1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131


//!  Region 3 :the dimensionless Helmholtz free energy 
//!     Speciphic Helmholtz free energy.
//!        tau :dimensionless temperature K
//1        delta: dimensionless density kg/m3

use crate::algo::fast_ipower::sac_pow;
use crate::common::constant::*;

//  Initialize coefphicients and exponents for region 3(Table 30, page 30)
pub const n1:f64 = 0.10658070028513e1;
	
pub const IJn:[IJnData;39] = [
	IJnData{I:0, J:0,n: -0.15732845290239E+02},
	IJnData{I:0, J:1, n: 0.20944396974307E+02},
	IJnData{I:0, J:2, n: -0.76867707878716E+01},
	IJnData{I:0, J:7, n: 0.26185947787954E+01},
	IJnData{I:0, J:10, n: -0.28080781148620E+01},

	IJnData{I:0, J:12, n: 0.12053369696517E+01},
	IJnData{I:0, J:23, n: -0.84566812812502E-02},
	IJnData{I:1, J:2, n: -0.12654315477714E+01},
	IJnData{I:1, J:6, n: -0.11524407806681E+01},
	IJnData{I:1, J:15, n: 0.88521043984318E+00},

	IJnData{I:1, J:17, n: -0.64207765181607E+00},
	IJnData{I:2, J:0, n: 0.38493460186671E+00},
	IJnData{I:2, J:2, n: -0.85214708824206E+00},
	IJnData{I:2, J:6, n: 0.48972281541877E+01},
	IJnData{I:2, J:7, n: -0.30502617256965E+01},

	IJnData{I:2, J:22, n: 0.39420536879154E-01},
	IJnData{I:2, J:26, n: 0.12558408424308E+00},
	IJnData{I:3, J:0, n: -0.27999329698710E+00},
	IJnData{I:3, J:2, n: 0.13899799569460E+01},
	IJnData{I:3, J:4, n: -0.20189915023570E+01},

	IJnData{I:3, J:16, n: -0.82147637173963E-02},
	IJnData{I:3, J:26, n: -0.47596035734923E+00},
	IJnData{I:4, J:0, n: 0.43984074473500E-01},
	IJnData{I:4, J:2, n: -0.44476435428739E+00},
	IJnData{I:4, J:4, n: 0.90572070719733E+00},

	IJnData{I:4, J:26, n: 0.70522450087967E+00},
	IJnData{I:5, J:1, n: 0.10770512626332E+00},
	IJnData{I:5, J:3, n: -0.32913623258954E+00},
	IJnData{I:5, J:26, n: -0.50871062041158E+00},
	IJnData{I:6, J:0, n: -0.22175400873096E-01},

	IJnData{I:6, J:2, n: 0.94260751665092E-01},
	IJnData{I:6, J:26, n: 0.16436278447961E+00},
	IJnData{I:7, J:2, n: -0.13503372241348E-01},
	IJnData{I:8, J:26, n: -0.14834345352472E-01},
	IJnData{I:9, J:2, n: 0.57922953628084E-03},

	IJnData{I:9, J:26, n: 0.32308904703711E-02},
	IJnData{I:10, J:0, n: 0.80964802996215E-04},
	IJnData{I:10, J:1, n: -0.16557679795037E-03},
	IJnData{I:11, J:26, n: -0.44923899061815E-04}];

/// Fundamental equation for region 3
pub fn phi_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64  = n1 * delta.ln();
	for k in 0..39{
		result += IJn[k].n * sac_pow(delta, IJn[k].I) * sac_pow(tau, IJn[k].J);
    	//result += IJn[k].n * delta.powi(IJn[k].I) * tau.powi(IJn[k].J);
	}
	return result;
}

/// First derivative in delta of fundamental equation for region 3
pub fn phi_delta_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64= n1 / delta;
	for k in 0..39
	{
	   result += IJn[k].n * IJn[k].I as f64* sac_pow(delta, IJn[k].I - 1) * sac_pow(tau, IJn[k].J);
	   //result += IJn[k].n * IJn[k].I as f64* delta.powi(IJn[k].I - 1) * tau.powi(IJn[k].J);
	}
	return  result;
}

/// Second derivative in delta of fundamental equation for region 3
pub fn phi_deltadelta_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64 = -n1 / delta / delta;
	for k in 0..39
    {
		 result += IJn[k].n *(IJn[k].I * (IJn[k].I - 1)) as f64 * sac_pow(delta, IJn[k].I - 2) * sac_pow(tau, IJn[k].J);
		// result += IJn[k].n *(IJn[k].I * (IJn[k].I - 1)) as f64 * delta.powi(IJn[k].I - 2) * tau.powi(IJn[k].J);
	 
	}
	return result;
}

/// First derivative in tau of fundamental equation for region 3
pub fn phi_tau_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64 = 0.0;
	for k in 0..39
    {	
		result += IJn[k].n * sac_pow(delta, IJn[k].I) * IJn[k].J as f64 * sac_pow(tau, IJn[k].J - 1);
		//result += IJn[k].n * delta.powi(IJn[k].I) * IJn[k].J as f64 * tau.powi(IJn[k].J - 1);

    }
	return result;
}

/// Second derivative in tau of fundamental equation for region 3
pub fn phi_tautau_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64 = 0.0;
	for k in 0..39
	{
		result += IJn[k].n * sac_pow(delta, IJn[k].I) * (IJn[k].J * (IJn[k].J - 1)) as f64 * sac_pow(tau, IJn[k].J - 2);
		//result += IJn[k].n * delta.powi(IJn[k].I) * (IJn[k].J * (IJn[k].J - 1)) as f64 * tau.powi(IJn[k].J - 2);
	}
	return result;
}

/// Second derivative in delta and tau of fundamental equation for region 3
pub fn phi_deltatau_reg3(tau:f64,delta:f64)->f64
{
	let mut result:f64 = 0.0;
	for k in 0..39{
		result += IJn[k].n * IJn[k].I as f64 * sac_pow(delta, IJn[k].I - 1) * IJn[k].J as f64* sac_pow(tau, IJn[k].J - 1);
		//result += IJn[k].n * IJn[k].I as f64 *delta.powi(IJn[k].I - 1) * IJn[k].J as f64* tau.powi(IJn[k].J - 1);
	}
	return result;
}