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1 /* dgetf2.f -- translated by f2c (version 20061008).
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2 You must link the resulting object file with libf2c:
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3 on Microsoft Windows system, link with libf2c.lib;
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4 on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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5 or, if you install libf2c.a in a standard place, with -lf2c -lm
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6 -- in that order, at the end of the command line, as in
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7 cc *.o -lf2c -lm
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8 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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9
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10 http://www.netlib.org/f2c/libf2c.zip
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11 */
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12
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13 #include "f2c.h"
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14 #include "blaswrap.h"
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15
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16 /* Table of constant values */
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17
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18 static integer c__1 = 1;
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19 static doublereal c_b8 = -1.;
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20
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21 /* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer *
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22 lda, integer *ipiv, integer *info)
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23 {
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24 /* System generated locals */
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25 integer a_dim1, a_offset, i__1, i__2, i__3;
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26 doublereal d__1;
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27
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28 /* Local variables */
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29 integer i__, j, jp;
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30 extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
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31 doublereal *, integer *, doublereal *, integer *, doublereal *,
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32 integer *), dscal_(integer *, doublereal *, doublereal *, integer
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33 *);
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34 doublereal sfmin;
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35 extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
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36 doublereal *, integer *);
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37 extern doublereal dlamch_(char *);
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38 extern integer idamax_(integer *, doublereal *, integer *);
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39 extern /* Subroutine */ int xerbla_(char *, integer *);
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40
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41
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42 /* -- LAPACK routine (version 3.2) -- */
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43 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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44 /* November 2006 */
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45
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46 /* .. Scalar Arguments .. */
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47 /* .. */
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48 /* .. Array Arguments .. */
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49 /* .. */
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50
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51 /* Purpose */
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52 /* ======= */
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53
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54 /* DGETF2 computes an LU factorization of a general m-by-n matrix A */
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55 /* using partial pivoting with row interchanges. */
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56
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57 /* The factorization has the form */
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58 /* A = P * L * U */
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59 /* where P is a permutation matrix, L is lower triangular with unit */
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60 /* diagonal elements (lower trapezoidal if m > n), and U is upper */
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61 /* triangular (upper trapezoidal if m < n). */
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62
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63 /* This is the right-looking Level 2 BLAS version of the algorithm. */
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64
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65 /* Arguments */
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66 /* ========= */
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67
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68 /* M (input) INTEGER */
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69 /* The number of rows of the matrix A. M >= 0. */
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70
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71 /* N (input) INTEGER */
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72 /* The number of columns of the matrix A. N >= 0. */
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73
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74 /* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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75 /* On entry, the m by n matrix to be factored. */
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76 /* On exit, the factors L and U from the factorization */
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77 /* A = P*L*U; the unit diagonal elements of L are not stored. */
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78
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79 /* LDA (input) INTEGER */
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80 /* The leading dimension of the array A. LDA >= max(1,M). */
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81
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82 /* IPIV (output) INTEGER array, dimension (min(M,N)) */
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83 /* The pivot indices; for 1 <= i <= min(M,N), row i of the */
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84 /* matrix was interchanged with row IPIV(i). */
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85
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86 /* INFO (output) INTEGER */
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87 /* = 0: successful exit */
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88 /* < 0: if INFO = -k, the k-th argument had an illegal value */
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89 /* > 0: if INFO = k, U(k,k) is exactly zero. The factorization */
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90 /* has been completed, but the factor U is exactly */
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91 /* singular, and division by zero will occur if it is used */
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92 /* to solve a system of equations. */
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93
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94 /* ===================================================================== */
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95
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96 /* .. Parameters .. */
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97 /* .. */
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98 /* .. Local Scalars .. */
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99 /* .. */
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100 /* .. External Functions .. */
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101 /* .. */
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102 /* .. External Subroutines .. */
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103 /* .. */
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104 /* .. Intrinsic Functions .. */
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105 /* .. */
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106 /* .. Executable Statements .. */
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107
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108 /* Test the input parameters. */
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109
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110 /* Parameter adjustments */
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111 a_dim1 = *lda;
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112 a_offset = 1 + a_dim1;
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113 a -= a_offset;
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114 --ipiv;
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115
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116 /* Function Body */
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117 *info = 0;
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118 if (*m < 0) {
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119 *info = -1;
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120 } else if (*n < 0) {
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121 *info = -2;
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122 } else if (*lda < max(1,*m)) {
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123 *info = -4;
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124 }
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125 if (*info != 0) {
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126 i__1 = -(*info);
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127 xerbla_("DGETF2", &i__1);
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128 return 0;
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129 }
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130
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131 /* Quick return if possible */
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132
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133 if (*m == 0 || *n == 0) {
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134 return 0;
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135 }
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136
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137 /* Compute machine safe minimum */
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138
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139 sfmin = dlamch_("S");
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140
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141 i__1 = min(*m,*n);
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142 for (j = 1; j <= i__1; ++j) {
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143
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144 /* Find pivot and test for singularity. */
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145
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146 i__2 = *m - j + 1;
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147 jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1);
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148 ipiv[j] = jp;
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149 if (a[jp + j * a_dim1] != 0.) {
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150
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151 /* Apply the interchange to columns 1:N. */
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152
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153 if (jp != j) {
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154 dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda);
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155 }
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156
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157 /* Compute elements J+1:M of J-th column. */
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158
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159 if (j < *m) {
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160 if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) {
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161 i__2 = *m - j;
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162 d__1 = 1. / a[j + j * a_dim1];
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163 dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1);
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164 } else {
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165 i__2 = *m - j;
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166 for (i__ = 1; i__ <= i__2; ++i__) {
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167 a[j + i__ + j * a_dim1] /= a[j + j * a_dim1];
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168 /* L20: */
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169 }
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170 }
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171 }
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172
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173 } else if (*info == 0) {
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174
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175 *info = j;
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176 }
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177
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178 if (j < min(*m,*n)) {
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179
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180 /* Update trailing submatrix. */
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181
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182 i__2 = *m - j;
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183 i__3 = *n - j;
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184 dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + (
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185 j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda);
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186 }
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187 /* L10: */
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188 }
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189 return 0;
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190
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191 /* End of DGETF2 */
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192
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193 } /* dgetf2_ */
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