1 | MODULE poisfft_hybrid_mod |
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2 | !------------------------------------------------------------------------------ |
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3 | ! |
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4 | ! Current revisions: |
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5 | ! ----------------- |
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6 | ! ddzu replaced by ddzu_pres due to changes in zu(0). |
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7 | ! |
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8 | ! Former revisions: |
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9 | ! ----------------- |
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10 | ! $Id: poisfft_hybrid.f90 667 2010-12-23 12:06:00Z suehring $ |
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11 | ! |
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12 | ! 415 2009-12-15 10:26:23Z raasch |
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13 | ! Dimension of array stat in cascade change to prevent type problems with |
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14 | ! mpi2 libraries |
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15 | ! |
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16 | ! 274 2009-03-26 15:11:21Z heinze |
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17 | ! Output of messages replaced by message handling routine. |
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18 | ! |
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19 | ! Feb. 2007 |
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20 | ! RCS Log replace by Id keyword, revision history cleaned up |
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21 | ! |
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22 | ! Revision 1.11 2004/04/30 12:43:14 raasch |
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23 | ! Renaming of fft routines, additional argument in calls of fft_y_m |
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24 | ! |
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25 | ! Revision 1.2 2002/12/19 16:08:31 raasch |
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26 | ! Preprocessor directive KKMP introduced (OMP does NOT work), |
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27 | ! array tri will be a shared array in OpenMP loop, to get better cache |
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28 | ! utilization, the i index (x-direction) will be executed in stride |
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29 | ! "istride" as outer loop and in a shorter inner loop, |
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30 | ! overlapping of computation and communication realized by new routine |
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31 | ! poisfft_hybrid_nodes, name of old routine poisfft_hybrid changed to |
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32 | ! poisfft_hybrid_omp, STOP statement replaced by call of subroutine local_stop |
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33 | ! |
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34 | ! |
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35 | ! Description: |
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36 | ! ------------ |
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37 | ! Solution of the Poisson equation with a 2D spectral method. |
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38 | ! Hybrid version for parallel computers using a 1D domain decomposition, |
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39 | ! realized with MPI, along x and parallelization with OPEN-MP along y |
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40 | ! (routine poisfft_hybrid_omp). In a second version (poisfft_hybrid_nodes), |
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41 | ! optimization is realized by overlapping of computation and communication |
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42 | ! and by simultaneously executing as many communication calls as switches |
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43 | ! per logical partition (LPAR) are available. This version comes into |
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44 | ! effect if more than one node is used and if the environment variable |
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45 | ! tasks_per_node is set in a way that it can be devided by switch_per_lpar |
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46 | ! without any rest. |
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47 | ! |
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48 | ! WARNING: In case of OpenMP, there are problems with allocating large |
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49 | ! arrays in parallel regions. |
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50 | ! |
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51 | ! Copyright Klaus Ketelsen / Siegfried Raasch May 2002 |
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52 | !------------------------------------------------------------------------------! |
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53 | |
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54 | USE fft_xy |
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55 | USE indices |
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56 | USE pegrid |
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57 | |
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58 | IMPLICIT NONE |
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59 | |
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60 | PRIVATE |
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61 | PUBLIC poisfft_hybrid, poisfft_hybrid_ini |
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62 | |
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63 | INTEGER, PARAMETER :: switch_per_lpar = 2 |
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64 | |
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65 | INTEGER, SAVE :: nxl_a, nxr_a, & ! total x dimension |
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66 | nxl_p, nxr_p, & ! partial x dimension |
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67 | nys_a, nyn_a, & ! total y dimension |
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68 | nys_p, nyn_p, & ! partial y dimension |
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69 | |
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70 | npe_s, & ! total number of PEs for solver |
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71 | nwords, & ! number of points to be exchanged |
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72 | ! with MPI_ALLTOALL |
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73 | n_omp_threads ! number of OpenMP threads |
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74 | |
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75 | ! |
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76 | !-- Variables for multi node version (cluster version) using routine |
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77 | !-- poisfft_hybrid_nodes |
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78 | INTEGER, SAVE :: comm_nodes, & ! communicater nodes |
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79 | comm_node_all, & ! communicater all PEs node version |
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80 | comm_tasks, & ! communicater tasks |
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81 | me, me_node, me_task,& ! identity of this PE |
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82 | nodes, & ! number of nodes |
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83 | tasks_per_logical_node = -1 ! default no cluster |
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84 | |
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85 | |
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86 | ! |
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87 | !-- Public interfaces |
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88 | INTERFACE poisfft_hybrid_ini |
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89 | MODULE PROCEDURE poisfft_hybrid_ini |
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90 | END INTERFACE poisfft_hybrid_ini |
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91 | |
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92 | INTERFACE poisfft_hybrid |
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93 | MODULE PROCEDURE poisfft_hybrid |
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94 | END INTERFACE poisfft_hybrid |
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95 | |
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96 | ! |
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97 | !-- Private interfaces |
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98 | INTERFACE poisfft_hybrid_omp |
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99 | MODULE PROCEDURE poisfft_hybrid_omp |
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100 | END INTERFACE poisfft_hybrid_omp |
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101 | |
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102 | INTERFACE poisfft_hybrid_omp_vec |
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103 | MODULE PROCEDURE poisfft_hybrid_omp_vec |
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104 | END INTERFACE poisfft_hybrid_omp_vec |
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105 | |
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106 | INTERFACE poisfft_hybrid_nodes |
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107 | MODULE PROCEDURE poisfft_hybrid_nodes |
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108 | END INTERFACE poisfft_hybrid_nodes |
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109 | |
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110 | INTERFACE tridia_hybrid |
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111 | MODULE PROCEDURE tridia_hybrid |
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112 | END INTERFACE tridia_hybrid |
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113 | |
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114 | INTERFACE cascade |
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115 | MODULE PROCEDURE cascade |
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116 | END INTERFACE cascade |
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117 | |
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118 | CONTAINS |
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119 | |
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120 | |
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121 | SUBROUTINE poisfft_hybrid_ini |
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122 | |
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123 | USE control_parameters |
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124 | USE pegrid |
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125 | |
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126 | IMPLICIT NONE |
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127 | |
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128 | CHARACTER(LEN=8) :: cdummy |
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129 | INTEGER :: idummy, istat |
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130 | INTEGER, DIMENSION(2) :: coords, dims |
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131 | |
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132 | LOGICAL, DIMENSION(2) :: period = .false., re_dims |
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133 | |
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134 | |
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135 | ! |
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136 | !-- Set the internal index values for the hybrid solver |
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137 | #if defined( __parallel ) |
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138 | npe_s = pdims(1) |
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139 | #else |
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140 | npe_s = 1 |
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141 | #endif |
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142 | nxl_a = 0 |
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143 | nxr_a = nx |
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144 | nxl_p = 0 |
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145 | nxr_p = ( ( nx+1 ) / npe_s ) - 1 |
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146 | nys_a = nys |
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147 | nyn_a = nyn |
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148 | nys_p = 0 |
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149 | nyn_p = ( ( ny+1 ) / npe_s ) - 1 |
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150 | |
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151 | nwords = ( nxr_p-nxl_p+1 ) * nz * ( nyn_p-nys_p+1 ) |
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152 | |
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153 | #if defined( __KKMP ) |
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154 | CALL LOCAL_GETENV( 'OMP_NUM_THREADS', 15, cdummy, idummy ) |
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155 | READ ( cdummy, '(I8)' ) n_omp_threads |
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156 | IF ( n_omp_threads > 1 ) THEN |
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157 | WRITE( message_string, * ) 'Number of OpenMP threads = ', & |
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158 | n_omp_threads |
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159 | CALL message( 'poisfft_hybrid_ini', 'PA0280', 0, 0, 0, 6, 0 ) |
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160 | ENDIF |
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161 | #else |
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162 | n_omp_threads = 1 |
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163 | #endif |
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164 | ! |
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165 | !-- Initialize the one-dimensional FFT routines |
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166 | CALL fft_init |
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167 | |
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168 | ! |
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169 | !-- Setup for multi node version (poisfft_hybrid_nodes) |
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170 | IF ( n_omp_threads == 1 .AND. & |
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171 | ( host(1:4) == 'ibmh' .OR. host(1:4) == 'ibmb' ) ) THEN |
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172 | |
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173 | IF ( tasks_per_node /= -9999 ) THEN |
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174 | ! |
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175 | !-- Multi node version requires that the available number of |
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176 | !-- switches per logical partition must be an integral divisor |
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177 | !-- of the chosen number of tasks per node |
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178 | IF ( MOD( tasks_per_node, switch_per_lpar ) == 0 ) THEN |
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179 | ! |
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180 | !-- Set the switch which decides about usage of the multi node |
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181 | !-- version |
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182 | IF ( tasks_per_node / switch_per_lpar > 1 .AND. & |
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183 | numprocs > tasks_per_node ) THEN |
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184 | tasks_per_logical_node = tasks_per_node / switch_per_lpar |
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185 | ENDIF |
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186 | |
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187 | IF ( tasks_per_logical_node > -1 ) THEN |
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188 | |
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189 | WRITE( message_string, * ) 'running optimized ', & |
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190 | 'multinode version', & |
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191 | '&switch_per_lpar = ', & |
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192 | switch_per_lpar, & |
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193 | '&tasks_per_lpar = ', & |
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194 | tasks_per_node, & |
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195 | 'tasks_per_logical_node = ', & |
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196 | tasks_per_logical_node |
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197 | CALL message( 'poisfft_hybrid_ini', 'PA0281', 0, 0, 0, 6, 0 ) |
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198 | |
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199 | ENDIF |
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200 | |
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201 | ENDIF |
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202 | ENDIF |
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203 | ENDIF |
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204 | |
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205 | ! |
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206 | !-- Determine sub-topologies for multi node version |
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207 | IF ( tasks_per_logical_node >= 2 ) THEN |
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208 | |
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209 | #if defined( __parallel ) |
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210 | nodes = ( numprocs + tasks_per_logical_node - 1 ) / & |
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211 | tasks_per_logical_node |
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212 | dims(1) = nodes |
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213 | dims(2) = tasks_per_logical_node |
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214 | |
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215 | CALL MPI_CART_CREATE( comm2d, 2, dims, period, .FALSE., & |
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216 | comm_node_all, istat ) |
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217 | CALL MPI_COMM_RANK( comm_node_all, me, istat ) |
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218 | |
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219 | re_dims(1) = .TRUE. |
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220 | re_dims(2) = .FALSE. |
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221 | CALL MPI_CART_SUB( comm_node_all, re_dims, comm_nodes, istat ) |
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222 | CALL MPI_COMM_RANK( comm_nodes, me_node, istat ) |
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223 | |
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224 | re_dims(1) = .FALSE. |
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225 | re_dims(2) = .TRUE. |
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226 | CALL MPI_CART_SUB( comm_node_all, re_dims, comm_tasks, istat ) |
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227 | CALL MPI_COMM_RANK( comm_tasks, me_task, istat ) |
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228 | |
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229 | ! write(0,*) 'who am i',myid,me,me_node,me_task,nodes,& |
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230 | ! tasks_per_logical_node |
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231 | #else |
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232 | message_string = 'parallel environment (MPI) required' |
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233 | CALL message( 'poisfft_hybrid_ini', 'PA0282', 1, 2, 0, 6, 0 ) |
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234 | #endif |
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235 | ENDIF |
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236 | |
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237 | END SUBROUTINE poisfft_hybrid_ini |
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238 | |
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239 | |
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240 | SUBROUTINE poisfft_hybrid( ar ) |
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241 | |
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242 | USE control_parameters |
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243 | USE interfaces |
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244 | |
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245 | IMPLICIT NONE |
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246 | |
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247 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar |
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248 | |
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249 | IF ( host(1:3) == 'nec' ) THEN |
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250 | CALL poisfft_hybrid_omp_vec( ar ) |
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251 | ELSE |
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252 | IF ( tasks_per_logical_node == -1 ) THEN |
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253 | CALL poisfft_hybrid_omp( ar ) |
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254 | ELSE |
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255 | CALL poisfft_hybrid_nodes( ar ) |
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256 | ENDIF |
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257 | ENDIF |
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258 | |
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259 | END SUBROUTINE poisfft_hybrid |
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260 | |
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261 | |
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262 | SUBROUTINE poisfft_hybrid_omp ( ar ) |
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263 | |
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264 | USE cpulog |
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265 | USE interfaces |
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266 | |
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267 | IMPLICIT NONE |
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268 | |
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269 | INTEGER, PARAMETER :: istride = 4 ! stride of i loop |
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270 | INTEGER :: i, ii, ir, iei, iouter, istat, j, jj, k, m, n, jthread |
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271 | |
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272 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar |
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273 | |
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274 | REAL, DIMENSION(0:nx) :: fftx_ar |
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275 | REAL, DIMENSION(0:ny,istride) :: ffty_ar |
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276 | |
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277 | REAL, DIMENSION(0:nx,nz) :: tri_ar |
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278 | |
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279 | REAL, DIMENSION(nxl_p:nxr_p,nz,nys_p:nyn_p,npe_s) :: work1, work2 |
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280 | #if defined( __KKMP ) |
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281 | INTEGER :: omp_get_thread_num |
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282 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
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283 | ALLOCATE( tri(5,0:nx,0:nz-1,n_omp_threads ) ) |
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284 | #else |
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285 | REAL, DIMENSION(5,0:nx,0:nz-1,1) :: tri |
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286 | #endif |
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287 | |
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288 | |
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289 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_omp', 'start' ) |
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290 | |
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291 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
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292 | |
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293 | !$OMP PARALLEL PRIVATE (i,iouter,ii,ir,iei,j,k,m,n,ffty_ar) |
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294 | !$OMP DO |
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295 | ! |
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296 | !-- Store grid points to be transformed on a 1d-array, do the fft |
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297 | !-- and sample the results on a 4d-array |
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298 | DO iouter = nxl_p, nxr_p, istride ! stride loop, better cache |
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299 | iei = MIN( iouter+istride-1, nxr_p ) |
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300 | DO k = 1, nz |
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301 | |
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302 | DO i = iouter, iei |
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303 | ii = nxl + i |
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304 | ir = i - iouter + 1 |
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305 | |
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306 | DO j = nys_a, nyn_a |
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307 | ffty_ar(j,ir) = ar(k,j,ii) |
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308 | ENDDO |
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309 | |
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310 | CALL fft_y( ffty_ar(:,ir), 'forward' ) |
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311 | ENDDO |
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312 | |
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313 | m = nys_a |
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314 | DO n = 1, npe_s |
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315 | DO j = nys_p, nyn_p |
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316 | DO i = iouter, iei |
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317 | ir = i - iouter + 1 |
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318 | work1(i,k,j,n) = ffty_ar(m,ir) |
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319 | ENDDO |
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320 | m = m+1 |
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321 | ENDDO |
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322 | ENDDO |
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323 | |
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324 | ENDDO |
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325 | ENDDO |
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326 | !$OMP END PARALLEL |
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327 | |
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328 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
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329 | |
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330 | #if defined( __parallel ) |
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331 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
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332 | |
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333 | CALL MPI_ALLTOALL( work1(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
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334 | work2(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
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335 | comm2d, istat ) |
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336 | |
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337 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
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338 | #else |
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339 | work2 = work1 |
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340 | #endif |
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341 | |
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342 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
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343 | |
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344 | #if defined( __KKMP ) |
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345 | !$OMP PARALLEL PRIVATE (i,j,jj,k,m,n,fftx_ar,tri_ar,jthread) |
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346 | !$OMP DO |
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347 | DO j = nys_p, nyn_p |
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348 | jthread = omp_get_thread_num() + 1 |
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349 | #else |
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350 | DO j = nys_p, nyn_p |
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351 | jthread = 1 |
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352 | #endif |
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353 | DO k = 1, nz |
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354 | |
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355 | m = nxl_a |
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356 | DO n = 1, npe_s |
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357 | DO i = nxl_p, nxr_p |
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358 | fftx_ar(m) = work2(i,k,j,n) |
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359 | m = m+1 |
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360 | ENDDO |
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361 | ENDDO |
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362 | |
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363 | CALL fft_x( fftx_ar, 'forward' ) |
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364 | |
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365 | DO i = nxl_a, nxr_a |
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366 | tri_ar(i,k) = fftx_ar(i) |
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367 | ENDDO |
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368 | |
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369 | ENDDO |
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370 | |
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371 | jj = myid * (nyn_p-nys_p+1) + j |
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372 | CALL tridia_hybrid( jj, tri_ar, tri(:,:,:,jthread)) |
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373 | |
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374 | DO k = 1, nz |
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375 | DO i = nxl_a, nxr_a |
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376 | fftx_ar(i) = tri_ar (i,k) |
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377 | ENDDO |
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378 | |
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379 | CALL fft_x( fftx_ar, 'backward' ) |
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380 | |
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381 | m = nxl_a |
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382 | DO n = 1, npe_s |
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383 | DO i = nxl_p, nxr_p |
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384 | work2(i,k,j,n) = fftx_ar(m) |
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385 | m = m+1 |
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386 | ENDDO |
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387 | ENDDO |
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388 | |
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389 | ENDDO |
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390 | ENDDO |
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391 | #if defined( __KKMP ) |
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392 | !$OMP END PARALLEL |
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393 | #endif |
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394 | |
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395 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
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396 | |
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397 | #if defined( __parallel ) |
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398 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
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399 | nwords = (nxr_p-nxl_p+1) * nz * (nyn_p-nys_p+1) |
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400 | |
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401 | CALL MPI_ALLTOALL( work2(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
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402 | work1(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
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403 | comm2d, istat ) |
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404 | |
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405 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
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406 | #else |
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407 | work1 = work2 |
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408 | #endif |
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409 | |
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410 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
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411 | |
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412 | !$OMP PARALLEL PRIVATE (i,iouter,ii,ir,iei,j,k,m,n,ffty_ar) |
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413 | !$OMP DO |
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414 | DO iouter = nxl_p, nxr_p, istride |
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415 | iei = MIN( iouter+istride-1, nxr_p ) |
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416 | DO k = 1, nz |
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417 | |
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418 | m = nys_a |
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419 | DO n = 1, npe_s |
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420 | DO j = nys_p, nyn_p |
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421 | DO i = iouter, iei |
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422 | ir = i - iouter + 1 |
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423 | ffty_ar(m,ir) = work1 (i,k,j,n) |
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424 | ENDDO |
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425 | m = m+1 |
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426 | ENDDO |
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427 | ENDDO |
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428 | |
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429 | DO i = iouter, iei |
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430 | ii = nxl + i |
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431 | ir = i - iouter + 1 |
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432 | CALL fft_y( ffty_ar(:,ir), 'backward' ) |
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433 | |
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434 | DO j = nys_a, nyn_a |
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435 | ar(k,j,ii) = ffty_ar(j,ir) |
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436 | ENDDO |
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437 | ENDDO |
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438 | |
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439 | ENDDO |
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440 | ENDDO |
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441 | !$OMP END PARALLEL |
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442 | |
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443 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
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444 | |
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445 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_omp', 'stop' ) |
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446 | |
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447 | #if defined( __KKMP ) |
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448 | DEALLOCATE( tri ) |
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449 | #endif |
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450 | |
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451 | END SUBROUTINE poisfft_hybrid_omp |
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452 | |
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453 | |
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454 | SUBROUTINE poisfft_hybrid_omp_vec ( ar ) |
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455 | |
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456 | USE cpulog |
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457 | USE interfaces |
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458 | |
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459 | IMPLICIT NONE |
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460 | |
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461 | INTEGER, PARAMETER :: istride = 4 ! stride of i loop |
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462 | INTEGER :: i, ii, ir, iei, iouter, istat, j, jj, k, m, n, jthread |
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463 | |
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464 | REAL, DIMENSION(0:nx,nz) :: tri_ar |
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465 | |
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466 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar |
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467 | |
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468 | REAL, DIMENSION(0:ny+3,nz,nxl_p:nxr_p) :: ffty_ar3 |
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469 | REAL, DIMENSION(0:nx+3,nz,nys_p:nyn_p) :: fftx_ar3 |
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470 | |
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471 | REAL, DIMENSION(nxl_p:nxr_p,nz,nys_p:nyn_p,npe_s) :: work1, work2 |
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472 | #if defined( __KKMP ) |
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473 | INTEGER :: omp_get_thread_num |
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474 | REAL, DIMENSION(:,:,:,:), ALLOCATABLE :: tri |
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475 | ALLOCATE( tri(5,0:nx,0:nz-1,n_omp_threads ) ) |
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476 | #else |
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477 | REAL, DIMENSION(5,0:nx,0:nz-1,1) :: tri |
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478 | #endif |
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479 | |
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480 | |
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481 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_vec', 'start' ) |
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482 | |
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483 | CALL cpu_log( log_point_s(7), 'fft_y_m', 'start' ) |
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484 | |
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485 | !$OMP PARALLEL PRIVATE (i,j,k,m,n) |
---|
486 | !$OMP DO |
---|
487 | ! |
---|
488 | !-- Store grid points to be transformed on a 1d-array, do the fft |
---|
489 | !-- and sample the results on a 4d-array |
---|
490 | DO i = nxl_p, nxr_p |
---|
491 | |
---|
492 | DO j = nys_a, nyn_a |
---|
493 | DO k = 1, nz |
---|
494 | ffty_ar3(j,k,i) = ar(k,j,i+nxl) |
---|
495 | ENDDO |
---|
496 | ENDDO |
---|
497 | |
---|
498 | CALL fft_y_m( ffty_ar3(:,:,i), ny+3, 'forward' ) |
---|
499 | ENDDO |
---|
500 | |
---|
501 | !$OMP DO |
---|
502 | DO k = 1, nz |
---|
503 | m = nys_a |
---|
504 | DO n = 1, npe_s |
---|
505 | DO j = nys_p, nyn_p |
---|
506 | DO i = nxl_p, nxr_p |
---|
507 | work1(i,k,j,n) = ffty_ar3(m,k,i) |
---|
508 | ENDDO |
---|
509 | m = m+1 |
---|
510 | ENDDO |
---|
511 | ENDDO |
---|
512 | ENDDO |
---|
513 | !$OMP END PARALLEL |
---|
514 | |
---|
515 | CALL cpu_log( log_point_s(7), 'fft_y_m', 'pause' ) |
---|
516 | |
---|
517 | #if defined( __parallel ) |
---|
518 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
519 | CALL MPI_ALLTOALL( work1(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
---|
520 | work2(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
---|
521 | comm2d, istat ) |
---|
522 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
523 | #else |
---|
524 | work2 = work1 |
---|
525 | #endif |
---|
526 | |
---|
527 | CALL cpu_log( log_point_s(33), 'fft_x_m + tridia', 'start' ) |
---|
528 | |
---|
529 | #if defined( __KKMP ) |
---|
530 | !$OMP PARALLEL PRIVATE (i,j,jj,k,m,n,tri_ar,jthread) |
---|
531 | !$OMP DO |
---|
532 | DO j = nys_p, nyn_p |
---|
533 | jthread = omp_get_thread_num() + 1 |
---|
534 | #else |
---|
535 | DO j = nys_p, nyn_p |
---|
536 | jthread = 1 |
---|
537 | #endif |
---|
538 | DO k = 1, nz |
---|
539 | |
---|
540 | m = nxl_a |
---|
541 | DO n = 1, npe_s |
---|
542 | DO i = nxl_p, nxr_p |
---|
543 | fftx_ar3(m,k,j) = work2(i,k,j,n) |
---|
544 | m = m+1 |
---|
545 | ENDDO |
---|
546 | ENDDO |
---|
547 | ENDDO |
---|
548 | |
---|
549 | CALL fft_x_m( fftx_ar3(:,:,j), 'forward' ) |
---|
550 | |
---|
551 | DO k = 1, nz |
---|
552 | DO i = nxl_a, nxr_a |
---|
553 | tri_ar(i,k) = fftx_ar3(i,k,j) |
---|
554 | ENDDO |
---|
555 | ENDDO |
---|
556 | |
---|
557 | jj = myid * (nyn_p-nys_p+1) + j |
---|
558 | CALL tridia_hybrid( jj, tri_ar, tri(:,:,:,jthread)) |
---|
559 | |
---|
560 | DO k = 1, nz |
---|
561 | DO i = nxl_a, nxr_a |
---|
562 | fftx_ar3(i,k,j) = tri_ar (i,k) |
---|
563 | ENDDO |
---|
564 | ENDDO |
---|
565 | |
---|
566 | CALL fft_x_m( fftx_ar3(:,:,j), 'backward' ) |
---|
567 | |
---|
568 | DO k = 1, nz |
---|
569 | m = nxl_a |
---|
570 | DO n = 1, npe_s |
---|
571 | DO i = nxl_p, nxr_p |
---|
572 | work2(i,k,j,n) = fftx_ar3(m,k,j) |
---|
573 | m = m+1 |
---|
574 | ENDDO |
---|
575 | ENDDO |
---|
576 | ENDDO |
---|
577 | |
---|
578 | ENDDO |
---|
579 | #if defined( __KKMP ) |
---|
580 | !$OMP END PARALLEL |
---|
581 | #endif |
---|
582 | |
---|
583 | CALL cpu_log( log_point_s(33), 'fft_x_m + tridia', 'stop' ) |
---|
584 | |
---|
585 | #if defined( __parallel ) |
---|
586 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'start' ) |
---|
587 | nwords = (nxr_p-nxl_p+1) * nz * (nyn_p-nys_p+1) |
---|
588 | CALL MPI_ALLTOALL( work2(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
---|
589 | work1(nxl_p,1,nys_p,1), nwords, MPI_REAL, & |
---|
590 | comm2d, istat ) |
---|
591 | CALL cpu_log( log_point_s(32), 'mpi_alltoall', 'stop' ) |
---|
592 | #else |
---|
593 | work1 = work2 |
---|
594 | #endif |
---|
595 | |
---|
596 | CALL cpu_log( log_point_s(7), 'fft_y_m', 'continue' ) |
---|
597 | |
---|
598 | !$OMP PARALLEL PRIVATE (i,iouter,ii,ir,iei,j,k,m,n) |
---|
599 | !$OMP DO |
---|
600 | DO k = 1, nz |
---|
601 | m = nys_a |
---|
602 | DO n = 1, npe_s |
---|
603 | DO j = nys_p, nyn_p |
---|
604 | DO i = nxl_p, nxr_p |
---|
605 | ffty_ar3(m,k,i) = work1(i,k,j,n) |
---|
606 | ENDDO |
---|
607 | m = m+1 |
---|
608 | ENDDO |
---|
609 | ENDDO |
---|
610 | ENDDO |
---|
611 | |
---|
612 | !$OMP DO |
---|
613 | DO i = nxl_p, nxr_p |
---|
614 | CALL fft_y_m( ffty_ar3(:,:,i), ny+3, 'backward' ) |
---|
615 | DO j = nys_a, nyn_a |
---|
616 | DO k = 1, nz |
---|
617 | ar(k,j,i+nxl) = ffty_ar3(j,k,i) |
---|
618 | ENDDO |
---|
619 | ENDDO |
---|
620 | ENDDO |
---|
621 | !$OMP END PARALLEL |
---|
622 | |
---|
623 | CALL cpu_log( log_point_s(7), 'fft_y_m', 'stop' ) |
---|
624 | |
---|
625 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_vec', 'stop' ) |
---|
626 | |
---|
627 | #if defined( __KKMP ) |
---|
628 | DEALLOCATE( tri ) |
---|
629 | #endif |
---|
630 | |
---|
631 | END SUBROUTINE poisfft_hybrid_omp_vec |
---|
632 | |
---|
633 | |
---|
634 | SUBROUTINE poisfft_hybrid_nodes ( ar ) |
---|
635 | |
---|
636 | USE cpulog |
---|
637 | USE interfaces |
---|
638 | |
---|
639 | IMPLICIT NONE |
---|
640 | |
---|
641 | INTEGER, PARAMETER :: istride = 4 ! stride of i loop |
---|
642 | INTEGER :: i, iei, ii, iouter, ir, istat, j, jj, k, m, & |
---|
643 | n, nn, nt, nw1, nw2 |
---|
644 | |
---|
645 | REAL, DIMENSION(1:nz,nys:nyn,nxl:nxr) :: ar |
---|
646 | |
---|
647 | REAL, DIMENSION(0:nx) :: fftx_ar |
---|
648 | REAL, DIMENSION(0:ny,istride) :: ffty_ar |
---|
649 | |
---|
650 | REAL, DIMENSION(0:nx,nz) :: tri_ar |
---|
651 | |
---|
652 | REAL, DIMENSION(nxl_p:nxr_p,nz,tasks_per_logical_node, & |
---|
653 | nodes,nys_p:nyn_p) :: work1,work2 |
---|
654 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
655 | |
---|
656 | |
---|
657 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_nodes', 'start' ) |
---|
658 | |
---|
659 | CALL cpu_log( log_point_s(7), 'fft_y', 'start' ) |
---|
660 | |
---|
661 | ! |
---|
662 | !-- Store grid points to be transformed on a 1d-array, do the fft |
---|
663 | !-- and sample the results on a 4d-array |
---|
664 | DO iouter = nxl_p, nxr_p, istride ! stride loop, better cache |
---|
665 | iei = MIN( iouter+istride-1, nxr_p ) |
---|
666 | DO k = 1, nz |
---|
667 | |
---|
668 | DO i = iouter, iei |
---|
669 | ii = nxl + i |
---|
670 | ir = i - iouter + 1 |
---|
671 | |
---|
672 | DO j = nys_a, nyn_a |
---|
673 | ffty_ar(j,ir) = ar(k,j,ii) |
---|
674 | ENDDO |
---|
675 | |
---|
676 | CALL fft_y( ffty_ar(:,ir), 'forward' ) |
---|
677 | ENDDO |
---|
678 | |
---|
679 | m = nys_a |
---|
680 | DO nn = 1, nodes |
---|
681 | DO nt = 1, tasks_per_logical_node |
---|
682 | DO j = nys_p, nyn_p |
---|
683 | DO i = iouter, iei |
---|
684 | ir = i - iouter + 1 |
---|
685 | work1(i,k,nt,nn,j) = ffty_ar(m,ir) |
---|
686 | ENDDO |
---|
687 | m = m+1 |
---|
688 | ENDDO |
---|
689 | ENDDO |
---|
690 | ENDDO |
---|
691 | |
---|
692 | ENDDO |
---|
693 | ENDDO |
---|
694 | |
---|
695 | CALL cpu_log( log_point_s(7), 'fft_y', 'pause' ) |
---|
696 | |
---|
697 | CALL cpu_log( log_point_s(32), 'alltoall_task', 'start' ) |
---|
698 | nw1 = SIZE( work1, 1 ) * SIZE( work1, 2 ) |
---|
699 | DO nn = 1, nodes |
---|
700 | DO j = nys_p, nyn_p |
---|
701 | #if defined( __parallel ) |
---|
702 | CALL MPI_ALLTOALL( work1(nxl_p,1,1,nn,j), nw1, MPI_REAL, & |
---|
703 | work2(nxl_p,1,1,nn,j), nw1, MPI_REAL, & |
---|
704 | comm_tasks, istat ) |
---|
705 | #endif |
---|
706 | ENDDO |
---|
707 | ENDDO |
---|
708 | CALL cpu_log( log_point_s(32), 'alltoall_task', 'stop' ) |
---|
709 | |
---|
710 | |
---|
711 | DO j = nys_p, nyn_p |
---|
712 | |
---|
713 | CALL cascade( 1, j, nys_p, nyn_p ) |
---|
714 | nw2 = nw1 * SIZE( work1, 3 ) |
---|
715 | CALL cpu_log( log_point_s(37), 'alltoall_node', 'start' ) |
---|
716 | #if defined( __parallel ) |
---|
717 | CALL MPI_ALLTOALL( work2(nxl_p,1,1,1,j), nw2, MPI_REAL, & |
---|
718 | work1(nxl_p,1,1,1,j), nw2, MPI_REAL, & |
---|
719 | comm_nodes, istat ) |
---|
720 | #endif |
---|
721 | CALL cpu_log( log_point_s(37), 'alltoall_node', 'pause' ) |
---|
722 | CALL cascade( 2, j, nys_p, nyn_p ) |
---|
723 | |
---|
724 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'start' ) |
---|
725 | DO k = 1, nz |
---|
726 | |
---|
727 | m = nxl_a |
---|
728 | DO nn = 1, nodes |
---|
729 | DO nt = 1, tasks_per_logical_node |
---|
730 | DO i = nxl_p, nxr_p |
---|
731 | fftx_ar(m) = work1(i,k,nt,nn,j) |
---|
732 | m = m+1 |
---|
733 | ENDDO |
---|
734 | ENDDO |
---|
735 | ENDDO |
---|
736 | |
---|
737 | CALL fft_x( fftx_ar, 'forward' ) |
---|
738 | |
---|
739 | DO i = nxl_a, nxr_a |
---|
740 | tri_ar(i,k) = fftx_ar(i) |
---|
741 | ENDDO |
---|
742 | |
---|
743 | ENDDO |
---|
744 | |
---|
745 | jj = myid * (nyn_p-nys_p+1) + j |
---|
746 | CALL tridia_hybrid( jj, tri_ar, tri(:,:,:) ) |
---|
747 | |
---|
748 | DO k = 1, nz |
---|
749 | DO i = nxl_a, nxr_a |
---|
750 | fftx_ar(i) = tri_ar(i,k) |
---|
751 | ENDDO |
---|
752 | |
---|
753 | CALL fft_x( fftx_ar, 'backward' ) |
---|
754 | |
---|
755 | m = nxl_a |
---|
756 | DO nn = 1, nodes |
---|
757 | DO nt = 1, tasks_per_logical_node |
---|
758 | DO i = nxl_p, nxr_p |
---|
759 | work1(i,k,nt,nn,j) = fftx_ar(m) |
---|
760 | m = m+1 |
---|
761 | ENDDO |
---|
762 | ENDDO |
---|
763 | ENDDO |
---|
764 | ENDDO |
---|
765 | |
---|
766 | CALL cpu_log( log_point_s(33), 'fft_x + tridia', 'stop' ) |
---|
767 | nw2 = nw1 * SIZE( work1, 3 ) |
---|
768 | CALL cpu_log( log_point_s(37), 'alltoall_node', 'continue' ) |
---|
769 | #if defined( __parallel ) |
---|
770 | CALL MPI_ALLTOALL( work1(nxl_p,1,1,1,j), nw2, MPI_REAL, & |
---|
771 | work2(nxl_p,1,1,1,j), nw2, MPI_REAL, & |
---|
772 | comm_nodes, istat ) |
---|
773 | #endif |
---|
774 | CALL cpu_log( log_point_s(37), 'alltoall_node', 'stop' ) |
---|
775 | |
---|
776 | ENDDO |
---|
777 | |
---|
778 | CALL cpu_log( log_point_s(32), 'alltoall_task', 'start' ) |
---|
779 | DO nn = 1, nodes |
---|
780 | DO j = nys_p, nyn_p |
---|
781 | #if defined( __parallel ) |
---|
782 | CALL MPI_ALLTOALL( work2(nxl_p,1,1,nn,j), nw1, MPI_REAL, & |
---|
783 | work1(nxl_p,1,1,nn,j), nw1, MPI_REAL, & |
---|
784 | comm_tasks, istat ) |
---|
785 | #endif |
---|
786 | ENDDO |
---|
787 | ENDDO |
---|
788 | CALL cpu_log( log_point_s(32), 'alltoall_task', 'stop' ) |
---|
789 | |
---|
790 | CALL cpu_log( log_point_s(7), 'fft_y', 'continue' ) |
---|
791 | |
---|
792 | DO iouter = nxl_p, nxr_p, istride |
---|
793 | iei = MIN( iouter+istride-1, nxr_p ) |
---|
794 | DO k = 1, nz |
---|
795 | |
---|
796 | m = nys_a |
---|
797 | DO nn = 1, nodes |
---|
798 | DO nt = 1, tasks_per_logical_node |
---|
799 | DO j = nys_p, nyn_p |
---|
800 | DO i = iouter, iei |
---|
801 | ir = i - iouter + 1 |
---|
802 | ffty_ar(m,ir) = work1(i,k,nt,nn,j) |
---|
803 | ENDDO |
---|
804 | m = m+1 |
---|
805 | ENDDO |
---|
806 | ENDDO |
---|
807 | ENDDO |
---|
808 | |
---|
809 | DO i = iouter, iei |
---|
810 | ii = nxl + i |
---|
811 | ir = i - iouter + 1 |
---|
812 | CALL fft_y( ffty_ar(:,ir), 'backward' ) |
---|
813 | |
---|
814 | DO j = nys_a, nyn_a |
---|
815 | ar(k,j,ii) = ffty_ar(j,ir) |
---|
816 | ENDDO |
---|
817 | ENDDO |
---|
818 | |
---|
819 | ENDDO |
---|
820 | ENDDO |
---|
821 | |
---|
822 | CALL cpu_log( log_point_s(7), 'fft_y', 'stop' ) |
---|
823 | |
---|
824 | CALL cpu_log( log_point_s(30), 'poisfft_hybrid_nodes', 'stop' ) |
---|
825 | |
---|
826 | END SUBROUTINE poisfft_hybrid_nodes |
---|
827 | |
---|
828 | |
---|
829 | |
---|
830 | SUBROUTINE tridia_hybrid( j, ar, tri ) |
---|
831 | |
---|
832 | USE arrays_3d |
---|
833 | USE control_parameters |
---|
834 | USE grid_variables |
---|
835 | |
---|
836 | IMPLICIT NONE |
---|
837 | |
---|
838 | INTEGER :: i, j, k, nnyh |
---|
839 | REAL, DIMENSION(0:nx,nz) :: ar |
---|
840 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
---|
841 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
---|
842 | |
---|
843 | nnyh = (ny+1) / 2 |
---|
844 | |
---|
845 | tri = 0.0 |
---|
846 | ! |
---|
847 | !-- Define constant elements of the tridiagonal matrix. |
---|
848 | DO k = 0, nz-1 |
---|
849 | DO i = 0,nx |
---|
850 | tri(2,i,k) = ddzu_pres(k+1) * ddzw(k+1) |
---|
851 | tri(3,i,k) = ddzu_pres(k+2) * ddzw(k+1) |
---|
852 | ENDDO |
---|
853 | ENDDO |
---|
854 | |
---|
855 | IF ( j <= nnyh ) THEN |
---|
856 | CALL maketri_hybrid( j ) |
---|
857 | ELSE |
---|
858 | CALL maketri_hybrid( ny+1-j) |
---|
859 | ENDIF |
---|
860 | CALL zerleg_hybrid |
---|
861 | CALL substi_hybrid( ar, tri ) |
---|
862 | |
---|
863 | CONTAINS |
---|
864 | |
---|
865 | SUBROUTINE maketri_hybrid( j ) |
---|
866 | |
---|
867 | !----------------------------------------------------------------------! |
---|
868 | ! maketri ! |
---|
869 | ! ! |
---|
870 | ! computes the i- and j-dependent component of the matrix ! |
---|
871 | !----------------------------------------------------------------------! |
---|
872 | |
---|
873 | USE constants |
---|
874 | |
---|
875 | IMPLICIT NONE |
---|
876 | |
---|
877 | INTEGER :: i, j, k, nnxh |
---|
878 | REAL :: a, c |
---|
879 | |
---|
880 | REAL, DIMENSION(0:nx) :: l |
---|
881 | |
---|
882 | |
---|
883 | nnxh = (nx+1) / 2 |
---|
884 | ! |
---|
885 | !-- Provide the tridiagonal matrix for solution of the Poisson equation |
---|
886 | !-- in Fourier space. The coefficients are computed following the method |
---|
887 | !-- of Schmidt et al. (DFVLR-Mitteilung 84-15) --> departs from Stephan |
---|
888 | !-- Siano's original version. |
---|
889 | DO i = 0,nx |
---|
890 | IF ( i >= 0 .AND. i < nnxh ) THEN |
---|
891 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * i ) / & |
---|
892 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
---|
893 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
894 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
---|
895 | ELSEIF ( i == nnxh ) THEN |
---|
896 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
897 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
---|
898 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
899 | FLOAT(ny+1) ) ) / ( dy * dy ) |
---|
900 | ELSE |
---|
901 | l(i) = 2.0 * ( 1.0 - COS( ( 2.0 * pi * ( nx+1-i ) ) / & |
---|
902 | FLOAT( nx+1 ) ) ) / ( dx * dx ) + & |
---|
903 | 2.0 * ( 1.0 - COS( ( 2.0 * pi * j ) / & |
---|
904 | FLOAT( ny+1 ) ) ) / ( dy * dy ) |
---|
905 | ENDIF |
---|
906 | ENDDO |
---|
907 | |
---|
908 | DO k = 0,nz-1 |
---|
909 | DO i = 0, nx |
---|
910 | a = -1.0 * ddzu_pres(k+2) * ddzw(k+1) |
---|
911 | c = -1.0 * ddzu_pres(k+1) * ddzw(k+1) |
---|
912 | tri(1,i,k) = a + c - l(i) |
---|
913 | ENDDO |
---|
914 | ENDDO |
---|
915 | IF ( ibc_p_b == 1 .OR. ibc_p_b == 2 ) THEN |
---|
916 | DO i = 0,nx |
---|
917 | tri(1,i,0) = tri(1,i,0) + tri(2,i,0) |
---|
918 | ENDDO |
---|
919 | ENDIF |
---|
920 | IF ( ibc_p_t == 1 ) THEN |
---|
921 | DO i = 0,nx |
---|
922 | tri(1,i,nz-1) = tri(1,i,nz-1) + tri(3,i,nz-1) |
---|
923 | ENDDO |
---|
924 | ENDIF |
---|
925 | |
---|
926 | END SUBROUTINE maketri_hybrid |
---|
927 | |
---|
928 | |
---|
929 | SUBROUTINE zerleg_hybrid |
---|
930 | |
---|
931 | !----------------------------------------------------------------------! |
---|
932 | ! zerleg ! |
---|
933 | ! ! |
---|
934 | ! Splitting of the tridiagonal matrix (Thomas algorithm) ! |
---|
935 | !----------------------------------------------------------------------! |
---|
936 | |
---|
937 | USE indices |
---|
938 | |
---|
939 | IMPLICIT NONE |
---|
940 | |
---|
941 | INTEGER :: i, k |
---|
942 | |
---|
943 | ! |
---|
944 | !-- Splitting |
---|
945 | DO i = 0, nx |
---|
946 | tri(4,i,0) = tri(1,i,0) |
---|
947 | ENDDO |
---|
948 | DO k = 1, nz-1 |
---|
949 | DO i = 0,nx |
---|
950 | tri(5,i,k) = tri(2,i,k) / tri(4,i,k-1) |
---|
951 | tri(4,i,k) = tri(1,i,k) - tri(3,i,k-1) * tri(5,i,k) |
---|
952 | ENDDO |
---|
953 | ENDDO |
---|
954 | |
---|
955 | END SUBROUTINE zerleg_hybrid |
---|
956 | |
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957 | SUBROUTINE substi_hybrid( ar, tri ) |
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958 | |
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959 | !----------------------------------------------------------------------! |
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960 | ! substi ! |
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961 | ! ! |
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962 | ! Substitution (Forward and Backward) (Thomas algorithm) ! |
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963 | !----------------------------------------------------------------------! |
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964 | |
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965 | IMPLICIT NONE |
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966 | |
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967 | INTEGER :: i, j, k |
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968 | REAL, DIMENSION(0:nx,nz) :: ar |
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969 | REAL, DIMENSION(0:nx,0:nz-1) :: ar1 |
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970 | REAL, DIMENSION(5,0:nx,0:nz-1) :: tri |
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971 | |
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972 | ! |
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973 | !-- Forward substitution |
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974 | DO i = 0, nx |
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975 | ar1(i,0) = ar(i,1) |
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976 | ENDDO |
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977 | DO k = 1, nz - 1 |
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978 | DO i = 0,nx |
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979 | ar1(i,k) = ar(i,k+1) - tri(5,i,k) * ar1(i,k-1) |
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980 | ENDDO |
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981 | ENDDO |
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982 | |
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983 | ! |
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984 | !-- Backward substitution |
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985 | DO i = 0,nx |
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986 | ar(i,nz) = ar1(i,nz-1) / tri(4,i,nz-1) |
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987 | ENDDO |
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988 | DO k = nz-2, 0, -1 |
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989 | DO i = 0,nx |
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990 | ar(i,k+1) = ( ar1(i,k) - tri(3,i,k) * ar(i,k+2) ) & |
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991 | / tri(4,i,k) |
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992 | ENDDO |
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993 | ENDDO |
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994 | |
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995 | END SUBROUTINE substi_hybrid |
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996 | |
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997 | END SUBROUTINE tridia_hybrid |
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998 | |
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999 | |
---|
1000 | SUBROUTINE cascade( loca, j, nys_p, nyn_p ) |
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1001 | |
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1002 | USE cpulog |
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1003 | |
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1004 | IMPLICIT NONE |
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1005 | |
---|
1006 | INTEGER :: ier, j, loca, nyn_p, nys_p, req, reqa(1) |
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1007 | INTEGER, SAVE :: tag = 10 |
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1008 | #if defined( __parallel ) |
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1009 | INTEGER, DIMENSION(MPI_STATUS_SIZE) :: stat |
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1010 | INTEGER, DIMENSION(MPI_STATUS_SIZE,1) :: stata |
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1011 | #endif |
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1012 | |
---|
1013 | REAL :: buf, buf1 |
---|
1014 | |
---|
1015 | |
---|
1016 | buf = 1.0 |
---|
1017 | buf1 = 1.1 |
---|
1018 | IF ( me_node == 0 ) THEN ! first node only |
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1019 | |
---|
1020 | SELECT CASE ( loca ) |
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1021 | |
---|
1022 | CASE ( 1 ) ! before alltoall |
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1023 | |
---|
1024 | IF( me_task > 0 ) THEN ! first task does not wait |
---|
1025 | #if defined( __parallel ) |
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1026 | CALL MPI_SENDRECV( buf, 1, MPI_REAL, me_task-1, 0, & |
---|
1027 | buf1, 1, MPI_REAL, me_task-1, 0, & |
---|
1028 | comm_tasks, stat, ierr ) |
---|
1029 | #endif |
---|
1030 | ELSEIF ( j > nys_p ) THEN |
---|
1031 | req = 0 |
---|
1032 | tag = MOD( tag-10, 10 ) + 10 |
---|
1033 | #if defined( __parallel ) |
---|
1034 | CALL MPI_IRECV( buf, 1, MPI_REAL, tasks_per_logical_node-1,& |
---|
1035 | tag, comm_tasks, req, ierr ) |
---|
1036 | reqa = req |
---|
1037 | CALL MPI_WAITALL( 1, reqa, stata, ierr ) |
---|
1038 | #endif |
---|
1039 | ENDIF |
---|
1040 | |
---|
1041 | CASE ( 2 ) ! after alltoall |
---|
1042 | |
---|
1043 | IF ( me_task < tasks_per_logical_node-1 ) THEN ! last task |
---|
1044 | #if defined( __parallel ) |
---|
1045 | CALL MPI_SENDRECV( buf, 1, MPI_REAL, me_task+1, 0, & |
---|
1046 | buf1, 1, MPI_REAL, me_task+1, 0, & |
---|
1047 | comm_tasks, stat, ierr) |
---|
1048 | #endif |
---|
1049 | ELSEIF ( j < nyn_p ) THEN |
---|
1050 | req = 0 |
---|
1051 | tag = MOD( tag-10, 10 ) + 10 |
---|
1052 | #if defined( __parallel ) |
---|
1053 | CALL MPI_ISEND( buf, 1, MPI_REAL, 0, tag, comm_tasks, req, & |
---|
1054 | ierr ) |
---|
1055 | #endif |
---|
1056 | ENDIF |
---|
1057 | |
---|
1058 | END SELECT |
---|
1059 | |
---|
1060 | ENDIF |
---|
1061 | |
---|
1062 | END SUBROUTINE cascade |
---|
1063 | |
---|
1064 | END MODULE poisfft_hybrid_mod |
---|