1 | !*********************************************************************** |
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2 | ! |
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3 | SUBROUTINE DLAMC1( BETA, T, RND, IEEE1 ) |
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4 | implicit none |
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5 | ! |
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6 | ! -- LAPACK auxiliary routine (version 3.1) -- |
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7 | ! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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8 | ! November 2006 |
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9 | ! |
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10 | ! .. Scalar Arguments .. |
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11 | LOGICAL IEEE1, RND |
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12 | INTEGER BETA, T |
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13 | ! .. |
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14 | ! |
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15 | ! Purpose |
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16 | ! ======= |
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17 | ! |
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18 | ! DLAMC1 determines the machine parameters given by BETA, T, RND, and |
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19 | ! IEEE1. |
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20 | ! |
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21 | ! Arguments |
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22 | ! ========= |
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23 | ! |
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24 | ! BETA (output) INTEGER |
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25 | ! The base of the machine. |
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26 | ! |
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27 | ! T (output) INTEGER |
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28 | ! The number of ( BETA ) digits in the mantissa. |
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29 | ! |
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30 | ! RND (output) LOGICAL |
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31 | ! Specifies whether proper rounding ( RND = .TRUE. ) or |
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32 | ! chopping ( RND = .FALSE. ) occurs in addition. This may not |
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33 | ! be a reliable guide to the way in which the machine performs |
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34 | ! its arithmetic. |
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35 | ! |
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36 | ! IEEE1 (output) LOGICAL |
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37 | ! Specifies whether rounding appears to be done in the IEEE |
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38 | ! 'round to nearest' style. |
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39 | ! |
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40 | ! Further Details |
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41 | ! =============== |
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42 | ! |
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43 | ! The routine is based on the routine ENVRON by Malcolm and |
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44 | ! incorporates suggestions by Gentleman and Marovich. See |
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45 | ! |
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46 | ! Malcolm M. A. (1972) Algorithms to reveal properties of |
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47 | ! floating-point arithmetic. Comms. of the ACM, 15, 949-951. |
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48 | ! |
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49 | ! Gentleman W. M. and Marovich S. B. (1974) More on algorithms |
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50 | ! that reveal properties of floating point arithmetic units. |
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51 | ! Comms. of the ACM, 17, 276-277. |
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52 | ! |
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53 | ! ===================================================================== |
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54 | ! |
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55 | ! .. Local Scalars .. |
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56 | LOGICAL FIRST, LIEEE1, LRND |
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57 | INTEGER LBETA, LT |
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58 | DOUBLE PRECISION A, B, C, F, ONE, QTR, SAVEC, T1, T2 |
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59 | ! .. |
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60 | ! .. External Functions .. |
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61 | DOUBLE PRECISION DLAMC3 |
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62 | EXTERNAL DLAMC3 |
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63 | ! .. |
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64 | ! .. Save statement .. |
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65 | SAVE FIRST, LIEEE1, LBETA, LRND, LT |
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66 | ! .. |
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67 | ! .. Data statements .. |
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68 | DATA FIRST / .TRUE. / |
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69 | ! .. |
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70 | ! .. Executable Statements .. |
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71 | ! |
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72 | IF( FIRST ) THEN |
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73 | ONE = 1 |
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74 | ! |
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75 | ! LBETA, LIEEE1, LT and LRND are the local values of BETA, |
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76 | ! IEEE1, T and RND. |
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77 | ! |
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78 | ! Throughout this routine we use the function DLAMC3 to ensure |
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79 | ! that relevant values are stored and not held in registers, or |
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80 | ! are not affected by optimizers. |
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81 | ! |
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82 | ! Compute a = 2.0**m with the smallest positive integer m such |
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83 | ! that |
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84 | ! |
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85 | ! fl( a + 1.0 ) = a. |
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86 | ! |
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87 | A = 1 |
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88 | C = 1 |
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89 | ! |
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90 | !+ WHILE( C.EQ.ONE )LOOP |
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91 | 10 CONTINUE |
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92 | IF( C.EQ.ONE ) THEN |
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93 | A = 2*A |
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94 | C = DLAMC3( A, ONE ) |
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95 | C = DLAMC3( C, -A ) |
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96 | GO TO 10 |
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97 | END IF |
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98 | !+ END WHILE |
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99 | ! |
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100 | ! Now compute b = 2.0**m with the smallest positive integer m |
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101 | ! such that |
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102 | ! |
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103 | ! fl( a + b ) .gt. a. |
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104 | ! |
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105 | B = 1 |
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106 | C = DLAMC3( A, B ) |
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107 | ! |
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108 | !+ WHILE( C.EQ.A )LOOP |
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109 | 20 CONTINUE |
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110 | IF( C.EQ.A ) THEN |
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111 | B = 2*B |
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112 | C = DLAMC3( A, B ) |
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113 | GO TO 20 |
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114 | END IF |
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115 | !+ END WHILE |
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116 | ! |
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117 | ! Now compute the base. a and c are neighbouring floating point |
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118 | ! numbers in the interval ( beta**t, beta**( t + 1 ) ) and so |
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119 | ! their difference is beta. Adding 0.25 to c is to ensure that it |
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120 | ! is truncated to beta and not ( beta - 1 ). |
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121 | ! |
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122 | QTR = ONE / 4 |
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123 | SAVEC = C |
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124 | C = DLAMC3( C, -A ) |
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125 | LBETA = C + QTR |
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126 | ! |
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127 | ! Now determine whether rounding or chopping occurs, by adding a |
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128 | ! bit less than beta/2 and a bit more than beta/2 to a. |
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129 | ! |
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130 | B = LBETA |
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131 | F = DLAMC3( B / 2, -B / 100 ) |
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132 | C = DLAMC3( F, A ) |
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133 | IF( C.EQ.A ) THEN |
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134 | LRND = .TRUE. |
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135 | ELSE |
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136 | LRND = .FALSE. |
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137 | END IF |
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138 | F = DLAMC3( B / 2, B / 100 ) |
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139 | C = DLAMC3( F, A ) |
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140 | IF( ( LRND ) .AND. ( C.EQ.A ) ) & |
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141 | &LRND = .FALSE. |
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142 | ! |
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143 | ! Try and decide whether rounding is done in the IEEE 'round to |
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144 | ! nearest' style. B/2 is half a unit in the last place of the two |
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145 | ! numbers A and SAVEC. Furthermore, A is even, i.e. has last bit |
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146 | ! zero, and SAVEC is odd. Thus adding B/2 to A should not change |
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147 | ! A, but adding B/2 to SAVEC should change SAVEC. |
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148 | ! |
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149 | T1 = DLAMC3( B / 2, A ) |
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150 | T2 = DLAMC3( B / 2, SAVEC ) |
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151 | LIEEE1 = ( T1.EQ.A ) .AND. ( T2.GT.SAVEC ) .AND. LRND |
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152 | ! |
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153 | ! Now find the mantissa, t. It should be the integer part of |
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154 | ! log to the base beta of a, however it is safer to determine t |
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155 | ! by powering. So we find t as the smallest positive integer for |
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156 | ! which |
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157 | ! |
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158 | ! fl( beta**t + 1.0 ) = 1.0. |
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159 | ! |
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160 | LT = 0 |
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161 | A = 1 |
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162 | C = 1 |
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163 | ! |
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164 | !+ WHILE( C.EQ.ONE )LOOP |
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165 | 30 CONTINUE |
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166 | IF( C.EQ.ONE ) THEN |
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167 | LT = LT + 1 |
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168 | A = A*LBETA |
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169 | C = DLAMC3( A, ONE ) |
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170 | C = DLAMC3( C, -A ) |
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171 | GO TO 30 |
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172 | END IF |
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173 | !+ END WHILE |
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174 | ! |
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175 | END IF |
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176 | ! |
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177 | BETA = LBETA |
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178 | T = LT |
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179 | RND = LRND |
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180 | IEEE1 = LIEEE1 |
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181 | FIRST = .FALSE. |
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182 | RETURN |
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183 | ! |
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184 | ! End of DLAMC1 |
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185 | ! |
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186 | END |
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187 | ! |
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