|  line  | 
 stmt  | 
 bran  | 
 cond  | 
 sub  | 
 pod  | 
 time  | 
 code  | 
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 /*  | 
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2
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 *+  | 
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3
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 *  Name:  | 
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4
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 *     palInvf  | 
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5
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6
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 *  Purpose:  | 
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7
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 *     Invert a linear model of the type produced by the palFitxy routine.  | 
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9
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 *  Language:  | 
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10
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 *     Starlink ANSI C  | 
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11
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    | 
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12
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 *  Type of Module:  | 
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13
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 *     Library routine  | 
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14
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15
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 *  Invocation:  | 
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16
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 *     palInvf ( double fwds[6], double bkwds[6], int *j )  | 
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17
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18
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 *  Arguments:  | 
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19
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 *     fwds = double[6] (Given)  | 
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20
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 *        model coefficients  | 
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21
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 *     bkwds = double[6] (Returned)  | 
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 *        inverse model  | 
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23
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 *     j = int (Returned)  | 
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24
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 *        status: 0 = OK, -1 = no inverse  | 
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25
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26
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 *  Description:  | 
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27
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 *     The models relate two sets of [x,y] coordinates as follows.  | 
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 *     Naming the elements of fwds:  | 
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 *     ---  | 
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 *        fwds[0] = A  | 
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31
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 *        fwds[1] = B  | 
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32
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 *        fwds[2] = C  | 
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33
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 *        fwds[3] = D  | 
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34
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 *        fwds[4] = E  | 
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35
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 *        fwds[5] = F  | 
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36
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 *     ---  | 
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37
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 *     where two sets of coordinates [x1,y1] and [x2,y2] are related  | 
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38
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 *     thus:  | 
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39
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 *     ---  | 
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40
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 *        x2 = A + B * x1 + C * y1  | 
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41
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 *        y2 = D + E * x1 + F * y1  | 
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42
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 *     ---  | 
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43
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 *     the present routine generates a new set of coefficients:  | 
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44
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 *     ---  | 
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 *        bkwds[0] = P  | 
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46
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 *        bkwds[1] = Q  | 
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47
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 *        bkwds[2] = R  | 
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48
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 *        bkwds[3] = S  | 
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49
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 *        bkwds[4] = T  | 
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50
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 *        bkwds[5] = U  | 
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51
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 *     ---  | 
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52
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 *     such that:  | 
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53
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 *     ---  | 
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54
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 *        x1 = P + Q * x2 + R * y2  | 
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55
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 *        y1 = S + T * x2 + U * y2  | 
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56
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 *     ---  | 
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57
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 *     Two successive calls to palInvf will thus deliver a set  | 
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58
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 *     of coefficients equal to the starting values.  | 
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59
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60
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 *  See also:  | 
| 
61
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 *     palFitxy, palPxy, palXy2xy and palDcmpf  | 
| 
62
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    | 
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63
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 *  Authors:  | 
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64
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 *     PTW: Pat Wallace (STFC)  | 
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65
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 *     GSB: Graham Bell (EAO)  | 
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66
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67
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 *  History:  | 
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68
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 *     1990-04-11 (PTW):  | 
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69
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 *        SLALIB implementation.  | 
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70
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 *     2004-12-26 (PTW):  | 
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71
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 *        Documentation updated.  | 
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72
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 *     2018-10-23 (GSB):  | 
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73
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 *        Initial version in C.  | 
| 
74
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75
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 *  Copyright:  | 
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76
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 *     Copyright P.T.Wallace.  All rights reserved.  | 
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77
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 *     Copyright (C) 2018 East Asian Observatory.  | 
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78
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79
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 *  Licence:  | 
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80
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 *     This program is free software; you can redistribute it and/or modify  | 
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81
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 *     it under the terms of the GNU General Public License as published by  | 
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82
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 *     the Free Software Foundation; either version 2 of the License, or  | 
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83
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 *     (at your option) any later version.  | 
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84
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 *  | 
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85
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 *     This program is distributed in the hope that it will be useful,  | 
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86
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 *     but WITHOUT ANY WARRANTY; without even the implied warranty of  | 
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87
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 *     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the  | 
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88
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 *     GNU General Public License for more details.  | 
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89
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 *  | 
| 
90
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 *     You should have received a copy of the GNU General Public License  | 
| 
91
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 *     along with this program (see SLA_CONDITIONS); if not, write to the  | 
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92
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 *     Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,  | 
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93
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 *     Boston, MA  02110-1301  USA  | 
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94
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 *-  | 
| 
95
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 */  | 
| 
96
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    | 
| 
97
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1
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 void palInvf ( double fwds[6], double bkwds[6], int *j ) {  | 
| 
98
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   double a, b, c, d, e, f, det;  | 
| 
99
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    | 
| 
100
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1
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   a = fwds[0];  | 
| 
101
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1
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   b = fwds[1];  | 
| 
102
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1
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   c = fwds[2];  | 
| 
103
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1
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   d = fwds[3];  | 
| 
104
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1
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   e = fwds[4];  | 
| 
105
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1
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   f = fwds[5];  | 
| 
106
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1
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   det = b * f - c * e;  | 
| 
107
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    | 
| 
108
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1
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 50
  
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   if ( det != 0.0 ) {  | 
| 
109
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1
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     bkwds[0] = (c * d - a * f) / det;  | 
| 
110
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1
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     bkwds[1] = f / det;  | 
| 
111
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1
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     bkwds[2] = -c / det;  | 
| 
112
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1
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     bkwds[3] = (a * e - b * d) / det;  | 
| 
113
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1
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     bkwds[4] = -e / det;  | 
| 
114
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1
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     bkwds[5] = b / det;  | 
| 
115
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1
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     *j = 0;  | 
| 
116
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   } else {  | 
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117
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0
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     *j = -1;  | 
| 
118
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   }  | 
| 
119
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1
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 }  |