[819] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * * |
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| 21 | // * Parts of this code which have been developed by QinetiQ Ltd * |
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| 22 | // * under contract to the European Space Agency (ESA) are the * |
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| 23 | // * intellectual property of ESA. Rights to use, copy, modify and * |
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| 24 | // * redistribute this software for general public use are granted * |
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| 25 | // * in compliance with any licensing, distribution and development * |
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| 26 | // * policy adopted by the Geant4 Collaboration. This code has been * |
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| 27 | // * written by QinetiQ Ltd for the European Space Agency, under ESA * |
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| 28 | // * contract 17191/03/NL/LvH (Aurora Programme). * |
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| 29 | // * * |
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| 30 | // * By using, copying, modifying or distributing the software (or * |
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| 31 | // * any work based on the software) you agree to acknowledge its * |
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| 32 | // * use in resulting scientific publications, and indicate your * |
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| 33 | // * acceptance of all terms of the Geant4 Software license. * |
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| 34 | // ******************************************************************** |
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| 35 | // |
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| 36 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 37 | // |
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| 38 | // MODULE: G4Bessel.cc |
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| 39 | // |
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| 40 | // Version: B.1 |
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| 41 | // Date: 15/04/04 |
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| 42 | // Author: P R Truscott |
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| 43 | // Organisation: QinetiQ Ltd, UK |
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| 44 | // Customer: ESA/ESTEC, NOORDWIJK |
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| 45 | // Contract: 17191/03/NL/LvH |
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| 46 | // |
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| 47 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 48 | // |
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| 49 | // CHANGE HISTORY |
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| 50 | // -------------- |
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| 51 | // |
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| 52 | // 18 Noevmber 2003, P R Truscott, QinetiQ Ltd, UK |
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| 53 | // Created. |
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| 54 | // |
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| 55 | // 15 March 2004, P R Truscott, QinetiQ Ltd, UK |
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| 56 | // Beta release |
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| 57 | // |
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| 58 | // %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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| 59 | //////////////////////////////////////////////////////////////////////////////// |
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| 60 | // |
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| 61 | #include "G4Bessel.hh" |
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| 62 | //////////////////////////////////////////////////////////////////////////////// |
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| 63 | // |
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| 64 | G4Bessel::G4Bessel () |
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| 65 | {;} |
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| 66 | //////////////////////////////////////////////////////////////////////////////// |
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| 67 | // |
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| 68 | G4Bessel::~G4Bessel () |
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| 69 | {;} |
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| 70 | //////////////////////////////////////////////////////////////////////////////// |
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| 71 | // |
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| 72 | G4double G4Bessel::I0 (G4double x) |
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| 73 | { |
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| 74 | const G4double P1 = 1.0, |
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| 75 | P2 = 3.5156229, |
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| 76 | P3 = 3.0899424, |
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| 77 | P4 = 1.2067492, |
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| 78 | P5 = 0.2659732, |
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| 79 | P6 = 0.0360768, |
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| 80 | P7 = 0.0045813; |
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| 81 | const G4double Q1 = 0.39894228, |
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| 82 | Q2 = 0.01328592, |
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| 83 | Q3 = 0.00225319, |
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| 84 | Q4 =-0.00157565, |
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| 85 | Q5 = 0.00916281, |
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| 86 | Q6 =-0.02057706, |
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| 87 | Q7 = 0.02635537, |
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| 88 | Q8 =-0.01647633, |
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| 89 | Q9 = 0.00392377; |
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| 90 | |
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| 91 | G4double I = 0.0; |
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| 92 | if (std::fabs(x) < 3.75) |
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| 93 | { |
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| 94 | G4double y = std::pow(x/3.75, 2.0); |
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| 95 | I = P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7))))); |
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| 96 | } |
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| 97 | else |
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| 98 | { |
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| 99 | G4double ax = std::fabs(x); |
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| 100 | G4double y = 3.75/ax; |
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| 101 | I = std::exp(ax) / std::sqrt(ax) * |
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| 102 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*(Q7+y*(Q8+y*Q9)))))))); |
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| 103 | } |
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| 104 | return I; |
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| 105 | } |
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| 106 | //////////////////////////////////////////////////////////////////////////////// |
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| 107 | // |
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| 108 | G4double G4Bessel::K0 (G4double x) |
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| 109 | { |
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| 110 | const G4double P1 =-0.57721566, |
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| 111 | P2 = 0.42278420, |
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| 112 | P3 = 0.23069756, |
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| 113 | P4 = 0.03488590, |
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| 114 | P5 = 0.00262698, |
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| 115 | P6 = 0.00010750, |
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| 116 | P7 = 0.00000740; |
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| 117 | const G4double Q1 = 1.25331414, |
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| 118 | Q2 =-0.07832358, |
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| 119 | Q3 = 0.02189568, |
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| 120 | Q4 =-0.01062446, |
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| 121 | Q5 = 0.00587872, |
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| 122 | Q6 =-0.00251540, |
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| 123 | Q7 = 0.00053208; |
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| 124 | |
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| 125 | G4double K = 0.0; |
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| 126 | if (x <= 2.0) |
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| 127 | { |
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| 128 | G4double y = x * x / 4.0; |
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| 129 | K = (-std::log(x/2.0)) * I0(x) + |
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| 130 | P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7))))); |
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| 131 | } |
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| 132 | else |
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| 133 | { |
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| 134 | G4double y = 2.0 / x; |
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| 135 | K = std::exp(-x) / std::sqrt(x) * |
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| 136 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*Q7)))))); |
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| 137 | } |
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| 138 | return K; |
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| 139 | } |
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| 140 | //////////////////////////////////////////////////////////////////////////////// |
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| 141 | // |
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| 142 | G4double G4Bessel::I1 (G4double x) |
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| 143 | { |
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| 144 | const G4double P1 = 0.5, |
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| 145 | P2 = 0.87890594, |
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| 146 | P3 = 0.51498869, |
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| 147 | P4 = 0.15084934, |
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| 148 | P5 = 0.02658733, |
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| 149 | P6 = 0.00301532, |
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| 150 | P7 = 0.00032411; |
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| 151 | const G4double Q1 = 0.39894228, |
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| 152 | Q2 =-0.03988024, |
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| 153 | Q3 =-0.00362018, |
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| 154 | Q4 = 0.00163801, |
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| 155 | Q5 =-0.01031555, |
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| 156 | Q6 = 0.02282967, |
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| 157 | Q7 =-0.02895312, |
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| 158 | Q8 = 0.01787654, |
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| 159 | Q9 =-0.00420059; |
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| 160 | |
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| 161 | G4double I = 0.0; |
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| 162 | if (std::fabs(x) < 3.75) |
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| 163 | { |
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| 164 | G4double ax = std::fabs(x); |
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| 165 | G4double y = std::pow(x/3.75, 2.0); |
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| 166 | I = ax*(P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7)))))); |
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| 167 | } |
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| 168 | else |
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| 169 | { |
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| 170 | G4double ax = std::fabs(x); |
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| 171 | G4double y = 3.75/ax; |
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| 172 | I = std::exp(ax) / std::sqrt(ax) * |
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| 173 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*(Q7+y*(Q8+y*Q9)))))))); |
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| 174 | } |
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| 175 | if (x < 0.0) I = -I; |
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| 176 | return I; |
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| 177 | } |
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| 178 | //////////////////////////////////////////////////////////////////////////////// |
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| 179 | // |
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| 180 | G4double G4Bessel::K1 (G4double x) |
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| 181 | { |
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| 182 | const G4double P1 = 1.0, |
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| 183 | P2 = 0.15443144, |
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| 184 | P3 =-0.67278579, |
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| 185 | P4 =-0.18156897, |
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| 186 | P5 =-0.01919402, |
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| 187 | P6 =-0.00110404, |
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| 188 | P7 =-0.00004686; |
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| 189 | const G4double Q1 = 1.25331414, |
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| 190 | Q2 = 0.23498619, |
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| 191 | Q3 =-0.03655620, |
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| 192 | Q4 = 0.01504268, |
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| 193 | Q5 =-0.00780353, |
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| 194 | Q6 = 0.00325614, |
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| 195 | Q7 =-0.00068245; |
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| 196 | |
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| 197 | G4double K = 0.0; |
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| 198 | if (x <= 2.0) |
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| 199 | { |
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| 200 | G4double y = x * x / 4.0; |
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| 201 | K = std::log(x/2.0)*I1(x) + 1.0/x * |
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| 202 | (P1+y*(P2+y*(P3+y*(P4+y*(P5+y*(P6+y*P7)))))); |
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| 203 | } |
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| 204 | else |
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| 205 | { |
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| 206 | G4double y = 2.0 / x; |
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| 207 | K = std::exp(-x) / std::sqrt(x) * |
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| 208 | (Q1+y*(Q2+y*(Q3+y*(Q4+y*(Q5+y*(Q6+y*Q7)))))); |
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| 209 | } |
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| 210 | return K; |
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| 211 | } |
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| 212 | //////////////////////////////////////////////////////////////////////////////// |
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| 213 | // |
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| 214 | G4double G4Bessel::pI0 (G4double x) |
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| 215 | { |
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| 216 | const G4double A0 = 0.1250000000000E+00, |
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| 217 | A1 = 7.0312500000000E-02, |
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| 218 | A2 = 7.3242187500000E-02, |
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| 219 | A3 = 1.1215209960938E-01, |
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| 220 | A4 = 2.2710800170898E-01, |
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| 221 | A5 = 5.7250142097473E-01, |
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| 222 | A6 = 1.7277275025845E+00, |
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| 223 | A7 = 6.0740420012735E+00, |
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| 224 | A8 = 2.4380529699556E+01, |
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| 225 | A9 = 1.1001714026925E+02, |
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| 226 | A10 = 5.5133589612202E+02, |
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| 227 | A11 = 3.0380905109224E+03; |
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| 228 | |
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| 229 | G4double I = 0.0; |
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| 230 | if (x == 0.0) |
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| 231 | { |
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| 232 | I = 1.0; |
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| 233 | } |
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| 234 | else if (x < 18.0) |
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| 235 | { |
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| 236 | I = 1.0; |
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| 237 | G4double y = x * x; |
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| 238 | G4double s = 1.0; |
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| 239 | for (G4int i=1; i<101; i++) |
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| 240 | { |
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| 241 | s *= 0.25 * y / i / i; |
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| 242 | I += s; |
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| 243 | if (std::abs(s/I) < 1.0E-15) break; |
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| 244 | } |
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| 245 | } |
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| 246 | else |
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| 247 | { |
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| 248 | G4double y = 1.0 / x; |
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| 249 | I = std::exp(x) / std::sqrt(twopi*x) * |
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| 250 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*(A7+y*(A8+y*(A9+y*(A10+y*A11)))))))))))); |
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| 251 | } |
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| 252 | |
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| 253 | return I; |
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| 254 | } |
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| 255 | //////////////////////////////////////////////////////////////////////////////// |
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| 256 | // |
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| 257 | G4double G4Bessel::pI1 (G4double x) |
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| 258 | { |
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| 259 | const G4double A0 = -0.3750000000000E+00, |
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| 260 | A1 = -1.1718750000000E-01, |
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| 261 | A2 = -1.0253906250000E-01, |
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| 262 | A3 = -1.4419555664063E-01, |
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| 263 | A4 = -2.775764465332E-01, |
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| 264 | A5 = -6.7659258842468E-01, |
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| 265 | A6 = -1.9935317337513E+00, |
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| 266 | A7 = -6.8839142681099E+00, |
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| 267 | A8 = -2.7248827311269E+01, |
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| 268 | A9 = -1.2159789187654E+02, |
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| 269 | A10 = -6.0384407670507E+02, |
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| 270 | A11 = -3.3022722944809E+03; |
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| 271 | |
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| 272 | G4double I = 0.0; |
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| 273 | if (x == 0.0) |
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| 274 | { |
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| 275 | I = 0.0; |
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| 276 | } |
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| 277 | else if (x < 18.0) |
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| 278 | { |
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| 279 | I = 1.0; |
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| 280 | G4double y = x * x; |
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| 281 | G4double s = 1.0; |
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| 282 | for (G4int i=1; i<101; i++) |
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| 283 | { |
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| 284 | s *= 0.25 * y / i / (i+1.0); |
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| 285 | I += s; |
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| 286 | if (std::abs(s/I) < 1.0E-15) break; |
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| 287 | } |
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| 288 | I *= 0.5 * x; |
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| 289 | |
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| 290 | } |
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| 291 | else |
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| 292 | { |
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| 293 | G4double y = 1.0 / x; |
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| 294 | I = std::exp(x) / std::sqrt(twopi*x) * |
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| 295 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*(A7+y*(A8+y*(A9+y*(A10+y*A11)))))))))))); |
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| 296 | } |
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| 297 | |
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| 298 | return I; |
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| 299 | } |
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| 300 | //////////////////////////////////////////////////////////////////////////////// |
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| 301 | // |
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| 302 | G4double G4Bessel::pK0 (G4double x) |
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| 303 | { |
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| 304 | const G4double A0 = 0.1250000000000E+00, |
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| 305 | A1 = 0.2109375000000E+00, |
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| 306 | A2 = 1.0986328125000E+00, |
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| 307 | A3 = 1.1775970458984E+01, |
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| 308 | A4 = 2.1461706161499E+02, |
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| 309 | A5 = 5.9511522710323E+03, |
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| 310 | A6 = 2.3347645606175E+05, |
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| 311 | A7 = 1.2312234987631E+07; |
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| 312 | |
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| 313 | G4double K = 0.0; |
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| 314 | if (x == 0.0) |
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| 315 | { |
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| 316 | K = 1.0E+307; |
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| 317 | } |
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| 318 | else if (x < 9.0) |
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| 319 | { |
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| 320 | G4double y = x * x; |
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| 321 | G4double C = -std::log(x/2.0) - 0.5772156649015329; |
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| 322 | G4double s = 1.0; |
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| 323 | G4double t = 0.0; |
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| 324 | for (G4int i=1; i<51; i++) |
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| 325 | { |
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| 326 | s *= 0.25 * y / i / i; |
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| 327 | t += 1.0 / i ; |
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| 328 | K += s * (t+C); |
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| 329 | } |
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| 330 | K += C; |
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| 331 | } |
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| 332 | else |
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| 333 | { |
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| 334 | G4double y = 1.0 / x / x; |
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| 335 | K = 0.5 / x / pI0(x) * |
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| 336 | (1.0 + y*(A0+y*(A1+y*(A2+y*(A3+y*(A4+y*(A5+y*(A6+y*A7)))))))); |
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| 337 | } |
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| 338 | |
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| 339 | return K; |
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| 340 | } |
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| 341 | //////////////////////////////////////////////////////////////////////////////// |
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| 342 | // |
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| 343 | G4double G4Bessel::pK1 (G4double x) |
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| 344 | { |
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| 345 | G4double K = 0.0; |
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| 346 | if (x == 0.0) |
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| 347 | K = 1.0E+307; |
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| 348 | else |
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| 349 | K = (1.0/x - pI1(x)*pK0(x)) / pI0(x); |
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| 350 | return K; |
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| 351 | } |
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| 352 | //////////////////////////////////////////////////////////////////////////////// |
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| 353 | // |
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