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25 //
26 // G4Pow
27 //
28 // Class description:
29 //
30 // Utility singleton class for the fast computation of log and pow
31 // functions. Integer argument should be in the interval 0-512, no
32 // check is performed inside these methods for performance reasons.
33 // For factorial integer argument should be in the interval 0-170
34 // Computations with double arguments are fast for the interval
35 // 0.002-511.5 for all functions except exponent, which is computed
36 // for the interval 0-84.4, standard library is used in the opposite case
37
38 // Author: Vladimir Ivanchenko, 23.05.2009
39 // --------------------------------------------------------------------
40 #ifndef G4Pow_hh
41 #define G4Pow_hh 1
42
43 #include "G4DataVector.hh"
44 #include "G4Exp.hh"
45 #include "G4Log.hh"
46 #include "globals.hh"
47
48 class G4Pow
49 {
50 public:
51 static G4Pow* GetInstance();
52 ~G4Pow() = default;
53
54 // Fast computation of Z^1/3
55 //
56 inline G4double Z13(G4int Z) const;
57 G4double A13(G4double A) const;
58
59 // Fast computation of Z^2/3
60 //
61 inline G4double Z23(G4int Z) const;
62 inline G4double A23(G4double A) const;
63
64 // Fast computation of log(Z)
65 //
66 inline G4double logZ(G4int Z) const;
67 inline G4double logA(G4double A) const;
68 inline G4double logX(G4double x) const;
69
70 // Fast computation of log10(Z)
71 //
72 inline G4double log10Z(G4int Z) const;
73 inline G4double log10A(G4double A) const;
74
75 // Fast computation of exp(X)
76 //
77 inline G4double expA(G4double A) const;
78
79 // Fast computation of pow(Z,X)
80 //
81 inline G4double powZ(G4int Z, G4double y) const;
82 inline G4double powA(G4double A, G4double y) const;
83 G4double powN(G4double x, G4int n) const;
84
85 // Fast factorial
86 //
87 inline G4double factorial(G4int Z) const;
88 inline G4double logfactorial(G4int Z) const;
89
90 private:
91 G4Pow();
92
93 G4double A13Low(const G4double, const G4bool) const;
94 G4double A13High(const G4double, const G4bool) const;
95
96 inline G4double logBase(G4double x) const;
97
98 static G4Pow* fpInstance;
99
100 const G4double onethird = 1.0 / 3.0;
101 const G4int max2 = 5;
102
103 G4double maxA;
104 G4double maxLowA;
105 G4double maxA2;
106 G4double maxAexp;
107
108 G4DataVector ener;
109 G4DataVector logen;
110 G4DataVector pz13;
111 G4DataVector lowa13;
112 G4DataVector lz;
113 G4DataVector lz2;
114 G4DataVector fexp;
115 G4DataVector fact;
116 G4DataVector logfact;
117 };
118
119 // -----------------------------
120 // Inline methods implementation
121 // -----------------------------
122
123 inline G4double G4Pow::Z13(G4int Z) const { return pz13[Z]; }
124
125 inline G4double G4Pow::Z23(G4int Z) const
126 {
127 G4double x = Z13(Z);
128 return x * x;
129 }
130
131 inline G4double G4Pow::A23(G4double A) const
132 {
133 G4double x = A13(A);
134 return x * x;
135 }
136
137 inline G4double G4Pow::logZ(G4int Z) const { return lz[Z]; }
138
139 inline G4double G4Pow::logBase(G4double a) const
140 {
141 G4double res;
142 if(a <= maxA2)
143 {
144 G4int i = G4int(max2 * (a - 1) + 0.5);
145 if(i > max2)
146 {
147 i = max2;
148 }
149 G4double x = a / (G4double(i) / max2 + 1) - 1;
150 res = lz2[i] + x * (1.0 - (0.5 - onethird * x) * x);
151 }
152 else if(a <= maxA)
153 {
154 G4int i = G4int(a + 0.5);
155 G4double x = a / G4double(i) - 1;
156 res = lz[i] + x * (1.0 - (0.5 - onethird * x) * x);
157 }
158 else
159 {
160 res = G4Log(a);
161 }
162 return res;
163 }
164
165 inline G4double G4Pow::logA(G4double A) const
166 {
167 return (1.0 <= A ? logBase(A) : -logBase(1. / A));
168 }
169
170 inline G4double G4Pow::logX(G4double x) const
171 {
172 G4double res = 0.0;
173 G4double a = (1.0 <= x) ? x : 1.0 / x;
174
175 if(a <= maxA)
176 {
177 res = logBase(a);
178 }
179 else if(a <= ener[2])
180 {
181 res = logen[1] + logBase(a / ener[1]);
182 }
183 else if(a <= ener[3])
184 {
185 res = logen[2] + logBase(a / ener[2]);
186 }
187 else
188 {
189 res = G4Log(a);
190 }
191
192 if(1.0 > x)
193 {
194 res = -res;
195 }
196 return res;
197 }
198
199 inline G4double G4Pow::log10Z(G4int Z) const { return lz[Z] / lz[10]; }
200
201 inline G4double G4Pow::log10A(G4double A) const { return logX(A) / lz[10]; }
202
203 inline G4double G4Pow::expA(G4double A) const
204 {
205 G4double res;
206 G4double a = (0.0 <= A) ? A : -A;
207
208 if(a <= maxAexp)
209 {
210 G4int i = G4int(2 * a + 0.5);
211 G4double x = a - i * 0.5;
212 res = fexp[i] * (1.0 + x * (1.0 + 0.5 * (1.0 + onethird * x) * x));
213 }
214 else
215 {
216 res = G4Exp(a);
217 }
218 if(0.0 > A)
219 {
220 res = 1.0 / res;
221 }
222 return res;
223 }
224
225 inline G4double G4Pow::powZ(G4int Z, G4double y) const
226 {
227 return expA(y * lz[Z]);
228 }
229
230 inline G4double G4Pow::powA(G4double A, G4double y) const
231 {
232 return (0.0 == A ? 0.0 : expA(y * logX(A)));
233 }
234
235 inline G4double G4Pow::factorial(G4int Z) const { return fact[Z]; }
236
237 inline G4double G4Pow::logfactorial(G4int Z) const { return logfact[Z]; }
238
239 #endif
240