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diff --git a/Utilib/src/region4.c b/Utilib/src/region4.c
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+/*
+freesteam - IAPWS-IF97 steam tables library
+Copyright (C) 2004-2009 John Pye
+
+This program is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License
+as published by the Free Software Foundation; either version 2
+of the License, or (at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+*/
+
+#define FREESTEAM_BUILDING_LIB
+#include "region.h"
+
+#include <math.h>
+#include <stdlib.h>
+
+const double REGION4_N[11] = { 0, 0.11670521452767E+04, -0.72421316703206E+06
+ , -0.17073846940092E+02, 0.12020824702470E+05, -0.32325550322333E+07
+ , 0.14915108613530E+02, -0.48232657361591E+04, 0.40511340542057E+06
+ , -0.23855557567849E+00, 0.65017534844798E+03
+};
+
+#define REGION4_PSTAR 1e6 /* Pa */
+#define REGION4_TSTAR 1 /* K */
+
+/*------------------------------------------------------------------------------
+ REGION 4 SATURATION CURVE psat(T)
+*/
+
+double freesteam_region4_psat_T(double T){
+
+ double ups = T/REGION4_TSTAR + REGION4_N[9] / (T/REGION4_TSTAR - REGION4_N[10]);
+ double A = SQ(ups) + REGION4_N[1] * ups + REGION4_N[2];
+ double B = REGION4_N[3] * SQ(ups) + REGION4_N[4] * ups + REGION4_N[5];
+ double C = REGION4_N[6] * SQ(ups) + REGION4_N[7] * ups + REGION4_N[8];
+
+ double expr = 2. * C / (- B + sqrt(SQ(B) - 4. * A * C));
+ double psat = SQ(SQ(expr)) * REGION4_PSTAR;
+
+ /* fprintf(stderr,"freesteam_region4_psat_T = %f MPa\n", psat/1e6);*/
+ return psat;
+}
+
+/*------------------------------------------------------------------------------
+ REGION 4 SATURATION CURVE Tsat(p) (BACKWARDS EQUATION)
+*/
+
+double freesteam_region4_Tsat_p(double p){
+ double beta = pow(p/REGION4_PSTAR, 0.25);
+ double E = SQ(beta) + REGION4_N[3] * beta + REGION4_N[6];
+ double F = REGION4_N[1] * SQ(beta) + REGION4_N[4] * beta + REGION4_N[7];
+ double G = REGION4_N[2] * SQ(beta) + REGION4_N[5] * beta + REGION4_N[8];
+ double D = 2. * G / (-F - sqrt(SQ(F) - 4. * E * G));
+
+ double theta = 0.5 * (REGION4_N[10] + D - sqrt(SQ(REGION4_N[10] + D) - 4.0 * (REGION4_N[9] + REGION4_N[10] * D)));
+
+ /* FIXME iterative improve this estimate? is it necessary? */
+
+ return theta /* * REGION4_TSTAR = 1 {K} */;
+}
+
+/*------------------------------------------------------------------------------
+ REGION 4 DENSITIES rhof(T), rhog(T) (SUPPLEMENTARY EQUATIONS)
+*/
+
+
+
+/**
+ Coefficients for getSatDensWater_T
+*/
+const double REGION4_B[7]
+ = { 0, 1.99274064, 1.09965342, -0.510839303, -1.75493479, -45.5170352, -6.74694450E+05 };
+
+/**
+ Coefficients for getSatDensSteam_T
+*/
+const double REGION4_C[7]
+ = { 0, -2.03150240, -2.68302940, -5.38626492, -17.2991605, -44.7586581, -63.9201063 };
+
+
+double freesteam_region4_rhof_T(double T){
+ double tau = 1 - T / IAPWS97_TCRIT;
+
+ double tau_1_3 = pow(tau,1./3);
+
+ double tau_2_3 = SQ(tau_1_3);
+ double tau_5_3 = tau * tau_2_3;
+ double tau_16_3 = SQ(tau_5_3) * tau_5_3 * tau_1_3;
+ double tau_43_3 = SQ(tau_16_3) * SQ(tau_5_3) * tau_1_3;
+ double tau_110_3 = SQ(tau_43_3) * tau_16_3 * tau_5_3 * tau;
+
+ double delta = 1
+ + REGION4_B[1]*tau_1_3
+ + REGION4_B[2]*tau_2_3
+ + REGION4_B[3]*tau_5_3
+ + REGION4_B[4]*tau_16_3
+ + REGION4_B[5]*tau_43_3
+ + REGION4_B[6]*tau_110_3;
+
+ return delta * IAPWS97_RHOCRIT;
+
+ /* FIXME iteratively improve vf estimate */
+}
+
+double freesteam_region4_rhog_T(double T){
+ double tau = 1. - T / IAPWS97_TCRIT;
+
+ double tau_1_6 = pow(tau,1.0/6);
+
+ double tau_2_6 = SQ(tau_1_6);
+ double tau_4_6 = SQ(tau_2_6);
+ double tau_8_6 = SQ(tau_4_6);
+ double tau_16_6 = SQ(tau_8_6);
+ double tau_18_6 = tau_16_6 * tau_2_6;
+ double tau_37_6 = SQ(tau_18_6) * tau_1_6;
+ double tau_71_6 = tau_37_6 * tau_18_6 * tau_16_6;
+
+ double ln_delta =
+ REGION4_C[1]*tau_2_6
+ + REGION4_C[2]*tau_4_6
+ + REGION4_C[3]*tau_8_6
+ + REGION4_C[4]*tau_18_6
+ + REGION4_C[5]*tau_37_6
+ + REGION4_C[6]*tau_71_6;
+
+ return exp(ln_delta) * IAPWS97_RHOCRIT;
+
+ /* FIXME iteratively improve vg estimate */
+}
+
+
+/*------------------------------------------------------------------------------
+ INTERPOLATIONS FOR PROPERTIES WITHIN REGION 4
+*/
+
+double freesteam_region4_v_Tx(double T, double x){
+ double vf, vg;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ vf = freesteam_region1_v_pT(psat,T);
+ vg = freesteam_region2_v_pT(psat,T);
+ }else{
+ vf = 1./ freesteam_region4_rhof_T(T);
+ vg = 1./ freesteam_region4_rhog_T(T);
+ }
+ return vf + x*(vg - vf);
+}
+
+double freesteam_region4_u_Tx(double T, double x){
+ double uf, ug;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ uf = freesteam_region1_u_pT(psat,T);
+ ug = freesteam_region2_u_pT(psat,T);
+ }else{
+ double rhof, rhog;
+ rhof = freesteam_region4_rhof_T(T);
+ rhog = freesteam_region4_rhog_T(T);
+ uf = freesteam_region3_u_rhoT(rhof,T);
+ ug = freesteam_region3_u_rhoT(rhog,T);
+ }
+ return uf + x*(ug - uf);
+}
+
+double freesteam_region4_h_Tx(double T, double x){
+ double hf, hg;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ hf = freesteam_region1_h_pT(psat,T);
+ hg = freesteam_region2_h_pT(psat,T);
+ }else{
+ double rhof, rhog;
+ rhof = freesteam_region4_rhof_T(T);
+ rhog = freesteam_region4_rhog_T(T);
+ hf = freesteam_region3_h_rhoT(rhof,T);
+ hg = freesteam_region3_h_rhoT(rhog,T);
+ }
+ return hf + x*(hg - hf);
+}
+
+double freesteam_region4_s_Tx(double T, double x){
+ double sf, sg;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ sf = freesteam_region1_s_pT(psat,T);
+ sg = freesteam_region2_s_pT(psat,T);
+ }else{
+ double rhof, rhog;
+ rhof = freesteam_region4_rhof_T(T);
+ rhog = freesteam_region4_rhog_T(T);
+ sf = freesteam_region3_s_rhoT(rhof,T);
+ sg = freesteam_region3_s_rhoT(rhog,T);
+ }
+ return sf + x*(sg - sf);
+}
+
+double freesteam_region4_cp_Tx(double T, double x){
+ double cpf, cpg;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ cpf = freesteam_region1_cp_pT(psat,T);
+ cpg = freesteam_region2_cp_pT(psat,T);
+ }else{
+ double rhof, rhog;
+ rhof = freesteam_region4_rhof_T(T);
+ rhog = freesteam_region4_rhog_T(T);
+ cpf = freesteam_region3_cp_rhoT(rhof,T);
+ cpg = freesteam_region3_cp_rhoT(rhog,T);
+ }
+ return cpf + x*(cpg - cpf);
+}
+
+double freesteam_region4_cv_Tx(double T, double x){
+ double cvf, cvg;
+ if(T < REGION1_TMAX){
+ double psat = freesteam_region4_psat_T(T);
+ cvf = freesteam_region1_cv_pT(psat,T);
+ cvg = freesteam_region2_cv_pT(psat,T);
+ }else{
+ double rhof, rhog;
+ rhof = freesteam_region4_rhof_T(T);
+ rhog = freesteam_region4_rhog_T(T);
+ cvf = freesteam_region3_cv_rhoT(rhof,T);
+ cvg = freesteam_region3_cv_rhoT(rhog,T);
+ }
+ return cvf + x*(cvg - cvf);
+}
+
+/*------------------------------------------------------------------------------
+*/
+
+double freesteam_region4_dpsatdT_T(double T){
+ /* calculated this derivative using implicit differentiation of the
+ quadratic expression, then derivatives of beta and script-theta */
+ double beta = pow(freesteam_region4_psat_T(T)/REGION4_PSTAR, 0.25);
+#define N REGION4_N
+ double theta = T/REGION4_TSTAR + N[9] / (T/REGION4_TSTAR - N[10]);
+ double XBETA = (2.*beta + N[3])*SQ(theta) + (2.*beta*N[1] + N[4])*theta + 2.*N[2]*beta + N[5];
+ double XTHETA = (2.*theta + N[1])*SQ(beta) + (2.*N[3]*theta + N[4])*beta + 2.*N[6]*theta + N[7];
+
+ double dthetadT = (1 - N[9] / (T/REGION4_TSTAR - N[10]))/REGION4_TSTAR;
+ double dbetadtheta = -XTHETA/XBETA;
+ double dpdbeta = 4*SQ(beta)*beta*REGION4_PSTAR;
+#undef N
+
+ return dpdbeta * dbetadtheta * dthetadT;
+}
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