145480199568,0.841481631922268,0.842817783644968,0.844153935367669,
        0.845490087090369,0.846826238813070,0.848162390535770,0.849498542258470,
        0.850834693981171,0.852170845703871,0.853506997426572,0.854843149149272,
        0.856179300871973,0.857515452594673,0.858851604317373,0.860187756040074,
        0.861523907762774,0.862860059485475,0.864196211208175,0.865532362930875,
        0.866868514653576,0.868204666376276,0.869540818098977,0.870876969821677,
        0.872213121544378,0.873549273267078,0.874885424989778,0.876221576712479,
        0.877557728435179,0.878893880157880,0.880230031880580,0.881566183603280,
        0.882902335325981,0.884238487048681,0.885574638771382,0.886910790494082,
        0.888246942216783,0.889583093939483,0.890919245662183,0.892255397384884,
        0.893591549107584,0.894927700830285,0.896263852552985,0.897600004275685,
        0.898936155998386,0.900272307721086,0.901608459443787,0.902944611166487,
        0.904280762889188,0.905616914611888,0.906953066334588,0.908289218057289,
        0.909625369779989,0.910961521502690,0.912297673225390,0.913633824948090,
        0.914969976670791,0.916306128393491,0.917642280116192,0.919000395123209,
        0.920338788669353,0.921654913780206,0.922949140962045,0.924221834556595,
        0.925473352843603,0.926704048141686,0.927914266907520,0.929104349833374,
        0.930274631943016,0.931425442686031,0.932557106030558,0.933669940554492,
        0.934764259535182,0.935840371037602,0.936898578001085,0.937939178324610,
        0.938962464950653,0.939968725947663,0.940958244591156,0.941931299443453,
        0.942888164432106,0.943829108927011,0.944754397816244,0.945664291580614,
        0.946559046367014,0.947438914060509,0.948304142355261,0.949154974824251,
        0.949991650987844,0.950814406381226,0.951623472620704,0.952419077468909,
        0.953201444898923,0.953970795157311,0.954727344826145,0.955471306883966,
        0.956202890765733,0.956922302421791,0.957629744375846,0.958325415781975,
        0.959009512480699,0.959682227054106,0.960343748880064,0.960994264185543,
        0.961633956099033,0.962263004702097,0.962881587080076,0.963489877371918,
        0.964088046819229,0.964676263814465,0.965254693948328,0.965823500056402,
        0.966382842264975,0.966932878036132,0.967473762212069,0.968005647058694,
        0.968528682308485,0.969043015202643,0.969548790532545,0.970046150680502,
        0.970580611369582,0.971115072058662,0.971649532747743,0.972183993436823,
        0.972718454125903,0.973252914814983,0.973787375504063,0.974321836193144,
        0.974856296882223,0.975390757571304,0.975925218260384,0.976459678949464,
        0.976994139638544,0.977528600327624,0.978063061016705,0.978597521705785,
        0.979131982394865,0.979666443083945,0.980200903773025,0.980735364462105,
        0.981269825151186,0.981804285840266,0.982338746529346,0.982873207218426,
        0.983407667907506,0.983942128596586,0.984476589285667,0.985011049974747,
        0.985545510663827,0.986079971352907,0.986614432041987,0.987148892731067,
        0.987683353420148,0.988217814109228,0.988752274798308,0.989286735487388,
        0.989821196176468,0.990355656865548,0.990890117554629,0.991424578243709,
        0.991959038932789,0.992493499621869,0.993027960310949,0.993562421000029,
        0.994096881689110,0.994631342378190,0.995165803067270,0.995700263756350,
        0.996234724445430,0.996769185134510,0.997303645823591,0.997704491340401,
        0.998105336857211,0.998522611695603,0.998922580696883,0.999222557447843,
        0.999422541948483,0.999572530323963,0.999702520249380,0.999822510949763,
        0.999872507074923,0.999892505524987,0.999922503200083,0.999949226234537,
        0.999975949268991,0.999989310786218,0.999995991544832,1.0};
    constant Real[Ninterval, 4] Tcoef={{2.428119691060830e+012,-4.216479757645069e+008,
        9.287051822649143e+004,1.698508300000001e+002},{2.166914762300397e+012,
        -3.992111678478829e+008,9.062913441482277e+004,1.700999999999999e+002},
        {1.899159185577863e+012,-3.795555733430910e+008,8.878532320450363e+004,
        1.703092800000000e+002},{1.629916579808073e+012,-3.435128543022376e+008,
        8.477062663992558e+004,1.707856300000000e+002},{1.398839241865448e+012,
        -3.108983786183325e+008,8.093962908382615e+004,1.712651700000000e+002},
        {1.200574221723735e+012,-2.813879938533571e+008,7.728396604745965e+004,
        1.717479200000000e+002},{1.030417923000963e+012,-2.546836477814989e+008,
        7.379541586188905e+004,1.722339300000000e+002},{8.844001037952972e+011,
        -2.305189284572275e+008,7.046631066361128e+004,1.727232300000000e+002},
        {7.590860483164475e+011,-2.086514602087597e+008,6.728926490972207e+004,
        1.732158600000001e+002},{6.515463964671414e+011,-1.888629690497167e+008,
        6.425730760561715e+004,1.737118499999999e+002},{5.592552216502428e+011,
        -1.709551666980799e+008,6.136372775951276e+004,1.742112400000000e+002},
        {4.800416585372977e+011,-1.547489317359679e+008,5.860218639168952e+004,
        1.747140600000000e+002},{4.120619529393444e+011,-1.400824449235276e+008,
        5.596654048742052e+004,1.752203600000000e+002},{3.537140308461040e+011,
        -1.268087414876019e+008,5.345098341920615e+004,1.757301800000000e+002},
        {3.036357271971793e+011,-1.147956769847417e+008,5.105003430189027e+004,
        1.762435499999999e+002},{2.606525213033651e+011,-1.039230394931327e+008,
        4.875837260556154e+004,1.767605200000000e+002},{2.237609674834909e+011,
        -9.408262939444540e+007,4.657101751284228e+004,1.772811199999999e+002},
        {1.922419405902699e+011,-8.518143962347658e+007,4.448317923172022e+004,
        1.778053999999999e+002},{1.656321149901774e+011,-7.714416678199874e+007,
        4.249042535564808e+004,1.783334000000000e+002},{1.431407593855788e+011,
        -6.989094076846488e+007,4.058849075808411e+004,1.788651600000000e+002},
        {1.241037279204862e+011,-6.345000608556164e+007,3.880841089253586e+004,
        1.793900000000000e+002},{1.078897726938036e+011,-5.787323844457100e+007,
        3.719668427889198e+004,1.798900000000000e+002},{9.388245239329929e+010,
        -5.281986768088788e+007,3.566287663310264e+004,1.803899999999999e+002},
        {8.177026870962473e+010,-4.823785073207039e+007,3.420275088737812e+004,
        1.808900000000001e+002},{7.128653091837167e+010,-4.408054713844873e+007,
        3.281232303846304e+004,1.813900000000000e+002},{6.220419978100047e+010,
        -4.030623531248382e+007,3.148784749056206e+004,1.818900000000000e+002},
        {5.432814901566791e+010,-3.687745020027063e+007,3.022579953184881e+004,
        1.823900000000000e+002},{4.749233588110072e+010,-3.376066397124648e+007,
        2.902286362710196e+004,1.828899999999999e+002},{4.155352730607562e+010,
        -3.092570824858189e+007,2.787591713537610e+004,1.833900000000000e+002},
        {3.638967234175739e+010,-2.834555680690369e+007,2.678202091246125e+004,
        1.838900000000000e+002},{3.189545805614265e+010,-2.599587187121439e+007,
        2.573840508245055e+004,1.843899999999999e+002},{2.798050203785508e+010,
        -2.385478375872732e+007,2.474246009078133e+004,1.848900000000000e+002},
        {2.456737261968692e+010,-2.190263720157386e+007,2.379172636307514e+004,
        1.853900000000000e+002},{2.158887725624487e+010,-2.012168454337252e+007,
        2.288388355112532e+004,1.858900000000000e+002},{1.898760836682233e+010,
        -1.849598750549042e+007,2.201674428367421e+004,1.863900000000000e+002},
        {1.671373899396782e+010,-1.701114199658637e+007,2.118824358594005e+004,
        1.868900000000001e+002},{1.472442515376055e+010,-1.565417444528254e+007,
        2.039643299085866e+004,1.873900000000000e+002},{1.298254187769645e+010,
        -1.441336250162147e+007,1.963947244326254e+004,1.878900000000000e+002},
        {1.145612023308615e+010,-1.327813374098965e+007,1.891562443180674e+004,
        1.883899999999999e+002},{1.011726329520874e+010,-1.223890854106894e+007,
        1.822324676787706e+004,1.888899999999999e+002},{8.942115914174372e+009,
        -1.128706309621500e+007,1.756078856084207e+004,1.893899999999999e+002},
        {7.909709317744029e+009,-1.041475590863545e+007,1.692678236252691e+004,
        1.898900000000000e+002},{7.002011600872572e+009,-9.614913403719645e+006,
        1.631984148717728e+004,1.903899999999999e+002},{6.203335937528857e+009,
        -8.881122302459281e+006,1.573865385204634e+004,1.908899999999999e+002},
        {5.500000426851387e+009,-8.207563992121900e+006,1.518197779409089e+004,
        1.913900000000000e+002},{4.880147872846049e+009,-7.588969652936688e+006,
        1.464863839566741e+004,1.918900000000000e+002},{4.333458916781487e+009,
        -7.020558044503353e+006,1.413752314725710e+004,1.923900000000000e+002},
        {3.850903162697156e+009,-6.497982633829402e+006,1.364757825073601e+004,
        1.928900000000000e+002},{3.424640794532519e+009,-6.017301775739881e+006,
        1.317780570385806e+004,1.933900000000000e+002},{3.047820397687019e+009,
        -5.574930915074369e+006,1.272725963793938e+004,1.938900000000000e+002},
        {2.714455522862305e+009,-5.167610077477907e+006,1.229504347489282e+004,
        1.943900000000000e+002},{2.419310099883856e+009,-4.792372987537484e+006,
        1.188030713941842e+004,1.948900000000000e+002},{2.157814657986750e+009,
        -4.446521482506972e+006,1.148224448765968e+004,1.953900000000000e+002},
        {1.925958574178695e+009,-4.127595989843101e+006,1.110009063273798e+004,
        1.958900000000000e+002},{1.720235556842085e+009,-3.833356838509688e+006,
        1.073311982718851e+004,1.963900000000000e+002},{1.537568498602969e+009,
        -3.561761260770541e+006,1.038064313240985e+004,1.968900000000000e+002},
        {1.375254807055739e+009,-3.310945444478069e+006,1.004200642469327e+004,
        1.973900000000000e+002},{1.230926157318009e+009,-3.079209502474114e+006,
        9.716588529824085e+003,1.978900000000000e+002},{1.102501569080066e+009,
        -2.865000978909834e+006,9.403799307559229e+003,1.983899999999999e+002},
        {9.881431890151527e+008,-2.666899927117780e+006,9.103077924469371e+003,
        1.988900000000000e+002},{8.862460643504052e+008,-2.483611530634848e+006,
        8.813891493500507e+003,1.993900000000000e+002},{7.953869975993569e+008,
        -2.313948910499454e+006,8.535733187669037e+003,1.998900000000000e+002},
        {7.143138769691485e+008,-2.156827077065875e+006,8.268121128719055e+003,
        2.003900000000000e+002},{6.419280859884250e+008,-2.011254157318892e+006,
        8.010596993801432e+003,2.008900000000001e+002},{5.772519450401038e+008,
        -1.876319403262300e+006,7.762724544343183e+003,2.013900000000000e+002},
        {5.194272793309037e+008,-1.751190083800481e+006,7.524088760577367e+003,
        2.018899999999999e+002},{4.676942564542144e+008,-1.635102283023300e+006,
        7.294294502273217e+003,2.023900000000000e+002},{4.213813991521418e+008,
        -1.527355501832372e+006,7.072965529370125e+003,2.028900000000000e+002},
        {3.798929639616593e+008,-1.427306562607491e+006,6.859743479795654e+003,
        2.033900000000000e+002},{3.427034243188576e+008,-1.334365732814233e+006,
        6.654287012551113e+003,2.038900000000000e+002},{3.093461000479141e+008,
        -1.247990970222474e+006,6.456270819862391e+003,2.043900000000000e+002},
        {2.794066491203365e+008,-1.167684115936397e+006,6.265384847491296e+003,
        2.048900000000000e+002},{2.525185307660005e+008,-1.092987656856107e+006,
        6.081333540245373e+003,2.053899999999999e+002},{2.283558222313167e+008,
        -1.023480600819874e+006,5.903835032062275e+003,2.058900000000000e+002},
        {2.066285778103371e+008,-9.587754989355512e+005,5.732620476110842e+003,
        2.063899999999999e+002},{1.870796358504928e+008,-8.985159698708151e+005,
        5.567433409816551e+003,2.068900000000000e+002},{1.694800630152804e+008,
        -8.423737208584454e+005,5.408029086050894e+003,2.073900000000000e+002},
        {1.536254323472121e+008,-7.900460905552147e+005,5.254173889079566e+003,
        2.078900000000000e+002},{1.393350041292428e+008,-7.412546763455822e+005,
        5.105644838061499e+003,2.083900000000000e+002},{1.264461946876812e+008,
        -6.957420884142442e+005,4.962228931931791e+003,2.088900000000000e+002},
        {1.148149957717430e+008,-6.532714037371146e+005,4.823722794654673e+003,
        2.093900000000000e+002},{1.043126918759436e+008,-6.136238260582621e+005,
        4.689932103330038e+003,2.098900000000000e+002},{9.482399240733823e+007,
        -5.765972058455468e+005,4.560671161847407e+003,2.103900000000000e+002},
        {8.624641502669747e+007,-5.420050981894244e+005,4.435762520264600e+003,
        2.108900000000000e+002},{7.848790676326571e+007,-5.096749922949291e+005,
        4.315036509192491e+003,2.113899999999999e+002},{7.146637230514374e+007,
        -4.794475711409992e+005,4.198330916505517e+003,2.118899999999999e+002},
        {6.510826527489491e+007,-4.511754575867408e+005,4.085490594353537e+003,
        2.123900000000000e+002},{5.934772889807401e+007,-4.247223114761246e+005,
        3.976367129792119e+003,2.128900000000000e+002},{5.412562005348311e+007,
        -3.999618944172335e+005,3.870818517414752e+003,2.133899999999999e+002},
        {4.938925600232123e+007,-3.767775105272770e+005,3.768708878722507e+003,
        2.138899999999999e+002},{4.509087667312729e+007,-3.550607788424417e+005,
        3.669908110384081e+003,2.143900000000000e+002},{4.118807316164903e+007,
        -3.347115756562438e+005,3.574291699195102e+003,2.148900000000000e+002},
        {3.764247330924181e+007,-3.156368905942572e+005,3.481740374155148e+003,
        2.153899999999999e+002},{3.441971899342819e+007,-2.977505663723726e+005,
        3.392139916478927e+003,2.158900000000000e+002},{3.148883664649886e+007,
        -2.809726258964635e+005,3.305380896883451e+003,2.163899999999999e+002},
        {2.882206369704212e+007,-2.652289174340525e+005,3.221358471964407e+003,
        2.168900000000000e+002},{2.639430226411493e+007,-2.504505234176753e+005,
        3.139972148385238e+003,2.173900000000001e+002},{2.418303052952018e+007,
        -2.365735031462724e+005,3.061125608726445e+003,2.178900000000000e+002},
        {2.216790736643471e+007,-2.235384141346653e+005,2.984726499486276e+003,
        2.183900000000000e+002},{2.033061705830633e+007,-2.112900306234645e+005,
        2.910686262830227e+003,2.188900000000000e+002},{1.865461368328635e+007,
        -1.997769906568943e+005,2.838919956827780e+003,2.193900000000000e+002},
        {1.712501178845796e+007,-1.889515587375750e+005,2.769346100218770e+003,
        2.198900000000000e+002},{1.572830246673164e+007,-1.787692672877184e+005,
        2.701886501082210e+003,2.203900000000002e+002},{1.445234208083232e+007,
        -1.691887831467449e+005,2.636466131342296e+003,2.208899999999999e+002},
        {1.328611259790656e+007,-1.601715845366386e+005,2.573012964462273e+003,
        2.213899999999999e+002},{1.221967792218837e+007,-1.516818185846242e+005,
        2.511457857150583e+003,2.218899999999999e+002},{1.124402410901016e+007,
        -1.436860587692310e+005,2.451734410827016e+003,2.223900000000001e+002},
        {1.035100231090916e+007,-1.361531635944861e+005,2.393778859436568e+003,
        2.228900000000000e+002},{9.533236131047620e+006,-1.290541003018532e+005,
        2.337529949475997e+003,2.233899999999999e+002},{8.784032342642559e+006,
        -1.223617814028497e+005,2.282928828509020e+003,2.238899999999999e+002},
        {8.097324140450608e+006,-1.160509373912711e+005,2.229918944431192e+003,
        2.243900000000000e+002},{7.467609003399250e+006,-1.100979854201498e+005,
        2.178445944730142e+003,2.248900000000000e+002},{6.889898183747469e+006,
        -1.044809122220948e+005,2.128457581571682e+003,2.253900000000001e+002},
        {6.359654158917572e+006,-9.917915038790123e+004,2.079903618776534e+003,
        2.258900000000000e+002},{5.872759686767209e+006,-9.417349114733808e+004,
        2.032735749928480e+003,2.263900000000000e+002},{5.425475631504861e+006,
        -8.944598462814202e+004,1.986907513929262e+003,2.268900000000000e+002},
        {5.014390733055720e+006,-8.497983886637562e+004,1.942374214543448e+003,
        2.273900000000000e+002},{4.636415792979381e+006,-8.075936791787535e+004,
        1.899092852995913e+003,2.278900000000000e+002},{4.288733044060946e+006,
        -7.676988872480289e+004,1.857022047834165e+003,2.283900000000000e+002},
        {3.968773876673203e+006,-7.299765929671984e+004,1.816121971306828e+003,
        2.288899999999999e+002},{3.674202520100520e+006,-6.942982257803570e+004,
        1.776354286367471e+003,2.293900000000000e+002},{3.402892107203013e+006,
        -6.605434102471954e+004,1.737682082113611e+003,2.298900000000000e+002},
        {3.152896273279971e+006,-6.285993128052545e+004,1.700069813095759e+003,
        2.303899999999999e+002},{2.922447601033651e+006,-5.983603289980221e+004,
        1.663483248995434e+003,2.308899999999999e+002},{2.709926760057117e+006,
        -5.697273957445595e+004,1.627889413642931e+003,2.313900000000000e+002},
        {2.513861217833642e+006,-5.426077246627386e+004,1.593256539802403e+003,
        2.318900000000001e+002},{2.332900319601032e+006,-5.169142195505573e+004,
        1.559554014347537e+003,2.323900000000000e+002},{2.165813772476697e+006,
        -4.925652436360114e+004,1.526752336938422e+003,2.328900000000000e+002},
        {2.011475838578284e+006,-4.694841733751677e+004,1.494823071235126e+003,
        2.333899999999999e+002},{1.868856269356124e+006,-4.475990809519066e+004,
        1.463738803224226e+003,2.338900000000000e+002},{1.737013293432888e+006,
        -4.268424495431413e+004,1.433473101024697e+003,2.343900000000000e+002},
        {1.615084644443825e+006,-4.071508653570022e+004,1.404000474764923e+003,
        2.348899999999998e+002},{1.502280625890901e+006,-3.884647544872509e+004,
        1.375296339470493e+003,2.353900000000001e+002},{1.397877494187559e+006,
        -3.707281331859772e+004,1.347336979285312e+003,2.358900000000000e+002},
        {1.301213605644812e+006,-3.538884022447428e+004,1.320099513857462e+003,
        2.363899999999998e+002},{1.211679248380561e+006,-3.378960565339209e+004,
        1.293561863094709e+003,2.368900000000000e+002},{1.128718624184195e+006,
        -3.227045988925767e+004,1.267702720329528e+003,2.373900000000000e+002},
        {1.051819631323617e+006,-3.082702432545408e+004,1.242501517244634e+003,
        2.378900000000000e+002},{9.805119943329289e+005,-2.945517899158243e+004,
        1.217938398261965e+003,2.383900000000000e+002},{9.143661234246076e+005,
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        {-1.357244772388494e+001,-2.862919062243810e+001,5.296244024140553e+001,
        3.710000000000001e+002},{-1.717479675911297e+001,-2.874214450332900e+001,
        5.274508640521118e+001,3.711999999999999e+002},{-2.123801901866396e+001,
        -2.889134404513250e+001,5.252580043857113e+001,3.714000000000001e+002},
        {-2.619511142469762e+001,-2.907738790923127e+001,5.230424646131181e+001,
        3.716000000000000e+002},{-3.236073058364635e+001,-2.930723253179286e+001,
        5.208006194513168e+001,3.717999999999999e+002},{-4.022068942597398e+001,
        -2.958957539713408e+001,5.185280422638054e+001,3.720000000000000e+002},
        {-5.027803753687388e+001,-2.993866920656852e+001,5.162193160829787e+001,
        3.721999999999999e+002},{-6.436974496162212e+001,-3.035919422556437e+001,
        5.138671614373845e+001,3.724000000000002e+002},{-8.360686397848249e+001,
        -3.088595220083816e+001,5.114631483263473e+001,3.726000000000000e+002},
        {-1.100834389241486e+002,-3.155568586681570e+001,5.089950843562296e+001,
        3.728000000000001e+002},{-1.472841062914758e+002,-3.245099931262556e+001,
        5.064476196619719e+001,3.730000000000000e+002},{-2.021579877018242e+002,
        -3.370859211762419e+001,5.037989000027908e+001,3.732000000000001e+002},
        {-2.897791479469411e+002,-3.471839082840622e+001,5.017174758533965e+001,
        3.733500000000000e+002},{-4.370418417975305e+002,-3.595572803188362e+001,
        4.995306621058514e+001,3.735000000000001e+002},{-6.808564431390644e+002,
        -3.803753250618856e+001,4.971098502785520e+001,3.736561480000000e+002},
        {-1.079182893585270e+003,-4.178442673431590e+001,4.945933042367851e+001,
        3.738058199999999e+002},{-1.681835788759286e+003,-4.662329946397544e+001,
        4.925008325739737e+001,3.739180740000000e+002},{-2.582563222934587e+003,
        -5.134362044917342e+001,4.909428751215069e+001,3.739929099999999e+002},
        {-4.106828068576426e+003,-5.577687841590389e+001,4.896368572381315e+001,
        3.740490370000001e+002},{-5.107591845246606e+003,-6.580440293493800e+001,
        4.883933501194808e+001,3.740976804000001e+002},{-9.771765920564003e+003,
        -7.560712452291881e+001,4.870422526751046e+001,3.741425820000000e+002},
        {-8.755497642709564e+003,-8.742278426612906e+001,4.864183118847620e+001,
        3.741612909999998e+002},{-9.815118604201449e+003,-9.075723406919788e+001,
        4.861419440063168e+001,3.741687745999999e+002},{-1.598688798560589e+004,
        -9.374464327459545e+001,4.857016747633733e+001,3.741800000000001e+002},
        {-1.920875724714269e+004,-1.019624881152255e+002,4.852930969549549e+001,
        3.741899999999998e+002},{-1.636215913588905e+005,-7.659891465615223e+001,
        4.848251558276280e+001,3.741999999999999e+002},{-1.286897688417260e+006,
        1.186575607887113e+001,4.845730381784014e+001,3.742050000000000e+002},{
        8.838952576730371e+007,-4.445028478910222e+003,4.849792832024318e+001,
        3.742074999999999e+002}};
    constant Real[Ninterval, 4] ptcoef={{0.786553610980441,0.073986317581331,
        0.004029258982827,0.000095977628483},{0.804804842020852,
        0.075513868977931,0.004128852620146,0.000098693577477},{
        0.826483769874362,0.076781180144682,0.004214141994619,0.000101026437564},
        {0.852226781522051,0.079838214007716,0.004413722019840,
        0.000106516958458},{0.878734233127809,0.083011720420838,
        0.004622630654312,0.000112305941336},{0.905918938100631,
        0.086306406812799,0.004841289235230,0.000118409424841},{
        0.933873884997079,0.089726230581858,0.005070153132594,0.000124844693392},
        {0.962577238137988,0.093275895699320,0.005309687431187,
        0.000131629706447},{0.992070856558737,0.096959926219076,
        0.005560383405310,0.000138783529530},{1.022340779604642,
        0.100783239811202,0.005822748456693,0.000146326107976},{
        1.053408429650162,0.104750722856737,0.006097318061549,0.000154278611181},
        {1.085334401770672,0.108867191838833,0.006384645627683,
        0.000162663184614},{1.118066059070003,0.113138431880924,
        0.006685319756183,0.000171503506240},{1.151675830716446,
        0.117569521390065,0.006999950677252,0.000180824369499},{
        1.186152658253827,0.122166182229820,0.007329167943923,0.000190651710758},
        {1.221529325860328,0.126934198374854,0.007673642176701,
        0.000201013248529},{1.257786462283640,0.131879624460586,
        0.008034059624186,0.000211937791220},{1.294812956053328,
        0.137009131430195,0.008411150309429,0.000223456117470},{
        1.332050814897662,0.142331923230738,0.008805666323160,0.000235600452886},
        {1.369397755526468,0.147855890364265,0.009218393425041,
        0.000248404751272},{1.406816638143677,0.153467769902578,
        0.009641353399052,0.000261628465319},{1.444356079648527,
        0.158956456158090,0.010059134663008,0.000274788118369},{
        1.482496486580440,0.164593208638941,0.010491786565620,0.000288515879081},
        {1.521219525653765,0.170380509776158,0.010939707938024,
        0.000302831882662},{1.560542804418774,0.176320624445618,
        0.011403304275305,0.000317756801604},{1.600437543776211,
        0.182416074041046,0.011882987053658,0.000333311854289},{
        1.640936272107287,0.188669018847875,0.012379174551977,0.000349518813327},
        {1.681996400839473,0.195082050643184,0.012892290728097,
        0.000366400014143},{1.723656934024151,0.201657263429387,
        0.013422766529104,0.000383978363163},{1.765877582075693,
        0.208397225399801,0.013971038423670,0.000402277346453},{
        1.808673898875252,0.215304119402563,0.014537549727065,0.000421321037758},
        {1.852056948436205,0.222380208630733,0.015122749655067,
        0.000441134107092},{1.895976234842191,0.229628047386924,
        0.015727093310843,0.000461741828759},{1.940485837249081,
        0.237049568378319,0.016351042726376,0.000483170089585},{
        1.985535349395222,0.244647339911478,0.016995065014999,0.000505445397324},
        {2.031148612115400,0.252423430625727,0.017659634148470,
        0.000528594888329},{2.077302947391230,0.260380191193645,
        0.018345229588173,0.000552646335999},{2.124013371424510,
        0.268519730288320,0.019052337090330,0.000577628158512},{
        2.171233734600246,0.276844461955414,0.019781447908203,0.000603569426887},
        {2.219036879803186,0.285356138275785,0.020533059923821,
        0.000630499872733},{2.267319033113332,0.294057511278019,
        0.021307675460814,0.000658449896208},{2.316150758140982,
        0.302950218193697,0.022105804263753,0.000687450573315},{
        2.365499765564834,0.312036591386713,0.022927960463078,0.000717533664244},
        {2.415341254676885,0.321318803772746,0.023774664275808,
        0.000748731620229},{2.465702228666255,0.330798721201480,
        0.024646441777799,0.000781077591413},{2.516566337049237,
        0.340478491545039,0.025543824020845,0.000814605434250},{
        2.567900988365430,0.350360262236221,0.026467347650949,0.000849349718558},
        {2.619736333280843,0.360445798567964,0.027417555102175,
        0.000885345734951},{2.672048765758521,0.370737202172238,
        0.028394993495523,0.000922629502038},{2.724826587346702,
        0.381236432325441,0.029400215484282,0.000961237773163},{
        2.778063214522083,0.391945380908662,0.030433778913126,0.001001208043570},
        {2.831766036616288,0.402865857403683,0.031496246697041,
        0.001042578557225},{2.885908682390723,0.413999836240006,
        0.032588186505531,0.001085388313488},{2.940499375779766,
        0.425349047466033,0.033710171266653,0.001129677073668},{
        2.995518695471547,0.436915364909673,0.034862778477020,0.001175485367706},
        {3.050956509836956,0.448700547312638,0.036046590569830,
        0.001222854500461},{3.106820822095549,0.460706240111525,
        0.037262194688661,0.001271826558129},{3.163093309167843,
        0.472934226350843,0.038510182323064,0.001322444414376},{
        3.219746757773316,0.485386251264479,0.039791149597540,0.001374751736327},
        {3.276823378325092,0.498063672720634,0.041105697402525,
        0.001428792990668},{3.334256093194325,0.510968455863627,
        0.042454430092932,0.001484613449495},{3.392066452222572,
        0.524101941700382,0.043837957232333,0.001542259195759},{
        3.450267320729766,0.537465592429579,0.045256892052289,0.001601777129328},
        {3.508789067634338,0.551061252504325,0.046711851466142,
        0.001663214972080},{3.567677958706406,0.564890022697125,
        0.048203457357055,0.001726621273310},{3.626905151411771,
        0.578953490302442,0.049732334529406,0.001792045415320},{
        3.686462083749643,0.593253045708126,0.051299111947236,0.001859537618008},
        {3.746327635912001,0.607790095318200,0.052904422199431,
        0.001929148944129},{3.806521328539690,0.622565797973926,
        0.054548901665213,0.002000931304129},{3.867009632214078,
        0.637581603413359,0.056233189735702,0.002074937460871},{
        3.927782116924284,0.652838734378914,0.057957929579066,0.002151221034049},
        {3.988852365666806,0.668338275550249,0.059723767660887,
        0.002229836504888},{4.050192516216124,0.684081532186310,
        0.061531353270102,0.002310839220353},{4.111789278896813,
        0.700069639448781,0.063381339086498,0.002394285397225},{
        4.173651666210960,0.716303589828222,0.065274380831822,0.002480232126358},
        {4.235756676172436,0.732784540271985,0.067211136814012,
        0.002568737376544},{4.298085502042800,0.749513538707623,
        0.069192268324502,0.002659859998184},{4.360671661599279,
        0.766491347937005,0.071218439541212,0.002753659727090},{
        4.423438949366865,0.783719304937090,0.073290316468236,0.002850197187960},
        {4.486438551377852,0.801197930575199,0.075408568729196,
        0.002949533897579},{4.549635083346689,0.818928297908401,
        0.077573867304666,0.003051732268502},{4.613005208765145,
        0.836911289865486,0.079786885896258,0.003156855611648},{
        4.676574403683728,0.855147500168120,0.082048300614339,0.003264968139624},
        {4.740297050704474,0.873637909632577,0.084358789038483,
        0.003376134969544},{4.804190690507514,0.892383063052667,
        0.086719031350494,0.003490422125512},{4.868235121873531,
        0.911383726822147,0.089129709147211,0.003607896541475},{
        4.932419559693664,0.930640548615199,0.091591505998932,0.003728626063414},
        {4.996730104947655,0.950154145354210,0.094105107137860,
        0.003852679451797},{5.061189204396221,0.969924932558094,
        0.096671199500138,0.003980126383733},{5.125721774355183,
        0.989953806668835,0.099290470904280,0.004111037454977},{
        5.190399776670092,1.010240773734387,0.101963611687264,0.004245484181735},
        {5.255151436743157,1.030786704419071,0.104691312074425,
        0.004383539002791},{5.319997881680896,1.051591809289908,
        0.107474264565075,0.004525275280559},{5.384915083275455,
        1.072656564602096,0.110313162173150,0.004670767303162},{
        5.449915764807296,1.093981202980726,0.113208699187816,0.004820090285488},
        {5.514961084515890,1.115566214746911,0.116161570403907,
        0.004973320370546},{5.580069995165794,1.137411702858405,
        0.119172471924876,0.005130534630481},{5.645214917013816,
        1.159518032770311,0.122242100064668,0.005291811067763},{
        5.710397135075893,1.181885343682942,0.125371152069178,0.005457228615834},
        {5.775601905695197,1.204513844192818,0.128560325505952,
        0.005626867140010},{5.840835782784636,1.227403598430226,
        0.131810318497041,0.005800807438005},{5.906059494800497,
        1.250554880485784,0.135121829207348,0.005979131240455},{
        5.971301283679346,1.273967536407251,0.138495556564960,0.006161921211248},
        {6.036525184627135,1.297641782816887,0.141932199008561,
        0.006349260947941},{6.101742108554982,1.321577504276583,
        0.145432455530469,0.006541234981608},{6.166925944102037,
        1.345774777484733,0.148997024740760,0.006737928777106},{
        6.232083718610021,1.370233441641100,0.152626605432942,0.006939428732812},
        {6.297207184980851,1.394953425336797,0.156321895953925,
        0.007145822180530},{6.362277871137049,1.419934665093411,
        0.160083594379107,0.007357197385014},{6.427293032446297,
        1.445176960347283,0.163912398571472,0.007573643543593},{
        6.492248494825507,1.470680105264633,0.167809005838224,0.007795250785685},
        {6.557139915959902,1.496443877947695,0.171774112913575,
        0.008022110172037},{6.621948550316446,1.522468096828492,
        0.175808415864079,0.008254313693933},{6.686677764125916,
        1.548752416568682,0.179912610249625,0.008491954272338},{
        6.751318489523362,1.575296555162762,0.184087390680888,0.008735125756982},
        {6.815849328693517,1.602100243679581,0.188333450922353,
        0.008983922925176},{6.880294415977666,1.629162944906189,
        0.192651484067798,0.009238441480674},{6.944622895829550,
        1.656484438791168,0.197042181708333,0.009498778052406},{
        7.008826622849972,1.684064290571623,0.201506234762844,0.009765030192908},
        {7.072914856384893,1.711901963064116,0.206044333006924,
        0.010037296377091},{7.136877800207411,1.739997032582018,
        0.210657164762212,0.010315676000575},{7.200691051456989,
        1.768349094724015,0.215345417113497,0.010600269377903},{
        7.264377479650122,1.796957457787893,0.220109776102959,0.010891177740886},
        {7.327906141296870,1.825821737448506,0.224950925854684,
        0.011188503236811},{7.391293625276115,1.854941234807067,
        0.229869549469729,0.011492348926300},{7.454508371077754,
        1.884315510467502,0.234866328098409,0.011802818781492},{
        7.517569054229431,1.913943797155383,0.239941941727175,0.012120017683787},
        {7.580459415407503,1.943825542494100,0.245097068267364,
        0.012444051421826},{7.643171908708069,1.973960094001435,
        0.250332384098234,0.012775026689016},{7.705707996362623,
        2.004346732841488,0.255648563847159,0.013113051081326},{
        7.768059519623182,2.034984784600641,0.261046280194050,0.013458233094852},
        {7.830220904482947,2.065873531807347,0.266526203982097,
        0.013810682123266},{7.892188564751971,2.097012226673120,
        0.272089004114447,0.014170508455295},{7.953965487964128,
        2.128400080683881,0.277735347500195,0.014537823272081},{
        8.015523649434170,2.160036441620303,0.283465898846533,0.014912738644454},
        {8.076895462829125,2.191920302660508,0.289281321183433,
        0.015295367530163},{8.138044320167687,2.224051063573816,
        0.295182274777506,0.015685823771147},{8.198976439581513,
        2.256427805724049,0.301169418248213,0.016084222090402},{
        8.259707938402711,2.289049595720479,0.307243407828786,0.016490678089312},
        {8.320192607430975,2.321915814614592,0.313404897121920,
        0.016905308244463},{8.380470028810771,2.355025314333463,
        0.319654538135147,0.017328229904537},{8.440522518139051,
        2.388377335023929,0.325992979815505,0.017759561287442},{
        8.500322217978708,2.421971086721057,0.332420868948437,0.018199421476779},
        {8.559907453252212,2.455805402507063,0.338938850295470,
        0.018647930418875},{8.619247679352942,2.489879545144593,
        0.345547565459140,0.019105208919565},{8.678350338810887,
        2.524192502690502,0.352247654043904,0.019571378640574},{
        8.737200358793032,2.558743383285288,0.359039752909466,0.020046562096445},
        {8.795818738593697,2.593531090067868,0.365924496580261,
        0.020530882651035},{8.854183207405342,2.628554783799626,
        0.372902516607536,0.021024464514114},{8.912292637601727,
        2.663813451198047,0.379974442256104,0.021527432737748},{
        8.970164816146156,2.699305998657141,0.387140900144449,0.022039913212986},
        {9.027764581740044,2.735031616100854,0.394402513874834,
        0.022562032666223},{9.085123127706376,2.770989086540987,
        0.401759904933333,0.023093918655552},{9.142217145365851,
        2.807177536491606,0.409213691526334,0.023635699567366},{
        9.199057526581893,2.843595861945240,0.416764489523273,0.024187504612462},
        {9.255634156711325,2.880243086753219,0.424412911826686,
        0.024749463822588},{9.311949978406053,2.917118141884187,
        0.432159568722993,0.025321708046652},{9.368005011068972,
        2.954219981819242,0.440005067647167,0.025904368947099},{
        9.423798091407672,2.991547565855996,0.447950013236107,0.026497578996133},
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        14.721256475920658,4.646549038424966,0.565201580011704},{
        27.344634819583604,14.817934767851131,4.682300495420807,
        0.570846529867353},{27.713671593677677,14.914273470914237,
        4.717686824578717,0.576439888432411},{28.089691272397957,
        15.010280930582828,4.752709493736557,0.581981383336399},{
        28.472824854307039,15.105965165341871,4.787370055045711,
        0.587470774387750},{28.863193517870002,15.201334102546408,
        4.821670140178958,0.592907852495206},{29.260918302887685,
        15.296395505394935,4.855611456225897,0.598292438610054},{
        29.666132958462629,15.391156926950673,4.889195781620369,
        0.603624382689606},{30.078982460204806,15.485625755858862,
        4.922424962124026,0.608903562681821},{30.499592721193313,
        15.579809342711769,4.955300906990578,0.614129883531367},{
        30.928117472544855,15.673714785982705,4.987825585602939,
        0.619303276207172},{31.364710865969087,15.767349102050195,
        5.020001023779209,0.624423696751405},{31.809515123102404,
        15.860719254916436,5.051829300512150,0.629491125349948},{
        32.262705236081672,15.953831979977263,5.083312544958544,
        0.634505565424281},{32.724447907289544,16.046694000766831,
        5.114452933148136,0.639467042744666},{33.194897132039792,
        16.139312001629271,5.145252685204367,0.644375604564581},{
        33.674255019897664,16.231692414917958,5.175714062698377,
        0.649231318776222},{34.162693117856691,16.323841771582561,
        5.205839365624563,0.654034273086982},{34.660408283882070,
        16.415766446679168,5.235630930162420,0.658784574216433},{
        35.167590811037854,16.507472809522142,5.265091126045004,
        0.663482347114145},{35.684449944091867,16.598967127675568,
        5.294222354303641,0.668127734197491},{36.211206269977197,
        16.690255627599420,5.323027044937864,0.672720894609739},{
        36.748056707258620,16.781344600488524,5.351507654715894,
        0.677262003497751},{37.295248265383698,16.872240144915182,
        5.379666665308135,0.681751251309287},{37.852995971145809,
        16.962948488394094,5.407506580997999,0.686188843109573},{
        38.421564488506611,17.053475690433864,5.435029927062224,
        0.690574997916736},{39.001171266768537,17.143827988284571,
        5.462239247649191,0.694909948055925},{39.592097221535276,
        17.234011403696112,5.489137104365301,0.699193938531812},{
        40.194606324023972,17.324032074846357,5.515726074258302,
        0.703427226419012},{40.808938401803530,17.413896207928254,
        5.542008748346981,0.707610080270340},{41.435436776864577,
        17.503609730835098,5.567987730243535,0.711742779542350},{
        42.074330693130328,17.593178988541467,5.593665634167064,
        0.715825614037971},{42.725940101764373,17.682610023334441,
        5.619045084134955,0.719858883365846},{43.390590488356239,
        17.771908949085155,5.644128712167098,0.723842896416144},{
        44.070645121622796,17.861077799265878,5.668919158926054,
        0.727777970852333},{44.753184105407975,17.950153724907196,
        5.693419053900836,0.731664432618789},{45.474373691042267,
        18.039048771108984,5.717631098338662,0.735502615463705},{
        46.193899163412112,18.127899243718634,5.741557851475661,
        0.739292860480826},{46.996029946900421,18.216517946983732,
        5.765202097955019,0.743035515642772},{47.975217272766379,
        18.304869267108689,5.788566478022887,0.746730935410193},{
        46.875088973944962,18.397435734790200,5.811651899684304,
        0.750379480284763},{51.065991163454697,18.476818607729076,
        5.834469443821195,0.753981516503356},{49.333461744266728,
        18.573099243289850,5.857003438946910,0.757537415856357},{
        50.827892820844589,18.659006028627026,5.879277141033153,
        0.761047552504248},{51.658864029489543,18.747265541446783,
        5.901281540617321,0.764512309584712},{52.507342163173028,
        18.835468843734557,5.923021904004630,0.767932071140582},{
        53.373793178351164,18.923622470147773,5.944500865847515,
        0.771307225875759},{54.258789501497823,19.011732877688232,
        5.965721054625218,0.774638165973891},{55.162916478482941,
        19.099806756700104,5.986685091803454,0.777925286781048},{
        56.087116564192172,19.187850477830338,6.007395591520163,
        0.781168986499608},{57.032398932408853,19.275871118680147,
        6.027855159614455,0.784369665893400},{58.000369060093050,
        19.363875690575604,6.048066393969457,0.787527728003472},{
        59.016634487394832,19.451836730736815,6.068031895995421,
        0.790643577874778},{60.091857764934808,19.539739992232406,
        6.087754256968488,0.793717622293261},{61.240245331030316,
        19.627560573034796,6.107236083235058,0.796750269533514},{
        62.480561298708686,19.723763384189539,6.128269590423300,
        0.800019963066246},{61.700811904981713,19.825193831111250,
        6.149405839679586,0.803300925851243},{67.613280255293020,
        19.914643859675749,6.170653665148103,0.806593213984968},{
        65.160632861084636,20.026986310421218,6.191997393361786,
        0.809896884700018},{67.669033122940235,20.127441775170933,
        6.213461939269268,0.813211994514738},{69.158974688263967,
        20.233552143778557,6.235035431887980,0.816538605363333},{
        70.723256826348845,20.341932263338009,6.256723667414029,
        0.819876776933363},{72.367614994324157,20.452692130214967,
        6.278529139019087,0.823226571210103},{74.098101167452896,
        20.565950434907393,6.300454462542573,0.826588051543621},{
        75.921523426230067,20.681834359896129,6.322502386312879,
        0.829961282716883},{77.845391462064271,20.800480873586661,
        6.344675800844324,0.833346331019091},{79.877973252120924,
        20.922037773350514,6.366977749927341,0.836743264324587},{
        82.028526688840202,21.046664524133615,6.389411442986359,
        0.840152152177982},{84.307359657115470,21.174533750826306,
        6.411980268436992,0.843573065886157},{86.726134004965445,
        21.305832439883137,6.434687808816977,0.847006078617858},{
        89.298052645255225,21.440763800191853,6.457537857418896,
        0.850451265511744},{92.038364283034596,21.579548930296038,
        6.480534437230531,0.853908703793904},{94.965026588148092,
        21.722429035678608,6.503681822191650,0.857378472906041},{
        98.099651271544445,21.869668254286683,6.526984561549138,
        0.860860654645750},{101.469212866843510,22.021556781161863,
        6.550447508473278,0.864355333320771},{105.108611392323670,
        22.178415351638186,6.574075853974501,0.867862595919685},{
        109.065005486134880,22.340601002668283,6.597875168817166,
        0.871382532302410},{109.750042242080070,22.514375499939113,
        6.621849368866829,0.874915235415403},{122.164468808740280,
        22.670441678991452,6.646016608190354,0.878460801538834},{
        120.492493879440720,22.868998811452705,6.670353260952902,
        0.882019330576957},{127.651716860571530,23.050715346380404,
        6.694905768119855,0.885590923061522},{133.417901827374580,
        23.246144421955755,6.719657855196887,0.889175690895975},{
        139.724332490425070,23.449952674292600,6.744624090533837,
        0.892773744452224},{146.646067568266890,23.662885976357035,
        6.769813936652642,0.896385200660068},{154.272084490525660,
        23.885788232412818,6.795237725626818,0.900010181731173},{
        162.708903919517890,24.119617882190067,6.820906777869384,
        0.903648815653934},{172.084864641046120,24.365469173499047,
        6.846833542039902,0.907301236757100},{182.556942338038600,
        24.624596217120128,6.873031762800324,0.910967586354904},{
        194.319534415060760,24.898444814009999,6.899516681255775,
        0.914648013489756},{207.620595915041970,25.188686585937077,
        6.926305281144004,0.918342675792510},{222.788620730249990,
        25.497261589113076,6.953416591526287,0.922051740486512},{
        240.287692571162920,25.826419168838576,6.980872074207111,
        0.925775385569714},{256.799890482864780,26.185216782196846,
        7.008693832401432,0.929513801223933},{286.851617485832720,
        26.548780722767628,7.036921002156521,0.933267191524989},{
        308.757481229623580,26.973589993440147,7.065557892145567,
        0.937035776577968},{342.616615998311150,27.414357072890436,
        7.094674470820509,0.940819791613239},{381.652936748389780,
        27.901112273738025,7.124294167964932,0.944619499388744},{
        429.420511597585570,28.436458075451569,7.154472608250879,
        0.948435182728345},{488.956374804092890,29.029524488453990,
        7.185270948459126,0.952267155471084},{564.913569104604680,
        29.691719970341111,7.216763630423190,0.956115767213528},{
        662.593654854627520,30.440873759588669,7.249041648619902,
        0.959981411307655},{798.395259632387020,31.285522685311911,
        7.282225938437964,0.963864535640684},{984.858707574925800,
        32.266683177856073,7.316458408944520,0.967765657677109},{
        1240.731677732101800,33.435525835453468,7.351939105152393,
        0.971685384357021},{1599.976231716470900,34.896887003483748,
        7.388921872674265,0.975624447015660},{2129.911398579198200,
        36.824993793515745,7.427765289272872,0.979583747790001},{
        2973.337742375393600,38.358182172438710,7.458590833881339,
        0.982567188320956},{4392.068482735210600,40.182279884917335,
        7.491259295582522,0.985563285803890},{6744.182542887068800,
        43.093253924408778,7.527746112509292,0.988696515392235},{
        10586.401080300620000,48.112109166481709,7.566030993328872,
        0.991714705866086},{16414.657806854295000,54.433838984731196,
        7.598161821734584,0.993988954446224},{25171.400376638227000,
        60.516762902335024,7.622270849789598,0.995510777346757},{
        39924.646532205254000,66.237216173833630,7.642602684084054,
        0.996655475718842},{50014.862506044708000,78.880685852650700,
        7.662052700016630,0.997650144001249},{94512.909959942233000,
        91.545289401322989,7.683298623696445,0.998570741182521},{
        85789.631197521958000,106.331709600833660,7.693152458218265,
        0.998955116981272},{96484.149392753985000,110.551277570634270,
        7.697526525177595,0.999109011318793},{155745.736499270020000,
        114.483229466648910,7.704504194463604,0.999340021303733},{
        187336.117221347780000,124.858748457008220,7.710990375742048,
        0.999545993761771},{1561441.955568452100000,93.976965631416093,
        7.718432905786972,0.999752147562480},{12254471.880229050000000,-14.883471920491438,
        7.722448708901911,0.999855298039152},{-840729689.033797860000000,
        5473.418677569786300,7.715971952179429,0.999906892844623}};
    constant Real[Ninterval, 4] dltcoef={{-7.119202491756649e-001,-2.739402377062618e-001,
        -1.927672596844717e+000,3.108234546713844e+000},{-7.187746754592991e-001,
        -2.753459585506838e-001,-1.928038361308511e+000,3.106950869117843e+000},
        {-7.267169555982382e-001,-2.765215049130652e-001,-1.928347041349235e+000,
        3.105872508783626e+000},{-7.359380114100472e-001,-2.792612028934110e-001,
        -1.929054601531175e+000,3.103417366473884e+000},{-7.451596984095644e-001,
        -2.820546952208173e-001,-1.929773991238450e+000,3.100944868392513e+000},
        {-7.543868380432980e-001,-2.849025526846495e-001,-1.930505474697466e+000,
        3.098454883787075e+000},{-7.636195252102033e-001,-2.878055700919983e-001,
        -1.931249367470398e+000,3.095947126307967e+000},{-7.728608352753940e-001,
        -2.907644204639990e-001,-1.932005961304827e+000,3.093421411830454e+000},
        {-7.821138534967362e-001,-2.937798575560094e-001,-1.932775569789591e+000,
        3.090877503680519e+000},{-7.913807227613616e-001,-2.968525969010559e-001,
        -1.933558497589903e+000,3.088315215846500e+000},{-8.006644142147472e-001,
        -2.999834307075162e-001,-1.934355071871375e+000,3.085734309672668e+000},
        {-8.099668105946853e-001,-3.031731138060267e-001,-1.935165610880807e+000,
        3.083134597151535e+000},{-8.192918853252418e-001,-3.064225359625613e-001,
        -1.935990472438392e+000,3.080515785796513e+000},{-8.286413378736912e-001,
        -3.097325618705826e-001,-1.936830006147945e+000,3.077877633663473e+000},
        {-8.380195338699306e-001,-3.131039924173268e-001,-1.937684552795189e+000,
        3.075219949428117e+000},{-8.474270870580881e-001,-3.165378097414413e-001,
        -1.938554494310329e+000,3.072542437056092e+000},{-8.568696991541474e-001,
        -3.200348522413296e-001,-1.939440187491448e+000,3.069844902846438e+000},
        {-8.663006219851039e-001,-3.235963509846717e-001,-1.940342031243627e+000,
        3.067127048225000e+000},{-8.755969029666063e-001,-3.272238814054915e-001,
        -1.941260416087275e+000,3.064388625095321e+000},{-8.847451895324255e-001,
        -3.309187279025791e-001,-1.942195741563215e+000,3.061629384019479e+000},
        {-8.937320642447604e-001,-3.346053531802966e-001,-1.943129242827890e+000,
        3.058904739456490e+000},{-9.025917571346555e-001,-3.381523238866969e-001,
        -1.944028228246023e+000,3.056307824467905e+000},{-9.114372727199264e-001,
        -3.417348650176046e-001,-1.944936739647034e+000,3.053709701944858e+000},
        {-9.202705051593279e-001,-3.453529129795982e-001,-1.945854872015144e+000,
        3.051110359095721e+000},{-9.290943179147365e-001,-3.490064060917521e-001,
        -1.946782720180552e+000,3.048509783002059e+000},{-9.379113035378066e-001,
        -3.526952951802167e-001,-1.947720378827961e+000,3.045907960618840e+000},
        {-9.467220586520030e-001,-3.564195514784557e-001,-1.948667942508438e+000,
        3.043304878774594e+000},{-9.555308122884657e-001,-3.601791344616129e-001,
        -1.949625505711145e+000,3.040700524171566e+000},{-9.643382215985582e-001,
        -3.639740319079109e-001,-1.950593162835531e+000,3.038094883385813e+000},
        {-9.731477743382022e-001,-3.678042249680064e-001,-1.951571008256408e+000,
        3.035487942867281e+000},{-9.819604804460426e-001,-3.716697186165744e-001,
        -1.952559136308239e+000,3.032879688939842e+000},{-9.907792924725812e-001,
        -3.755705130003580e-001,-1.953557641352945e+000,3.030270107801308e+000},
        {-9.996061903488108e-001,-3.795066236033756e-001,-1.954566617769396e+000,
        3.027659185523410e+000},{-1.008442332217312e+000,-3.834780801466576e-001,
        -1.955586159975327e+000,3.025046908051736e+000},{-1.017291187118612e+000,
        -3.874849056387030e-001,-1.956616362486219e+000,3.022433261205659e+000},
        {-1.026154224708753e+000,-3.915271430094308e-001,-1.957657319899389e+000,
        3.019818230678225e+000},{-1.035032728246099e+000,-3.956048454200966e-001,
        -1.958709126923303e+000,3.017201802035997e+000},{-1.043929801274928e+000,
        -3.997180632397729e-001,-1.959771878421853e+000,3.014583960718895e+000},
        {-1.052846917422804e+000,-4.038668640643446e-001,-1.960845669410642e+000,
        3.011964692039990e+000},{-1.061785874617104e+000,-4.080513211658256e-001,
        -1.961930595091244e+000,3.009343981185274e+000},{-1.070749281155416e+000,
        -4.122715113299520e-001,-1.963026750875285e+000,3.006721813213400e+000},
        {-1.079738284824320e+000,-4.165275287976867e-001,-1.964134232385564e+000,
        3.004098173055395e+000},{-1.088755056537119e+000,-4.208194669364273e-001,
        -1.965253135509263e+000,3.001473045514344e+000},{-1.097802354172137e+000,
        -4.251474262252926e-001,-1.966383556395710e+000,2.998846415265045e+000},
        {-1.106880826500578e+000,-4.295115260316672e-001,-1.967525591470941e+000,
        2.996218266853638e+000},{-1.115992785290996e+000,-4.339118828275575e-001,
        -1.968679337486387e+000,2.993588584697207e+000},{-1.125140601947682e+000,
        -4.383486216067864e-001,-1.969844891518973e+000,2.990957353083350e+000},
        {-1.134325959887290e+000,-4.428218781489602e-001,-1.971022350993147e+000,
        2.988324556169727e+000},{-1.143550497239480e+000,-4.473317957093480e-001,
        -1.972211813704686e+000,2.985690177983577e+000},{-1.152816353482765e+000,
        -4.518785235407696e-001,-1.973413377839173e+000,2.983054202421210e+000},
        {-1.162124575492226e+000,-4.564622237902882e-001,-1.974627141987564e+000,
        2.980416613247473e+000},{-1.171478417504371e+000,-4.610830531229002e-001,
        -1.975853205189499e+000,2.977777394095186e+000},{-1.180878493083438e+000,
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        -4.384508863125920e+000,1.961103344743806e+000},{-9.638803576032707e+001,
        -1.441179912568236e+001,-4.422583856657013e+000,1.955219658422624e+000},
        {-1.006355886419617e+002,-1.478104683078891e+001,-4.461628093181375e+000,
        1.949284456050977e+000},{-1.051313454597849e+002,-1.516621147525332e+001,
        -4.501682994351671e+000,1.943296415304725e+000},{-1.098726320850258e+002,
        -1.557562130758561e+001,-4.543476494807336e+000,1.937154374999355e+000},
        {-1.148328382566474e+002,-1.599730363449987e+001,-4.585776601560153e+000,
        1.931045251398180e+000},{-1.200188108246691e+002,-1.643068297329990e+001,
        -4.628499471591676e+000,1.924981823573037e+000},{-1.254402600577610e+002,
        -1.687609306545174e+001,-4.671650064463239e+000,1.918963711773316e+000},
        {-1.311072854774274e+002,-1.733387495899903e+001,-4.715233405571223e+000,
        1.912990539037578e+000},{-1.370304007377400e+002,-1.780437708974399e+001,
        -4.759254580973940e+000,1.907061931185782e+000},{-1.432205478371830e+002,
        -1.828795544632071e+001,-4.803718732234705e+000,1.901177516818668e+000},
        {-1.496891184999602e+002,-1.878497370717625e+001,-4.848631051484921e+000,
        1.895336927323218e+000},{-1.564479780964446e+002,-1.929580338699566e+001,
        -4.893996776657341e+000,1.889539796883510e+000},{-1.635094896114932e+002,
        -1.982082401614414e+001,-4.939821186869632e+000,1.883785762496075e+000},
        {-1.708865276896965e+002,-2.036042337835779e+001,-4.986109598005116e+000,
        1.878074463988980e+000},{-1.785925165319611e+002,-2.091499764565038e+001,
        -5.032867358670587e+000,1.872405544044007e+000},{-1.866414510420746e+002,
        -2.148495164496683e+001,-5.080099846220948e+000,1.866778648221036e+000},
        {-1.950479162106498e+002,-2.207069912489180e+001,-5.127812463129048e+000,
        1.861193424984080e+000},{-2.038271353278870e+002,-2.267266292380108e+001,
        -5.176010633724887e+000,1.855649525728495e+000},{-2.129949758145855e+002,
        -2.329127536217849e+001,-5.224699800985325e+000,1.850146604808510e+000},
        {-2.225680072626292e+002,-2.392697840643329e+001,-5.273885423907177e+000,
        1.844684319564753e+000},{-2.325635046039472e+002,-2.458022411269052e+001,
        -5.323572974870670e+000,1.839262330351306e+000},{-2.429995182741653e+002,
        -2.525147478994882e+001,-5.373767937627715e+000,1.833880300561732e+000},
        {-2.538948748098448e+002,-2.594120350769362e+001,-5.424475805224988e+000,
        1.828537896653741e+000},{-2.652692415314800e+002,-2.664989431255637e+001,
        -5.475702078602022e+000,1.823234788172320e+000},{-2.771431560702175e+002,
        -2.737804267118220e+001,-5.527452265174031e+000,1.817970647770634e+000},
        {-2.895380660742452e+002,-2.812615585599748e+001,-5.579731877863270e+000,
        1.812745151228864e+000},{-3.024763750171533e+002,-2.889475333428489e+001,
        -5.632546434409225e+000,1.807557977470461e+000},{-3.159814902028902e+002,
        -2.968436718887993e+001,-5.685901456916128e+000,1.802408808575871e+000},
        {-3.300778700110466e+002,-3.049554255611214e+001,-5.739802471693491e+000,
        1.797297329793238e+000},{-3.447910678389576e+002,-3.132883810210219e+001,
        -5.794255009340000e+000,1.792223229546456e+000},{-3.601477887192862e+002,
        -3.218482647037611e+001,-5.849264605126227e+000,1.787186199439965e+000},
        {-3.761759502852180e+002,-3.306409475164691e+001,-5.904836799592490e+000,
        1.782185934260666e+000},{-3.929047215975117e+002,-3.396724504852546e+001,
        -5.960977139338727e+000,1.777222131976677e+000},{-4.103646058482501e+002,
        -3.489489490975335e+001,-6.017691178152736e+000,1.772294493733011e+000},
        {-4.285874676385886e+002,-3.584767798721607e+001,-6.074984478170861e+000,
        1.767402723844187e+000},{-4.476066601835161e+002,-3.682624437371988e+001,
        -6.132862611514633e+000,1.762546529783868e+000},{-4.674570002533873e+002,
        -3.783126149387554e+001,-6.191331161679662e+000,1.757725622171409e+000},
        {-4.881749356184829e+002,-3.886341433245930e+001,-6.250395725677553e+000,
        1.752939714755772e+000},{-5.097985523417300e+002,-3.992340630042679e+001,
        -6.310061915750649e+000,1.748188524396310e+000},{-5.323676746229096e+002,
        -4.101195973874807e+001,-6.370335361660072e+000,1.743471771041181e+000},
        {-5.559239469182820e+002,-4.212981655933941e+001,-6.431221712923479e+000,
        1.738789177703054e+000},{-5.805109168157189e+002,-4.327773889908156e+001,
        -6.492726641214050e+000,1.734140470432367e+000},{-6.061741146091180e+002,
        -4.445650981673200e+001,-6.554855842839679e+000,1.729525378288342e+000},
        {-6.329602015454766e+002,-4.566693587314825e+001,-6.617615040532088e+000,
        1.724943633307832e+000},{-6.609250424371172e+002,-4.690982976130863e+001,
        -6.681009994698973e+000,1.720394970472067e+000},{-6.901042593869157e+002,
        -4.818608458142636e+001,-6.745046467541486e+000,1.715879127671711e+000},
        {-7.205706164247110e+002,-4.949651492478494e+001,-6.809730323163137e+000,
        1.711395845671781e+000},{-7.523401581588573e+002,-5.084211154381994e+001,
        -6.875067360429169e+000,1.706944868064385e+000},{-7.854200256589894e+002,
        -5.222382897866345e+001,-6.941063483168687e+000,1.702525941248357e+000},
        {-8.210353457106370e+002,-5.364030461686616e+001,-7.007725542909286e+000,
        1.698138814375824e+000},{-8.554766922517680e+002,-5.510143617018551e+001,
        -7.075055206156207e+000,1.693783239359508e+000},{-8.945408949715370e+002,
        -5.659285841589260e+001,-7.143067888804235e+000,1.689458970942078e+000},
        {-9.336319987298878e+002,-5.812951993780914e+001,-7.211759170575077e+000,
        1.685165765209987e+000},{-9.748070167487797e+002,-5.970600021779582e+001,
        -7.281141145128838e+000,1.680903383115732e+000},{-1.017797161099866e+003,
        -6.132462116161106e+001,-7.351218688149022e+000,1.676671586493826e+000},
        {-1.062683684456890e+003,-6.298650584026640e+001,-7.421998074872098e+000,
        1.672470140103473e+000},{-1.109551487921742e+003,-6.469280936461375e+001,
        -7.493485645708336e+000,1.668298811149195e+000},{-1.158489280848639e+003,
        -6.644471976211437e+001,-7.565687809091735e+000,1.664157369235286e+000},
        {-1.209589622929883e+003,-6.824345904605310e+001,-7.638611044176486e+000,
        1.660045586320429e+000},{-1.262949116295308e+003,-7.009028388353097e+001,
        -7.712261903592744e+000,1.655963236672332e+000},{-1.318668341934761e+003,
        -7.198648673326566e+001,-7.786647015696424e+000,1.651910096822905e+000},
        {-1.378234074012758e+003,-7.393131086849101e+001,-7.861773788109874e+000,
        1.647885945523818e+000},{-1.442265174772427e+003,-7.592462610887877e+001,
        -7.937649607034357e+000,1.643890563702867e+000},{-1.511481571183503e+003,
        -7.796562144522292e+001,-8.014283223597630e+000,1.639923734421354e+000},
        {-1.586722725865685e+003,-8.026846357280738e+001,-8.098960584225544e+000,
        1.635617913591073e+000},{-1.668825233579326e+003,-8.268094464949859e+001,
        -8.186167899408106e+000,1.631266166750611e+000},{-1.751894172577563e+003,
        -8.522351785771092e+001,-8.276024876610972e+000,1.626867109373032e+000},
        {-1.847472908821830e+003,-8.787922432899295e+001,-8.368677996958821e+000,
        1.622419288010019e+000},{-1.946491084587533e+003,-9.068266529460510e+001,
        -8.464253729359603e+000,1.617921174006821e+000},{-2.053978412575095e+003,
        -9.363129093939379e+001,-8.562915811238364e+000,1.613371162616998e+000},
        {-2.169922983260752e+003,-9.673869964576350e+001,-8.664826684394154e+000,
        1.608767561543369e+000},{-2.295197216249843e+003,-1.000170527865890e+002,
        -8.770163821231140e+000,1.604108587787459e+000},{-2.430785442417563e+003,
        -1.034797311140764e+002,-8.879118505262669e+000,1.599392359891713e+000},
        {-2.577801026632838e+003,-1.071414867500088e+002,-8.991897240203381e+000,
        1.594616890192578e+000},{-2.737506932622896e+003,-1.110186171022473e+002,
        -9.108723338184889e+000,1.589780076274507e+000},{-2.911339732177706e+003,
        -1.151291662320393e+002,-9.229838713457117e+000,1.584879691522251e+000},
        {-3.100938315519513e+003,-1.194931571822090e+002,-9.355505914598652e+000,
        1.579913374653328e+000},{-3.308178313364557e+003,-1.241328611774950e+002,
        -9.486010432931598e+000,1.574878618093619e+000},{-3.535213086559769e+003,
        -1.290731114786262e+002,-9.621663331956111e+000,1.569772755037022e+000},
        {-3.784523337361933e+003,-1.343416691601648e+002,-9.762804252286623e+000,
        1.564592945003904e+000},{-4.058976804769223e+003,-1.399696522448835e+002,
        -9.909804855879647e+000,1.559336157681449e+000},{-4.361900810987743e+003,
        -1.459920399445989e+002,-1.006307278746745e+001,1.553999154791511e+000},
        {-4.697170408589283e+003,-1.524482682241805e+002,-1.022305624605249e+001,
        1.548578469686142e+000},{-5.069316087288656e+003,-1.593829353173996e+002,
        -1.039024927974076e+001,1.543070384316234e+000},{-5.483655244797968e+003,
        -1.668466418498926e+002,-1.056519794058328e+001,1.537470903152320e+000},
        {-5.946453353590173e+003,-1.748969941438437e+002,-1.074850746706512e+001,
        1.531775723555805e+000},{-6.470411734157407e+003,-1.835913253448870e+002,
        -1.094085372023932e+001,1.525980202000237e+000},{-7.043187071142154e+003,
        -1.930474897871591e+002,-1.114297042220280e+001,1.520079315421806e+000},
        {-7.711933761545253e+003,-2.032681531837435e+002,-1.135574068537159e+001,
        1.514067616830629e+000},{-8.457541572806047e+003,-2.144378352863221e+002,
        -1.158005302355428e+001,1.507939179287543e+000},{-9.310061797401568e+003,
        -2.266315901380780e+002,-1.181700489705569e+001,1.501687551187454e+000},
        {-1.028612055393173e+004,-2.399941811640263e+002,-1.206779207559716e+001,
        1.495305668348962e+000},{-1.140941135333577e+004,-2.546856980795141e+002,
        -1.233378335486043e+001,1.488785783609071e+000},{-1.270936879154894e+004,
        -2.708950151984197e+002,-1.261654223773738e+001,1.482119368890722e+000},
        {-1.422287401592777e+004,-2.888462620691078e+002,-1.291786359692049e+001,
        1.475297002040697e+000},{-1.599657041959849e+004,-3.088070502047960e+002,
        -1.323981906420460e+001,1.468308231964111e+000},{-1.809004382910636e+004,
        -3.310990266311976e+002,-1.358481369182558e+001,1.461141416796625e+000},
        {-2.058025235609896e+004,-3.561115228088582e+002,-1.395565733388563e+001,
        1.453783528293291e+000},{-2.356778164825942e+004,-3.843193794845403e+002,
        -1.435565545638336e+001,1.446219913491735e+000},{-2.718581393635035e+004,
        -4.163064498517156e+002,-1.478872591139304e+001,1.438434001794348e+000},
        {-3.161318342772590e+004,-4.527969315541988e+002,-1.525955085475275e+001,
        1.430406941556335e+000},{-3.710725880796295e+004,-4.946758410121437e+002,
        -1.577378467014829e+001,1.422117144536678e+000},{-4.396402756633394e+004,
        -5.431789342797099e+002,-1.633827036775515e+001,1.413539708353296e+000},
        {-5.273878604465988e+004,-5.996007772929380e+002,-1.696157367093251e+001,
        1.404645675124891e+000},{-6.407490165878369e+004,-6.659850765960473e+002,
        -1.765417026519191e+001,1.395401054361457e+000},{-7.904776202793667e+004,
        -7.447144090654609e+002,-1.842951853955794e+001,1.385765574728270e+000},
        {-9.926766194745344e+004,-8.390379482241829e+002,-1.930485080869606e+001,
        1.375690927154873e+000},{-1.273095825071022e+005,-9.532400246900349e+002,
        -2.030280355373593e+001,1.365118418615304e+000},{-1.674562138620607e+005,
        -1.092995537492447e+003,-2.145377509289186e+001,1.353975640846269e+000},
        {-2.272198539857275e+005,-1.265667878999013e+003,-2.279974485733070e+001,
        1.342171664024869e+000},{-3.205446595310491e+005,-1.480352798561740e+003,
        -2.440067528762999e+001,1.329589871746868e+000},{-4.757004171335059e+005,
        -1.745534398035771e+003,-2.634638501786641e+001,1.316076873033058e+000},
        {-7.277874286905073e+005,-2.104072122532931e+003,-2.876388941251714e+001,
        1.301424533021810e+000},{-1.158269327743195e+006,-2.638285390348861e+003,
        -3.185184183947293e+001,1.285339230723633e+000},{-1.959002083113540e+006,
        -3.532523254029535e+003,-3.592185311796366e+001,1.267385221467623e+000},
        {-3.596005342715708e+006,-3.892843755514912e+003,-4.023498447113133e+001,
        1.252292339125201e+000},{-7.337307110377396e+006,-3.598464703219049e+003,
        -4.636507095266333e+001,1.235307228164419e+000},{-1.605717610482991e+007,
        -3.192373063618026e+003,-5.564203153249309e+001,1.214800598771303e+000},
        {-3.619723757401069e+007,-6.348690590601902e+003,-6.892252303788369e+001,
        1.191007390096094e+000},{-8.251938353183653e+007,-1.344847387729171e+004,
        -8.574522926416114e+001,1.168783843757871e+000},{-2.040599684077241e+008,
        -1.069786567964125e+004,-1.061289066146439e+002,1.150438269719548e+000},
        {-5.121867096552509e+008,1.456135255074863e+004,-1.331224976907382e+002,
        1.133590960463892e+000},{-1.208283139664454e+009,1.667633657013471e+004,
        -1.694988472006016e+002,1.115407413029604e+000},{-2.713573785229895e+009,
        -2.376510051574436e+005,-2.229542789125316e+002,1.093221801784601e+000},
        {-5.496859099556583e+009,-4.498406556454219e+005,-2.698490407608527e+002,
        1.081141798451352e+000},{-1.281003550443853e+010,-1.454397978181947e+005,
        -3.068797733762085e+002,1.075521362860637e+000},{-3.803997568288454e+010,
        7.244080350807136e+005,-3.862216588136204e+002,1.065839017041407e+000},
        {-1.282594878189864e+011,3.702125120753230e+006,-5.256416986606254e+002,
        1.055309382343471e+000},{-4.144936674091608e+011,2.980984288420191e+006,
        -6.792080235153045e+002,1.041458768913244e+000},{-8.964984509224136e+011,
        -5.905430282043110e+006,-8.516642522807352e+002,1.031926967645291e+000},
        {-7.355836465490852e+015,4.518177895310270e+010,-6.933068977626010e+004,
        1.025706312840203e+000}};
    constant Real[Ninterval, 4] dvtcoef={{3.665200884480820e-001,
        3.768263375039013e-002,2.190792329657455e-003,5.503960828374045e-005},{
        3.740100562223658e-001,3.839687254278058e-002,2.241470067816089e-003,
        5.651517998086539e-005},{3.828499115332361e-001,3.899054527468819e-002,
        2.284797395124333e-003,5.778081864475580e-005},{3.933222065720126e-001,
        4.041224383597725e-002,2.385959187504062e-003,6.075322570198209e-005},{
        4.040330124879073e-001,4.188279732592867e-002,2.491507351266832e-003,
        6.387796804156671e-005},{4.149858832885122e-001,4.340369917802586e-002,
        2.601623832550185e-003,6.716271877677985e-005},{4.261843979498587e-001,
        4.497658031312836e-002,2.716504756553497e-003,7.061574208320139e-005},{
        4.376320460159308e-001,4.660304907537514e-002,2.836349505162887e-003,
        7.424557939372635e-005},{4.493322760556361e-001,4.828479016768840e-002,
        2.961367887534022e-003,7.806127539077438e-005},{4.612885541291512e-001,
        5.002349607708437e-002,3.091775532306176e-003,8.207225038864295e-005},{
        4.735043599311913e-001,5.182093843609277e-002,3.227799262656286e-003,
        8.628847726670128e-005},{4.859830663248401e-001,5.367889630080813e-002,
        3.369672145850532e-003,9.072034242183301e-005},{4.987281155931236e-001,
        5.559927072115295e-002,3.517642230639391e-003,9.537893269130447e-005},{
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        8.459822722289890e-001},{5.417031709599584e+008,-1.429287025490565e+004,
        1.349265846505103e+002,8.629254292602316e-001},{1.260427879479906e+009,
        -1.145901868204451e+004,1.733305321359170e+002,8.814128590616269e-001},
        {2.813184466308078e+009,2.559435030649040e+005,2.304564317758250e+002,
        9.042234397623542e-001},{5.626351338748589e+009,4.809820508206572e+005,
        2.799571429006732e+002,9.167366942666617e-001},{1.296968662926528e+010,
        1.817347953863243e+005,3.184401164168030e+002,9.225727665578075e-001},{
        3.830247925197880e+010,-6.819911380346881e+005,4.005374222642562e+002,
        9.326388658049110e-001},{1.287778778901221e+011,-3.655758707469311e+006,
        5.430609568313491e+002,9.435863614001090e-001},{4.268494326672124e+011,
        -3.288472239150366e+006,7.033859556657586e+002,9.579454741567478e-001},
        {1.034173853201191e+012,4.083865055613008e+006,8.820734693646336e+002,
        9.677749072712484e-001},{7.360535318331335e+015,-4.520887554536115e+010,
        6.939753852333379e+004,9.741584695812871e-001}};
    constant Real[Ninterval, 4] dlcoef={{-1.238492681682227e+010,
        2.155273044551285e+006,-4.784064764172629e+002,3.108234546713846e+000},
        {-1.105429598046165e+010,2.040848348264662e+006,-4.669490356904236e+002,
        3.106950869117842e+000},{-9.690084649689146e+009,1.940606112928544e+006,
        -4.575230025626220e+002,3.105872508783625e+000},{-8.318064398350635e+009,
        1.756735969737722e+006,-4.369950152503960e+002,3.103417366473883e+000},
        {-7.140296347581058e+009,1.590320343200648e+006,-4.174017246617847e+002,
        3.100944868392514e+000},{-6.129570508708958e+009,1.439711927840652e+006,
        -3.987007300239189e+002,3.098454883787075e+000},{-5.261965140039352e+009,
        1.303395508058584e+006,-3.808503361523602e+002,3.095947126307966e+000},
        {-4.517289395063499e+009,1.180016669264855e+006,-3.638116590837542e+002,
        3.093421411830455e+000},{-3.878070615519906e+009,1.068342896840991e+006,
        -3.475472372378163e+002,3.090877503680521e+000},{-3.329405690851281e+009,
        9.672641008273838e+005,-3.320217101263023e+002,3.088315215846500e+000},
        {-2.858440705800047e+009,8.757716096217774e+005,-3.172010279329125e+002,
        3.085734309672665e+000},{-2.454126160678405e+009,7.929540898201873e+005,
        -3.030530265360140e+002,3.083134597151535e+000},{-2.107077441640843e+009,
        7.179881425904200e+005,-2.895465270173005e+002,3.080515785796512e+000},
        {-1.809136833923553e+009,6.501257495370673e+005,-2.766520552391303e+002,
        3.077877633663473e+000},{-1.553367992062939e+009,5.886942597143862e+005,
        -2.643417895971250e+002,3.075219949428117e+000},{-1.333788491394850e+009,
        5.330816167622649e+005,-2.525887134919396e+002,3.072542437056091e+000},
        {-1.145286689441753e+009,4.827368491822371e+005,-2.413675362576479e+002,
        3.069844902846438e+000},{-9.842004535366566e+008,4.371863251742306e+005,
        -2.306539304447653e+002,3.067127048225000e+000},{-8.481738668343931e+008,
        3.960467172138331e+005,-2.204253861258150e+002,3.064388625095322e+000},
        {-7.331751535883956e+008,3.589111400199431e+005,-2.106602384512079e+002,
        3.061629384019479e+000},{-6.358170209106354e+008,3.259263366450451e+005,
        -2.015181373167670e+002,3.058904739456489e+000},{-5.528785395381644e+008,
        2.973604756002514e+005,-1.932383784377713e+002,3.056307824467903e+000},
        {-4.812120579273270e+008,2.714695510765162e+005,-1.853567632253349e+002,
        3.053709701944857e+000},{-4.192283489842466e+008,2.479880869216736e+005,
        -1.778517183038584e+002,3.051110359095722e+000},{-3.655664548207343e+008,
        2.266781162415372e+005,-1.707029553047223e+002,3.048509783002060e+000},
        {-3.190676294329081e+008,2.073267347249426e+005,-1.638913968450548e+002,
        3.045907960618840e+000},{-2.787357163663924e+008,1.897427160373918e+005,
        -1.573990874235835e+002,3.043304878774594e+000},{-2.437229798017070e+008,
        1.737549055396368e+005,-1.512091344388983e+002,3.040700524171564e+000},
        {-2.132978996593800e+008,1.592092608304189e+005,-1.453056252302879e+002,
        3.038094883385813e+000},{-1.868371040328432e+008,1.459677646993695e+005,
        -1.396735798552919e+002,3.035487942867281e+000},{-1.638025501528403e+008,
        1.339061001971329e+005,-1.342988785546285e+002,3.032879688939840e+000},
        {-1.437323978319605e+008,1.229125376644445e+005,-1.291682166376668e+002,
        3.030270107801310e+000},{-1.262309428194057e+008,1.128866441350699e+005,
        -1.242690519881137e+002,3.027659185523409e+000},{-1.109546795986899e+008,
        1.037377107884577e+005,-1.195895502947782e+002,3.025046908051736e+000},
        {-9.761012432391328e+007,9.538426669141714e+004,-1.151185537187768e+002,
        3.022433261205660e+000},{-8.594246238515522e+007,8.775266482730758e+004,
        -1.108455268357315e+002,3.019818230678227e+000},{-7.573256602113859e+007,
        8.077656161927809e+004,-1.067605270066560e+002,3.017201802035995e+000},
        {-6.679050808234609e+007,7.439599879519979e+004,-1.028541631348516e+002,
        3.014583960718893e+000},{-5.895272357387779e+007,6.855689098463632e+004,
        -9.911756599444276e+001,3.011964692039987e+000},{-5.207642434522393e+007,
        6.321021881030477e+004,-9.554235139999366e+001,3.009343981185272e+000},
        {-4.603952482299992e+007,5.831185001665622e+004,-9.212060006254087e+001,
        3.006721813213399e+000},{-4.073465329002590e+007,5.382164282445671e+004,
        -8.884481728610524e+001,3.004098173055394e+000},{-3.606947830186065e+007,
        4.970338252471794e+004,-8.570791975358135e+001,3.001473045514342e+000},
        {-3.196365751713583e+007,4.592422769921850e+004,-8.270320400275625e+001,
        2.998846415265044e+000},{-2.834709613390578e+007,4.245437522415161e+004,
        -7.982432520669138e+001,2.996218266853638e+000},{-2.515904141651271e+007,
        3.926683364274947e+004,-7.706527859170076e+001,2.993588584697207e+000},
        {-2.234661006197257e+007,3.633710429345421e+004,-7.442037731654195e+001,
        2.990957353083351e+000},{-1.986350933749488e+007,3.364291054328384e+004,
        -7.188423367010003e+001,2.988324556169726e+000},{-1.766954634469551e+007,
        3.116404764577806e+004,-6.945174434254167e+001,2.985690177983576e+000},
        {-1.572958710525628e+007,2.888213723781383e+004,-6.711807172295707e+001,
        2.983054202421209e+000},{-1.401292644023167e+007,2.678046159635360e+004,
        -6.487862947013215e+001,2.980416613247471e+000},{-1.249270190404953e+007,
        2.484380595914790e+004,-6.272906834224337e+001,2.977777394095186e+000},
        {-1.114546757050897e+007,2.305832820575798e+004,-6.066526313144936e+001,
        2.975136528464554e+000},{-9.950639193150809e+006,2.141140730200463e+004,
        -5.868329902325385e+001,2.972493999722552e+000},{-8.890218298855454e+006,
        1.989154845489648e+004,-5.677946086303228e+001,2.969849791102278e+000},
        {-7.948405774843407e+006,1.848826513773720e+004,-5.495022127059669e+001,
        2.967203885702293e+000},{-7.111322017747801e+006,1.719198739978693e+004,
        -5.319223050409758e+001,2.964556266485915e+000},{-6.366802347563332e+006,
        1.599398533656803e+004,-5.150230698139536e+001,2.961906916280511e+000},
        {-5.704155755187705e+006,1.488628445368870e+004,-4.987742750713409e+001,
        2.959255817776730e+000},{-5.113936916982337e+006,1.386158907991517e+004,
        -4.831471847609879e+001,2.956602953527748e+000},{-4.587897845661234e+006,
        1.291324557621612e+004,-4.681144900015597e+001,2.953948305948456e+000},
        {-4.118721316950063e+006,1.203515316230080e+004,-4.536502121962786e+001,
        2.951291857314630e+000},{-3.699968686669407e+006,1.122173374498905e+004,
        -4.397296471188466e+001,2.948633589762085e+000},{-3.325990419032289e+006,
        1.046788709710375e+004,-4.263292938338680e+001,2.945973485285792e+000},
        {-2.991756337877007e+006,9.768928695956120e+003,-4.134267792650781e+001,
        2.943311525738965e+000},{-2.692851052844252e+006,9.120574676046892e+003,
        -4.010008148277442e+001,2.940647692832129e+000},{-2.425364090781395e+006,
        8.518894238993196e+003,-3.890311277023815e+001,2.937981968132176e+000},
        {-2.185839011929014e+006,7.960282125333197e+003,-3.774984110719230e+001,
        2.935314333061347e+000},{-1.971208238001473e+006,7.441427276955104e+003,
        -3.663842719615118e+001,2.932644768896239e+000},{-1.778765554998854e+006,
        6.959293235989100e+003,-3.556711877550735e+001,2.929973256766761e+000},
        {-1.606107055594805e+006,6.511088393081703e+003,-3.453424555743582e+001,
        2.927299777655057e+000},{-1.451097834519724e+006,6.094246543433254e+003,
        -3.353821526499588e+001,2.924624312394422e+000},{-1.311849093123074e+006,
        5.706410424466297e+003,-3.257750979381026e+001,2.921946841668166e+000},
        {-1.186680867573490e+006,5.345410405839227e+003,-3.165068106360730e+001,
        2.919267346008474e+000},{-1.074098219451101e+006,5.009249251722629e+003,
        -3.075634760904577e+001,2.916585805795216e+000},{-9.727750675061081e+005,
        4.696089510241781e+003,-2.989319134752533e+001,2.913902201254751e+000},
        {-8.815305960940811e+005,4.404238143974260e+003,-2.905995415563471e+001,
        2.911216512458684e+000},{-7.993100073168422e+005,4.132133894522016e+003,
        -2.825543489024561e+001,2.908528719322610e+000},{-7.251808108065209e+005,
        3.878340434733169e+003,-2.747848687199868e+001,2.905838801604811e+000},
        {-6.583036582047840e+005,3.641529386009533e+003,-2.672801450587870e+001,
        2.903146738904952e+000},{-5.979351488970650e+005,3.420477830640781e+003,
        -2.600297151102254e+001,2.900452510662714e+000},{-5.434106276898081e+005,
        3.214056119358886e+003,-2.530235797279994e+001,2.897756096156425e+000},
        {-4.941345433408149e+005,3.021220273636314e+003,-2.462521817165470e+001,
        2.895057474501652e+000},{-4.495775001488223e+005,2.841007253447881e+003,
        -2.397063865119245e+001,2.892356624649757e+000},{-4.092637696142438e+005,
        2.672525730358106e+003,-2.333774582158626e+001,2.889653525386433e+000},
        {-3.727690426212300e+005,2.514952386918597e+003,-2.272570432440947e+001,
        2.886948155330209e+000},{-3.397130883384123e+005,2.367525415691009e+003,
        -2.213371501440320e+001,2.884240492930909e+000},{-3.097553540585333e+005,
        2.229539894807050e+003,-2.156101328018909e+001,2.881530516468100e+000},
        {-2.825898974603600e+005,2.100342961405521e+003,-2.100686736953992e+001,
        2.878818204049503e+000},{-2.579442208981614e+005,1.979331007278646e+003,
        -2.047057696315193e+001,2.876103533609366e+000},{-2.355710977468511e+005,
        1.865943220530542e+003,-1.995147135640385e+001,2.873386482906805e+000},
        {-2.152510718952486e+005,1.759661471895166e+003,-1.944890854277082e+001,
        2.870667029524125e+000},{-1.967854522379427e+005,1.660004272608494e+003,
        -1.896227340604679e+001,2.867945150865090e+000},{-1.799963227248120e+005,
        1.566525526716963e+003,-1.849097676756957e+001,2.865220824153183e+000},
        {-1.647232316787083e+005,1.478811021808096e+003,-1.803445403318663e+001,
        2.862494026429800e+000},{-1.508223569587723e+005,1.396476642378965e+003,
        -1.759216415836827e+001,2.859764734552452e+000},{-1.381636164814771e+005,
        1.319165275775219e+003,-1.716358843294191e+001,2.857032925192887e+000},
        {-1.266302756204947e+005,1.246545535418823e+003,-1.674822959952733e+001,
        2.854298574835218e+000},{-1.161168631137604e+005,1.178309260666872e+003,
        -1.634561076107631e+001,2.851561659773991e+000},{-1.065283929681333e+005,
        1.114170085655529e+003,-1.595527452413494e+001,2.848822156112222e+000},
        {-9.777902898360457e+004,1.053861608696577e+003,-1.557678207604774e+001,
        2.846080039759405e+000},{-8.979154479537536e+004,9.971361867131301e+002,
        -1.520971239323694e+001,2.843335286429471e+000},{-8.249581780149181e+004,
        9.437630558793404e+002,-1.485366135803301e+001,2.840587871638727e+000},
        {-7.582881406187733e+004,8.935276800414810e+002,-1.450824112401567e+001,
        2.837837770703734e+000},{-6.973331684484918e+004,8.462300547482139e+002,
        -1.417307927722939e+001,2.835084958739184e+000},{-6.415772301025310e+004,
        8.016839926065475e+002,-1.384781823535527e+001,2.832329410655682e+000},
        {-5.905519971849246e+004,7.597158559545809e+002,-1.353211453405775e+001,
        2.829571101157552e+000},{-5.438340177539967e+004,7.201638399218540e+002,
        -1.322563825532957e+001,2.826810004740545e+000},{-5.010398989213503e+004,
        6.828770586818224e+002,-1.292807241099001e+001,2.824046095689559e+000},
        {-4.618216375504041e+004,6.477146970338505e+002,-1.263911237047971e+001,
        2.821279348076278e+000},{-4.258637278865216e+004,6.145453580284924e+002,
        -1.235846534594279e+001,2.818509735756785e+000},{-3.928799334523628e+004,
        5.832463833869973e+002,-1.208584987510642e+001,2.815737232369135e+000},
        {-3.626107008446607e+004,5.537032511254856e+002,-1.182099533490190e+001,
        2.812961811330881e+000},{-3.348198605783714e+004,5.258089299140838e+002,
        -1.156364146280048e+001,2.810183445836552e+000},{-3.092930799948825e+004,
        4.994634350699143e+002,-1.131353793886240e+001,2.807402108855102e+000},
        {-2.858356718774496e+004,4.745733110816813e+002,-1.107044395139554e+001,
        2.804617773127295e+000},{-2.642699292972316e+004,4.510511035622531e+002,
        -1.083412778305086e+001,2.801830411163054e+000},{-2.444349338561342e+004,
        4.288151035012024e+002,-1.060436646834351e+001,2.799039995238765e+000},
        {-2.261838452021139e+004,4.077888022404431e+002,-1.038094537815669e+001,
        2.796246497394526e+000},{-2.093827593537573e+004,3.879005747406519e+002,
        -1.016365789510950e+001,2.793449889431356e+000},{-1.939098963577922e+004,
        3.690833932437830e+002,-9.952305091079492e+000,2.790650142908357e+000},
        {-1.796543440841462e+004,3.512744857770907e+002,-9.746695394200888e+000,
        2.787847229139806e+000},{-1.665145478671165e+004,3.344149940989051e+002,
        -9.546644276491429e+000,2.785041119192228e+000},{-1.543982996581212e+004,
        3.184498209919203e+002,-9.351973998366489e+000,2.782231783881397e+000},
        {-1.432210669598613e+004,3.033272642915332e+002,-9.162513291636291e+000,
        2.779419193769276e+000},{-1.329059840415068e+004,2.889988870529622e+002,
        -8.978097130361970e+000,2.776603319160937e+000},{-1.233825052722389e+004,
        2.754192080986946e+002,-8.798566446195549e+000,2.773784130101386e+000},
        {-1.145863709207734e+004,2.625455884031810e+002,-8.623767918906500e+000,
        2.770961596372379e+000},{-1.064587614821500e+004,2.503379954642477e+002,
        -8.453553723390042e+000,2.768135687489127e+000},{-9.894583021419403e+003,
        2.387588397329175e+002,-8.287781316214854e+000,2.765306372696999e+000},
        {-9.199834391098546e+003,2.277728276390388e+002,-8.126313229068519e+000,
        2.762473620968123e+000},{-8.557121363365739e+003,2.173468013975267e+002,
        -7.969016862161412e+000,2.759637400997958e+000},{-7.962313251536238e+003,
        2.074496022604224e+002,-7.815764293296074e+000,2.756797681201794e+000},
        {-7.411623241071581e+003,1.980519411509770e+002,-7.666432093866367e+000,
        2.753954429711179e+000},{-6.901589290252236e+003,1.891262933062386e+002,
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        {-1.502516407943721e+001,-3.039461566365826e+000,-1.607093118455835e+000,
        1.537470903152320e+000},{-1.620820834955008e+001,-3.185571181481919e+000,
        -1.629078606872898e+000,1.531775723555805e+000},{-1.756861317903349e+001,
        -3.342859695130933e+000,-1.652227062158571e+000,1.525980202000237e+000},
        {-1.896992968076159e+001,-3.514753551909730e+000,-1.676629844756208e+000,
        1.520079315421806e+000},{-2.070940498674979e+001,-3.698607679814522e+000,
        -1.702409666201476e+000,1.514067616830629e+000},{-2.258006445102759e+001,
        -3.900361852777759e+000,-1.729670196587357e+000,1.507939179287543e+000},
        {-2.472640864504724e+001,-4.119997968335903e+000,-1.758560156062154e+000,
        1.501687551187454e+000},{-2.717555760930571e+001,-4.360330688942441e+000,
        -1.789232432463443e+000,1.495305668348961e+000},{-2.998453612050399e+001,
        -4.624174865325230e+000,-1.821864001930955e+000,1.488785783609070e+000},
        {-3.322400657923019e+001,-4.914848588452856e+000,-1.856657070400842e+000,
        1.482119368890723e+000},{-3.698227739969207e+001,-5.236285870597177e+000,
        -1.893843826546765e+000,1.475297002040697e+000},{-4.137073781469906e+001,
        -5.593179752915376e+000,-1.933692326201029e+000,1.468308231964111e+000},
        {-4.653129624345377e+001,-5.991165877519198e+000,-1.976513837575755e+000,
        1.461141416796625e+000},{-5.264671942271787e+001,-6.437059666295744e+000,
        -2.022672094596102e+000,1.453783528293291e+000},{-5.995516440181747e+001,
        -6.939166169402911e+000,-2.072595066915272e+000,1.446219913491736e+000},
        {-6.877091752349767e+001,-7.507688498893050e+000,-2.126790093032183e+000,
        1.438434001794347e+000},{-7.951434352644553e+001,-8.155272910741649e+000,
        -2.185863560319914e+000,1.430406941556337e+000},{-9.282260741855799e+001,
        -8.896990368881466e+000,-2.250548709297550e+000,1.422117144536678e+000},
        {-1.092705800731509e+002,-9.755978248450887e+000,-2.321727653966861e+000,
        1.413539708353296e+000},{-1.303440861742615e+002,-1.075180658002727e+001,
        -2.400520525131451e+000,1.404645675124892e+000},{-1.573817172536041e+002,
        -1.192284129304266e+001,-2.488271989475859e+000,1.395401054361456e+000},
        {-1.929469781047582e+002,-1.330915824062231e+001,-2.586733173534589e+000,
        1.385765574728271e+000},{-2.407515409275657e+002,-1.496747918474029e+001,
        -2.698134813608466e+000,1.375690927154873e+000},{-3.067296511299643e+002,
        -1.697224306116501e+001,-2.825409191622562e+000,1.365118418615304e+000},
        {-4.007152627101729e+002,-1.942210540851691e+001,-2.972493248817588e+000,
        1.353975640846269e+000},{-5.399185840310040e+002,-2.244503642183699e+001,
        -3.144822779164391e+000,1.342171664024869e+000},{-7.560716744000814e+002,
        -2.620100919290446e+001,-3.350155100053136e+000,1.329589871746869e+000},
        {-1.113449606842879e+003,-3.084021110135518e+001,-3.600109952519693e+000,
        1.316076873033058e+000},{-1.690504862425243e+003,-3.710261655467448e+001,
        -3.911155756406296e+000,1.301424533021810e+000},{-2.670061268217115e+003,
        -4.640046513281821e+001,-4.309071967361942e+000,1.285339230723633e+000},
        {-4.481748438342077e+003,-6.187707883736660e+001,-4.834386672670042e+000,
        1.267385221467624e+000},{-8.164522417664276e+003,-6.838329256029518e+001,
        -5.390905548063032e+000,1.252292339125201e+000},{-1.652878983123607e+004,
        -6.410911523659486e+001,-6.181751840615706e+000,1.235307228164419e+000},
        {-3.589814816980765e+004,-5.850303396906464e+001,-7.379682885213981e+000,
        1.214800598771303e+000},{-8.037263246538142e+004,-1.135710262603827e+002,
        -9.097826769016773e+000,1.191007390096093e+000},{-1.821922090737477e+005,
        -2.354776316590442e+002,-1.127469694751144e+001,1.168783843757871e+000},
        {-4.484262360427870e+005,-1.929406030066214e+002,-1.390923719646678e+001,
        1.150438269719548e+000},{-1.121046496283366e+006,2.244014433727998e+002,
        -1.739509749280907e+001,1.133590960463892e+000},{-2.637332052450561e+006,
        2.537931543190984e+002,-2.209765636576909e+001,1.115407413029603e+000},
        {-5.907648512403362e+006,-4.012624018357776e+003,-2.901240599782692e+001,
        1.093221801784601e+000},{-1.195665812647725e+007,-7.565697091202631e+003,
        -3.507390000142389e+001,1.081141798451352e+000},{-2.784190228559279e+007,
        -2.474660221277177e+003,-3.985563387169906e+001,1.075521362860637e+000},
        {-8.260002532389586e+007,1.207599307914400e+004,-5.010461096457156e+001,
        1.065839017041407e+000},{-2.783054150157432e+008,6.191392637195736e+004,
        -6.812180721814856e+001,1.055309382343470e+000},{-8.984303648430897e+008,
        4.972036367617193e+004,-8.797612069577760e+001,1.041458768913245e+000},
        {-1.938721107426129e+009,-9.947883920780817e+004,-1.102739497257638e+002,
        1.031926967645291e+000},{-1.596711708673011e+013,7.576033677883548e+008,
        -8.980126598064539e+003,1.025706312840203e+000}};
    constant Real[Ninterval, 4] dvcoef={{4.918869918230695e+005,-1.567555888877598e+002,
        5.437208630256651e-001,5.503960828374048e-005},{4.550378123449924e+005,
        -1.523735197978206e+002,5.428795951631563e-001,5.651517998086538e-005},
        {4.154435854155241e+005,-1.485249049854512e+002,5.421736401433307e-001,
        5.778081864475579e-005},{3.741482472743288e+005,-1.409517385019123e+002,
        5.405774106280010e-001,6.075322570198208e-005},{3.367178855870678e+005,
        -1.337561394903371e+002,5.389802274088923e-001,6.387796804156671e-005},
        {3.032331897449884e+005,-1.269325231900327e+002,5.373822526407004e-001,
        6.716271877677984e-005},{2.729783236073526e+005,-1.204513648774790e+002,
        5.357833746302725e-001,7.061574208320135e-005},{2.457737771951380e+005,
        -1.143004549600878e+002,5.341836871213043e-001,7.424557939372635e-005},
        {2.212418903451594e+005,-1.084606313277702e+002,5.325831835730194e-001,
        7.806127539077440e-005},{1.991932319373264e+005,-1.029188757389579e+002,
        5.309819330350911e-001,8.207225038864295e-005},{1.793568834640014e+005,
        -9.765862295132199e+001,5.293799351427024e-001,8.628847726670124e-005},
        {1.614383537622045e+005,-9.266330277412550e+001,5.277772334623126e-001,
        9.072034242183298e-005},{1.453621714686960e+005,-8.792412794039890e+001,
        5.261738672668539e-001,9.537893269130447e-005},{1.308585174350236e+005,
        -8.342408029607272e+001,5.245698186895845e-001,1.002758063548368e-004},
        {1.178099872852326e+005,-7.915315147317665e+001,5.229651805648193e-001,
        1.054230003569786e-004},{1.060542653282609e+005,-7.509881556093026e+001,
        5.213599463406871e-001,1.108333568850558e-004},{9.549308124088842e+004,
        -7.125147962403636e+001,5.197541987519517e-001,1.165201514339942e-004},
        {8.600354913972432e+004,-6.759972330879310e+001,5.181479357221414e-001,
        1.224975427286338e-004},{7.761649543341427e+004,-6.414066678887514e+001,
        5.165412858073596e-001,1.287802891593490e-004},{7.020537948517055e+004,
        -6.086565981704204e+001,5.149343233861899e-001,1.353838849828343e-004},
        {6.362526510536840e+004,-5.781701794798269e+001,5.133590847200070e-001,
        1.421827481986982e-004},{5.777602598727927e+004,-5.506082706782908e+001,
        5.118681842941606e-001,1.489285080947021e-004},{5.249423222977891e+004,
        -5.245136198830269e+001,5.103869134700294e-001,1.559450852216556e-004},
        {4.772771403525848e+004,-4.998041590145706e+001,5.089152331130584e-001,
        1.632411903229066e-004},{4.341758916708818e+004,-4.763947665576765e+001,
        5.074530908455733e-001,1.708257343021365e-004},{3.952482258441854e+004,
        -4.542149360328381e+001,5.060004500938848e-001,1.787078304444174e-004},
        {3.599853857184100e+004,-4.331871999300164e+001,5.045572556408491e-001,
        1.868967966091156e-004},{3.281073717790914e+004,-4.132521822148750e+001,
        5.031234772300364e-001,1.954021573940050e-004},{2.991928864379426e+004,
        -3.943405746218934e+001,5.016990585808311e-001,2.042336462698480e-004},
        {2.730136743929938e+004,-3.764000095251405e+001,5.002839707362081e-001,
        2.134012076848843e-004},{2.492659063635537e+004,-3.593720253748594e+001,
        4.988781632750814e-001,2.229149991386049e-004},{2.276955125736159e+004,
        -3.432046079500933e+001,4.974815975109458e-001,2.327853932242566e-004},
        {2.081432755389784e+004,-3.278542777406340e+001,4.960942426492074e-001,
        2.430229796396210e-004},{1.903499917129547e+004,-3.132692253363413e+001,
        4.947160448050079e-001,2.536385671655345e-004},{1.741916761544805e+004,
        -2.994121669633407e+001,4.933469804327021e-001,2.646431856117704e-004},
        {1.594856799673893e+004,-2.862400374594620e+001,4.919870030103821e-001,
        2.760480877298892e-004},{1.461071366209510e+004,-2.737169558264001e+001,
        4.906360810069271e-001,2.878647510927006e-004},{1.339168327690314e+004,
        -2.618061339571608e+001,4.892941746173027e-001,3.001048799400484e-004},
        {1.228253049325166e+004,-2.504768084200302e+001,4.879612544780885e-001,
        3.127804069906575e-004},{1.126892157829276e+004,-2.396930264453291e+001,
        4.866372742930647e-001,3.259034952198203e-004},{1.034662065878251e+004,
        -2.294316241182801e+001,4.853222187890683e-001,3.394865396027453e-004},
        {9.503700936201338e+003,-2.196597276324068e+001,4.840160361000067e-001,
        3.535421688234263e-004},{8.734018189448401e+003,-2.103534947204093e+001,
        4.827187038678896e-001,3.680832469489622e-004},{8.031366011875803e+003,
        -2.014888458104759e+001,4.814301896622395e-001,3.831228750692300e-004},
        {7.388578355618841e+003,-1.930410181604127e+001,4.801504565658148e-001,
        3.986743929019504e-004},{6.800574870580942e+003,-1.849890723067505e+001,
        4.788794784376936e-001,4.147513803631108e-004},{6.262968091501257e+003,
        -1.773131649952538e+001,4.776172260185485e-001,4.313676591028885e-004},
        {5.770389109765950e+003,-1.699924277022264e+001,4.763636637585473e-001,
        4.485372940071114e-004},{5.319190052222050e+003,-1.630094266002941e+001,
        4.751187671980786e-001,4.662745946644320e-004},{4.905748845902255e+003,
        -1.563469347603085e+001,4.738825069166632e-001,4.845941167994040e-004},
        {4.526685334231427e+003,-1.499884943133974e+001,4.726548535498104e-001,
        5.035106636716925e-004},{4.178772802276819e+003,-1.439183882285007e+001,
        4.714357786189442e-001,5.230392874416343e-004},{3.859530682062243e+003,
        -1.381226047506382e+001,4.702252575271995e-001,5.431952905025171e-004},
        {3.566271424600439e+003,-1.325870013942056e+001,4.690232613675992e-001,
        5.639942267798111e-004},{3.296870650297050e+003,-1.272989003696022e+001,
        4.678297654512661e-001,5.854519029978606e-004},{3.049276098691007e+003,
        -1.222459719155169e+001,4.666447430986029e-001,6.075843799142949e-004},
        {2.821484408536768e+003,-1.174163338947488e+001,4.654681678733132e-001,
        6.304079735227145e-004},{2.611896527283416e+003,-1.127992855916830e+001,
        4.643000166997424e-001,6.539392562240592e-004},{2.419079453141731e+003,
        -1.083846133076433e+001,4.631402651077743e-001,6.781950579671866e-004},
        {2.241307272262556e+003,-1.041617660727023e+001,4.619888855086836e-001,
        7.031924673592141e-004},{2.077658736699405e+003,-1.001223689974768e+001,
        4.608458599404298e-001,7.289488327461664e-004},{1.926777017074004e+003,
        -9.625702150971902e+000,4.597111603812837e-001,7.554817632645456e-004},
        {1.787519449312663e+003,-9.255727615109393e+000,4.585847646064639e-001,
        7.828091298644552e-004},{1.659179395402279e+003,-8.901591924409631e+000,
        4.574666539228491e-001,8.109490663049823e-004},{1.540633616703145e+003,
        -8.562472211245941e+000,4.563568005087656e-001,8.399199701224020e-004},
        {1.431161858142325e+003,-8.237690859137757e+000,4.552551859319501e-001,
        8.697405035720722e-004},{1.330023377555299e+003,-7.926573334195409e+000,
        4.541617883382710e-001,9.004295945446778e-004},{1.236573482343776e+003,
        -7.628487285308340e+000,4.530765866476337e-001,9.320064374575882e-004},
        {1.150117985277077e+003,-7.342803184259996e+000,4.519995585201517e-001,
        9.644904941221798e-004},{1.070158684587523e+003,-7.068970548333955e+000,
        4.509306856964692e-001,9.979014945878772e-004},{9.961748371914198e+002,
        -6.806438520833332e+000,4.498699469983624e-001,1.032259437963822e-003},
        {9.276477356080152e+002,-6.554674171966223e+000,4.488173216777321e-001,
        1.067584593218963e-003},{8.641833883415839e+002,-6.313201947850644e+000,
        4.477727918978972e-001,1.103897499961509e-003},{8.053877216782303e+002,
        -6.081553232617854e+000,4.467363378201690e-001,1.141218969198647e-003},
        {7.508679837063625e+002,-5.859273363957273e+000,4.457079396593727e-001,
        1.179570084077442e-003},{7.003121955106866e+002,-5.645950416545300e+000,
        4.446875799042271e-001,1.218972200607816e-003},{6.534229224786275e+002,
        -5.441184593317924e+000,4.436752399301383e-001,1.259446948368720e-003},
        {6.098701132482534e+002,-5.244576566367364e+000,4.426709003094503e-001,
        1.301016231198290e-003},{5.694693580848956e+002,-5.055795182260655e+000,
        4.416745463024567e-001,1.343702227869144e-003},{5.319187630216652e+002,
        -4.874464882088055e+000,4.406861567650555e-001,1.387527392749791e-003},
        {4.970284952496925e+002,-4.700273550639881e+000,4.397057168100576e-001,
        1.432514456453111e-003},{4.646073398256017e+002,-4.532911236187518e+000,
        4.387332091303748e-001,1.478686426473104e-003},{4.344436320778534e+002,
        -4.372067882144371e+000,4.377686155875123e-001,1.526066587810795e-003},
        {4.063942942181745e+002,-4.217474280320218e+000,4.368119214276980e-001,
        1.574678503590567e-003},{3.802841770186233e+002,-4.068850532622352e+000,
        4.358631089330863e-001,1.624546015667824e-003},{3.559769108797973e+002,
        -3.925944939917800e+000,4.349221629490394e-001,1.675693245229227e-003},
        {3.333402909463835e+002,-3.788512906615899e+000,4.339890675369079e-001,
        1.728144593386517e-003},{3.122536180170024e+002,-3.656321586479176e+000,
        4.330638070558099e-001,1.781924741765163e-003},{2.925902763184365e+002,
        -3.529142319538135e+000,4.321463655932412e-001,1.837058653088838e-003},
        {2.742740781970119e+002,-3.406778654781579e+000,4.312367299211879e-001,
        1.893571571760979e-003},{2.571759037143193e+002,-3.289008496189263e+000,
        4.303348822713388e-001,1.951489024444565e-003},{2.412316234199518e+002,
        -3.175655844670625e+000,4.294408108599679e-001,2.010836820641156e-003},
        {2.263479765419118e+002,-3.066528653226592e+000,4.285544996055142e-001,
        2.071641053270657e-003},{2.124540881441975e+002,-2.961454863028191e+000,
        4.276759349468488e-001,2.133928099252665e-003},{1.994738967239204e+002,
        -2.860263446005821e+000,4.268051024338398e-001,2.197724620090749e-003},
        {1.873507685079785e+002,-2.762800207342723e+000,4.259419892085835e-001,
        2.263057562460898e-003},{1.760176881347635e+002,-2.668907362024899e+000,
        4.250865807774918e-001,2.329954158805295e-003},{1.654238211245136e+002,
        -2.578442894138812e+000,4.242388645871290e-001,2.398441927932571e-003},
        {1.555155973132484e+002,-2.491265813149157e+000,4.233988271501935e-001,
        2.468548675625884e-003},{1.462467369395943e+002,-2.407244188793173e+000,
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        3.211290782525183e+000,1.272231405920666e+000,8.930912596503021e-001,
        3.974693046888215e-001},{3.338918141302322e+000,1.303068219692468e+000,
        9.016763420849130e-001,4.004583724710529e-001},{3.471892018272730e+000,
        1.334706240150083e+000,9.103540397044045e-001,4.034364899924997e-001},{
        3.610440645775533e+000,1.367167120982722e+000,9.191252214485987e-001,
        4.064035668556145e-001},{3.754800508814665e+000,1.400473111418473e+000,
        9.279907688104051e-001,4.093595161310653e-001},{3.905216477735271e+000,
        1.434647058532653e+000,9.369515758788880e-001,4.123042542968515e-001},{
        4.065670804884121e+000,1.469678174488928e+000,9.460086192933500e-001,
        4.152377011781764e-001},{4.237761502904625e+000,1.505565867821763e+000,
        9.551628791098028e-001,4.181597798876018e-001},{4.423332904730818e+000,
        1.542298398896243e+000,9.644154775777063e-001,4.210704167656975e-001},{
        4.624516092786303e+000,1.583704725720241e+000,9.746473707878920e-001,
        4.242404029888883e-001},{4.850196574686571e+000,1.626991736963335e+000,
        9.851937689726753e-001,4.274553962053975e-001},{5.056790030629979e+000,
        1.672846557345158e+000,9.960690537668240e-001,4.307167462684177e-001},{
        5.322780585611914e+000,1.720316041896115e+000,1.007293551783249e+000,
        4.340258706136082e-001},{5.581856116174721e+000,1.770664322860376e+000,
        1.018880860299036e+000,4.373842594703593e-001},{5.866088407465559e+000,
        1.823520560177389e+000,1.030853140388873e+000,4.407934798537482e-001},{
        6.171923002120571e+000,1.879189565923113e+000,1.043230569280668e+000,
        4.442551829095663e-001},{6.501535536191801e+000,1.937885751613769e+000,
        1.056035595849955e+000,4.477711093076880e-001},{6.857377194386117e+000,
        1.999844889612192e+000,1.069292431020710e+000,4.513430963808631e-001},{
        7.242214043652889e+000,2.065326797427353e+000,1.083027227973919e+000,
        4.549730857610047e-001},{7.659178646510535e+000,2.134618343011173e+000,
        1.097268285542566e+000,4.586631318040277e-001},{8.111827066134506e+000,
        2.208036973520845e+000,1.112046277772487e+000,4.624154109045757e-001},{
        8.604208529071581e+000,2.285934758959754e+000,1.127394514184514e+000,
        4.662322318172514e-001},{9.140948252644797e+000,2.368703086413673e+000,
        1.143349235435159e+000,4.701160471199221e-001},{9.727346257355944e+000,
        2.456778125271054e+000,1.159949950207535e+000,4.740694659762598e-001},{
        1.036949636473117e+001,2.550647201445953e+000,1.177239820295516e+000,
        4.780952683808142e-001},{1.107442943815378e+001,2.650856267473131e+000,
        1.195266102140809e+000,4.821964211012327e-001},{1.185028605617332e+001,
        2.758018689992081e+000,1.214080654794935e+000,4.863760955695670e-001},{
        1.270652798974013e+001,2.872825592971998e+000,1.233740526395416e+000,
        4.906376880197966e-001},{1.365419174621447e+001,2.996058162729545e+000,
        1.254308633466170e+000,4.949848422233832e-001},{1.470620059822895e+001,
        3.128602227412618e+000,1.275854551067133e+000,4.994214752410865e-001},{
        1.587774199700023e+001,3.271465705618580e+000,1.298455434935754e+000,
        5.039518066908264e-001},{1.720674254013149e+001,3.425586345730544e+000,
        1.322197606263238e+000,5.085803921309422e-001},{1.863402248089567e+001,
        3.593353579496717e+000,1.347174025974930e+000,5.133121612816782e-001},{
        2.032390211918452e+001,3.774153760759719e+000,1.373499219827730e+000,
        5.181524619605369e-001},{2.218601347832784e+001,3.971869398731903e+000,
        1.401284417001323e+000,5.231071115480921e-001},{2.431252464422925e+001,
        4.187482117105547e+000,1.430671346578243e+000,5.281824536278078e-001},{
        2.673985851010544e+001,4.423583955149483e+000,1.461812601611662e+000,
        5.333854293394883e-001},{2.952491937183151e+001,4.682968036424375e+000,
        1.494883366150635e+000,5.387236561640727e-001},{3.273828578159125e+001,
        4.968928762622564e+000,1.530083871593750e+000,5.442055229446516e-001},{
        3.646825750913934e+001,5.285374439016692e+000,1.567644134852697e+000,
        5.498403020789376e-001},{4.082633712570511e+001,5.636970657586560e+000,
        1.607829829067538e+000,5.556382833229866e-001},{4.595475926455129e+001,
        6.029324175734520e+000,1.650949619985925e+000,5.616109344677590e-001},{
        5.203696918320384e+001,6.469220871161562e+000,1.697364417633431e+000,
        5.677710957231201e-001},{5.931241581636025e+001,6.964936570782171e+000,
        1.747499159582017e+000,5.741332167790794e-001},{6.809776191782187e+001,
        7.526647036007701e+000,1.801857981792066e+000,5.807136484549547e-001},{
        7.881778054554678e+001,8.166974540194117e+000,1.861043982241702e+000,
        5.875310049495474e-001},{9.207856359262058e+001,8.901415236315513e+000,
        1.925786076833259e+000,5.946066185193436e-001},{1.085962925592044e+002,
        9.751235331139156e+000,1.996968777326911e+000,6.019651167819492e-001},{
        1.296612727594772e+002,1.073953725331416e+001,2.075696926484503e+000,
        6.096351651125727e-001},{1.568149508938095e+002,1.190149594899319e+001,
        2.163329563019325e+000,6.176504358167556e-001},{1.925895489261716e+002,
        1.327895255374134e+001,2.261610095071371e+000,6.260508899137490e-001},{
        2.407894220277205e+002,1.492863095592906e+001,2.372777247256969e+000,
        6.348845111387734e-001},{3.074933991972216e+002,1.692543720677949e+001,
        2.499777113694852e+000,6.442096900359834e-001},{4.028115941258301e+002,
        1.936864049070909e+001,2.646574749423806e+000,6.540985866240505e-001},{
        5.444627680553028e+002,2.238732251366779e+001,2.818658896530704e+000,
        6.646420006807281e-001},{7.654263901392872e+002,2.613984326739216e+001,
        3.023895327133340e+000,6.759566538738164e-001},{1.132473145221229e+003,
        3.077464245663644e+001,3.274097890822487e+000,6.881964979202373e-001},{
        1.728456306009293e+003,3.703669144378617e+001,3.586095407785845e+000,
        7.015710980094141e-001},{2.746345210190641e+003,4.636511685430635e+001,
        3.986312539776484e+000,7.163772638856115e-001},{4.641775374977525e+003,
        6.199723710600262e+001,4.516428772903993e+000,7.330575520262050e-001},{
        8.525657962231340e+003,6.810054194649604e+001,5.081630948855855e+000,
        7.472071449747022e-001},{1.741572862879567e+004,6.219045752188775e+001,
        5.890642485434674e+000,7.632728136051337e-001},{3.813458054210775e+004,
        5.370618375512508e+001,7.124228169883730e+000,7.828757764751582e-001},{
        8.589158440190039e+004,1.090981683303350e+002,8.902873285623791e+000,
        8.059157661363586e-001},{1.951303750681718e+005,2.375849575768755e+002,
        1.117514113283684e+001,8.277377240352704e-001},{4.782548713012288e+005,
        1.986473214368117e+002,1.394735114459777e+001,8.459822722289891e-001},{
        1.185655347397813e+006,-2.174684780917248e+002,1.762979102357640e+001,
        8.629254292602320e-001},{2.750846962420604e+006,-1.629109294341851e+002,
        2.259666061556802e+001,8.814128590616266e-001},{6.123913630880820e+006,
        4.322208699496733e+003,2.998861227777463e+001,9.042234397623542e-001},{
        1.223685185147719e+007,8.090218357744150e+003,3.638774289535504e+001,
        9.167366942666613e-001},{2.818621443600825e+007,3.085711548192580e+003,
        4.135729893033309e+001,9.225727665578074e-001},{8.316585285067827e+007,
        -1.136324148807467e+004,5.196252092604191e+001,9.326388658049112e-001},
        {2.794244200228550e+008,-6.113667992222013e+004,7.038061963269288e+001,
        9.435863614001085e-001},{9.252325428804928e+008,-5.487463721818197e+004,
        9.110802490104044e+001,9.579454741567480e-001},{2.237265034221097e+009,
        6.896819415082679e+004,1.142108494843807e+002,9.677749072712486e-001},{
        1.597732512872630e+013,-7.580581567199930e+008,8.988788796440838e+003,
        9.741584695812871e-001}};
    constant Real[Ninterval, 4] hlcoef={{7.395064117384627e+009,-1.280865388176200e+006,
        2.821575750527614e+002,1.833836171003976e-001},{6.597504135407492e+009,
        -1.212511325876777e+006,2.753491351615672e+002,1.841406426859871e-001},
        {5.780271674084454e+009,-1.152633155136978e+006,2.697490006419553e+002,
        1.847764786820451e-001},{4.958860729534658e+009,-1.042899311995140e+006,
        2.575580906113897e+002,1.862237508639398e-001},{4.254225882522524e+009,
        -9.436430636231016e+005,2.459280611632260e+002,1.876807622923263e-001},
        {3.649929287231926e+009,-8.538684890799312e+005,2.348330720290646e+002,
        1.891475943673219e-001},{3.131540328303725e+009,-7.726606490030770e+005,
        2.242477593033248e+002,1.906244199793511e-001},{2.686884429215740e+009,
        -6.992021917100513e+005,2.141484795719950e+002,1.921113515976508e-001},
        {2.305436681190764e+009,-6.327500405900241e+005,2.045124826635191e+002,
        1.936085324364108e-001},{1.978225892136117e+009,-5.726354169435729e+005,
        1.953183098525792e+002,1.951160756856359e-001},{1.697521363709874e+009,
        -5.182511799267425e+005,1.865453222831365e+002,1.966341253040380e-001},
        {1.456683048691095e+009,-4.690492050108880e+005,1.781740380829120e+002,
        1.981627952385604e-001},{1.250074360886440e+009,-4.245346083004282e+005,
        1.701855963205966e+002,1.997022606387281e-001},{1.072800606962726e+009,
        -3.842582037066196e+005,1.625621803354005e+002,2.012526666726048e-001},
        {9.207021541607516e+008,-3.478163169361438e+005,1.552869834519622e+002,
        2.028141285158312e-001},{7.901943344753319e+008,-3.148419383589053e+005,
        1.483437057813515e+002,2.043868226073761e-001},{6.782161334430934e+008,
        -2.850048993978956e+005,1.417170959818027e+002,2.059708649963459e-001},
        {5.825727219202920e+008,-2.580214571990632e+005,1.353924992211892e+002,
        2.075664330398644e-001},{5.018477901925672e+008,-2.336618459414496e+005,
        1.293563597550240e+002,2.091736741482984e-001},{4.336339749859386e+008,
        -2.116826692784306e+005,1.235956428311352e+002,2.107927362153820e-001},
        {3.759101976651321e+008,-1.921682462515702e+005,1.182042406216403e+002,
        2.123911161514204e-001},{3.267571477181848e+008,-1.752745050595466e+005,
        1.133228792803702e+002,2.139142206063779e-001},{2.843020873596044e+008,
        -1.599683613280694e+005,1.086775876446765e+002,2.154377045739531e-001},
        {2.475979262638457e+008,-1.460916038079511e+005,1.042554766441906e+002,
        2.169615822712266e-001},{2.158340827399827e+008,-1.335024950386115e+005,
        1.000444324122937e+002,2.184858675939239e-001},{1.883207309006085e+008,
        -1.220742895035692e+005,9.603307088337355e+001,2.200105741258566e-001},
        {1.644651841228906e+008,-1.116932087097448e+005,9.221068373842154e+001,
        2.215357151481048e-001},{1.437632632379007e+008,-1.022574640228438e+005,
        8.856720217299345e+001,2.230613036479431e-001},{1.257801607275091e+008,
        -9.367549193296053e+004,8.509314677627712e+001,2.245873523275273e-001},
        {1.101454874055535e+008,-8.586529010338520e+004,8.177959848067110e+001,
        2.261138736123414e-001},{9.653972368356156e+007,-7.875303244948787e+004,
        7.861815481978856e+001,2.276408796594130e-001},{8.468871988652200e+007,
        -7.227239695689626e+004,7.560090235615557e+001,2.291683823653079e-001},
        {7.435767250336401e+007,-6.636379223835093e+004,7.272038489459962e+001,
        2.306963933739068e-001},{6.534286001294021e+007,-6.097342167031716e+004,
        6.996957046343296e+001,2.322249240839693e-001},{5.747027807155222e+007,
        -5.605298520200417e+004,6.734183209615867e+001,2.337539856564991e-001},
        {5.058892155208572e+007,-5.155884014645571e+004,6.483091539577785e+001,
        2.352835890219054e-001},{4.456897749091873e+007,-4.745168641553626e+004,
        6.243092046710518e+001,2.368137448869720e-001},{3.929797808634566e+007,
        -4.369602037553607e+004,6.013627711697743e+001,2.383444637416446e-001},
        {3.467909626236541e+007,-4.025982723829874e+004,5.794172688510435e+001,
        2.398757558656324e-001},{3.062784360211651e+007,-3.711410238256247e+004,
        5.584230094500428e+001,2.414076313348311e-001},{2.707199455967587e+007,
        -3.423274054960324e+004,5.383330780575171e+001,2.429401000275848e-001},
        {2.394806063151847e+007,-3.159200650084850e+004,5.191030928225440e+001,
        2.444731716307669e-001},{2.120145854494023e+007,-2.917049319028297e+004,
        5.006911233397096e+001,2.460068556457158e-001},{1.878470848130406e+007,
        -2.694879400670043e+004,4.830575024370947e+001,2.475411613940012e-001},
        {1.665640139112113e+007,-2.490930349109187e+004,4.661646985518280e+001,
        2.490760980230453e-001},{1.478065625824185e+007,-2.303608166989841e+004,
        4.499772037807755e+001,2.506116745115950e-001},{1.312624886938225e+007,
        -2.131466500927661e+004,4.344614015879794e+001,2.521478996750478e-001},
        {1.166585545469223e+007,-1.973190580002538e+004,4.195854541513062e+001,
        2.536847821706443e-001},{1.037575804683703e+007,-1.827588228385652e+004,
        4.053192137337701e+001,2.552223305025196e-001},{9.235229821301350e+006,
        -1.693575336267236e+004,3.916341110770780e+001,2.567605530266264e-001},
        {8.226161529454760e+006,-1.570166014825697e+004,3.785030689607822e+001,
        2.582994579555294e-001},{7.332714409838634e+006,-1.456463239248035e+004,
        3.659004174391924e+001,2.598390533630776e-001},{6.541067280596239e+006,
        -1.351651109839700e+004,3.538018157148768e+001,2.613793471889549e-001},
        {5.839089097217685e+006,-1.254985887421323e+004,3.421841707983741e+001,
        2.629203472431124e-001},{5.216174993443639e+006,-1.165790355620624e+004,
        3.310255732922824e+001,2.644620612100892e-001},{4.663018167146263e+006,
        -1.083446843025749e+004,3.203052265688924e+001,2.660044966532249e-001},
        {4.171444464302824e+006,-1.007391792850541e+004,3.100033862903940e+001,
        2.675476610187589e-001},{3.734291063599596e+006,-9.371112234283090e+003,
        3.001013038565671e+001,2.690915616398324e-001},{3.345264196959495e+006,
        -8.721357281608769e+003,2.905811682622430e+001,2.706362057403845e-001},
        {2.998804824052956e+006,-8.120359510245587e+003,2.814260537246550e+001,
        2.721816004389522e-001},{2.690059117043254e+006,-7.564203866773062e+003,
        2.726198786072066e+001,2.737277527523759e-001},{2.414722165518809e+006,
        -7.049301389752438e+003,2.641473480407623e+001,2.752746695994082e-001},
        {2.169006576676412e+006,-6.572371181362734e+003,2.559939204631222e+001,
        2.768223578042399e-001},{1.949589547380671e+006,-6.130413910998713e+003,
        2.481457654061498e+001,2.783708240999319e-001},{1.753513335070667e+006,
        -5.720675273235230e+003,2.405897188170692e+001,2.799200751317631e-001},
        {1.578181984153911e+006,-5.340636910887383e+003,2.333132571024671e+001,
        2.814701174605012e-001},{1.421296797534924e+006,-4.987988415116040e+003,
        2.263044564557126e+001,2.830209575655875e-001},{1.280826297625475e+006,
        -4.660611060652745e+003,2.195519632940761e+001,2.845726018482448e-001},
        {1.154967887885402e+006,-4.356559333855659e+003,2.130449633293048e+001,
        2.861250566345134e-001},{1.042131487251255e+006,-4.074049315833184e+003,
        2.067731557349638e+001,2.876783281782094e-001},{9.409048828988477e+005,
        -3.811441190960783e+003,2.007267232055989e+001,2.892324226638147e-001},
        {8.500340926125752e+005,-3.567227768237408e+003,1.948963084447095e+001,
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        8.275700180218225e-001},{2.530004736674350e-001,-5.950549117251455e-002,
        3.526743712965212e-001,8.292652958829614e-001},{2.559752230366451e-001,
        -5.594177412647441e-002,3.521262910014856e-001,8.309392897040731e-001},
        {2.592422310622398e-001,-5.237959267551613e-002,3.516177751155357e-001,
        8.325922910059250e-001},{2.628065531267236e-001,-4.881568009199424e-002,
        3.511480607379117e-001,8.342245873328724e-001},{2.666738567720074e-001,
        -4.524682709852055e-002,3.507164162151467e-001,8.358364623005091e-001},
        {2.708504884539047e-001,-4.166987608244501e-002,3.503221398361055e-001,
        8.374281956429612e-001},{2.753433071879429e-001,-3.808171199029962e-002,
        3.499645585884929e-001,8.390000632598814e-001},{2.801599037196582e-001,
        -3.447926077765695e-002,3.496430270117127e-001,8.405523372631366e-001},
        {2.853083921105367e-001,-3.085947960555782e-002,3.493569260683962e-001,
        8.420852860231959e-001},{2.907976806313661e-001,-2.721935651026936e-002,
        3.491056621189848e-001,8.435991742151832e-001},{2.966371720783940e-001,
        -2.355589928273860e-002,3.488886658983132e-001,8.450942628646833e-001},
        {3.028370462889118e-001,-1.986613619310260e-002,3.487053916015641e-001,
        8.465708093931487e-001},{3.094081917821564e-001,-1.614710890028537e-002,
        3.485553159714244e-001,8.480290676631032e-001},{3.163620364755382e-001,
        -1.239586542273052e-002,3.484379374449686e-001,8.494692880229420e-001},
        {3.237109529050010e-001,-8.609462422221065e-003,3.483527753712113e-001,
        8.508917173514538e-001},{3.314679191860245e-001,-4.784954014192033e-003,
        3.482993692124245e-001,8.522965991020172e-001},{3.396466627040896e-001,
        -9.193907609769285e-004,3.482772778363755e-001,8.536841733464595e-001},
        {3.482573639782674e-001,2.990234168183047e-003,3.482860786936271e-001,
        8.550546768185773e-001},{3.573435870189764e-001,6.946512750374164e-003,
        3.483253684425491e-001,8.564083429573437e-001},{3.668456015562940e-001,
        1.095357014539229e-002,3.483947564910607e-001,8.577454019497183e-001},{
        3.768666032330697e-001,1.501283216327796e-002,3.484938791513281e-001,
        8.590660807729463e-001},{3.872502858387614e-001,1.912964792928498e-002,
        3.486223735021649e-001,8.603706032376969e-001},{3.978260416786913e-001,
        2.330753852682181e-002,3.487799024495905e-001,8.616591900276418e-001},{
        4.132101935168742e-001,2.749646402204903e-002,3.489662637387618e-001,
        8.629320587422359e-001},{4.184545943199193e-001,3.190595255298934e-002,
        3.491805658203261e-001,8.641894239321634e-001},{4.362824413649418e-001,
        3.618297429472679e-002,3.494237843557785e-001,8.654314971271906e-001},{
        4.482605603718436e-001,4.065324239822417e-002,3.496942108258070e-001,
        8.666584870394793e-001},{4.622330316257493e-001,4.516985999042349e-002,
        3.499923862104077e-001,8.678705992003968e-001},{4.768622286036364e-001,
        4.976455970008947e-002,3.503178747560284e-001,8.690680364449238e-001},{
        4.921745241725010e-001,5.444066904880778e-002,3.506704352553635e-001,
        8.702509987148481e-001},{5.081973839874943e-001,5.920156908963686e-002,
        3.510498387111092e-001,8.714196831463595e-001},{5.249595720422131e-001,
        6.405069424380409e-002,3.514558679881682e-001,8.725742841082431e-001},{
        5.424905347559086e-001,6.899154202103656e-002,3.518883174461503e-001,
        8.737149932396073e-001},{5.608210429624480e-001,7.402766394847896e-002,
        3.523469926362302e-001,8.748419994872339e-001},{5.799822127345404e-001,
        7.916267804090524e-002,3.528317099190555e-001,8.759554891424319e-001},{
        6.004830519290501e-001,8.439587774540482e-002,3.533423051135982e-001,
        8.770556458774835e-001},{6.225303530662254e-001,8.972780116427569e-002,
        3.538786230951095e-001,8.781426507816023e-001},{6.463610750175416e-001,
        9.515751995040138e-002,3.544405351945316e-001,8.792166823964106e-001},{
        6.722471844825647e-001,1.012426405366949e-001,3.550840958618995e-001,
        8.803766342353709e-001},{7.038651077223995e-001,1.075468486721946e-001,
        3.557708387936919e-001,8.815427655306450e-001},{7.251393379424058e-001,
        1.142877363408631e-001,3.565023423314873e-001,8.827152564770329e-001},{
        7.642524395207234e-001,1.210851585997144e-001,3.572820846551236e-001,
        8.838942963354349e-001},{7.967358094127701e-001,1.283613467605374e-001,
        3.581108233391086e-001,8.850800842450453e-001},{8.338699793357391e-001,
        1.359403244468062e-001,3.589921197256534e-001,8.862728294157951e-001},{
        8.739157757386329e-001,1.438882241405927e-001,3.599284806768164e-001,
        8.874727525584538e-001},{9.171674240348069e-001,1.522338614296611e-001,
        3.609228706786188e-001,8.886800863594736e-001},{9.639566900146391e-001,
        1.610089362976866e-001,3.619784903446237e-001,8.898950765022780e-001},{
        1.014658245902457e+000,1.702483983739543e-001,3.630988007319633e-001,
        8.911179826999973e-001},{1.069696500740114e+000,1.799908580537642e-001,
        3.642875508037436e-001,8.923490798353885e-001},{1.129553586989754e+000,
        1.902790629163924e-001,3.655488084631469e-001,8.935886592217480e-001},{
        1.194778730658964e+000,2.011604495101677e-001,3.668869957374470e-001,
        8.948370300007601e-001},{1.265999604715109e+000,2.126877807800234e-001,
        3.683069287846877e-001,8.960945206957666e-001},{1.343935603653501e+000,
        2.249198920053187e-001,3.698138634914989e-001,8.973614809419384e-001},{
        1.429414190654427e+000,2.379225551311867e-001,3.714135476414637e-001,
        8.986382834183703e-001},{1.523389963185659e+000,2.517694999845817e-001,
        3.731122807290428e-001,8.999253260114501e-001},{1.626967987465184e+000,
        2.665436073713666e-001,3.749169828303232e-001,9.012230342439003e-001},{
        1.741431587530111e+000,2.823383211013446e-001,3.768352741049624e-001,
        9.025318640101248e-001},{1.868275831068914e+000,2.992593167802703e-001,
        3.788755669150111e-001,9.038523046659105e-001},{2.009247253435497e+000,
        3.174264875499637e-001,3.810471728982508e-001,9.051848825296176e-001},{
        2.166391087168643e+000,3.369763061640536e-001,3.833604278633734e-001,
        9.065301648630008e-001},{2.349101814944340e+000,3.579901484020978e-001,
        3.858270141057033e-001,9.078887644133517e-001},{2.531929749610997e+000,
        3.810226519207810e-001,3.884588003903566e-001,9.092613446151097e-001},{
        2.767188003052499e+000,4.055286490868840e-001,3.912727602985009e-001,
        9.106486255694756e-001},{3.016217450507473e+000,4.324970058988013e-001,
        3.942818356613025e-001,9.120513915273417e-001},{3.303389261208595e+000,
        4.618306962042632e-001,3.975063679209401e-001,9.134704971443424e-001},{
        3.631549916126941e+000,4.939281587987267e-001,4.009666241813926e-001,
        9.149068790734376e-001},{4.008482779288279e+000,5.291694395449363e-001,
        4.046862435629703e-001,9.163615656490546e-001},{4.443846750534742e+000,
        5.680030693371376e-001,4.086922722032931e-001,9.178356901063999e-001},{
        4.949731196871531e+000,6.109615086616571e-001,4.130158106084739e-001,
        9.193305059167702e-001},{5.541409643335976e+000,6.586807872014066e-001,
        4.176928163006187e-001,9.208474050863027e-001},{6.238372675901206e+000,
        7.119257358914435e-001,4.227651072505875e-001,9.223879401412338e-001},{
        7.065766386999059e+000,7.716226265930281e-001,4.282816280479594e-001,
        9.239538507389419e-001},{8.056416694649682e+000,8.389018864217007e-001,
        4.343000631122791e-001,9.255470961380512e-001},{9.253723462876144e+000,
        9.151544772853499e-001,4.408889145566523e-001,9.271698951653059e-001},{
        1.071584561649215e+001,1.002107267105648e+000,4.481302092757962e-001,
        9.288247758812972e-001},{1.253214033900518e+001,1.101808734948876e+000,
        4.561233615389971e-001,9.305146379456196e-001},{1.477897062418504e+001,
        1.217485995326902e+000,4.649880047213420e-001,9.322428318295400e-001},{
        1.766908561621815e+001,1.351719349121241e+000,4.748770243380275e-001,
        9.340132606989513e-001},{2.138486266524388e+001,1.509883643514754e+000,
        4.859733964211321e-001,9.358305148113010e-001},{2.628754637519723e+001,
        1.697451202895145e+000,4.985169448163012e-001,9.377000442304936e-001},{
        3.289856626810693e+001,1.922256316265470e+000,5.128135873286412e-001,
        9.396284013530487e-001},{4.205492727375339e+001,2.194581754116503e+000,
        5.292667488868058e-001,9.416235666436306e-001},{5.514876558372439e+001,
        2.528063775283584e+000,5.484198767596652e-001,9.436954119389488e-001},{
        7.462633427723064e+001,2.940368260878233e+000,5.710261164676607e-001,
        9.458563710445010e-001},{1.050184348991562e+002,3.453462949853480e+000,
        5.981648072853771e-001,9.481224427923183e-001},{1.555495965673860e+002,
        4.087350044552481e+000,6.314608944041468e-001,9.505147490704314e-001},{
        2.376339218745235e+002,4.944818621598538e+000,6.732270162071558e-001,
        9.530620700536182e-001},{3.778931105604901e+002,6.223871768745157e+000,
        7.270999546100488e-001,9.558052023498382e-001},{6.392510022959895e+002,
        8.369904048358965e+000,7.988184626507228e-001,9.588050299738381e-001},{
        1.175214125741375e+003,9.200515050596998e+000,8.756729054310770e-001,
        9.612797327158309e-001},{2.404391521144330e+003,8.351201828031256e+000,
        9.861434004464017e-001,9.640175305607321e-001},{5.280178052685498e+003,
        7.052137331238425e+000,1.155225153751228e+000,9.672632864915536e-001},{
        1.195185547887987e+004,1.436266930835130e+001,1.399691464502437e+000,
        9.709593911907505e-001},{2.738163303986884e+004,3.128192142643308e+001,
        1.713086045447508e+000,9.743575124934957e-001},{6.813367902015221e+004,
        2.245954110359909e+001,2.098339086431259e+000,9.771334786926074e-001},{
        1.719549070722432e+005,-4.567581958920449e+001,2.615376615379705e+000,
        9.796670698052391e-001},{4.072927452321919e+005,-5.632241381576800e+001,
        3.317614691567385e+000,9.823925310148151e-001},{9.174334612404156e+005,
        5.978559879130236e+002,4.355002072346393e+000,9.857167565271496e-001},{
        1.863229120547296e+006,1.146180212440694e+003,5.277266586606779e+000,
        9.875311446084982e-001},{4.352587282561689e+006,3.435290432960140e+002,
        6.013725056438802e+000,9.883772225822374e-001},{1.294720023425507e+007,
        -1.952316825630777e+003,7.598845776825704e+000,9.898384444052550e-001},
        {4.368922580067658e+007,-9.798242269889981e+003,1.040268251220144e+001,
        9.914339076346728e-001},{1.412163489780696e+008,-7.929973860030538e+003,
        1.348982180175535e+001,9.935448201066974e-001},{3.054619794272863e+008,
        1.543075051399528e+004,1.697364990930417e+001,9.950069147908655e-001},{
        2.513842293016319e+012,-1.192762798969687e+008,1.413409677685541e+003,
        9.959656981502529e-001}};
    constant Real[Ninterval, 4] hvcoef={{3.418719024828741e+009,-6.021500887201227e+005,
        1.372239895761628e+002,8.595917694423992e-001},{3.054310565670096e+009,
        -5.705938691014666e+005,1.340221742560438e+002,8.599600896018758e-001},
        {2.680326377990845e+009,-5.429463074242631e+005,1.313866487967003e+002,
        8.602696780537780e-001},{2.303779913727746e+009,-4.921392562770898e+005,
        1.256410111646926e+002,8.609751352703259e-001},{1.980129780009944e+009,
        -4.460960668130493e+005,1.201498857905039e+002,8.616864231415984e-001},
        {1.702029460983321e+009,-4.043727836958034e+005,1.149020405579111e+002,
        8.624035880113733e-001},{1.463001841507740e+009,-3.665601613605881e+005,
        1.098863963717011e+002,8.631267209320035e-001},{1.257578888846852e+009,
        -3.322921639231642e+005,1.050926221990266e+002,8.638558834346060e-001},
        {1.081020151317802e+009,-3.012351730865443e+005,1.005107466086200e+002,
        8.645911520991180e-001},{9.292788756444820e+008,-2.730884033777993e+005,
        9.613135173247430e+001,8.653325887404106e-001},{7.988592072529383e+008,
        -2.475781452734592e+005,9.194535249523334e+001,8.660802702489665e-001},
        {6.867517994789405e+008,-2.244567953084133e+005,8.794416126688296e+001,
        8.668342586830016e-001},{5.903993090097249e+008,-2.035004093727184e+005,
        8.411943557310387e+001,8.675946462312558e-001},{5.075739967569540e+008,
        -1.845052128758624e+005,8.046328280923146e+001,8.683615102740704e-001},
        {4.363803981359935e+008,-1.672877964071615e+005,7.696824858217629e+001,
        8.691349132544352e-001},{3.751811369685484e+008,-1.516810195389626e+005,
        7.362707753938845e+001,8.699149478489386e-001},{3.225757764446142e+008,
        -1.375342639486588e+005,7.043297686856677e+001,8.707016766933142e-001},
        {2.775632019164234e+008,-1.247180148068888e+005,6.737939987231324e+001,
        8.714951927224426e-001},{2.395047937120040e+008,-1.131276569986563e+005,
        6.446029045026621e+001,8.722955738779207e-001},{2.072894646248908e+008,
        -1.026516293164950e+005,6.166981089182345e+001,8.731028981691641e-001},
        {1.799822430252400e+008,-9.333464537306117e+004,5.905402123864285e+001,
        8.739009311042776e-001},{1.566914275764715e+008,-8.525624087305536e+004,
        5.668205775153147e+001,8.746623083398238e-001},{1.365420998913238e+008,
        -7.792553082576592e+004,5.442145459347433e+001,8.754247647693702e-001},
        {1.190945653358361e+008,-7.126911585540987e+004,5.226630523340383e+001,
        8.761882924491433e-001},{1.039717710388903e+008,-6.522111942123056e+004,
        5.021104820325436e+001,8.769528833328070e-001},{9.085238634246235e+007,
        -5.972253866425365e+004,4.825044784911309e+001,8.777185292709222e-001},
        {7.945976285392952e+007,-5.472031010955200e+004,4.637957044109646e+001,
        8.784852220104472e-001},{6.955828718931271e+007,-5.016689134145316e+004,
        4.459376897054184e+001,8.792529531942909e-001},{6.094432939926156e+007,
        -4.601943690028419e+004,4.288866070740672e+001,8.800217143609221e-001},
        {5.344423567813414e+007,-4.223952028854783e+004,4.126011513927500e+001,
        8.807914969440196e-001},{4.690790693157751e+007,-3.879248539780872e+004,
        3.970423429382681e+001,8.815622922721852e-001},{4.120636628965157e+007,
        -3.564715093489797e+004,3.821734102078233e+001,8.823340915687035e-001},
        {3.622900976104898e+007,-3.277545861657008e+004,3.679596497500520e+001,
        8.831068859513512e-001},{3.187967036644944e+007,-3.015203386420734e+004,
        3.543682780067873e+001,8.838806664322682e-001},{2.807613578829654e+007,
        -2.775406516810798e+004,3.413683515396600e+001,8.846554239178743e-001},
        {2.474692036340034e+007,-2.556090563904067e+004,3.289306188961926e+001,
        8.854311492088450e-001},{2.183049697968674e+007,-2.355393699418945e+004,
        3.170274439968934e+001,8.862078330001338e-001},{1.927347019859899e+007,
        -2.171631328406215e+004,3.056326941876671e+001,8.869854658810615e-001},
        {1.702981751333125e+007,-2.003282321642497e+004,2.947216618883089e+001,
        8.877640383354423e-001},{1.505930006594837e+007,-1.848966312427858e+004,
        2.842709641996708e+001,8.885435407417774e-001},{1.332750187738691e+007,
        -1.707439527076683e+004,2.742584914811091e+001,8.893239633734973e-001},
        {1.180409908173095e+007,-1.577569115143173e+004,2.646632952888870e+001,
        8.901052963992563e-001},{1.046300091887967e+007,-1.458332162795913e+004,
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        {5.640453232697693e-002,-1.937878816798458e-001,4.163696706650428e-002,
        1.098802638310406e+000},{5.003932121783335e-002,-1.927430817480175e-001,
        3.949389537115199e-002,1.099027440295432e+000},{4.370356344501013e-002,
        -1.917964562372977e-001,3.734334623333660e-002,1.099242193923410e+000},
        {3.738474704089313e-002,-1.909490901638774e-001,3.518427175977259e-002,
        1.099446659306848e+000},{3.106990814761928e-002,-1.902022738733920e-001,
        3.301558205824082e-002,1.099640587342539e+000},{2.471924771693251e-002,
        -1.895570588253832e-001,3.083614013868847e-002,1.099823719208536e+000},
        {1.834223327637784e-002,-1.890154314600311e-001,2.864476241935234e-002,
        1.099995785825217e+000},{1.195094886503533e-002,-1.885798454355235e-001,
        2.644021168354557e-002,1.100156507277238e+000},{5.557050709009414e-003,
        -1.882515929288725e-001,2.418461128139228e-002,1.100307943910574e+000},
        {-8.014493909795158e-004,-1.880402684286048e-001,2.194575815737601e-002,
        1.100445109478535e+000},{-7.135417654424650e-003,-1.879436446578345e-001,
        1.972726442004061e-002,1.100567996583830e+000},{-1.345870138684300e-002,
        -1.879591637675092e-001,1.752795451986745e-002,1.100676931096945e+000},
        {-1.978471856691031e-002,-1.880845063496110e-001,1.534670037602332e-002,
        1.100772233147846e+000},{-2.612655707280306e-002,-1.883175768416115e-001,
        1.318241876916896e-002,1.100854217210090e+000},{-3.249697575622967e-002,
        -1.886564925021107e-001,1.103406890701701e-002,1.100923192183922e+000},
        {-3.890850468817631e-002,-1.890995704946074e-001,8.900650115975411e-003,
        1.100979461478381e+000},{-4.537347157514723e-002,-1.896453182395342e-001,
        6.781199688611053e-003,1.101023323092393e+000},{-5.190403204992995e-002,
        -1.902924240651144e-001,4.674790850459827e-003,1.101055069694875e+000},
        {-5.851225277558175e-002,-1.910397473018965e-001,2.580530837908182e-003,
        1.101074988703860e+000},{-6.521011476274589e-002,-1.918863113150857e-001,
        4.975591027557807e-004,1.101083362364609e+000},{-7.200957075288722e-002,
        -1.928312955496475e-001,-1.574954392253073e-003,1.101080467826757e+000},
        {-7.892258128041750e-002,-1.938740289010325e-001,-3.637810776014087e-003,
        1.101066577220491e+000},{-8.596114095058548e-002,-1.950139836709728e-001,
        -5.691783782005860e-003,1.101041957731749e+000},{-9.313731870582566e-002,
        -1.962507697828389e-001,-7.737621177713153e-003,1.101006871676471e+000},
        {-1.004633132706661e-001,-1.975841292444321e-001,-9.776046115403617e-003,
        1.100961576573900e+000},{-1.079514189138674e-001,-1.990139329502044e-001,
        -1.180775839988235e-002,1.100906325218945e+000},{-1.156141501458894e-001,
        -2.005401741857532e-001,-1.383343570756720e-002,1.100841365753626e+000},
        {-1.234641865756744e-001,-2.021629669142985e-001,-1.585373471362041e-002,
        1.100766941737587e+000},{-1.315144632458761e-001,-2.038825407987732e-001,
        -1.786929218092619e-002,1.100683292217720e+000},{-1.397781622796490e-001,
        -2.056992389395121e-001,-1.988072597730302e-002,1.100590651796894e+000},
        {-1.482687849379858e-001,-2.076135142055186e-001,-2.188863604735403e-002,
        1.100489250701797e+000},{-1.570001127509399e-001,-2.096259281418626e-001,
        -2.389360532338351e-002,1.100379314849913e+000},{-1.659863131041873e-001,
        -2.117371469439204e-001,-2.589620060511024e-002,1.100261065915656e+000},
        {-1.752419465890530e-001,-2.139479403721047e-001,-2.789697337688882e-002,
        1.100134721395630e+000},{-1.847819278769801e-001,-2.162591809460440e-001,
        -2.989646059049550e-002,1.100000494673090e+000},{-1.946216794315628e-001,
        -2.186718402076742e-001,-3.189518541573153e-002,1.099858595081566e+000},
        {-2.047770670769773e-001,-2.211869893365289e-001,-3.389365793731571e-002,
        1.099709227967682e+000},{-2.152644567239538e-001,-2.238057975178256e-001,
        -3.589237582835234e-002,1.099552594753185e+000},{-2.261007643374610e-001,
        -2.265295306054332e-001,-3.789182498937845e-002,1.099388892996184e+000},
        {-2.373034676588316e-001,-2.293595508675275e-001,-3.989248015126330e-002,
        1.099218316451631e+000},{-2.488906597672881e-001,-2.322973162338434e-001,
        -4.189480545039329e-002,1.099041055131017e+000},{-2.608810484226545e-001,
        -2.353443803241083e-001,-4.389925497691962e-002,1.098857295361356e+000},
        {-2.732940302195583e-001,-2.385023915702908e-001,-4.590627329721378e-002,
        1.098667219843396e+000},{-2.861497020009324e-001,-2.417730936839753e-001,
        -4.791629594706479e-002,1.098471007709130e+000},{-2.994689199938831e-001,
        -2.451583253792444e-001,-4.992974990525140e-002,1.098268834578575e+000},
        {-3.132732751354347e-001,-2.486600214001266e-001,-5.194705404153135e-002,
        1.098060872615857e+000},{-3.275852638322766e-001,-2.522802108711590e-001,
        -5.396861955037104e-002,1.097847290584594e+000},{-3.424281663994858e-001,
        -2.560210205428296e-001,-5.599485034861269e-002,1.097628253902595e+000},
        {-3.578293520435974e-001,-2.598846367187872e-001,-5.802614356800304e-002,
        1.097403924695883e+000},{-3.737991995924480e-001,-2.638735869985462e-001,
        -6.006288915407318e-002,1.097174461852052e+000},{-3.903902600560969e-001,
        -2.679898530112919e-001,-6.210547303843708e-002,1.096940021072966e+000},
        {-4.076012547942460e-001,-2.722364457397745e-001,-6.415427156013318e-002,
        1.096700754925520e+000},{-4.254343891046640e-001,-2.766161117295213e-001,
        -6.620965819623846e-002,1.096456812898149e+000},{-4.438339027573641e-001,
        -2.811320490392464e-001,-6.827199959147826e-002,1.096208341444035e+000},
        {-4.644750403946706e-001,-2.857679946652489e-001,-7.034170236902584e-002,
        1.095955484037268e+000},{-4.820890817525319e-001,-2.906000672424869e-001,
        -7.241891749894044e-002,1.095698381226341e+000},{-5.047134822541359e-001,
        -2.955056304565424e-001,-7.450444780138031e-002,1.095437170699271e+000},
        {-5.258914498568529e-001,-3.006012937060756e-001,-7.659813906378293e-002,
        1.095171987136068e+000},{-5.484047930470472e-001,-3.058375854914676e-001,
        -7.870062238535235e-002,1.094902962737344e+000},{-5.718129216158286e-001,
        -3.112278431359212e-001,-8.081217584455191e-002,1.094630226742015e+000},
        {-5.961547440676940e-001,-3.167755376343922e-001,-8.293313841275786e-002,
        1.094353905753897e+000},{-6.214708520460160e-001,-3.224842528277391e-001,
        -8.506384586954169e-002,1.094074123729523e+000},{-6.478032148383646e-001,
        -3.283576921832907e-001,-8.720463098789563e-002,1.093791002023522e+000},
        {-6.751957491746247e-001,-3.343996727291274e-001,-8.935582375150214e-002,
        1.093504659433427e+000},{-7.036936171960371e-001,-3.406141369349701e-001,
        -9.151775149673061e-002,1.093215212243908e+000},{-7.333438920356818e-001,
        -3.470051435467684e-001,-9.369073911646579e-002,1.092922774270491e+000},
        {-7.649284588825603e-001,-3.535701423882779e-001,-9.587512294577692e-002,
        1.092627456902683e+000},{-7.987573127935487e-001,-3.603086226499994e-001,
        -9.807123530043556e-002,1.092329369146623e+000},{-8.351881293636163e-001,
        -3.672179068043334e-001,-1.002794318903687e-001,1.092028617667189e+000},
        {-8.746337064830027e-001,-3.750216293989062e-001,-1.027084493542587e-001,
        1.091696779574096e+000},{-9.182631668618914e-001,-3.831991324672869e-001,
        -1.051985063743867e-001,1.091355729081559e+000},{-9.598866647526484e-001,
        -3.918556861719648e-001,-1.077524800454063e-001,1.091005198961375e+000},
        {-1.010790497453898e+000,-4.008622937465624e-001,-1.103741544582843e-001,
        1.090644908830807e+000},{-1.061585597914184e+000,-4.104074244317262e-001,
        -1.130664113126074e-001,1.090274564104240e+000},{-1.116923652713534e+000,
        -4.204470439736384e-001,-1.158334219482580e-001,1.089893855365184e+000},
        {-1.176390470616413e+000,-4.310341925159665e-001,-1.186791465288392e-001,
        1.089502456776096e+000},{-1.240398358090701e+000,-4.422099547341248e-001,
        -1.216079485825098e-001,1.089100025144463e+000},{-1.309411351967095e+000,
        -4.540194728668653e-001,-1.246245298507227e-001,1.088686198529077e+000},
        {-1.383952478324663e+000,-4.665124525546056e-001,-1.277339645466649e-001,
        1.088260594774788e+000},{-1.464613539394650e+000,-4.797437255410850e-001,
        -1.309417379885211e-001,1.087822809897360e+000},{-1.552065595474018e+000,
        -4.937739146636258e-001,-1.342537901400978e-001,1.087372416299330e+000},
        {-1.647071854814870e+000,-5.086701932065426e-001,-1.376765649336416e-001,
        1.086908960794945e+000},{-1.750503179964703e+000,-5.245071629179311e-001,
        -1.412170662450014e-001,1.086431962418652e+000},{-1.863356315547510e+000,
        -5.413678789587019e-001,-1.448829215901497e-001,1.085940909987632e+000},
        {-1.986775922871999e+000,-5.593450423418901e-001,-1.486824548572708e-001,
        1.085435259383995e+000},{-2.122081131299789e+000,-5.785423947412177e-001,
        -1.526247696085506e-001,1.084914430516412e+000},{-2.270797351520379e+000,
        -5.990763602365653e-001,-1.567198447858746e-001,1.084377803914027e+000},
        {-2.434695501360245e+000,-6.210779709042096e-001,-1.609786450924524e-001,
        1.083824716897111e+000},{-2.615838531681118e+000,-6.446951619454530e-001,
        -1.654132486612294e-001,1.083254459258780e+000},{-2.816639044616160e+000,
        -6.700954812249659e-001,-1.700369953943099e-001,1.082666268379815e+000},
        {-3.039928700415489e+000,-6.974693316356091e-001,-1.748646598439750e-001,
        1.082059323683556e+000},{-3.292219758098840e+000,-7.270000140981027e-001,
        -1.799127335700266e-001,1.081432740319499e+000},{-3.564782476198684e+000,
        -7.591050350223508e-001,-1.851990623476152e-001,1.080785561941540e+000},
        {-3.884190359823099e+000,-7.937345882311215e-001,-1.907452448062669e-001,
        1.080116752418797e+000},{-4.237141139726640e+000,-8.315523945506937e-001,
        -1.965727692029269e-001,1.079425186076460e+000},{-4.639142492737927e+000,
        -8.727752413556356e-001,-2.027083906666977e-001,1.078709637232685e+000},
        {-5.097189675608282e+000,-9.178820437390601e-001,-2.091811202970346e-001,
        1.077968766554805e+000},{-5.621762464449057e+000,-9.673950144480338e-001,
        -2.160241562151455e-001,1.077201106424277e+000},{-6.225833712033967e+000,
        -1.021929051176963e+000,-2.232753772451849e-001,1.076405043117602e+000},
        {-6.925601260591495e+000,-1.082212356404202e+000,-2.309782180242463e-001,
        1.075578795840945e+000},{-7.741476361496349e+000,-1.149112657464135e+000,
        -2.391827511126749e-001,1.074720391772839e+000},{-8.699439370277643e+000,
        -1.223670757770951e+000,-2.479470365689759e-001,1.073827636152860e+000},
        {-9.832921391371407e+000,-1.307143891200575e+000,-2.573388201788544e-001,
        1.072898076168983e+000},{-1.118545570250340e+001,-1.401062230883758e+000,
        -2.674376916575652e-001,1.071928957010234e+000},{-1.281446878655493e+001,
        -1.507303306245227e+000,-2.783378567732671e-001,1.070917167920417e+000},
        {-1.479678827882319e+001,-1.628191020093895e+000,-2.901517399548284e-001,
        1.069859175350126e+000},{-1.724144136142261e+001,-1.766576297530559e+000,
        -3.030148579310907e-001,1.068750939259828e+000},{-2.027826987203854e+001,
        -1.926337376059677e+000,-3.170912838064992e-001,1.067587807127434e+000},
        {-2.413687940816858e+001,-2.111734868657410e+000,-3.325851366637468e-001,
        1.066364378021886e+000},{-2.909401840847157e+001,-2.329151580543732e+000,
        -3.497470819764231e-001,1.065074325623783e+000},{-3.559985600470116e+001,
        -2.586219259879967e+000,-3.688972788252130e-001,1.063710165062041e+000},
        {-4.432903871576617e+001,-2.893237376748189e+000,-3.904455236187271e-001,
        1.062262938236866e+000},{-5.635486800356907e+001,-3.263787309390394e+000,
        -4.149289589297027e-001,1.060721782952100e+000},{-7.345422356224562e+001,
        -3.715852360320928e+000,-4.430674062157222e-001,1.059073327378870e+000},
        {-9.872541030429800e+001,-4.272847713002282e+000,-4.758525332055549e-001,
        1.057300816644650e+000},{-1.379029789580371e+002,-4.963698528158174e+000,
        -5.146977811000596e-001,1.055382812700357e+000},{-2.025227956751322e+002,
        -5.816502032157165e+000,-5.617124713275824e-001,1.053291185212563e+000},
        {-3.066576906266529e+002,-6.965314926095712e+000,-6.198853650303311e-001,
        1.050987862948901e+000},{-4.830543755124683e+002,-8.666062419141326e+000,
        -6.938823513423141e-001,1.048419277617361e+000},{-8.084833331246175e+002,
        -1.148692234324379e+001,-7.910281397083958e-001,1.045506157577100e+000},
        {-1.468144450984898e+003,-1.270342041479051e+001,-8.932720264828298e-001,
        1.043022458452853e+000},{-2.960185006157666e+003,-1.204645827816411e+001,
        -1.037687543523871e+000,1.040192609451484e+000},{-6.394379648177180e+003,
        -1.133095662667407e+001,-1.255214139021270e+000,1.036731981255395e+000},
        {-1.421291626844065e+004,-2.176830415540717e+001,-1.565859480023533e+000,
        1.032664478961364e+000},{-3.188506981409266e+004,-4.472235675466877e+001,
        -1.957122092195666e+000,1.028823550217078e+000},{-7.717088076510136e+004,
        -4.157109709425348e+001,-2.425675063473610e+000,1.025629204891293e+000},
        {-1.893604841837793e+005,1.988107110128464e+001,-3.037933999829498e+000,
        1.022682315051265e+000},{-4.362759910617617e+005,4.356252894797460e+000,
        -3.857056802145624e+000,1.019493900338764e+000},{-9.667858531739716e+005,
        -7.110743222205122e+002,-5.068028151693111e+000,1.015606411778339e+000},
        {-1.926807175753026e+006,-1.308643373681819e+003,-6.100046763833379e+000,
        1.013498423615123e+000},{-4.430874958584904e+006,-5.255191972894967e+002,
        -6.892511697752738e+000,1.012521645013935e+000},{-1.306500915854772e+007,
        1.740498999891739e+003,-8.577603939805345e+000,1.010846737556340e+000},
        {-4.389793234302502e+007,9.560482174458750e+003,-1.148948797863325e+001,
        1.009039661353492e+000},{-1.453953316964447e+008,8.587054210867187e+003,
        -1.476464101007846e+001,1.006692766581286e+000},{-3.516933123906404e+008,
        -1.085943267171107e+004,-1.840303816166151e+001,1.005101578506159e+000},
        {-2.510574163087101e+012,1.191163343802633e+008,-1.412900529450008e+003,
        1.004074865378772e+000}};
    constant Real[Ninterval, 4] slcoef={{1.177557139507648e+010,-1.993514199606193e+006,
        4.143546065409241e+002,2.641402961120132e-001},{1.048671143722957e+010,
        -1.884478673305442e+006,4.037631012049168e+002,2.652511930832029e-001},
        {9.168562051007404e+009,-1.788981183928967e+006,3.950602310696419e+002,
        2.661829932674829e-001},{7.846446101028213e+009,-1.614583713308304e+006,
        3.761535139366466e+002,2.682996669625260e-001},{6.715017635832893e+009,
        -1.457222530950107e+006,3.581621886022840e+002,2.704246269918255e-001},
        {5.747015349679062e+009,-1.315240915328985e+006,3.410420212198932e+002,
        2.725579055981067e-001},{4.918630356754790e+009,-1.187122828234776e+006,
        3.247498175022562e+002,2.746996665285123e-001},{4.209783796072495e+009,
        -1.071515458129660e+006,3.092453129575851e+002,2.768499837872521e-001},
        {3.603174902826428e+009,-9.671924631452678e+005,2.944898874475471e+002,
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        1.581230920983324e+002,3.266020040491545e+000,4.399786317612097e-001,
        9.689968887258295e-001},{2.515136935955693e+002,4.116442075807741e+000,
        4.756363207390761e-001,9.707903327720178e-001},{4.255666011618887e+002,
        5.543864685060169e+000,5.231660521339230e-001,9.727536601397832e-001},{
        7.825530244524709e+002,6.095169952013788e+000,5.741651534308233e-001,
        9.743751414991224e-001},{1.601387467228535e+003,5.526394469524922e+000,
        6.475446574462375e-001,9.761711567563309e-001},{3.517379521473430e+003,
        4.655838112548601e+000,7.599439282112659e-001,9.783035737380645e-001},{
        7.962846678376361e+003,9.518793744286704e+000,9.225514220968945e-001,
        9.807363487766135e-001},{1.824488327643979e+004,2.078256392728106e+001,
        1.131128321260709e+000,9.829773592443036e-001},{4.540306810221719e+004,
        1.488976251891372e+001,1.387654000750968e+000,9.848111708264992e-001},{
        1.145958554994318e+005,-3.053821008062807e+001,1.732038158743400e+000,
        9.864872284392217e-001},{2.714454865411694e+005,-3.766348045575876e+001,
        2.199850765561659e+000,9.882925910565035e-001},{6.114567935601252e+005,
        3.983023186009633e+002,2.891002115453413e+000,9.904976309221367e-001},{
        1.241850100485509e+006,7.637348298339904e+002,3.505557353710815e+000,
        9.917024335783234e-001},{2.901091663911621e+006,2.287151249154257e+002,
        3.996356201581334e+000,9.922645331286384e-001},{8.629777329944847e+006,
        -1.301634709362246e+003,5.052771746981934e+000,9.932357014649955e-001},
        {2.912091392721209e+007,-6.531467250818030e+003,6.921517889213511e+000,
        9.942966215510268e-001},{9.412813865309173e+007,-5.286393541194419e+003,
        8.979056034617720e+000,9.957010756859428e-001},{2.036070618782550e+008,
        1.028469165095266e+004,1.130107943827922e+001,9.966743300764792e-001},{
        1.674526211291653e+012,-7.945254783461587e+007,9.414997405411956e+002,
        9.973127499065179e-001}};
    constant Real[Ninterval, 4] svcoef={{-1.167161242280822e+010,
        1.878696788040639e+006,-3.414627808635271e+002,1.257192752866231e+000},
        {-1.035354888344887e+010,1.770211704883063e+006,-3.314921184815092e+002,
        1.256278981521677e+000},{-9.010871046855169e+009,1.675234821593873e+006,
        -3.233186928839511e+002,1.255515159251215e+000},{-7.670087323896805e+009,
        1.503104694936961e+006,-3.056454829469166e+002,1.253788981093666e+000},
        {-6.528525227742667e+009,1.348617412883818e+006,-2.889263517656612e+002,
        1.252068489141656e+000},{-5.556819130397623e+009,1.209977756821469e+006,
        -2.731107664395464e+002,1.250353786912934e+000},{-4.729570822211771e+009,
        1.085555117462545e+006,-2.581498340050509e+002,1.248644873308041e+000},
        {-4.025383319196040e+009,9.738978630494837e+005,-2.439979849174128e+002,
        1.246941821048949e+000},{-3.425938223747980e+009,8.736974103745150e+005,
        -2.306117633794419e+002,1.245244670239726e+000},{-2.915696321437560e+009,
        7.837826255347068e+005,-2.179503198145804e+002,1.243553497923841e+000},
        {-2.481383208327286e+009,7.030988445381357e+005,-2.059747132443750e+002,
        1.241868349123961e+000},{-2.111686390084153e+009,6.307004543248878e+005,
        -1.946483220668824e+002,1.240189304980033e+000},{-1.797034775339657e+009,
        5.657386555897944e+005,-1.839360670319048e+002,1.238516382333624e+000},
        {-1.529214800743476e+009,5.074499659892993e+005,-1.738049564593241e+002,
        1.236849634718179e+000},{-1.301273763706718e+009,4.551518279503796e+005,
        -1.642239738649408e+002,1.235189150544434e+000},{-1.107273660839951e+009,
        4.082289549017351e+005,-1.551633835517684e+002,1.233534955827648e+000},
        {-9.421731741085697e+008,3.661311815312429e+005,-1.465954002475946e+002,
        1.231887143503433e+000},{-8.023146343545597e+008,3.283866390101237e+005,
        -1.384935880133614e+002,1.230245745364984e+000},{-6.852307594168044e+008,
        2.946092675025202e+005,-1.308334802778386e+002,1.228610827813656e+000},
        {-5.870901801301618e+008,2.644005082934081e+005,-1.235917413237229e+002,
        1.226982459618363e+000},{-5.047068181055782e+008,2.378107583024218e+005,
        -1.168778656810235e+002,1.225392995014713e+000},{-4.351080450261749e+008,
        2.149782115590958e+005,-1.108542675702452e+002,1.223894955882774e+000},
        {-3.754631816409877e+008,1.944610872742684e+005,-1.051729507319718e+002,
        1.222412562340188e+000},{-3.243003876591392e+008,1.760126494519494e+005,
        -9.981271620297964e+001,1.220945658781368e+000},{-2.803704024187839e+008,
        1.594135405147079e+005,-9.475377996554323e+001,1.219494091303989e+000},
        {-2.426161580886689e+008,1.444689114102572e+005,-8.997767687518686e+001,
        1.218057707682420e+000},{-2.101376500670390e+008,1.310052300243061e+005,
        -8.546716076385087e+001,1.216636357341712e+000},{-1.821729409586426e+008,
        1.188682298364962e+005,-8.120612512230242e+001,1.215229891332141e+000},
        {-1.580713395011833e+008,1.079202781593172e+005,-7.717951465716868e+001,
        1.213838162304302e+000},{-1.372810899764895e+008,9.803887891483332e+004,
        -7.337325952167046e+001,1.212461024484717e+000},{-1.193305568497935e+008,
        8.911463290966404e+004,-6.977419934441511e+001,1.211098333651978e+000},
        {-1.038177842631264e+008,8.104994158345387e+004,-6.637002475122108e+001,
        1.209749947113391e+000},{-9.040040036718562e+007,7.375769881825958e+004,
        -6.314921765813308e+001,1.208415723682116e+000},{-7.878443856624676e+007,
        6.715992689454205e+004,-6.010099316854539e+001,1.207095523654803e+000},
        {-6.871974414947894e+007,6.118702847513706e+004,-5.721525561719147e+001,
        1.205789208789701e+000},{-5.999133752771001e+007,5.577663404305128e+004,
        -5.448254540510249e+001,1.204496642285233e+000},{-5.241543869142986e+007,
        5.087295055300280e+004,-5.189400007463385e+001,1.203217688759031e+000},
        {-4.583415581126005e+007,4.642596046130997e+004,-4.944131149429202e+001,
        1.201952214227427e+000},{-4.011228675603470e+007,4.239086070618492e+004,
        -4.711669043018321e+001,1.200700086085366e+000},{-3.513311357163611e+007,
        3.872739999770453e+004,-4.491282933447061e+001,1.199461173086765e+000},
        {-3.079702502223688e+007,3.539954399663577e+004,-4.282287446858340e+001,
        1.198235345325283e+000},{-2.701759418906320e+007,3.237483582224888e+004,
        -4.084039003202591e+001,1.197022474215511e+000},{-2.372076973145581e+007,
        2.962417023636633e+004,-3.895933616247480e+001,1.195822432474547e+000},
        {-2.084264185672811e+007,2.712136254406240e+004,-3.717403962809318e+001,
        1.194635094103993e+000},{-1.832795661554030e+007,2.484284118361123e+004,
        -3.547917043105402e+001,1.193460334372309e+000},{-1.612910315484070e+007,
        2.276740549221483e+004,-3.386972055424017e+001,1.192298029797559e+000},
        {-1.420493817465342e+007,2.087595838808486e+004,-3.234098209159364e+001,
        1.191148058130523e+000},{-1.251978525903208e+007,1.915127628793518e+004,
        -3.088852777905769e+001,1.190010298338169e+000},{-1.104283839085355e+007,
        1.757784331955985e+004,-2.950819407825404e+001,1.188884630587475e+000},
        {-9.747385274891593e+006,1.614165584070271e+004,-2.819606332104048e+001,
        1.187770936229595e+000},{-8.610258724756623e+006,1.483007183595590e+004,
        -2.694844841479200e+001,1.186669097784365e+000},{-7.611347860356514e+006,
        1.363167257285838e+004,-2.576187830531837e+001,1.185578998925132e+000},
        {-6.733210449194347e+006,1.253614352179986e+004,-2.463308451072768e+001,
        1.184500524463906e+000},{-5.960664814163764e+006,1.153415408137276e+004,
        -2.355898800825970e+001,1.183433560336828e+000},{-5.280521597699627e+006,
        1.061726682066825e+004,-2.253668783797127e+001,1.182377993589938e+000},
        {-4.681293638655025e+006,9.777843148067454e+003,-2.156344973986173e+001,
        1.181333712365246e+000},{-4.152968837995382e+006,9.008964808911329e+003,
        -2.063669596087836e+001,1.180300605887091e+000},{-3.686828565114908e+006,
        8.304365766483923e+003,-1.975399574397403e+001,1.179278564448786e+000},
        {-3.275266327776558e+006,7.658365108421354e+003,-1.891305611231615e+001,
        1.178267479399534e+000},{-2.911625574521497e+006,7.065807076565250e+003,
        -1.811171341970251e+001,1.177267243131628e+000},{-2.590114661892789e+006,
        6.522019111917333e+003,-1.734792596167091e+001,1.176277749067896e+000},
        {-2.305650275370526e+006,6.022753490926198e+003,-1.661976587626541e+001,
        1.175298891649416e+000},{-2.053788951097264e+006,5.564153643271859e+003,
        -1.592541287535999e+001,1.174330566323474e+000},{-1.830650417503742e+006,
        5.142717130166380e+003,-1.526314768679637e+001,1.173372669531767e+000},
        {-1.632819252290972e+006,4.755254885285894e+003,-1.463134563215786e+001,
        1.172425098698841e+000},{-1.457310558157280e+006,4.398869159670537e+003,
        -1.402847159348952e+001,1.171487752220765e+000},{-1.301502456237975e+006,
        4.070921570400577e+003,-1.345307431038991e+001,1.170560529454023e+000},
        {-1.163093581080859e+006,3.769009894238661e+003,-1.290378157209061e+001,
        1.169643330704624e+000},{-1.040059054359292e+006,3.490944949502028e+003,
        -1.237929552902521e+001,1.168736057217427e+000},{-9.306220845951777e+005,
        3.234732704043220e+003,-1.187838848926460e+001,1.167838611165672e+000},
        {-8.332175097131218e+005,2.998554122300491e+003,-1.139989865622131e+001,
        1.166950895640710e+000},{-7.464663784985374e+005,2.780749557180561e+003,
        -1.094272640598105e+001,1.166072814641923e+000},{-6.691556891366435e+005,
        2.579804982448421e+003,-1.050583075721938e+001,1.165204273066841e+000},
        {-6.002151747908264e+005,2.394337509561513e+003,-1.008822589061445e+001,
        1.164345176701438e+000},{-5.387000166680566e+005,2.223083665065604e+003,
        -9.688978048092071e+000,1.163495432210602e+000},{-4.837771715710186e+005,
        2.064889150637393e+003,-9.307202614248977e+000,1.162654947128783e+000},
        {-4.347104808441157e+005,1.918698359847450e+003,-8.942061260376542e+000,
        1.161823629850803e+000},{-3.908482209910512e+005,1.783545349089750e+003,
        -8.592759344255985e+000,1.161001389622835e+000},{-3.516161249361212e+005,
        1.658547033549894e+003,-8.258543553706538e+000,1.160188136533529e+000},
        {-3.165035478016587e+005,1.542893819027835e+003,-7.938699394039895e+000,
        1.159383781505299e+000},{-2.850598559817247e+005,1.435844989118608e+003,
        -7.632549251081720e+000,1.158588236285744e+000},{-2.568853836992341e+005,
        1.336721560377161e+003,-7.339450190895453e+000,1.157801413439231e+000},
        {-2.316252113167582e+005,1.244900875868593e+003,-7.058792075603022e+000,
        1.157023226338597e+000},{-2.089652497780896e+005,1.159812303640403e+003,
        -6.789995822552769e+000,1.156253589156990e+000},{-1.886260028704987e+005,
        1.080931941447458e+003,-6.532511605482741e+000,1.155492416859840e+000},
        {-1.703595756576603e+005,1.007779146610457e+003,-6.285817340840077e+000,
        1.154739625196958e+000},{-1.539455303444279e+005,9.399125006097200e+002,
        -6.049417130211369e+000,1.153995130694738e+000},{-1.391878353597992e+005,
        8.769265149992824e+002,-5.822839859171091e+000,1.153258850648495e+000},
        {-1.259118679027340e+005,8.184484746241886e+002,-5.605637854535695e+000,
        1.152530703114902e+000},{-1.139626359191102e+005,7.641359827753867e+002,
        -5.397385660782585e+000,1.151810606904539e+000},{-1.032013550357087e+005,
        7.136737153582978e+002,-5.197678765965424e+000,1.151098481574539e+000},
        {-9.350496389204710e+004,6.667719731724156e+002,-5.006132610481427e+000,
        1.150394247421343e+000},{-8.476330492175093e+004,6.231638226625424e+002,
        -4.822381409307250e+000,1.149697825473546e+000},{-7.687824464670279e+004,
        5.826035987524953e+002,-4.646077237885241e+000,1.149009137484835e+000},
        {-6.976204933005408e+004,5.448649346498113e+002,-4.476889054980945e+000,
        1.148328105927014e+000},{-6.333647369305392e+004,5.097393221858990e+002,
        -4.314501843141601e+000,1.147654653983123e+000},{-5.753143008675712e+004,
        4.770344420945451e+002,-4.158615740492024e+000,1.146988705540629e+000},
        {-5.228434076819440e+004,4.465730200783362e+002,-4.008945287331126e+000,
        1.146330185184698e+000},{-4.753914508465970e+004,4.181914609969991e+002,
        -3.865218653140307e+000,1.145679018191555e+000},{-4.324567909424259e+004,
        3.917388090779465e+002,-3.727176949977069e+000,1.145035130521896e+000},
        {-3.935897394044224e+004,3.670756753534608e+002,-3.594573558074095e+000,
        1.144398448814387e+000},{-3.583878264355163e+004,3.440733666158342e+002,
        -3.467173508311998e+000,1.143768900379221e+000},{-3.264892946834709e+004,
        3.226129150306674e+002,-3.344752869211387e+000,1.143146413191748e+000},
        {-2.975703079636661e+004,3.025844320516610e+002,-3.227098213411754e+000,
        1.142530915886152e+000},{-2.713396553903700e+004,2.838862715090525e+002,
        -3.114006060655961e+000,1.141922337749209e+000},{-2.475361222892791e+004,
        2.664244520011594e+002,-3.005282394893281e+000,1.141320608714076e+000},
        {-2.259246929329500e+004,2.501119931930805e+002,-2.900742176144558e+000,
        1.140725659354155e+000},{-2.062942089795645e+004,2.348684065079063e+002,
        -2.800208902194028e+000,1.140137420877001e+000},{-1.884547713413705e+004,
        2.206191719071575e+002,-2.703514177914426e+000,1.139555825118279e+000},
        {-1.722353739702725e+004,2.072952590638357e+002,-2.610497311259647e+000,
        1.138980804535772e+000},{-1.574820565669981e+004,1.948327142632579e+002,
        -2.521004936730899e+000,1.138412292203431e+000},{-1.440561272630618e+004,
        1.831722652704424e+002,-2.434890653346931e+000,1.137850221805471e+000},
        {-1.318326353872169e+004,1.722589632456998e+002,-2.352014682990452e+000,
        1.137294527630510e+000},{-1.206988185328727e+004,1.620418365675164e+002,
        -2.272243543846235e+000,1.136745144565746e+000},{-1.105529962362607e+004,
        1.524736029253813e+002,-2.195449748531088e+000,1.136202008091175e+000},
        {-1.013034181716861e+004,1.435103830129309e+002,-2.121511510792387e+000,
        1.135665054273839e+000},{-9.286710899115280e+003,1.351114286113316e+002,
        -2.050312467770768e+000,1.135134219762123e+000},{-8.516925185585011e+003,
        1.272389163739304e+002,-1.981741426500199e+000,1.134609441780069e+000},
        {-7.814215167392292e+003,1.198576991982375e+002,-1.915692106619513e+000,
        1.134090658121731e+000},{-7.172456309463685e+003,1.129351140608649e+002,
        -1.852062910163217e+000,1.133577807145568e+000},{-6.586111850428207e+003,
        1.064408049999422e+002,-1.790756700400648e+000,1.133070827768850e+000},
        {-6.050171835345558e+003,1.003465460629108e+002,-1.731680587420741e+000,
        1.132569659462107e+000},{-5.560092621539761e+003,9.462607475690936e+001,
        -1.674745725978995e+000,1.132074242243597e+000},{-5.111765690517253e+003,
        8.925496645655235e+001,-1.619867130786789e+000,1.131584516673807e+000},
        {-4.701461004393561e+003,8.421047987386929e+001,-1.566963488558861e+000,
        1.131100423849972e+000},{-4.325801937265625e+003,7.947145063101340e+001,
        -1.515956992240450e+000,1.130621905400621e+000},{-3.981719970706350e+003,
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        1.062403035055771e+000},{-1.100635026079546e+000,-3.011556050874361e-001,
        -1.237127306959247e-001,1.061984783130254e+000},{-1.168634591893341e+000,
        -3.117499794663595e-001,-1.258134320829727e-001,1.061558004172562e+000},
        {-1.242871047312425e+000,-3.230176068616857e-001,-1.279969998819422e-001,
        1.061122363622202e+000},{-1.324102816333368e+000,-3.350198128649087e-001,
        -1.302689135412735e-001,1.060677505215274e+000},{-1.413204046652451e+000,
        -3.478252360881645e-001,-1.326351679601656e-001,1.060223048975250e+000},
        {-1.511185630627330e+000,-3.615109178443726e-001,-1.351023368667481e-001,
        1.059758588960120e+000},{-1.619221197038109e+000,-3.761635786122374e-001,
        -1.376776459309125e-001,1.059283690729083e+000},{-1.738677889702752e+000,
        -3.918811400429350e-001,-1.403690573333936e-001,1.058797888485215e+000},
        {-1.871154359990751e+000,-4.087745223058986e-001,-1.431853680336985e-001,
        1.058300681842389e+000},{-2.018526589606020e+000,-4.269697926301481e-001,
        -1.461363243040554e-001,1.057791532154715e+000},{-2.185501792184186e+000,
        -4.465841288025065e-001,-1.492328186957302e-001,1.057269858334624e+000},
        {-2.364687153396257e+000,-4.679154024903533e-001,-1.524865743220330e-001,
        1.056735032070606e+000},{-2.576475123351074e+000,-4.908877748574237e-001,
        -1.559120016473587e-001,1.056186372337097e+000},{-2.809603261630487e+000,
        -5.159839044005667e-001,-1.595231052389059e-001,1.055623138920609e+000},
        {-3.075454975098822e+000,-5.433260214541975e-001,-1.633376814220988e-001,
        1.055044525513794e+000},{-3.378476048700296e+000,-5.732358362636583e-001,
        -1.673748772676717e-001,1.054449650639562e+000},{-3.725624075390214e+000,
        -6.060595365408650e-001,-1.716566425727572e-001,1.053837547969356e+000},
        {-4.125513088548122e+000,-6.422048242798819e-001,-1.762080296688844e-001,
        1.053207154504926e+000},{-4.588900079051337e+000,-6.821546123391310e-001,
        -1.810577742248455e-001,1.052557296675667e+000},{-5.129342151488261e+000,
        -7.264844420275155e-001,-1.862390135536310e-001,1.051886673785578e+000},
        {-5.764097830251668e+000,-7.758847747289787e-001,-1.917901826032635e-001,
        1.051193838170567e+000},{-6.515378231730130e+000,-8.311897985680916e-001,
        -1.977561416081993e-001,1.050477171237241e+000},{-7.412109909279641e+000,
        -8.934149834663464e-001,-2.041896093864123e-001,1.049734854297595e+000},
        {-8.492455381030945e+000,-9.638065423607585e-001,-2.111530046471992e-001,
        1.048964832761054e+000},{-9.807474389689094e+000,-1.043907256650206e+000,
        -2.187208392607184e-001,1.048164771754150e+000},{-1.142992555561826e+001,
        -1.135606773901190e+000,-2.269829647144973e-001,1.047332000543470e+000},
        {-1.344511926099734e+001,-1.241495308018550e+000,-2.360481455742939e-001,
        1.046463442140266e+000},{-1.600738269476274e+001,-1.364375395477736e+000,
        -2.460518881297009e-001,1.045555523007033e+000},{-1.929939535516280e+001,
        -1.508513275807175e+000,-2.571603987700460e-001,1.044604055466647e+000},
        {-2.362120150582920e+001,-1.678967132778218e+000,-2.695862540141585e-001,
        1.043604082766197e+000},{-2.942152881801653e+001,-1.882583607807427e+000,
        -2.836015162163547e-001,1.042549669910840e+000},{-3.741453654687421e+001,
        -2.128389007332268e+000,-2.995629186888021e-001,1.041433617232253e+000},
        {-4.878270682458398e+001,-2.428336462205647e+000,-3.179486577792697e-001,
        1.040247057754742e+000},{-6.558832836460495e+001,-2.797988793419757e+000,
        -3.394177234686278e-001,1.038978876337398e+000},{-9.164855359795394e+001,
        -3.256574496899152e+000,-3.649096511422550e-001,1.037614844862927e+000},
        {-1.346442592691005e+002,-3.822745465072996e+000,-3.958270232324012e-001,
        1.036136285584020e+000},{-2.039488892785857e+002,-4.585663115601926e+000,
        -4.341576010582943e-001,1.034517909421716e+000},{-3.213729265046176e+002,
        -5.715603682655638e+000,-4.830053729894114e-001,1.032724118072463e+000},
        {-5.380530697149483e+002,-7.590740438263201e+000,-5.472440337555892e-001,
        1.030702209952531e+000},{-9.773668143802523e+002,-8.397564013673986e+000,
        -6.149721615017588e-001,1.028987687176493e+000},{-1.971206182132680e+003,
        -7.954972432593549e+000,-7.107673680064054e-001,1.027043503002403e+000},
        {-4.259063749453282e+003,-7.470160381920227e+000,-8.552169229520203e-001,
        1.024677777723123e+000},{-9.468420868233850e+003,-1.441169226818975e+001,
        -1.061676619743433e+000,1.021911421684383e+000},{-2.124426475615268e+004,
        -2.969103328338514e+001,-1.321932106107769e+000,1.019310988957590e+000},
        {-5.142304350768700e+004,-2.757198727294517e+001,-1.633808439690381e+000,
        1.017155605087379e+000},{-1.261916077251016e+005,1.340795831729274e+001,
        -2.041513938530926e+000,1.015172127346691e+000},{-2.907555625955585e+005,
        3.100216772602235e+000,-2.587089312710111e+000,1.013030579652139e+000},
        {-6.443400705406987e+005,-4.736727283746432e+002,-3.393782437455662e+000,
        1.010424690909639e+000},{-1.284212584824039e+006,-8.719164629810688e+002,
        -4.081415290704422e+000,1.009013628657760e+000},{-2.953254945900618e+006,
        -3.499079388487411e+002,-4.609510455745138e+000,1.008360191314845e+000},
        {-8.708278203444760e+006,1.160570409967432e+003,-5.732506388098228e+000,
        1.007240267626251e+000},{-2.925999835917269e+007,6.373124182370374e+003,
        -7.673217433665648e+000,1.006032670356375e+000},{-9.691364693490808e+007,
        5.724533606825865e+003,-9.856016988972671e+000,1.004465302443802e+000},
        {-2.344230326747042e+008,-7.237460849943119e+003,-1.228103670994250e+001,
        1.003403193772207e+000},{-1.674594981779917e+012,7.945262725742146e+007,
        -9.424323791757101e+002,1.002718092569686e+000}};

    record crit
      extends Modelica.Icons.Record;
      constant SI.Temperature TCRIT=374.18;
      constant SI.Pressure PCRIT=4056290.0;
      constant SI.Density DCRIT=508.0;

    end crit;

    record data
      constant SI.SpecificHeatCapacity R_s=81.4888564372;
      // 8.314471/0.102032
      constant SI.MolarMass MM=0.102032;
      extends crit;
      constant SI.SpecificEnthalpy HCRIT=389653;
      constant SI.SpecificEntropy SCRIT=1562.135;
      extends fcrit;
      extends triple;

    end data;

    record fcrit
      extends Modelica.Icons.Record;
      constant SI.Temperature FTCRIT=374.209;
      constant SI.Pressure FPCRIT=4059280.0;
      constant SI.Density FDCRIT=511.9;

    end fcrit;

    record Ideal
      extends Common.EOSIdealCoeff(nc=5, a={-1.019535e+0,9.047135e+0,-1.629789e+0,
            -9.723916e+0,-3.927170e+0});

    end Ideal;

    record ReferenceStates
      extends Modelica.Icons.Record;
      constant SI.SpecificEnthalpy h0=1.0;
      constant SI.SpecificEntropy s0=1.0;

    end ReferenceStates;

    record Residual
      extends Common.EOSResidualCoeff(
        nc=21,
        ns1=8,
        c={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,2.0,2.0,2.0,2.0,2.0,2.0,
            3.0,3.0,3.0,4.0},
        d={2.0,1.0,3.0,6.0,6.0,1.0,1.0,2.0,5.0,2.0,2.0,4.0,1.0,4.0,1.0,2.0,4.0,
            1.0,5.0,3.0,10.0},
        t={-0.5,0.0,0.0,0.0,1.5,1.5,2.0,2.0,1.0,3.0,5.0,1.0,5.0,5.0,6.0,10.0,
            10.0,10.0,18.0,22.0,50.0},
        n={0.5586817000e-01,0.4982230000e+00,0.2458698000e-01,0.8570145000e-03,
            0.4788584000e-03,-0.1800808000e+01,0.2671641000e+00,-0.4781652000e-01,
            0.1423987000e-01,0.3324062000e+00,-0.7485907000e-02,
            0.1017263000e-03,-0.5184567000e+00,-0.8692288000e-01,
            0.2057144000e+00,-0.5000457000e-02,0.4603262000e-03,-0.3497836000e-02,
            0.6995038000e-02,-0.1452184000e-01,-0.1285458000e-03});

    end Residual;

    record triple
      extends Modelica.Icons.Record;
      constant SI.Temperature TTRIPLE=169.85;
      constant SI.Pressure PTRIPLE=389.563789;
      constant SI.Density DLTRIPLE=1591.107453;
      constant SI.Density DVTRIPLE=0.028172;

    end triple;

    record CoeffsThermalConductivity
      extends Modelica.Icons.Record;
      constant Real a_0=-1.05248e-2 "Empirical parameter, [W/(m K)]";
      constant Real a_1=8.00982e-5 "Empirical parameter, [W/(m K^2)]";
      constant Real b[4]={1.836526,5.126143,-1.436883,0.626144}
        "Empirical parameter, [-]";
      constant Real lambda_reducing=2.055e-3 "Reducing factor, [W/(m K)]";
      constant Real q_d=1.89202e9
        "Modified effective cutoff wave number, [1/m]";
      constant Real xi_0=1.94e-10 "Critical Amplitude, [m]";
      constant Real GAMMA=0.0496 "Amplitude, [-]";
      constant Real T_ref=561.411 "Arbitrary reference temperature, [K]";
      constant Real p_crit=4059.28 "Critical pressure, [kPa]";
      constant Real rho_crit=5.049886 "Critical density, [mol/L]";
      constant Real nu=0.63 "Universal exponent, [-]";
      constant Real gamma=1.239 "Universal exponent, [-]";
      constant Real R_0=1.03 "Universal amplitude, [-]";

    end CoeffsThermalConductivity;

    record CoeffsSurfaceTension
      extends Modelica.Icons.Record;
      constant Integer nterm=1;
      constant Real sigmak[nterm]={0.06016} "Empirical parameter";
      constant Real sigexp[nterm]={1.26} "Empirical parameter";

    end CoeffsSurfaceTension;
  end R134aData;
  annotation (Documentation(info="<html>
<p>
Calculation of fluid properties for Tetrafluoroethane (R134a) in the fluid region of 0.0039 bar (Triple pressure) to 700 bar and 169.85 Kelvin (Triple temperature) to 455 Kelvin.
</p>
<h4>Restriction</h4>
<p>
The functions provided by this package shall be used inside of the restricted limits according to the referenced literature.
</p>
<ul>
 <li>
      <strong> 0.0039 bar &le; p &le; 700 bar </strong>
 </li>
 <li>
      <strong> 169.85 Kelvin &le; T &le; 455 Kelvin  </strong>
 </li>
 <li>
      <strong> explicit for pressure and specific enthalpy </strong>
 </li>
</ul>

<p><strong>References</strong></p>
<dl><dt>Baehr, H.D. and Tillner-Roth, R.: </dt>
<dd><strong>Thermodynamic Properties of Environmentally Acceptable Refrigerants -
Equations of State and Tables for Ammonia, R22, R134a, R152a, and R123</strong>. Springer-Verlag, Berlin (Germany), 1994.</dd>
</dl>
<dl><dt>Klein, McLinden and Laesecke: </dt>
<dd><strong>An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures</strong>.
Int. J. Refrig., Vol. 20, No.3, pp. 208-217, 1997.</dd>
</dl>
<dl><dt>McLinden, Klein. and Perkins: </dt>
<dd><strong>An extended corresponding states model for the thermal conductivity
of refrigerants and refrigerant mixtures</strong>.
Int. J. Refrig., 23 (2000) 43-63.</dd>
</dl>
<dl><dt>Okada and Higashi: </dt>
<dd><strong>Surface tension correlation of HFC-134a and HCFC-123</strong>.
Proceedings of the Joint Meeting of IIR Commissions B1, B2, E1, and E2, Padua, Italy, pp. 541-548, 1994.</dd>
</dl>

<h4>Verification</h4>
<p>
The verification report for the development of this library is provided
<a href=\"modelica://Modelica/Resources/Documentation/Media/MoMoLib_VerificationResults_XRG.pdf\">here</a>.
</p>

<h4>Acknowledgment</h4>
<p>
This library was developed by XRG Simulation GmbH as part of the <a href=\"http://www.cleansky.eu/\">Clean Sky</a> JTI project (Project title: MoMoLib-Modelica Model Library Development for Media, Magnetic Systems and Wavelets; Project number: 296369; Theme: JTI-CS-2011-1-SGO-02-026: Modelica Model Library Development Part I). The partial financial support for the development of this library by the European Union is highly appreciated.
</p>

<p>
Some parts of this library refer to the ThermoFluid library developed at Lund University (<a href=\"http://thermofluid.sourceforge.net/\">http://thermofluid.sourceforge.net</a>).
</p>

<p>
Copyright &copy; 2013-2020, Modelica Association and contributors
</p>
</html>"));
end R134a;