1 | !> @file temperton_fft_mod.f90 |
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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 | ! |
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7 | ! |
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8 | ! Former revisions: |
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9 | ! ----------------- |
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10 | ! $Id: temperton_fft_mod.f90 4180 2019-08-21 14:37:54Z scharf $ |
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11 | ! GOTO statements replaced, file re-formatted corresponding to coding standards |
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12 | ! |
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13 | ! |
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14 | ! Description: |
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15 | ! ------------ |
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16 | !> Fast Fourier transformation developed by Clive Temperton, ECMWF. |
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17 | !------------------------------------------------------------------------------! |
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18 | MODULE temperton_fft |
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19 | |
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20 | USE kinds |
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21 | |
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22 | IMPLICIT NONE |
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23 | |
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24 | PRIVATE |
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25 | |
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26 | PUBLIC set99, fft991cy |
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27 | |
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28 | INTEGER(iwp), PARAMETER :: nfft = 32 !< maximum length of calls to *fft |
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29 | INTEGER(iwp), PARAMETER :: nout = 6 !< standard output stream |
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30 | |
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31 | CONTAINS |
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32 | |
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33 | !------------------------------------------------------------------------------! |
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34 | ! Description: |
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35 | ! ------------ |
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36 | !> Calls Fortran-versions of fft's. |
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37 | !> |
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38 | !> Method: |
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39 | !> |
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40 | !> Subroutine 'fft991cy' - multiple fast real periodic transform |
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41 | !> supersedes previous routine 'fft991cy'. |
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42 | !> |
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43 | !> Real transform of length n performed by removing redundant |
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44 | !> operations from complex transform of length n. |
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45 | !> |
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46 | !> a is the array containing input & output data. |
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47 | !> work is an area of size (n+1)*min(lot,nfft). |
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48 | !> trigs is a previously prepared list of trig function values. |
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49 | !> ifax is a previously prepared list of factors of n. |
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50 | !> inc is the increment within each data 'vector' |
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51 | !> (e.g. inc=1 for consecutively stored data). |
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52 | !> jump is the increment between the start of each data vector. |
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53 | !> n is the length of the data vectors. |
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54 | !> lot is the number of data vectors. |
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55 | !> isign = +1 for transform from spectral to gridpoint |
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56 | !> = -1 for transform from gridpoint to spectral. |
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57 | !> |
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58 | !> ordering of coefficients: |
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59 | !> a(0),b(0),a(1),b(1),a(2),b(2),.,a(n/2),b(n/2) |
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60 | !> where b(0)=b(n/2)=0; (n+2) locations required. |
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61 | !> |
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62 | !> ordering of data: |
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63 | !> x(0),x(1),x(2),.,x(n-1), 0 , 0 ; (n+2) locations required. |
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64 | !> |
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65 | !> Vectorization is achieved on cray by doing the transforms |
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66 | !> in parallel. |
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67 | !> |
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68 | !> n must be composed of factors 2,3 & 5 but does not have to be even. |
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69 | !> |
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70 | !> definition of transforms: |
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71 | !> |
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72 | !> isign=+1: x(j)=sum(k=0,.,n-1)(c(k)*exp(2*i*j*k*pi/n)) |
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73 | !> where c(k)=a(k)+i*b(k) and c(n-k)=a(k)-i*b(k) |
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74 | !> |
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75 | !> isign=-1: a(k)=(1/n)*sum(j=0,.,n-1)(x(j)*cos(2*j*k*pi/n)) |
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76 | !> b(k)=-(1/n)*sum(j=0,.,n-1)(x(j)*sin(2*j*k*pi/n)) |
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77 | !> |
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78 | !> calls fortran-versions of fft's !!! |
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79 | !> dimension a(n),work(n),trigs(n),ifax(1) |
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80 | !------------------------------------------------------------------------------! |
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81 | SUBROUTINE fft991cy( a, work, trigs, ifax, inc, jump, n, lot, isign ) |
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82 | |
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83 | USE kinds |
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84 | |
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85 | IMPLICIT NONE |
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86 | |
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87 | INTEGER(iwp) :: inc !< |
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88 | INTEGER(iwp) :: isign !< |
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89 | INTEGER(iwp) :: jump !< |
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90 | INTEGER(iwp) :: lot !< |
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91 | INTEGER(iwp) :: n !< |
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92 | |
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93 | REAL(wp) :: a(*) !< |
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94 | REAL(wp) :: trigs(*) !< |
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95 | REAL(wp) :: work(*) !< |
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96 | INTEGER(iwp) :: ifax(*) !< |
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97 | |
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98 | INTEGER(iwp) :: i !< |
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99 | INTEGER(iwp) :: ia !< |
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100 | INTEGER(iwp) :: ibase !< |
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101 | INTEGER(iwp) :: ierr !< |
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102 | INTEGER(iwp) :: ifac !< |
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103 | INTEGER(iwp) :: igo !< |
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104 | INTEGER(iwp) :: ii !< |
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105 | INTEGER(iwp) :: istart !< |
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106 | INTEGER(iwp) :: ix !< |
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107 | INTEGER(iwp) :: iz !< |
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108 | INTEGER(iwp) :: j !< |
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109 | INTEGER(iwp) :: jbase !< |
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110 | INTEGER(iwp) :: jj !< |
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111 | INTEGER(iwp) :: k !< |
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112 | INTEGER(iwp) :: la !< |
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113 | INTEGER(iwp) :: nb !< |
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114 | INTEGER(iwp) :: nblox !< |
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115 | INTEGER(iwp) :: nfax !< |
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116 | INTEGER(iwp) :: nvex !< |
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117 | INTEGER(iwp) :: nx !< |
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118 | |
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119 | |
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120 | IF ( ifax(10) /= n ) CALL set99( trigs, ifax, n ) |
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121 | nfax = ifax(1) |
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122 | nx = n + 1 |
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123 | IF ( MOD(n,2) == 1 ) nx = n |
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124 | nblox = 1 + (lot-1) / nfft |
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125 | nvex = lot - (nblox-1) * nfft |
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126 | |
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127 | |
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128 | IF ( isign == 1 ) THEN |
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129 | ! |
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130 | !-- Backward fft: spectral to gridpoint transform |
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131 | |
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132 | istart = 1 |
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133 | DO nb = 1, nblox |
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134 | |
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135 | ia = istart |
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136 | i = istart |
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137 | !DIR$ IVDEP |
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138 | !CDIR NODEP |
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139 | !OCL NOVREC |
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140 | DO j = 1, nvex |
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141 | a(i+inc) = 0.5_wp * a(i) |
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142 | i = i + jump |
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143 | ENDDO |
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144 | IF ( MOD(n,2) /= 1 ) THEN |
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145 | i = istart + n * inc |
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146 | DO j = 1, nvex |
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147 | a(i) = 0.5_wp * a(i) |
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148 | i = i + jump |
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149 | ENDDO |
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150 | ENDIF |
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151 | ia = istart + inc |
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152 | la = 1 |
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153 | igo = + 1 |
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154 | |
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155 | DO k = 1, nfax |
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156 | |
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157 | ifac = ifax(k+1) |
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158 | ierr = -1 |
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159 | IF ( igo /= -1 ) THEN |
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160 | CALL rpassm( a(ia), a(ia+la*inc), work(1), work(ifac*la+1), trigs, inc, 1, jump, & |
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161 | nx, nvex, n, ifac, la, ierr ) |
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162 | ELSE |
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163 | CALL rpassm( work(1), work(la+1), a(ia), a(ia+ifac*la*inc), trigs, 1, inc, nx, & |
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164 | jump, nvex, n, ifac, la, ierr ) |
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165 | ENDIF |
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166 | ! |
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167 | !-- Following messages shouldn't appear in PALM applications |
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168 | IF ( ierr /= 0 ) THEN |
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169 | SELECT CASE (ierr) |
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170 | CASE (:-1) |
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171 | WRITE (nout,'(A,I5,A)') ' Vector length =',nvex,', greater than nfft' |
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172 | CASE (0) |
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173 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
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174 | CASE (1:) |
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175 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
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176 | END SELECT |
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177 | RETURN |
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178 | ENDIF |
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179 | |
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180 | la = ifac * la |
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181 | igo = -igo |
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182 | ia = istart |
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183 | |
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184 | ENDDO |
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185 | ! |
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186 | !-- If necessary, copy results back to a |
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187 | IF ( MOD(nfax,2) /= 0 ) THEN |
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188 | ibase = 1 |
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189 | jbase = ia |
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190 | DO jj = 1, nvex |
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191 | i = ibase |
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192 | j = jbase |
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193 | DO ii = 1, n |
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194 | a(j) = work(i) |
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195 | i = i + 1 |
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196 | j = j + inc |
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197 | ENDDO |
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198 | ibase = ibase + nx |
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199 | jbase = jbase + jump |
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200 | ENDDO |
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201 | ENDIF |
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202 | ! |
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203 | !-- Fill in zeros at end |
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204 | ix = istart + n*inc |
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205 | !DIR$ IVDEP |
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206 | !CDIR NODEP |
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207 | !OCL NOVREC |
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208 | DO j = 1, nvex |
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209 | a(ix) = 0.0_wp |
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210 | a(ix+inc) = 0.0_wp |
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211 | ix = ix + jump |
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212 | ENDDO |
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213 | istart = istart + nvex*jump |
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214 | nvex = nfft |
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215 | |
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216 | ENDDO |
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217 | |
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218 | ELSEIF ( isign == -1 ) THEN |
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219 | ! |
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220 | !-- Forward fft: gridpoint to spectral transform |
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221 | istart = 1 |
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222 | DO nb = 1, nblox |
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223 | ia = istart |
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224 | la = n |
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225 | igo = + 1 |
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226 | |
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227 | DO k = 1, nfax |
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228 | |
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229 | ifac = ifax(nfax+2-k) |
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230 | la = la / ifac |
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231 | ierr = -1 |
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232 | IF ( igo /= -1 ) THEN |
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233 | CALL qpassm( a(ia), a(ia+ifac*la*inc), work(1), work(la+1), trigs, inc, 1, jump, & |
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234 | nx, nvex, n, ifac, la, ierr ) |
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235 | ELSE |
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236 | CALL qpassm( work(1), work(ifac*la+1), a(ia), a(ia+la*inc), trigs, 1, inc, nx, & |
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237 | jump, nvex, n, ifac, la, ierr ) |
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238 | ENDIF |
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239 | ! |
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240 | !-- Following messages shouldn't appear in PALM applications |
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241 | IF ( ierr /= 0 ) THEN |
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242 | SELECT CASE (ierr) |
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243 | CASE (:-1) |
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244 | WRITE (nout,'(A,I5,A)') ' Vector length =',nvex,', greater than nfft' |
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245 | CASE (0) |
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246 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', not catered for' |
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247 | CASE (1:) |
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248 | WRITE (nout,'(A,I3,A)') ' Factor =',ifac,', only catered for if la*ifac=n' |
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249 | END SELECT |
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250 | RETURN |
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251 | ENDIF |
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252 | |
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253 | igo = -igo |
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254 | ia = istart + inc |
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255 | |
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256 | ENDDO |
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257 | ! |
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258 | !-- If necessary, copy results back to a |
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259 | IF ( MOD(nfax,2) /= 0 ) THEN |
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260 | ibase = 1 |
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261 | jbase = ia |
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262 | DO jj = 1, nvex |
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263 | i = ibase |
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264 | j = jbase |
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265 | DO ii = 1, n |
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266 | a(j) = work(i) |
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267 | i = i + 1 |
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268 | j = j + inc |
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269 | ENDDO |
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270 | ibase = ibase + nx |
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271 | jbase = jbase + jump |
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272 | ENDDO |
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273 | ENDIF |
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274 | ! |
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275 | !-- Shift a(0) and fill in zero imag parts |
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276 | ix = istart |
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277 | !DIR$ IVDEP |
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278 | !CDIR NODEP |
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279 | !OCL NOVREC |
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280 | DO j = 1, nvex |
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281 | a(ix) = a(ix+inc) |
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282 | a(ix+inc) = 0.0_wp |
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283 | ix = ix + jump |
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284 | ENDDO |
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285 | IF ( MOD(n,2) /= 1 ) THEN |
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286 | iz = istart + (n+1) * inc |
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287 | DO j = 1, nvex |
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288 | a(iz) = 0.0_wp |
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289 | iz = iz + jump |
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290 | ENDDO |
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291 | ENDIF |
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292 | istart = istart + nvex * jump |
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293 | nvex = nfft |
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294 | |
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295 | ENDDO |
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296 | |
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297 | ENDIF |
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298 | |
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299 | END SUBROUTINE fft991cy |
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300 | |
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301 | !------------------------------------------------------------------------------! |
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302 | ! Description: |
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303 | ! ------------ |
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304 | !> Performs one pass through data as part of |
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305 | !> multiple real fft (fourier analysis) routine. |
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306 | !> |
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307 | !> Method: |
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308 | !> |
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309 | !> a is first real input vector |
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310 | !> equivalence b(1) with a(ifac*la*inc1+1) |
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311 | !> c is first real output vector |
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312 | !> equivalence d(1) with c(la*inc2+1) |
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313 | !> trigs is a precalculated list of sines & cosines |
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314 | !> inc1 is the addressing increment for a |
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315 | !> inc2 is the addressing increment for c |
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316 | !> inc3 is the increment between input vectors a |
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317 | !> inc4 is the increment between output vectors c |
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318 | !> lot is the number of vectors |
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319 | !> n is the length of the vectors |
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320 | !> ifac is the current factor of n |
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321 | !> la = n/(product of factors used so far) |
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322 | !> ierr is an error indicator: |
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323 | !> 0 - pass completed without error |
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324 | !> 1 - lot greater than nfft |
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325 | !> 2 - ifac not catered for |
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326 | !> 3 - ifac only catered for if la=n/ifac |
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327 | !------------------------------------------------------------------------------! |
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328 | SUBROUTINE qpassm( a, b, c, d, trigs, inc1, inc2, inc3, inc4, lot, n, ifac, la, ierr ) |
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329 | |
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330 | USE kinds |
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331 | |
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332 | IMPLICIT NONE |
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333 | |
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334 | INTEGER(iwp) :: ierr !< |
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335 | INTEGER(iwp) :: ifac !< |
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336 | INTEGER(iwp) :: inc1 !< |
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337 | INTEGER(iwp) :: inc2 !< |
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338 | INTEGER(iwp) :: inc3 !< |
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339 | INTEGER(iwp) :: inc4 !< |
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340 | INTEGER(iwp) :: la !< |
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341 | INTEGER(iwp) :: lot !< |
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342 | INTEGER(iwp) :: n !< |
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343 | |
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344 | ! |
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345 | !-- Arrays are dimensioned with n |
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346 | REAL(wp) :: a(*) !< |
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347 | REAL(wp) :: b(*) !< |
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348 | REAL(wp) :: c(*) !< |
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349 | REAL(wp) :: d(*) !< |
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350 | REAL(wp) :: trigs(*) !< |
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351 | |
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352 | REAL(wp) :: a0 !< |
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353 | REAL(wp) :: a1 !< |
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354 | REAL(wp) :: a10 !< |
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355 | REAL(wp) :: a11 !< |
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356 | REAL(wp) :: a2 !< |
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357 | REAL(wp) :: a20 !< |
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358 | REAL(wp) :: a21 !< |
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359 | REAL(wp) :: a3 !< |
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360 | REAL(wp) :: a4 !< |
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361 | REAL(wp) :: a5 !< |
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362 | REAL(wp) :: a6 !< |
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363 | REAL(wp) :: b0 !< |
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364 | REAL(wp) :: b1 !< |
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365 | REAL(wp) :: b10 !< |
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366 | REAL(wp) :: b11 !< |
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367 | REAL(wp) :: b2 !< |
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368 | REAL(wp) :: b20 !< |
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369 | REAL(wp) :: b21 !< |
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370 | REAL(wp) :: b3 !< |
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371 | REAL(wp) :: b4 !< |
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372 | REAL(wp) :: b5 !< |
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373 | REAL(wp) :: b6 !< |
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374 | REAL(wp) :: c1 !< |
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375 | REAL(wp) :: c2 !< |
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376 | REAL(wp) :: c3 !< |
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377 | REAL(wp) :: c4 !< |
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378 | REAL(wp) :: c5 !< |
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379 | REAL(wp) :: qrt5 !< |
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380 | REAL(wp) :: s1 !< |
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381 | REAL(wp) :: s2 !< |
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382 | REAL(wp) :: s3 !< |
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383 | REAL(wp) :: s4 !< |
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384 | REAL(wp) :: s5 !< |
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385 | REAL(wp) :: sin36 !< |
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386 | REAL(wp) :: sin45 !< |
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387 | REAL(wp) :: sin60 !< |
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388 | REAL(wp) :: sin72 !< |
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389 | REAL(wp) :: z !< |
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390 | REAL(wp) :: zqrt5 !< |
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391 | REAL(wp) :: zsin36 !< |
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392 | REAL(wp) :: zsin45 !< |
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393 | REAL(wp) :: zsin60 !< |
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394 | REAL(wp) :: zsin72 !< |
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395 | |
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396 | INTEGER(iwp) :: i !< |
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397 | INTEGER(iwp) :: ia !< |
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398 | INTEGER(iwp) :: ib !< |
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399 | INTEGER(iwp) :: ibase !< |
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400 | INTEGER(iwp) :: ic !< |
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401 | INTEGER(iwp) :: id !< |
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402 | INTEGER(iwp) :: ie !< |
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403 | INTEGER(iwp) :: if !< |
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404 | INTEGER(iwp) :: ig !< |
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405 | INTEGER(iwp) :: igo !< |
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406 | INTEGER(iwp) :: ih !< |
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407 | INTEGER(iwp) :: iink !< |
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408 | INTEGER(iwp) :: ijk !< |
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409 | INTEGER(iwp) :: ijump !< |
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410 | INTEGER(iwp) :: j !< |
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411 | INTEGER(iwp) :: ja !< |
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412 | INTEGER(iwp) :: jb !< |
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413 | INTEGER(iwp) :: jbase !< |
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414 | INTEGER(iwp) :: jc !< |
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415 | INTEGER(iwp) :: jd !< |
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416 | INTEGER(iwp) :: je !< |
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417 | INTEGER(iwp) :: jf !< |
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418 | INTEGER(iwp) :: jink !< |
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419 | INTEGER(iwp) :: k !< |
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420 | INTEGER(iwp) :: kb !< |
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421 | INTEGER(iwp) :: kc !< |
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422 | INTEGER(iwp) :: kd !< |
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423 | INTEGER(iwp) :: ke !< |
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424 | INTEGER(iwp) :: kf !< |
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425 | INTEGER(iwp) :: kstop !< |
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426 | INTEGER(iwp) :: l !< |
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427 | INTEGER(iwp) :: m !< |
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428 | |
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429 | |
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430 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
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431 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
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432 | |
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433 | |
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434 | ierr = 0 |
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435 | |
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436 | IF ( lot > nfft ) THEN |
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437 | ierr = 1 |
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438 | RETURN |
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439 | ENDIF |
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440 | |
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441 | m = n / ifac |
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442 | iink = la * inc1 |
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443 | jink = la * inc2 |
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444 | ijump = (ifac-1) * iink |
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445 | kstop = ( n-ifac ) / ( 2*ifac ) |
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446 | |
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447 | ibase = 0 |
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448 | jbase = 0 |
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449 | igo = ifac - 1 |
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450 | IF ( igo == 7 ) igo = 6 |
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451 | |
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452 | IF (igo < 1 .OR. igo > 6 ) THEN |
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453 | ierr = 2 |
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454 | RETURN |
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455 | ENDIF |
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456 | |
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457 | |
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458 | SELECT CASE ( igo ) |
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459 | |
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460 | ! |
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461 | !-- Coding for factor 2 |
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462 | CASE ( 1 ) |
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463 | ia = 1 |
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464 | ib = ia + iink |
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465 | ja = 1 |
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466 | jb = ja + (2*m-la) * inc2 |
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467 | |
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468 | IF ( la /= m ) THEN |
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469 | |
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470 | DO l = 1, la |
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471 | i = ibase |
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472 | j = jbase |
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473 | !DIR$ IVDEP |
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474 | !CDIR NODEP |
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475 | !OCL NOVREC |
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476 | DO ijk = 1, lot |
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477 | c(ja+j) = a(ia+i) + a(ib+i) |
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478 | c(jb+j) = a(ia+i) - a(ib+i) |
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479 | i = i + inc3 |
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480 | j = j + inc4 |
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481 | ENDDO |
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482 | ibase = ibase + inc1 |
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483 | jbase = jbase + inc2 |
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484 | ENDDO |
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485 | |
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486 | ja = ja + jink |
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487 | jink = 2 * jink |
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488 | jb = jb - jink |
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489 | ibase = ibase + ijump |
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490 | ijump = 2 * ijump + iink |
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491 | |
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492 | IF ( ja /= jb ) THEN |
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493 | |
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494 | DO k = la, kstop, la |
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495 | kb = k + k |
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496 | c1 = trigs(kb+1) |
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497 | s1 = trigs(kb+2) |
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498 | jbase = 0 |
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499 | DO l = 1, la |
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500 | i = ibase |
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501 | j = jbase |
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502 | !DIR$ IVDEP |
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503 | !CDIR NODEP |
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504 | !OCL NOVREC |
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505 | DO ijk = 1, lot |
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506 | c(ja+j) = a(ia+i) + (c1*a(ib+i)+s1*b(ib+i)) |
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507 | c(jb+j) = a(ia+i) - (c1*a(ib+i)+s1*b(ib+i)) |
---|
508 | d(ja+j) = (c1*b(ib+i)-s1*a(ib+i)) + b(ia+i) |
---|
509 | d(jb+j) = (c1*b(ib+i)-s1*a(ib+i)) - b(ia+i) |
---|
510 | i = i + inc3 |
---|
511 | j = j + inc4 |
---|
512 | ENDDO |
---|
513 | ibase = ibase + inc1 |
---|
514 | jbase = jbase + inc2 |
---|
515 | ENDDO |
---|
516 | |
---|
517 | ibase = ibase + ijump |
---|
518 | ja = ja + jink |
---|
519 | jb = jb - jink |
---|
520 | ENDDO |
---|
521 | |
---|
522 | IF ( ja > jb ) RETURN |
---|
523 | |
---|
524 | ENDIF |
---|
525 | |
---|
526 | jbase = 0 |
---|
527 | DO l = 1, la |
---|
528 | i = ibase |
---|
529 | j = jbase |
---|
530 | !DIR$ IVDEP |
---|
531 | !CDIR NODEP |
---|
532 | !OCL NOVREC |
---|
533 | DO ijk = 1, lot |
---|
534 | c(ja+j) = a(ia+i) |
---|
535 | d(ja+j) = -a(ib+i) |
---|
536 | i = i + inc3 |
---|
537 | j = j + inc4 |
---|
538 | |
---|
539 | ENDDO |
---|
540 | ibase = ibase + inc1 |
---|
541 | jbase = jbase + inc2 |
---|
542 | ENDDO |
---|
543 | |
---|
544 | ELSE |
---|
545 | |
---|
546 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
547 | DO l = 1, la |
---|
548 | i = ibase |
---|
549 | j = jbase |
---|
550 | !DIR$ IVDEP |
---|
551 | !CDIR NODEP |
---|
552 | !OCL NOVREC |
---|
553 | DO ijk = 1, lot |
---|
554 | c(ja+j) = z*(a(ia+i)+a(ib+i)) |
---|
555 | c(jb+j) = z*(a(ia+i)-a(ib+i)) |
---|
556 | i = i + inc3 |
---|
557 | j = j + inc4 |
---|
558 | ENDDO |
---|
559 | ibase = ibase + inc1 |
---|
560 | jbase = jbase + inc2 |
---|
561 | ENDDO |
---|
562 | |
---|
563 | ENDIF |
---|
564 | |
---|
565 | ! |
---|
566 | !-- Coding for factor 3 |
---|
567 | CASE ( 2 ) |
---|
568 | |
---|
569 | ia = 1 |
---|
570 | ib = ia + iink |
---|
571 | ic = ib + iink |
---|
572 | ja = 1 |
---|
573 | jb = ja + (2*m-la) * inc2 |
---|
574 | jc = jb |
---|
575 | |
---|
576 | IF ( la /= m ) THEN |
---|
577 | |
---|
578 | DO l = 1, la |
---|
579 | i = ibase |
---|
580 | j = jbase |
---|
581 | !DIR$ IVDEP |
---|
582 | !CDIR NODEP |
---|
583 | !OCL NOVREC |
---|
584 | DO ijk = 1, lot |
---|
585 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
586 | c(jb+j) = a(ia+i) - 0.5_wp*(a(ib+i)+a(ic+i)) |
---|
587 | d(jb+j) = sin60*(a(ic+i)-a(ib+i)) |
---|
588 | i = i + inc3 |
---|
589 | j = j + inc4 |
---|
590 | ENDDO |
---|
591 | ibase = ibase + inc1 |
---|
592 | jbase = jbase + inc2 |
---|
593 | ENDDO |
---|
594 | |
---|
595 | ja = ja + jink |
---|
596 | jink = 2 * jink |
---|
597 | jb = jb + jink |
---|
598 | jc = jc - jink |
---|
599 | ibase = ibase + ijump |
---|
600 | ijump = 2 * ijump + iink |
---|
601 | |
---|
602 | IF ( ja /= jc ) THEN |
---|
603 | |
---|
604 | DO k = la, kstop, la |
---|
605 | kb = k + k |
---|
606 | kc = kb + kb |
---|
607 | c1 = trigs(kb+1) |
---|
608 | s1 = trigs(kb+2) |
---|
609 | c2 = trigs(kc+1) |
---|
610 | s2 = trigs(kc+2) |
---|
611 | |
---|
612 | jbase = 0 |
---|
613 | DO l = 1, la |
---|
614 | i = ibase |
---|
615 | j = jbase |
---|
616 | !DIR$ IVDEP |
---|
617 | !CDIR NODEP |
---|
618 | !OCL NOVREC |
---|
619 | DO ijk = 1, lot |
---|
620 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c2*a(ic+i)+s2*b(ic+i)) |
---|
621 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c2*b(ic+i)-s2*a(ic+i)) |
---|
622 | a2 = a(ia+i) - 0.5_wp*a1 |
---|
623 | b2 = b(ia+i) - 0.5_wp*b1 |
---|
624 | a3 = sin60*((c1*a(ib+i)+s1*b(ib+i))-(c2*a(ic+i)+s2*b(ic+i))) |
---|
625 | b3 = sin60*((c1*b(ib+i)-s1*a(ib+i))-(c2*b(ic+i)-s2*a(ic+i))) |
---|
626 | c(ja+j) = a(ia+i) + a1 |
---|
627 | d(ja+j) = b(ia+i) + b1 |
---|
628 | c(jb+j) = a2 + b3 |
---|
629 | d(jb+j) = b2 - a3 |
---|
630 | c(jc+j) = a2 - b3 |
---|
631 | d(jc+j) = -(b2+a3) |
---|
632 | i = i + inc3 |
---|
633 | j = j + inc4 |
---|
634 | ENDDO |
---|
635 | ibase = ibase + inc1 |
---|
636 | jbase = jbase + inc2 |
---|
637 | ENDDO |
---|
638 | ibase = ibase + ijump |
---|
639 | ja = ja + jink |
---|
640 | jb = jb + jink |
---|
641 | jc = jc - jink |
---|
642 | ENDDO |
---|
643 | |
---|
644 | IF ( ja > jc ) RETURN |
---|
645 | |
---|
646 | ENDIF |
---|
647 | |
---|
648 | jbase = 0 |
---|
649 | DO l = 1, la |
---|
650 | i = ibase |
---|
651 | j = jbase |
---|
652 | !DIR$ IVDEP |
---|
653 | !CDIR NODEP |
---|
654 | !OCL NOVREC |
---|
655 | DO ijk = 1, lot |
---|
656 | c(ja+j) = a(ia+i) + 0.5_wp*(a(ib+i)-a(ic+i)) |
---|
657 | d(ja+j) = -sin60*(a(ib+i)+a(ic+i)) |
---|
658 | c(jb+j) = a(ia+i) - (a(ib+i)-a(ic+i)) |
---|
659 | i = i + inc3 |
---|
660 | j = j + inc4 |
---|
661 | ENDDO |
---|
662 | ibase = ibase + inc1 |
---|
663 | jbase = jbase + inc2 |
---|
664 | ENDDO |
---|
665 | |
---|
666 | ELSE |
---|
667 | |
---|
668 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
669 | zsin60 = z*sin60 |
---|
670 | DO l = 1, la |
---|
671 | i = ibase |
---|
672 | j = jbase |
---|
673 | !DIR$ IVDEP |
---|
674 | !CDIR NODEP |
---|
675 | !OCL NOVREC |
---|
676 | DO ijk = 1, lot |
---|
677 | c(ja+j) = z*(a(ia+i)+(a(ib+i)+a(ic+i))) |
---|
678 | c(jb+j) = z*(a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i))) |
---|
679 | d(jb+j) = zsin60*(a(ic+i)-a(ib+i)) |
---|
680 | i = i + inc3 |
---|
681 | j = j + inc4 |
---|
682 | ENDDO |
---|
683 | ibase = ibase + inc1 |
---|
684 | jbase = jbase + inc2 |
---|
685 | ENDDO |
---|
686 | |
---|
687 | ENDIF |
---|
688 | |
---|
689 | ! |
---|
690 | !-- Coding for factor 4 |
---|
691 | CASE ( 3 ) |
---|
692 | |
---|
693 | ia = 1 |
---|
694 | ib = ia + iink |
---|
695 | ic = ib + iink |
---|
696 | id = ic + iink |
---|
697 | ja = 1 |
---|
698 | jb = ja + (2*m-la) * inc2 |
---|
699 | jc = jb + 2*m*inc2 |
---|
700 | jd = jb |
---|
701 | |
---|
702 | IF ( la /= m ) THEN |
---|
703 | |
---|
704 | DO l = 1, la |
---|
705 | |
---|
706 | i = ibase |
---|
707 | j = jbase |
---|
708 | !DIR$ IVDEP |
---|
709 | !CDIR NODEP |
---|
710 | !OCL NOVREC |
---|
711 | DO ijk = 1, lot |
---|
712 | c(ja+j) = (a(ia+i)+a(ic+i)) + (a(ib+i)+a(id+i)) |
---|
713 | c(jc+j) = (a(ia+i)+a(ic+i)) - (a(ib+i)+a(id+i)) |
---|
714 | c(jb+j) = a(ia+i) - a(ic+i) |
---|
715 | d(jb+j) = a(id+i) - a(ib+i) |
---|
716 | i = i + inc3 |
---|
717 | j = j + inc4 |
---|
718 | ENDDO |
---|
719 | ibase = ibase + inc1 |
---|
720 | jbase = jbase + inc2 |
---|
721 | ENDDO |
---|
722 | |
---|
723 | ja = ja + jink |
---|
724 | jink = 2 * jink |
---|
725 | jb = jb + jink |
---|
726 | jc = jc - jink |
---|
727 | jd = jd - jink |
---|
728 | ibase = ibase + ijump |
---|
729 | ijump = 2 * ijump + iink |
---|
730 | |
---|
731 | IF ( jb /= jc ) THEN |
---|
732 | |
---|
733 | DO k = la, kstop, la |
---|
734 | kb = k + k |
---|
735 | kc = kb + kb |
---|
736 | kd = kc + kb |
---|
737 | c1 = trigs(kb+1) |
---|
738 | s1 = trigs(kb+2) |
---|
739 | c2 = trigs(kc+1) |
---|
740 | s2 = trigs(kc+2) |
---|
741 | c3 = trigs(kd+1) |
---|
742 | s3 = trigs(kd+2) |
---|
743 | jbase = 0 |
---|
744 | DO l = 1, la |
---|
745 | i = ibase |
---|
746 | j = jbase |
---|
747 | !DIR$ IVDEP |
---|
748 | !CDIR NODEP |
---|
749 | !OCL NOVREC |
---|
750 | DO ijk = 1, lot |
---|
751 | a0 = a(ia+i) + (c2*a(ic+i)+s2*b(ic+i)) |
---|
752 | a2 = a(ia+i) - (c2*a(ic+i)+s2*b(ic+i)) |
---|
753 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c3*a(id+i)+s3*b(id+i)) |
---|
754 | a3 = (c1*a(ib+i)+s1*b(ib+i)) - (c3*a(id+i)+s3*b(id+i)) |
---|
755 | b0 = b(ia+i) + (c2*b(ic+i)-s2*a(ic+i)) |
---|
756 | b2 = b(ia+i) - (c2*b(ic+i)-s2*a(ic+i)) |
---|
757 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c3*b(id+i)-s3*a(id+i)) |
---|
758 | b3 = (c1*b(ib+i)-s1*a(ib+i)) - (c3*b(id+i)-s3*a(id+i)) |
---|
759 | c(ja+j) = a0 + a1 |
---|
760 | c(jc+j) = a0 - a1 |
---|
761 | d(ja+j) = b0 + b1 |
---|
762 | d(jc+j) = b1 - b0 |
---|
763 | c(jb+j) = a2 + b3 |
---|
764 | c(jd+j) = a2 - b3 |
---|
765 | d(jb+j) = b2 - a3 |
---|
766 | d(jd+j) = -(b2+a3) |
---|
767 | i = i + inc3 |
---|
768 | j = j + inc4 |
---|
769 | ENDDO |
---|
770 | ibase = ibase + inc1 |
---|
771 | jbase = jbase + inc2 |
---|
772 | ENDDO |
---|
773 | ibase = ibase + ijump |
---|
774 | ja = ja + jink |
---|
775 | jb = jb + jink |
---|
776 | jc = jc - jink |
---|
777 | jd = jd - jink |
---|
778 | ENDDO |
---|
779 | |
---|
780 | IF ( jb > jc ) RETURN |
---|
781 | |
---|
782 | ENDIF |
---|
783 | |
---|
784 | sin45 = SQRT( 0.5_wp ) |
---|
785 | jbase = 0 |
---|
786 | DO l = 1, la |
---|
787 | i = ibase |
---|
788 | j = jbase |
---|
789 | !DIR$ IVDEP |
---|
790 | !CDIR NODEP |
---|
791 | !OCL NOVREC |
---|
792 | DO ijk = 1, lot |
---|
793 | c(ja+j) = a(ia+i) + sin45*(a(ib+i)-a(id+i)) |
---|
794 | c(jb+j) = a(ia+i) - sin45*(a(ib+i)-a(id+i)) |
---|
795 | d(ja+j) = -a(ic+i) - sin45*(a(ib+i)+a(id+i)) |
---|
796 | d(jb+j) = a(ic+i) - sin45*(a(ib+i)+a(id+i)) |
---|
797 | i = i + inc3 |
---|
798 | j = j + inc4 |
---|
799 | ENDDO |
---|
800 | ibase = ibase + inc1 |
---|
801 | jbase = jbase + inc2 |
---|
802 | ENDDO |
---|
803 | |
---|
804 | ELSE |
---|
805 | |
---|
806 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
807 | DO l = 1, la |
---|
808 | i = ibase |
---|
809 | j = jbase |
---|
810 | !DIR$ IVDEP |
---|
811 | !CDIR NODEP |
---|
812 | !OCL NOVREC |
---|
813 | DO ijk = 1, lot |
---|
814 | c(ja+j) = z*((a(ia+i)+a(ic+i))+(a(ib+i)+a(id+i))) |
---|
815 | c(jc+j) = z*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) |
---|
816 | c(jb+j) = z*(a(ia+i)-a(ic+i)) |
---|
817 | d(jb+j) = z*(a(id+i)-a(ib+i)) |
---|
818 | i = i + inc3 |
---|
819 | j = j + inc4 |
---|
820 | ENDDO |
---|
821 | ibase = ibase + inc1 |
---|
822 | jbase = jbase + inc2 |
---|
823 | ENDDO |
---|
824 | |
---|
825 | ENDIF |
---|
826 | |
---|
827 | ! |
---|
828 | !-- Coding for factor 5 |
---|
829 | CASE ( 4 ) |
---|
830 | |
---|
831 | ia = 1 |
---|
832 | ib = ia + iink |
---|
833 | ic = ib + iink |
---|
834 | id = ic + iink |
---|
835 | ie = id + iink |
---|
836 | ja = 1 |
---|
837 | jb = ja + (2*m-la) * inc2 |
---|
838 | jc = jb + 2*m*inc2 |
---|
839 | jd = jc |
---|
840 | je = jb |
---|
841 | |
---|
842 | IF ( la /= m ) THEN |
---|
843 | |
---|
844 | DO l = 1, la |
---|
845 | i = ibase |
---|
846 | j = jbase |
---|
847 | !DIR$ IVDEP |
---|
848 | !CDIR NODEP |
---|
849 | !OCL NOVREC |
---|
850 | DO ijk = 1, lot |
---|
851 | a1 = a(ib+i) + a(ie+i) |
---|
852 | a3 = a(ib+i) - a(ie+i) |
---|
853 | a2 = a(ic+i) + a(id+i) |
---|
854 | a4 = a(ic+i) - a(id+i) |
---|
855 | a5 = a(ia+i) - 0.25_wp*(a1+a2) |
---|
856 | a6 = qrt5*(a1-a2) |
---|
857 | c(ja+j) = a(ia+i) + (a1+a2) |
---|
858 | c(jb+j) = a5 + a6 |
---|
859 | c(jc+j) = a5 - a6 |
---|
860 | d(jb+j) = -sin72*a3 - sin36*a4 |
---|
861 | d(jc+j) = -sin36*a3 + sin72*a4 |
---|
862 | i = i + inc3 |
---|
863 | j = j + inc4 |
---|
864 | ENDDO |
---|
865 | ibase = ibase + inc1 |
---|
866 | jbase = jbase + inc2 |
---|
867 | ENDDO |
---|
868 | |
---|
869 | ja = ja + jink |
---|
870 | jink = 2 * jink |
---|
871 | jb = jb + jink |
---|
872 | jc = jc + jink |
---|
873 | jd = jd - jink |
---|
874 | je = je - jink |
---|
875 | ibase = ibase + ijump |
---|
876 | ijump = 2 * ijump + iink |
---|
877 | |
---|
878 | IF ( jb /= jd ) THEN |
---|
879 | |
---|
880 | DO k = la, kstop, la |
---|
881 | kb = k + k |
---|
882 | kc = kb + kb |
---|
883 | kd = kc + kb |
---|
884 | ke = kd + kb |
---|
885 | c1 = trigs(kb+1) |
---|
886 | s1 = trigs(kb+2) |
---|
887 | c2 = trigs(kc+1) |
---|
888 | s2 = trigs(kc+2) |
---|
889 | c3 = trigs(kd+1) |
---|
890 | s3 = trigs(kd+2) |
---|
891 | c4 = trigs(ke+1) |
---|
892 | s4 = trigs(ke+2) |
---|
893 | jbase = 0 |
---|
894 | DO l = 1, la |
---|
895 | i = ibase |
---|
896 | j = jbase |
---|
897 | !DIR$ IVDEP |
---|
898 | !CDIR NODEP |
---|
899 | !OCL NOVREC |
---|
900 | DO ijk = 1, lot |
---|
901 | a1 = (c1*a(ib+i)+s1*b(ib+i)) + (c4*a(ie+i)+s4*b(ie+i)) |
---|
902 | a3 = (c1*a(ib+i)+s1*b(ib+i)) - (c4*a(ie+i)+s4*b(ie+i)) |
---|
903 | a2 = (c2*a(ic+i)+s2*b(ic+i)) + (c3*a(id+i)+s3*b(id+i)) |
---|
904 | a4 = (c2*a(ic+i)+s2*b(ic+i)) - (c3*a(id+i)+s3*b(id+i)) |
---|
905 | b1 = (c1*b(ib+i)-s1*a(ib+i)) + (c4*b(ie+i)-s4*a(ie+i)) |
---|
906 | b3 = (c1*b(ib+i)-s1*a(ib+i)) - (c4*b(ie+i)-s4*a(ie+i)) |
---|
907 | b2 = (c2*b(ic+i)-s2*a(ic+i)) + (c3*b(id+i)-s3*a(id+i)) |
---|
908 | b4 = (c2*b(ic+i)-s2*a(ic+i)) - (c3*b(id+i)-s3*a(id+i)) |
---|
909 | a5 = a(ia+i) - 0.25_wp*(a1+a2) |
---|
910 | a6 = qrt5*(a1-a2) |
---|
911 | b5 = b(ia+i) - 0.25_wp*(b1+b2) |
---|
912 | b6 = qrt5*(b1-b2) |
---|
913 | a10 = a5 + a6 |
---|
914 | a20 = a5 - a6 |
---|
915 | b10 = b5 + b6 |
---|
916 | b20 = b5 - b6 |
---|
917 | a11 = sin72*b3 + sin36*b4 |
---|
918 | a21 = sin36*b3 - sin72*b4 |
---|
919 | b11 = sin72*a3 + sin36*a4 |
---|
920 | b21 = sin36*a3 - sin72*a4 |
---|
921 | c(ja+j) = a(ia+i) + (a1+a2) |
---|
922 | c(jb+j) = a10 + a11 |
---|
923 | c(je+j) = a10 - a11 |
---|
924 | c(jc+j) = a20 + a21 |
---|
925 | c(jd+j) = a20 - a21 |
---|
926 | d(ja+j) = b(ia+i) + (b1+b2) |
---|
927 | d(jb+j) = b10 - b11 |
---|
928 | d(je+j) = -(b10+b11) |
---|
929 | d(jc+j) = b20 - b21 |
---|
930 | d(jd+j) = -(b20+b21) |
---|
931 | i = i + inc3 |
---|
932 | j = j + inc4 |
---|
933 | ENDDO |
---|
934 | ibase = ibase + inc1 |
---|
935 | jbase = jbase + inc2 |
---|
936 | ENDDO |
---|
937 | ibase = ibase + ijump |
---|
938 | ja = ja + jink |
---|
939 | jb = jb + jink |
---|
940 | jc = jc + jink |
---|
941 | jd = jd - jink |
---|
942 | je = je - jink |
---|
943 | ENDDO |
---|
944 | |
---|
945 | IF ( jb > jd ) RETURN |
---|
946 | |
---|
947 | ENDIF |
---|
948 | |
---|
949 | jbase = 0 |
---|
950 | DO l = 1, la |
---|
951 | i = ibase |
---|
952 | j = jbase |
---|
953 | !DIR$ IVDEP |
---|
954 | !CDIR NODEP |
---|
955 | !OCL NOVREC |
---|
956 | DO ijk = 1, lot |
---|
957 | a1 = a(ib+i) + a(ie+i) |
---|
958 | a3 = a(ib+i) - a(ie+i) |
---|
959 | a2 = a(ic+i) + a(id+i) |
---|
960 | a4 = a(ic+i) - a(id+i) |
---|
961 | a5 = a(ia+i) + 0.25_wp*(a3-a4) |
---|
962 | a6 = qrt5*(a3+a4) |
---|
963 | c(ja+j) = a5 + a6 |
---|
964 | c(jb+j) = a5 - a6 |
---|
965 | c(jc+j) = a(ia+i) - (a3-a4) |
---|
966 | d(ja+j) = -sin36*a1 - sin72*a2 |
---|
967 | d(jb+j) = -sin72*a1 + sin36*a2 |
---|
968 | i = i + inc3 |
---|
969 | j = j + inc4 |
---|
970 | ENDDO |
---|
971 | ibase = ibase + inc1 |
---|
972 | jbase = jbase + inc2 |
---|
973 | ENDDO |
---|
974 | |
---|
975 | ELSE |
---|
976 | |
---|
977 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
978 | zqrt5 = z * qrt5 |
---|
979 | zsin36 = z * sin36 |
---|
980 | zsin72 = z * sin72 |
---|
981 | DO l = 1, la |
---|
982 | i = ibase |
---|
983 | j = jbase |
---|
984 | !DIR$ IVDEP |
---|
985 | !CDIR NODEP |
---|
986 | !OCL NOVREC |
---|
987 | DO ijk = 1, lot |
---|
988 | a1 = a(ib+i) + a(ie+i) |
---|
989 | a3 = a(ib+i) - a(ie+i) |
---|
990 | a2 = a(ic+i) + a(id+i) |
---|
991 | a4 = a(ic+i) - a(id+i) |
---|
992 | a5 = z*(a(ia+i)-0.25_wp*(a1+a2)) |
---|
993 | a6 = zqrt5*(a1-a2) |
---|
994 | c(ja+j) = z*(a(ia+i)+(a1+a2)) |
---|
995 | c(jb+j) = a5 + a6 |
---|
996 | c(jc+j) = a5 - a6 |
---|
997 | d(jb+j) = -zsin72*a3 - zsin36*a4 |
---|
998 | d(jc+j) = -zsin36*a3 + zsin72*a4 |
---|
999 | i = i + inc3 |
---|
1000 | j = j + inc4 |
---|
1001 | ENDDO |
---|
1002 | ibase = ibase + inc1 |
---|
1003 | jbase = jbase + inc2 |
---|
1004 | ENDDO |
---|
1005 | |
---|
1006 | ENDIF |
---|
1007 | |
---|
1008 | ! |
---|
1009 | !-- Coding for factor 6 |
---|
1010 | CASE ( 5 ) |
---|
1011 | |
---|
1012 | ia = 1 |
---|
1013 | ib = ia + iink |
---|
1014 | ic = ib + iink |
---|
1015 | id = ic + iink |
---|
1016 | ie = id + iink |
---|
1017 | if = ie + iink |
---|
1018 | ja = 1 |
---|
1019 | jb = ja + (2*m-la) * inc2 |
---|
1020 | jc = jb + 2*m*inc2 |
---|
1021 | jd = jc + 2*m*inc2 |
---|
1022 | je = jc |
---|
1023 | jf = jb |
---|
1024 | |
---|
1025 | IF ( la /= m ) THEN |
---|
1026 | |
---|
1027 | DO l = 1, la |
---|
1028 | i = ibase |
---|
1029 | j = jbase |
---|
1030 | !DIR$ IVDEP |
---|
1031 | !CDIR NODEP |
---|
1032 | !OCL NOVREC |
---|
1033 | DO ijk = 1, lot |
---|
1034 | a11 = (a(ic+i)+a(if+i)) + (a(ib+i)+a(ie+i)) |
---|
1035 | c(ja+j) = (a(ia+i)+a(id+i)) + a11 |
---|
1036 | c(jc+j) = (a(ia+i)+a(id+i)-0.5_wp*a11) |
---|
1037 | d(jc+j) = sin60*((a(ic+i)+a(if+i))-(a(ib+i)+a(ie+i))) |
---|
1038 | a11 = (a(ic+i)-a(if+i)) + (a(ie+i)-a(ib+i)) |
---|
1039 | c(jb+j) = (a(ia+i)-a(id+i)) - 0.5_wp*a11 |
---|
1040 | d(jb+j) = sin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1041 | c(jd+j) = (a(ia+i)-a(id+i)) + a11 |
---|
1042 | i = i + inc3 |
---|
1043 | j = j + inc4 |
---|
1044 | ENDDO |
---|
1045 | ibase = ibase + inc1 |
---|
1046 | jbase = jbase + inc2 |
---|
1047 | ENDDO |
---|
1048 | ja = ja + jink |
---|
1049 | jink = 2 * jink |
---|
1050 | jb = jb + jink |
---|
1051 | jc = jc + jink |
---|
1052 | jd = jd - jink |
---|
1053 | je = je - jink |
---|
1054 | jf = jf - jink |
---|
1055 | ibase = ibase + ijump |
---|
1056 | ijump = 2 * ijump + iink |
---|
1057 | |
---|
1058 | IF ( jc /= jd ) THEN |
---|
1059 | |
---|
1060 | DO k = la, kstop, la |
---|
1061 | kb = k + k |
---|
1062 | kc = kb + kb |
---|
1063 | kd = kc + kb |
---|
1064 | ke = kd + kb |
---|
1065 | kf = ke + kb |
---|
1066 | c1 = trigs(kb+1) |
---|
1067 | s1 = trigs(kb+2) |
---|
1068 | c2 = trigs(kc+1) |
---|
1069 | s2 = trigs(kc+2) |
---|
1070 | c3 = trigs(kd+1) |
---|
1071 | s3 = trigs(kd+2) |
---|
1072 | c4 = trigs(ke+1) |
---|
1073 | s4 = trigs(ke+2) |
---|
1074 | c5 = trigs(kf+1) |
---|
1075 | s5 = trigs(kf+2) |
---|
1076 | jbase = 0 |
---|
1077 | DO l = 1, la |
---|
1078 | i = ibase |
---|
1079 | j = jbase |
---|
1080 | !DIR$ IVDEP |
---|
1081 | !CDIR NODEP |
---|
1082 | !OCL NOVREC |
---|
1083 | DO ijk = 1, lot |
---|
1084 | a1 = c1*a(ib+i) + s1*b(ib+i) |
---|
1085 | b1 = c1*b(ib+i) - s1*a(ib+i) |
---|
1086 | a2 = c2*a(ic+i) + s2*b(ic+i) |
---|
1087 | b2 = c2*b(ic+i) - s2*a(ic+i) |
---|
1088 | a3 = c3*a(id+i) + s3*b(id+i) |
---|
1089 | b3 = c3*b(id+i) - s3*a(id+i) |
---|
1090 | a4 = c4*a(ie+i) + s4*b(ie+i) |
---|
1091 | b4 = c4*b(ie+i) - s4*a(ie+i) |
---|
1092 | a5 = c5*a(if+i) + s5*b(if+i) |
---|
1093 | b5 = c5*b(if+i) - s5*a(if+i) |
---|
1094 | a11 = (a2+a5) + (a1+a4) |
---|
1095 | a20 = (a(ia+i)+a3) - 0.5_wp*a11 |
---|
1096 | a21 = sin60*((a2+a5)-(a1+a4)) |
---|
1097 | b11 = (b2+b5) + (b1+b4) |
---|
1098 | b20 = (b(ia+i)+b3) - 0.5_wp*b11 |
---|
1099 | b21 = sin60*((b2+b5)-(b1+b4)) |
---|
1100 | c(ja+j) = (a(ia+i)+a3) + a11 |
---|
1101 | d(ja+j) = (b(ia+i)+b3) + b11 |
---|
1102 | c(jc+j) = a20 - b21 |
---|
1103 | d(jc+j) = a21 + b20 |
---|
1104 | c(je+j) = a20 + b21 |
---|
1105 | d(je+j) = a21 - b20 |
---|
1106 | a11 = (a2-a5) + (a4-a1) |
---|
1107 | a20 = (a(ia+i)-a3) - 0.5_wp*a11 |
---|
1108 | a21 = sin60*((a4-a1)-(a2-a5)) |
---|
1109 | b11 = (b5-b2) - (b4-b1) |
---|
1110 | b20 = (b3-b(ia+i)) - 0.5_wp*b11 |
---|
1111 | b21 = sin60*((b5-b2)+(b4-b1)) |
---|
1112 | c(jb+j) = a20 - b21 |
---|
1113 | d(jb+j) = a21 - b20 |
---|
1114 | c(jd+j) = a11 + (a(ia+i)-a3) |
---|
1115 | d(jd+j) = b11 + (b3-b(ia+i)) |
---|
1116 | c(jf+j) = a20 + b21 |
---|
1117 | d(jf+j) = a21 + b20 |
---|
1118 | i = i + inc3 |
---|
1119 | j = j + inc4 |
---|
1120 | ENDDO |
---|
1121 | ibase = ibase + inc1 |
---|
1122 | jbase = jbase + inc2 |
---|
1123 | ENDDO |
---|
1124 | ibase = ibase + ijump |
---|
1125 | ja = ja + jink |
---|
1126 | jb = jb + jink |
---|
1127 | jc = jc + jink |
---|
1128 | jd = jd - jink |
---|
1129 | je = je - jink |
---|
1130 | jf = jf - jink |
---|
1131 | ENDDO |
---|
1132 | |
---|
1133 | IF ( jc > jd ) RETURN |
---|
1134 | |
---|
1135 | ENDIF |
---|
1136 | |
---|
1137 | jbase = 0 |
---|
1138 | DO l = 1, la |
---|
1139 | i = ibase |
---|
1140 | j = jbase |
---|
1141 | !DIR$ IVDEP |
---|
1142 | !CDIR NODEP |
---|
1143 | !OCL NOVREC |
---|
1144 | DO ijk = 1, lot |
---|
1145 | c(ja+j) = (a(ia+i)+0.5_wp*(a(ic+i)-a(ie+i))) + sin60*(a(ib+i)-a(if+i)) |
---|
1146 | d(ja+j) = -(a(id+i)+0.5_wp*(a(ib+i)+a(if+i))) - sin60*(a(ic+i)+a(ie+i)) |
---|
1147 | c(jb+j) = a(ia+i) - (a(ic+i)-a(ie+i)) |
---|
1148 | d(jb+j) = a(id+i) - (a(ib+i)+a(if+i)) |
---|
1149 | c(jc+j) = (a(ia+i)+0.5_wp*(a(ic+i)-a(ie+i))) - sin60*(a(ib+i)-a(if+i)) |
---|
1150 | d(jc+j) = -(a(id+i)+0.5_wp*(a(ib+i)+a(if+i))) + sin60*(a(ic+i)+a(ie+i)) |
---|
1151 | i = i + inc3 |
---|
1152 | j = j + inc4 |
---|
1153 | ENDDO |
---|
1154 | ibase = ibase + inc1 |
---|
1155 | jbase = jbase + inc2 |
---|
1156 | ENDDO |
---|
1157 | |
---|
1158 | ELSE |
---|
1159 | |
---|
1160 | z = 1.0_wp/REAL(n,KIND=wp) |
---|
1161 | zsin60 = z*sin60 |
---|
1162 | DO l = 1, la |
---|
1163 | i = ibase |
---|
1164 | j = jbase |
---|
1165 | !DIR$ IVDEP |
---|
1166 | !CDIR NODEP |
---|
1167 | !OCL NOVREC |
---|
1168 | DO ijk = 1, lot |
---|
1169 | a11 = (a(ic+i)+a(if+i)) + (a(ib+i)+a(ie+i)) |
---|
1170 | c(ja+j) = z*((a(ia+i)+a(id+i))+a11) |
---|
1171 | c(jc+j) = z*((a(ia+i)+a(id+i))-0.5_wp*a11) |
---|
1172 | d(jc+j) = zsin60*((a(ic+i)+a(if+i))-(a(ib+i)+a(ie+i))) |
---|
1173 | a11 = (a(ic+i)-a(if+i)) + (a(ie+i)-a(ib+i)) |
---|
1174 | c(jb+j) = z*((a(ia+i)-a(id+i))-0.5_wp*a11) |
---|
1175 | d(jb+j) = zsin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1176 | c(jd+j) = z*((a(ia+i)-a(id+i))+a11) |
---|
1177 | i = i + inc3 |
---|
1178 | j = j + inc4 |
---|
1179 | ENDDO |
---|
1180 | ibase = ibase + inc1 |
---|
1181 | jbase = jbase + inc2 |
---|
1182 | ENDDO |
---|
1183 | |
---|
1184 | ENDIF |
---|
1185 | |
---|
1186 | ! |
---|
1187 | !-- Coding for factor 8 |
---|
1188 | CASE ( 6 ) |
---|
1189 | |
---|
1190 | IF ( la /= m ) THEN |
---|
1191 | ierr = 3 |
---|
1192 | RETURN |
---|
1193 | ENDIF |
---|
1194 | |
---|
1195 | ia = 1 |
---|
1196 | ib = ia + iink |
---|
1197 | ic = ib + iink |
---|
1198 | id = ic + iink |
---|
1199 | ie = id + iink |
---|
1200 | if = ie + iink |
---|
1201 | ig = if + iink |
---|
1202 | ih = ig + iink |
---|
1203 | ja = 1 |
---|
1204 | jb = ja + la * inc2 |
---|
1205 | jc = jb + 2*m*inc2 |
---|
1206 | jd = jc + 2*m*inc2 |
---|
1207 | je = jd + 2*m*inc2 |
---|
1208 | z = 1.0_wp / REAL( n, KIND=wp ) |
---|
1209 | zsin45 = z * SQRT( 0.5_wp ) |
---|
1210 | |
---|
1211 | DO l = 1, la |
---|
1212 | i = ibase |
---|
1213 | j = jbase |
---|
1214 | |
---|
1215 | !DIR$ IVDEP |
---|
1216 | !CDIR NODEP |
---|
1217 | !OCL NOVREC |
---|
1218 | DO ijk = 1, lot |
---|
1219 | c(ja+j) = z*(((a(ia+i)+a(ie+i))+(a(ic+i)+a(ig+i)))+((a(id+i)+ a(ih+i))+(a(ib+i)+a(if+i)))) |
---|
1220 | c(je+j) = z*(((a(ia+i)+a(ie+i))+(a(ic+i)+a(ig+i)))-((a(id+i)+ a(ih+i))+(a(ib+i)+a(if+i)))) |
---|
1221 | c(jc+j) = z*((a(ia+i)+a(ie+i))-(a(ic+i)+a(ig+i))) |
---|
1222 | d(jc+j) = z*((a(id+i)+a(ih+i))-(a(ib+i)+a(if+i))) |
---|
1223 | c(jb+j) = z*(a(ia+i)-a(ie+i)) + zsin45*((a(ih+i)-a(id+i))-(a(if+i)-a(ib+i))) |
---|
1224 | c(jd+j) = z*(a(ia+i)-a(ie+i)) - zsin45*((a(ih+i)-a(id+i))-(a(if+i)-a(ib+i))) |
---|
1225 | d(jb+j) = zsin45*((a(ih+i)-a(id+i))+(a(if+i)-a(ib+i))) + z*(a(ig+i)-a(ic+i)) |
---|
1226 | d(jd+j) = zsin45*((a(ih+i)-a(id+i))+(a(if+i)-a(ib+i))) - z*(a(ig+i)-a(ic+i)) |
---|
1227 | i = i + inc3 |
---|
1228 | j = j + inc4 |
---|
1229 | ENDDO |
---|
1230 | ibase = ibase + inc1 |
---|
1231 | jbase = jbase + inc2 |
---|
1232 | ENDDO |
---|
1233 | |
---|
1234 | END SELECT |
---|
1235 | |
---|
1236 | END SUBROUTINE qpassm |
---|
1237 | |
---|
1238 | !------------------------------------------------------------------------------! |
---|
1239 | ! Description: |
---|
1240 | ! ------------ |
---|
1241 | !> Same as qpassm, but for backward fft |
---|
1242 | !------------------------------------------------------------------------------! |
---|
1243 | SUBROUTINE rpassm( a, b, c, d, trigs, inc1, inc2, inc3, inc4, lot, n, ifac, la, ierr ) |
---|
1244 | |
---|
1245 | USE kinds |
---|
1246 | |
---|
1247 | IMPLICIT NONE |
---|
1248 | |
---|
1249 | INTEGER(iwp) :: ierr !< |
---|
1250 | INTEGER(iwp) :: ifac !< |
---|
1251 | INTEGER(iwp) :: inc1 !< |
---|
1252 | INTEGER(iwp) :: inc2 !< |
---|
1253 | INTEGER(iwp) :: inc3 !< |
---|
1254 | INTEGER(iwp) :: inc4 !< |
---|
1255 | INTEGER(iwp) :: la !< |
---|
1256 | INTEGER(iwp) :: lot !< |
---|
1257 | INTEGER(iwp) :: n !< |
---|
1258 | ! |
---|
1259 | !-- Arrays are dimensioned with n |
---|
1260 | REAL(wp) :: a(*) !< |
---|
1261 | REAL(wp) :: b(*) !< |
---|
1262 | REAL(wp) :: c(*) !< |
---|
1263 | REAL(wp) :: d(*) !< |
---|
1264 | REAL(wp) :: trigs(*) !< |
---|
1265 | |
---|
1266 | REAL(wp) :: c1 !< |
---|
1267 | REAL(wp) :: c2 !< |
---|
1268 | REAL(wp) :: c3 !< |
---|
1269 | REAL(wp) :: c4 !< |
---|
1270 | REAL(wp) :: c5 !< |
---|
1271 | REAL(wp) :: qqrt5 !< |
---|
1272 | REAL(wp) :: qrt5 !< |
---|
1273 | REAL(wp) :: s1 !< |
---|
1274 | REAL(wp) :: s2 !< |
---|
1275 | REAL(wp) :: s3 !< |
---|
1276 | REAL(wp) :: s4 !< |
---|
1277 | REAL(wp) :: s5 !< |
---|
1278 | REAL(wp) :: sin36 !< |
---|
1279 | REAL(wp) :: sin45 !< |
---|
1280 | REAL(wp) :: sin60 !< |
---|
1281 | REAL(wp) :: sin72 !< |
---|
1282 | REAL(wp) :: ssin36 !< |
---|
1283 | REAL(wp) :: ssin45 !< |
---|
1284 | REAL(wp) :: ssin60 !< |
---|
1285 | REAL(wp) :: ssin72 !< |
---|
1286 | |
---|
1287 | INTEGER(iwp) :: i !< |
---|
1288 | INTEGER(iwp) :: ia !< |
---|
1289 | INTEGER(iwp) :: ib !< |
---|
1290 | INTEGER(iwp) :: ibase !< |
---|
1291 | INTEGER(iwp) :: ic !< |
---|
1292 | INTEGER(iwp) :: id !< |
---|
1293 | INTEGER(iwp) :: ie !< |
---|
1294 | INTEGER(iwp) :: if !< |
---|
1295 | INTEGER(iwp) :: igo !< |
---|
1296 | INTEGER(iwp) :: iink !< |
---|
1297 | INTEGER(iwp) :: ijk !< |
---|
1298 | INTEGER(iwp) :: j !< |
---|
1299 | INTEGER(iwp) :: ja !< |
---|
1300 | INTEGER(iwp) :: jb !< |
---|
1301 | INTEGER(iwp) :: jbase !< |
---|
1302 | INTEGER(iwp) :: jc !< |
---|
1303 | INTEGER(iwp) :: jd !< |
---|
1304 | INTEGER(iwp) :: je !< |
---|
1305 | INTEGER(iwp) :: jf !< |
---|
1306 | INTEGER(iwp) :: jg !< |
---|
1307 | INTEGER(iwp) :: jh !< |
---|
1308 | INTEGER(iwp) :: jink !< |
---|
1309 | INTEGER(iwp) :: jump !< |
---|
1310 | INTEGER(iwp) :: k !< |
---|
1311 | INTEGER(iwp) :: kb !< |
---|
1312 | INTEGER(iwp) :: kc !< |
---|
1313 | INTEGER(iwp) :: kd !< |
---|
1314 | INTEGER(iwp) :: ke !< |
---|
1315 | INTEGER(iwp) :: kf !< |
---|
1316 | INTEGER(iwp) :: kstop !< |
---|
1317 | INTEGER(iwp) :: l !< |
---|
1318 | INTEGER(iwp) :: m !< |
---|
1319 | |
---|
1320 | REAL(wp) :: a10(nfft) !< |
---|
1321 | REAL(wp) :: a11(nfft) !< |
---|
1322 | REAL(wp) :: a20(nfft) !< |
---|
1323 | REAL(wp) :: a21(nfft) !< |
---|
1324 | REAL(wp) :: b10(nfft) !< |
---|
1325 | REAL(wp) :: b11(nfft) !< |
---|
1326 | REAL(wp) :: b20(nfft) !< |
---|
1327 | REAL(wp) :: b21(nfft) !< |
---|
1328 | |
---|
1329 | |
---|
1330 | DATA sin36/0.587785252292473_wp/, sin72/0.951056516295154_wp/, & |
---|
1331 | qrt5/0.559016994374947_wp/, sin60/0.866025403784437_wp/ |
---|
1332 | |
---|
1333 | |
---|
1334 | ierr = 0 |
---|
1335 | |
---|
1336 | m = n / ifac |
---|
1337 | iink = la * inc1 |
---|
1338 | jink = la * inc2 |
---|
1339 | jump = (ifac-1) * jink |
---|
1340 | kstop = (n-ifac) / (2*ifac) |
---|
1341 | |
---|
1342 | IF ( lot > nfft ) THEN |
---|
1343 | ierr = 1 |
---|
1344 | RETURN |
---|
1345 | ENDIF |
---|
1346 | ibase = 0 |
---|
1347 | jbase = 0 |
---|
1348 | igo = ifac - 1 |
---|
1349 | IF ( igo == 7 ) igo = 6 |
---|
1350 | IF ( igo < 1 .OR. igo > 6 ) THEN |
---|
1351 | ierr = 2 |
---|
1352 | RETURN |
---|
1353 | ENDIF |
---|
1354 | |
---|
1355 | |
---|
1356 | SELECT CASE ( igo ) |
---|
1357 | ! |
---|
1358 | !-- Coding for factor 2 |
---|
1359 | CASE ( 1 ) |
---|
1360 | |
---|
1361 | ia = 1 |
---|
1362 | ib = ia + (2*m-la) * inc1 |
---|
1363 | ja = 1 |
---|
1364 | jb = ja + jink |
---|
1365 | |
---|
1366 | IF ( la /= m ) THEN |
---|
1367 | |
---|
1368 | DO l = 1, la |
---|
1369 | i = ibase |
---|
1370 | j = jbase |
---|
1371 | !DIR$ IVDEP |
---|
1372 | !CDIR NODEP |
---|
1373 | !OCL NOVREC |
---|
1374 | DO ijk = 1, lot |
---|
1375 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1376 | c(jb+j) = a(ia+i) - a(ib+i) |
---|
1377 | i = i + inc3 |
---|
1378 | j = j + inc4 |
---|
1379 | ENDDO |
---|
1380 | ibase = ibase + inc1 |
---|
1381 | jbase = jbase + inc2 |
---|
1382 | ENDDO |
---|
1383 | |
---|
1384 | ia = ia + iink |
---|
1385 | iink = 2 * iink |
---|
1386 | ib = ib - iink |
---|
1387 | ibase = 0 |
---|
1388 | jbase = jbase + jump |
---|
1389 | jump = 2 * jump + jink |
---|
1390 | |
---|
1391 | IF ( ia /= ib ) THEN |
---|
1392 | |
---|
1393 | DO k = la, kstop, la |
---|
1394 | kb = k + k |
---|
1395 | c1 = trigs(kb+1) |
---|
1396 | s1 = trigs(kb+2) |
---|
1397 | ibase = 0 |
---|
1398 | DO l = 1, la |
---|
1399 | i = ibase |
---|
1400 | j = jbase |
---|
1401 | !DIR$ IVDEP |
---|
1402 | !CDIR NODEP |
---|
1403 | !OCL NOVREC |
---|
1404 | DO ijk = 1, lot |
---|
1405 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1406 | d(ja+j) = b(ia+i) - b(ib+i) |
---|
1407 | c(jb+j) = c1*(a(ia+i)-a(ib+i)) - s1*(b(ia+i)+b(ib+i)) |
---|
1408 | d(jb+j) = s1*(a(ia+i)-a(ib+i)) + c1*(b(ia+i)+b(ib+i)) |
---|
1409 | i = i + inc3 |
---|
1410 | j = j + inc4 |
---|
1411 | ENDDO |
---|
1412 | ibase = ibase + inc1 |
---|
1413 | jbase = jbase + inc2 |
---|
1414 | ENDDO |
---|
1415 | ia = ia + iink |
---|
1416 | ib = ib - iink |
---|
1417 | jbase = jbase + jump |
---|
1418 | ENDDO |
---|
1419 | |
---|
1420 | IF ( ia > ib ) RETURN |
---|
1421 | |
---|
1422 | ENDIF |
---|
1423 | |
---|
1424 | ibase = 0 |
---|
1425 | DO l = 1, la |
---|
1426 | i = ibase |
---|
1427 | j = jbase |
---|
1428 | !DIR$ IVDEP |
---|
1429 | !CDIR NODEP |
---|
1430 | !OCL NOVREC |
---|
1431 | DO ijk = 1, lot |
---|
1432 | c(ja+j) = a(ia+i) |
---|
1433 | c(jb+j) = -b(ia+i) |
---|
1434 | i = i + inc3 |
---|
1435 | j = j + inc4 |
---|
1436 | ENDDO |
---|
1437 | ibase = ibase + inc1 |
---|
1438 | jbase = jbase + inc2 |
---|
1439 | ENDDO |
---|
1440 | |
---|
1441 | ELSE |
---|
1442 | |
---|
1443 | DO l = 1, la |
---|
1444 | i = ibase |
---|
1445 | j = jbase |
---|
1446 | !DIR$ IVDEP |
---|
1447 | !CDIR NODEP |
---|
1448 | !OCL NOVREC |
---|
1449 | DO ijk = 1, lot |
---|
1450 | c(ja+j) = 2.0_wp*(a(ia+i)+a(ib+i)) |
---|
1451 | c(jb+j) = 2.0_wp*(a(ia+i)-a(ib+i)) |
---|
1452 | i = i + inc3 |
---|
1453 | j = j + inc4 |
---|
1454 | ENDDO |
---|
1455 | ibase = ibase + inc1 |
---|
1456 | jbase = jbase + inc2 |
---|
1457 | ENDDO |
---|
1458 | |
---|
1459 | ENDIF |
---|
1460 | |
---|
1461 | ! |
---|
1462 | !-- Coding for factor 3 |
---|
1463 | CASE ( 2 ) |
---|
1464 | |
---|
1465 | ia = 1 |
---|
1466 | ib = ia + (2*m-la) * inc1 |
---|
1467 | ic = ib |
---|
1468 | ja = 1 |
---|
1469 | jb = ja + jink |
---|
1470 | jc = jb + jink |
---|
1471 | |
---|
1472 | IF ( la /= m ) THEN |
---|
1473 | |
---|
1474 | DO l = 1, la |
---|
1475 | i = ibase |
---|
1476 | j = jbase |
---|
1477 | !DIR$ IVDEP |
---|
1478 | !CDIR NODEP |
---|
1479 | !OCL NOVREC |
---|
1480 | DO ijk = 1, lot |
---|
1481 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1482 | c(jb+j) = (a(ia+i)-0.5_wp*a(ib+i)) - (sin60*(b(ib+i))) |
---|
1483 | c(jc+j) = (a(ia+i)-0.5_wp*a(ib+i)) + (sin60*(b(ib+i))) |
---|
1484 | i = i + inc3 |
---|
1485 | j = j + inc4 |
---|
1486 | ENDDO |
---|
1487 | ibase = ibase + inc1 |
---|
1488 | jbase = jbase + inc2 |
---|
1489 | ENDDO |
---|
1490 | ia = ia + iink |
---|
1491 | iink = 2 * iink |
---|
1492 | ib = ib + iink |
---|
1493 | ic = ic - iink |
---|
1494 | jbase = jbase + jump |
---|
1495 | jump = 2 * jump + jink |
---|
1496 | |
---|
1497 | IF ( ia /= ic ) THEN |
---|
1498 | |
---|
1499 | DO k = la, kstop, la |
---|
1500 | kb = k + k |
---|
1501 | kc = kb + kb |
---|
1502 | c1 = trigs(kb+1) |
---|
1503 | s1 = trigs(kb+2) |
---|
1504 | c2 = trigs(kc+1) |
---|
1505 | s2 = trigs(kc+2) |
---|
1506 | ibase = 0 |
---|
1507 | DO l = 1, la |
---|
1508 | i = ibase |
---|
1509 | j = jbase |
---|
1510 | !DIR$ IVDEP |
---|
1511 | !CDIR NODEP |
---|
1512 | !OCL NOVREC |
---|
1513 | DO ijk = 1, lot |
---|
1514 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
1515 | d(ja+j) = b(ia+i) + (b(ib+i)-b(ic+i)) |
---|
1516 | c(jb+j) = c1*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))-(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1517 | - s1*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))+(sin60*(a(ib+i)- a(ic+i)))) |
---|
1518 | d(jb+j) = s1*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))-(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1519 | + c1*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))+(sin60*(a(ib+i)- a(ic+i)))) |
---|
1520 | c(jc+j) = c2*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))+(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1521 | - s2*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))-(sin60*(a(ib+i)- a(ic+i)))) |
---|
1522 | d(jc+j) = s2*((a(ia+i)-0.5_wp*(a(ib+i)+a(ic+i)))+(sin60*(b(ib+i)+ b(ic+i)))) & |
---|
1523 | + c2*((b(ia+i)-0.5_wp*(b(ib+i)-b(ic+i)))-(sin60*(a(ib+i)- a(ic+i)))) |
---|
1524 | i = i + inc3 |
---|
1525 | j = j + inc4 |
---|
1526 | ENDDO |
---|
1527 | ibase = ibase + inc1 |
---|
1528 | jbase = jbase + inc2 |
---|
1529 | ENDDO |
---|
1530 | ia = ia + iink |
---|
1531 | ib = ib + iink |
---|
1532 | ic = ic - iink |
---|
1533 | jbase = jbase + jump |
---|
1534 | ENDDO |
---|
1535 | |
---|
1536 | IF ( ia > ic ) RETURN |
---|
1537 | |
---|
1538 | ENDIF |
---|
1539 | |
---|
1540 | ibase = 0 |
---|
1541 | DO l = 1, la |
---|
1542 | i = ibase |
---|
1543 | j = jbase |
---|
1544 | !DIR$ IVDEP |
---|
1545 | !CDIR NODEP |
---|
1546 | !OCL NOVREC |
---|
1547 | DO ijk = 1, lot |
---|
1548 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1549 | c(jb+j) = (0.5_wp*a(ia+i)-a(ib+i)) - (sin60*b(ia+i)) |
---|
1550 | c(jc+j) = -(0.5_wp*a(ia+i)-a(ib+i)) - (sin60*b(ia+i)) |
---|
1551 | i = i + inc3 |
---|
1552 | j = j + inc4 |
---|
1553 | ENDDO |
---|
1554 | ibase = ibase + inc1 |
---|
1555 | jbase = jbase + inc2 |
---|
1556 | ENDDO |
---|
1557 | |
---|
1558 | ELSE |
---|
1559 | |
---|
1560 | ssin60 = 2.0_wp * sin60 |
---|
1561 | DO l = 1, la |
---|
1562 | i = ibase |
---|
1563 | j = jbase |
---|
1564 | !DIR$ IVDEP |
---|
1565 | !CDIR NODEP |
---|
1566 | !OCL NOVREC |
---|
1567 | DO ijk = 1, lot |
---|
1568 | c(ja+j) = 2.0_wp*(a(ia+i)+a(ib+i)) |
---|
1569 | c(jb+j) = (2.0_wp*a(ia+i)-a(ib+i)) - (ssin60*b(ib+i)) |
---|
1570 | c(jc+j) = (2.0_wp*a(ia+i)-a(ib+i)) + (ssin60*b(ib+i)) |
---|
1571 | i = i + inc3 |
---|
1572 | j = j + inc4 |
---|
1573 | ENDDO |
---|
1574 | ibase = ibase + inc1 |
---|
1575 | jbase = jbase + inc2 |
---|
1576 | ENDDO |
---|
1577 | |
---|
1578 | ENDIF |
---|
1579 | |
---|
1580 | ! |
---|
1581 | !-- Coding for factor 4 |
---|
1582 | CASE ( 3 ) |
---|
1583 | |
---|
1584 | ia = 1 |
---|
1585 | ib = ia + (2*m-la) * inc1 |
---|
1586 | ic = ib + 2*m*inc1 |
---|
1587 | id = ib |
---|
1588 | ja = 1 |
---|
1589 | jb = ja + jink |
---|
1590 | jc = jb + jink |
---|
1591 | jd = jc + jink |
---|
1592 | |
---|
1593 | IF ( la /= m ) THEN |
---|
1594 | |
---|
1595 | DO l = 1, la |
---|
1596 | i = ibase |
---|
1597 | j = jbase |
---|
1598 | !DIR$ IVDEP |
---|
1599 | !CDIR NODEP |
---|
1600 | !OCL NOVREC |
---|
1601 | DO ijk = 1, lot |
---|
1602 | c(ja+j) = (a(ia+i)+a(ic+i)) + a(ib+i) |
---|
1603 | c(jb+j) = (a(ia+i)-a(ic+i)) - b(ib+i) |
---|
1604 | c(jc+j) = (a(ia+i)+a(ic+i)) - a(ib+i) |
---|
1605 | c(jd+j) = (a(ia+i)-a(ic+i)) + b(ib+i) |
---|
1606 | i = i + inc3 |
---|
1607 | j = j + inc4 |
---|
1608 | ENDDO |
---|
1609 | ibase = ibase + inc1 |
---|
1610 | jbase = jbase + inc2 |
---|
1611 | ENDDO |
---|
1612 | ia = ia + iink |
---|
1613 | iink = 2 * iink |
---|
1614 | ib = ib + iink |
---|
1615 | ic = ic - iink |
---|
1616 | id = id - iink |
---|
1617 | jbase = jbase + jump |
---|
1618 | jump = 2 * jump + jink |
---|
1619 | |
---|
1620 | IF ( ib /= ic ) THEN |
---|
1621 | |
---|
1622 | DO k = la, kstop, la |
---|
1623 | kb = k + k |
---|
1624 | kc = kb + kb |
---|
1625 | kd = kc + kb |
---|
1626 | c1 = trigs(kb+1) |
---|
1627 | s1 = trigs(kb+2) |
---|
1628 | c2 = trigs(kc+1) |
---|
1629 | s2 = trigs(kc+2) |
---|
1630 | c3 = trigs(kd+1) |
---|
1631 | s3 = trigs(kd+2) |
---|
1632 | ibase = 0 |
---|
1633 | DO l = 1, la |
---|
1634 | i = ibase |
---|
1635 | j = jbase |
---|
1636 | !DIR$ IVDEP |
---|
1637 | !CDIR NODEP |
---|
1638 | !OCL NOVREC |
---|
1639 | DO ijk = 1, lot |
---|
1640 | c(ja+j) = (a(ia+i)+a(ic+i)) + (a(ib+i)+a(id+i)) |
---|
1641 | d(ja+j) = (b(ia+i)-b(ic+i)) + (b(ib+i)-b(id+i)) |
---|
1642 | c(jc+j) = c2*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) - s2*((b(ia+i)-b(ic+i))& |
---|
1643 | -(b(ib+i)-b(id+i))) |
---|
1644 | d(jc+j) = s2*((a(ia+i)+a(ic+i))-(a(ib+i)+a(id+i))) + c2*((b(ia+i)-b(ic+i))& |
---|
1645 | -(b(ib+i)-b(id+i))) |
---|
1646 | c(jb+j) = c1*((a(ia+i)-a(ic+i))-(b(ib+i)+b(id+i))) - s1*((b(ia+i)+b(ic+i))& |
---|
1647 | +(a(ib+i)-a(id+i))) |
---|
1648 | d(jb+j) = s1*((a(ia+i)-a(ic+i))-(b(ib+i)+b(id+i))) + c1*((b(ia+i)+b(ic+i))& |
---|
1649 | +(a(ib+i)-a(id+i))) |
---|
1650 | c(jd+j) = c3*((a(ia+i)-a(ic+i))+(b(ib+i)+b(id+i))) - s3*((b(ia+i)+b(ic+i))& |
---|
1651 | -(a(ib+i)-a(id+i))) |
---|
1652 | d(jd+j) = s3*((a(ia+i)-a(ic+i))+(b(ib+i)+b(id+i))) + c3*((b(ia+i)+b(ic+i))& |
---|
1653 | -(a(ib+i)-a(id+i))) |
---|
1654 | i = i + inc3 |
---|
1655 | j = j + inc4 |
---|
1656 | ENDDO |
---|
1657 | ibase = ibase + inc1 |
---|
1658 | jbase = jbase + inc2 |
---|
1659 | ENDDO |
---|
1660 | ia = ia + iink |
---|
1661 | ib = ib + iink |
---|
1662 | ic = ic - iink |
---|
1663 | id = id - iink |
---|
1664 | jbase = jbase + jump |
---|
1665 | ENDDO |
---|
1666 | |
---|
1667 | IF ( ib > ic ) RETURN |
---|
1668 | |
---|
1669 | ENDIF |
---|
1670 | |
---|
1671 | ibase = 0 |
---|
1672 | sin45 = SQRT( 0.5_wp ) |
---|
1673 | DO l = 1, la |
---|
1674 | i = ibase |
---|
1675 | j = jbase |
---|
1676 | !DIR$ IVDEP |
---|
1677 | !CDIR NODEP |
---|
1678 | !OCL NOVREC |
---|
1679 | DO ijk = 1, lot |
---|
1680 | c(ja+j) = a(ia+i) + a(ib+i) |
---|
1681 | c(jb+j) = sin45*((a(ia+i)-a(ib+i))-(b(ia+i)+b(ib+i))) |
---|
1682 | c(jc+j) = b(ib+i) - b(ia+i) |
---|
1683 | c(jd+j) = -sin45*((a(ia+i)-a(ib+i))+(b(ia+i)+b(ib+i))) |
---|
1684 | i = i + inc3 |
---|
1685 | j = j + inc4 |
---|
1686 | ENDDO |
---|
1687 | ibase = ibase + inc1 |
---|
1688 | jbase = jbase + inc2 |
---|
1689 | ENDDO |
---|
1690 | |
---|
1691 | ELSE |
---|
1692 | |
---|
1693 | DO l = 1, la |
---|
1694 | i = ibase |
---|
1695 | j = jbase |
---|
1696 | !DIR$ IVDEP |
---|
1697 | !CDIR NODEP |
---|
1698 | !OCL NOVREC |
---|
1699 | DO ijk = 1, lot |
---|
1700 | c(ja+j) = 2.0_wp*((a(ia+i)+a(ic+i))+a(ib+i)) |
---|
1701 | c(jb+j) = 2.0_wp*((a(ia+i)-a(ic+i))-b(ib+i)) |
---|
1702 | c(jc+j) = 2.0_wp*((a(ia+i)+a(ic+i))-a(ib+i)) |
---|
1703 | c(jd+j) = 2.0_wp*((a(ia+i)-a(ic+i))+b(ib+i)) |
---|
1704 | i = i + inc3 |
---|
1705 | j = j + inc4 |
---|
1706 | ENDDO |
---|
1707 | ibase = ibase + inc1 |
---|
1708 | jbase = jbase + inc2 |
---|
1709 | ENDDO |
---|
1710 | |
---|
1711 | ENDIF |
---|
1712 | |
---|
1713 | ! |
---|
1714 | !-- Coding for factor 5 |
---|
1715 | CASE ( 4 ) |
---|
1716 | |
---|
1717 | ia = 1 |
---|
1718 | ib = ia + (2*m-la) * inc1 |
---|
1719 | ic = ib + 2*m*inc1 |
---|
1720 | id = ic |
---|
1721 | ie = ib |
---|
1722 | ja = 1 |
---|
1723 | jb = ja + jink |
---|
1724 | jc = jb + jink |
---|
1725 | jd = jc + jink |
---|
1726 | je = jd + jink |
---|
1727 | |
---|
1728 | IF ( la /= m ) THEN |
---|
1729 | |
---|
1730 | DO l = 1, la |
---|
1731 | i = ibase |
---|
1732 | j = jbase |
---|
1733 | !DIR$ IVDEP |
---|
1734 | !CDIR NODEP |
---|
1735 | !OCL NOVREC |
---|
1736 | DO ijk = 1, lot |
---|
1737 | c(ja+j) = a(ia+i) + (a(ib+i)+a(ic+i)) |
---|
1738 | c(jb+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qrt5*(a(ib+i)-a(ic+i))) - & |
---|
1739 | (sin72*b(ib+i)+sin36*b(ic+i)) |
---|
1740 | c(jc+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qrt5*(a(ib+i)-a(ic+i))) - & |
---|
1741 | (sin36*b(ib+i)-sin72*b(ic+i)) |
---|
1742 | c(jd+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qrt5*(a(ib+i)-a(ic+i))) + & |
---|
1743 | (sin36*b(ib+i)-sin72*b(ic+i)) |
---|
1744 | c(je+j) = ((a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qrt5*(a(ib+i)-a(ic+i))) + & |
---|
1745 | (sin72*b(ib+i)+sin36*b(ic+i)) |
---|
1746 | i = i + inc3 |
---|
1747 | j = j + inc4 |
---|
1748 | ENDDO |
---|
1749 | ibase = ibase + inc1 |
---|
1750 | jbase = jbase + inc2 |
---|
1751 | ENDDO |
---|
1752 | ia = ia + iink |
---|
1753 | iink = 2 * iink |
---|
1754 | ib = ib + iink |
---|
1755 | ic = ic + iink |
---|
1756 | id = id - iink |
---|
1757 | ie = ie - iink |
---|
1758 | jbase = jbase + jump |
---|
1759 | jump = 2 * jump + jink |
---|
1760 | |
---|
1761 | IF ( ib /= id ) THEN |
---|
1762 | |
---|
1763 | DO k = la, kstop, la |
---|
1764 | kb = k + k |
---|
1765 | kc = kb + kb |
---|
1766 | kd = kc + kb |
---|
1767 | ke = kd + kb |
---|
1768 | c1 = trigs(kb+1) |
---|
1769 | s1 = trigs(kb+2) |
---|
1770 | c2 = trigs(kc+1) |
---|
1771 | s2 = trigs(kc+2) |
---|
1772 | c3 = trigs(kd+1) |
---|
1773 | s3 = trigs(kd+2) |
---|
1774 | c4 = trigs(ke+1) |
---|
1775 | s4 = trigs(ke+2) |
---|
1776 | ibase = 0 |
---|
1777 | DO l = 1, la |
---|
1778 | i = ibase |
---|
1779 | j = jbase |
---|
1780 | !DIR$ IVDEP |
---|
1781 | !CDIR NODEP |
---|
1782 | !OCL NOVREC |
---|
1783 | DO ijk = 1, lot |
---|
1784 | a10(ijk) = (a(ia+i)-0.25_wp*((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i)))) + & |
---|
1785 | qrt5*((a(ib+i)+a(ie+i))-(a(ic+i)+a(id+i))) |
---|
1786 | a20(ijk) = (a(ia+i)-0.25_wp*((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i)))) - & |
---|
1787 | qrt5*((a(ib+i)+a(ie+i))-(a(ic+i)+a(id+i))) |
---|
1788 | b10(ijk) = (b(ia+i)-0.25_wp*((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i)))) + & |
---|
1789 | qrt5*((b(ib+i)-b(ie+i))-(b(ic+i)-b(id+i))) |
---|
1790 | b20(ijk) = (b(ia+i)-0.25_wp*((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i)))) - & |
---|
1791 | qrt5*((b(ib+i)-b(ie+i))-(b(ic+i)-b(id+i))) |
---|
1792 | a11(ijk) = sin72*(b(ib+i)+b(ie+i)) + sin36*(b(ic+i)+b(id+i)) |
---|
1793 | a21(ijk) = sin36*(b(ib+i)+b(ie+i)) - sin72*(b(ic+i)+b(id+i)) |
---|
1794 | b11(ijk) = sin72*(a(ib+i)-a(ie+i)) + sin36*(a(ic+i)-a(id+i)) |
---|
1795 | b21(ijk) = sin36*(a(ib+i)-a(ie+i)) - sin72*(a(ic+i)-a(id+i)) |
---|
1796 | c(ja+j) = a(ia+i) + ((a(ib+i)+a(ie+i))+(a(ic+i)+a(id+i))) |
---|
1797 | d(ja+j) = b(ia+i) + ((b(ib+i)-b(ie+i))+(b(ic+i)-b(id+i))) |
---|
1798 | c(jb+j) = c1*(a10(ijk)-a11(ijk)) - s1*(b10(ijk)+b11(ijk)) |
---|
1799 | d(jb+j) = s1*(a10(ijk)-a11(ijk)) + c1*(b10(ijk)+b11(ijk)) |
---|
1800 | c(je+j) = c4*(a10(ijk)+a11(ijk)) - s4*(b10(ijk)-b11(ijk)) |
---|
1801 | d(je+j) = s4*(a10(ijk)+a11(ijk)) + c4*(b10(ijk)-b11(ijk)) |
---|
1802 | c(jc+j) = c2*(a20(ijk)-a21(ijk)) - s2*(b20(ijk)+b21(ijk)) |
---|
1803 | d(jc+j) = s2*(a20(ijk)-a21(ijk)) + c2*(b20(ijk)+b21(ijk)) |
---|
1804 | c(jd+j) = c3*(a20(ijk)+a21(ijk)) - s3*(b20(ijk)-b21(ijk)) |
---|
1805 | d(jd+j) = s3*(a20(ijk)+a21(ijk)) + c3*(b20(ijk)-b21(ijk)) |
---|
1806 | |
---|
1807 | i = i + inc3 |
---|
1808 | j = j + inc4 |
---|
1809 | ENDDO |
---|
1810 | ibase = ibase + inc1 |
---|
1811 | jbase = jbase + inc2 |
---|
1812 | ENDDO |
---|
1813 | ia = ia + iink |
---|
1814 | ib = ib + iink |
---|
1815 | ic = ic + iink |
---|
1816 | id = id - iink |
---|
1817 | ie = ie - iink |
---|
1818 | jbase = jbase + jump |
---|
1819 | ENDDO |
---|
1820 | |
---|
1821 | IF ( ib > id ) RETURN |
---|
1822 | |
---|
1823 | ENDIF |
---|
1824 | |
---|
1825 | ibase = 0 |
---|
1826 | DO l = 1, la |
---|
1827 | i = ibase |
---|
1828 | j = jbase |
---|
1829 | !DIR$ IVDEP |
---|
1830 | !CDIR NODEP |
---|
1831 | !OCL NOVREC |
---|
1832 | DO ijk = 1, lot |
---|
1833 | c(ja+j) = (a(ia+i)+a(ib+i)) + a(ic+i) |
---|
1834 | c(jb+j) = (qrt5*(a(ia+i)-a(ib+i))+(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1835 | (sin36*b(ia+i)+sin72*b(ib+i)) |
---|
1836 | c(je+j) = -(qrt5*(a(ia+i)-a(ib+i))+(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1837 | (sin36*b(ia+i)+sin72*b(ib+i)) |
---|
1838 | c(jc+j) = (qrt5*(a(ia+i)-a(ib+i))-(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1839 | (sin72*b(ia+i)-sin36*b(ib+i)) |
---|
1840 | c(jd+j) = -(qrt5*(a(ia+i)-a(ib+i))-(0.25_wp*(a(ia+i)+a(ib+i))-a(ic+i))) - & |
---|
1841 | (sin72*b(ia+i)-sin36*b(ib+i)) |
---|
1842 | i = i + inc3 |
---|
1843 | j = j + inc4 |
---|
1844 | ENDDO |
---|
1845 | ibase = ibase + inc1 |
---|
1846 | jbase = jbase + inc2 |
---|
1847 | ENDDO |
---|
1848 | |
---|
1849 | ELSE |
---|
1850 | |
---|
1851 | qqrt5 = 2.0_wp * qrt5 |
---|
1852 | ssin36 = 2.0_wp * sin36 |
---|
1853 | ssin72 = 2.0_wp * sin72 |
---|
1854 | DO l = 1, la |
---|
1855 | i = ibase |
---|
1856 | j = jbase |
---|
1857 | !DIR$ IVDEP |
---|
1858 | !CDIR NODEP |
---|
1859 | !OCL NOVREC |
---|
1860 | DO ijk = 1, lot |
---|
1861 | c(ja+j) = 2.0_wp*(a(ia+i)+(a(ib+i)+a(ic+i))) |
---|
1862 | c(jb+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1863 | - (ssin72*b(ib+i)+ssin36*b(ic+i)) |
---|
1864 | c(jc+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1865 | - (ssin36*b(ib+i)-ssin72*b(ic+i)) |
---|
1866 | c(jd+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))-qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1867 | + (ssin36*b(ib+i)-ssin72*b(ic+i)) |
---|
1868 | c(je+j) = (2.0_wp*(a(ia+i)-0.25_wp*(a(ib+i)+a(ic+i)))+qqrt5*(a(ib+i)-a(ic+i))) & |
---|
1869 | + (ssin72*b(ib+i)+ssin36*b(ic+i)) |
---|
1870 | i = i + inc3 |
---|
1871 | j = j + inc4 |
---|
1872 | ENDDO |
---|
1873 | ibase = ibase + inc1 |
---|
1874 | jbase = jbase + inc2 |
---|
1875 | ENDDO |
---|
1876 | |
---|
1877 | ENDIF |
---|
1878 | |
---|
1879 | ! |
---|
1880 | !-- Coding for factor 6 |
---|
1881 | CASE ( 5 ) |
---|
1882 | |
---|
1883 | ia = 1 |
---|
1884 | ib = ia + (2*m-la) * inc1 |
---|
1885 | ic = ib + 2*m*inc1 |
---|
1886 | id = ic + 2*m*inc1 |
---|
1887 | ie = ic |
---|
1888 | if = ib |
---|
1889 | ja = 1 |
---|
1890 | jb = ja + jink |
---|
1891 | jc = jb + jink |
---|
1892 | jd = jc + jink |
---|
1893 | je = jd + jink |
---|
1894 | jf = je + jink |
---|
1895 | |
---|
1896 | IF ( la /= m ) THEN |
---|
1897 | |
---|
1898 | DO l = 1, la |
---|
1899 | i = ibase |
---|
1900 | j = jbase |
---|
1901 | !DIR$ IVDEP |
---|
1902 | !CDIR NODEP |
---|
1903 | !OCL NOVREC |
---|
1904 | DO ijk = 1, lot |
---|
1905 | c(ja+j) = (a(ia+i)+a(id+i)) + (a(ib+i)+a(ic+i)) |
---|
1906 | c(jd+j) = (a(ia+i)-a(id+i)) - (a(ib+i)-a(ic+i)) |
---|
1907 | c(jb+j) = ((a(ia+i)-a(id+i))+0.5_wp*(a(ib+i)-a(ic+i))) - (sin60*(b(ib+i)+b(ic+i))) |
---|
1908 | c(jf+j) = ((a(ia+i)-a(id+i))+0.5_wp*(a(ib+i)-a(ic+i))) + (sin60*(b(ib+i)+b(ic+i))) |
---|
1909 | c(jc+j) = ((a(ia+i)+a(id+i))-0.5_wp*(a(ib+i)+a(ic+i))) - (sin60*(b(ib+i)-b(ic+i))) |
---|
1910 | c(je+j) = ((a(ia+i)+a(id+i))-0.5_wp*(a(ib+i)+a(ic+i))) + (sin60*(b(ib+i)-b(ic+i))) |
---|
1911 | i = i + inc3 |
---|
1912 | j = j + inc4 |
---|
1913 | ENDDO |
---|
1914 | ibase = ibase + inc1 |
---|
1915 | jbase = jbase + inc2 |
---|
1916 | ENDDO |
---|
1917 | ia = ia + iink |
---|
1918 | iink = 2 * iink |
---|
1919 | ib = ib + iink |
---|
1920 | ic = ic + iink |
---|
1921 | id = id - iink |
---|
1922 | ie = ie - iink |
---|
1923 | if = if - iink |
---|
1924 | jbase = jbase + jump |
---|
1925 | jump = 2 * jump + jink |
---|
1926 | |
---|
1927 | IF ( ic /= id ) THEN |
---|
1928 | |
---|
1929 | DO k = la, kstop, la |
---|
1930 | kb = k + k |
---|
1931 | kc = kb + kb |
---|
1932 | kd = kc + kb |
---|
1933 | ke = kd + kb |
---|
1934 | kf = ke + kb |
---|
1935 | c1 = trigs(kb+1) |
---|
1936 | s1 = trigs(kb+2) |
---|
1937 | c2 = trigs(kc+1) |
---|
1938 | s2 = trigs(kc+2) |
---|
1939 | c3 = trigs(kd+1) |
---|
1940 | s3 = trigs(kd+2) |
---|
1941 | c4 = trigs(ke+1) |
---|
1942 | s4 = trigs(ke+2) |
---|
1943 | c5 = trigs(kf+1) |
---|
1944 | s5 = trigs(kf+2) |
---|
1945 | ibase = 0 |
---|
1946 | DO l = 1, la |
---|
1947 | i = ibase |
---|
1948 | j = jbase |
---|
1949 | !DIR$ IVDEP |
---|
1950 | !CDIR NODEP |
---|
1951 | !OCL NOVREC |
---|
1952 | DO ijk = 1, lot |
---|
1953 | a11(ijk) = (a(ie+i)+a(ib+i)) + (a(ic+i)+a(if+i)) |
---|
1954 | a20(ijk) = (a(ia+i)+a(id+i)) - 0.5_wp*a11(ijk) |
---|
1955 | a21(ijk) = sin60*((a(ie+i)+a(ib+i))-(a(ic+i)+a(if+i))) |
---|
1956 | b11(ijk) = (b(ib+i)-b(ie+i)) + (b(ic+i)-b(if+i)) |
---|
1957 | b20(ijk) = (b(ia+i)-b(id+i)) - 0.5_wp*b11(ijk) |
---|
1958 | b21(ijk) = sin60*((b(ib+i)-b(ie+i))-(b(ic+i)-b(if+i))) |
---|
1959 | |
---|
1960 | c(ja+j) = (a(ia+i)+a(id+i)) + a11(ijk) |
---|
1961 | d(ja+j) = (b(ia+i)-b(id+i)) + b11(ijk) |
---|
1962 | c(jc+j) = c2*(a20(ijk)-b21(ijk)) - s2*(b20(ijk)+a21(ijk)) |
---|
1963 | d(jc+j) = s2*(a20(ijk)-b21(ijk)) + c2*(b20(ijk)+a21(ijk)) |
---|
1964 | c(je+j) = c4*(a20(ijk)+b21(ijk)) - s4*(b20(ijk)-a21(ijk)) |
---|
1965 | d(je+j) = s4*(a20(ijk)+b21(ijk)) + c4*(b20(ijk)-a21(ijk)) |
---|
1966 | |
---|
1967 | a11(ijk) = (a(ie+i)-a(ib+i)) + (a(ic+i)-a(if+i)) |
---|
1968 | b11(ijk) = (b(ie+i)+b(ib+i)) - (b(ic+i)+b(if+i)) |
---|
1969 | a20(ijk) = (a(ia+i)-a(id+i)) - 0.5_wp*a11(ijk) |
---|
1970 | a21(ijk) = sin60*((a(ie+i)-a(ib+i))-(a(ic+i)-a(if+i))) |
---|
1971 | b20(ijk) = (b(ia+i)+b(id+i)) + 0.5_wp*b11(ijk) |
---|
1972 | b21(ijk) = sin60*((b(ie+i)+b(ib+i))+(b(ic+i)+b(if+i))) |
---|
1973 | |
---|
1974 | c(jd+j) = c3*((a(ia+i)-a(id+i))+a11(ijk)) - s3*((b(ia+i)+b(id+i))-b11(ijk)) |
---|
1975 | d(jd+j) = s3*((a(ia+i)-a(id+i))+a11(ijk)) + c3*((b(ia+i)+b(id+i))-b11(ijk)) |
---|
1976 | c(jb+j) = c1*(a20(ijk)-b21(ijk)) - s1*(b20(ijk)-a21(ijk)) |
---|
1977 | d(jb+j) = s1*(a20(ijk)-b21(ijk)) + c1*(b20(ijk)-a21(ijk)) |
---|
1978 | c(jf+j) = c5*(a20(ijk)+b21(ijk)) - s5*(b20(ijk)+a21(ijk)) |
---|
1979 | d(jf+j) = s5*(a20(ijk)+b21(ijk)) + c5*(b20(ijk)+a21(ijk)) |
---|
1980 | |
---|
1981 | i = i + inc3 |
---|
1982 | j = j + inc4 |
---|
1983 | ENDDO |
---|
1984 | ibase = ibase + inc1 |
---|
1985 | jbase = jbase + inc2 |
---|
1986 | ENDDO |
---|
1987 | ia = ia + iink |
---|
1988 | ib = ib + iink |
---|
1989 | ic = ic + iink |
---|
1990 | id = id - iink |
---|
1991 | ie = ie - iink |
---|
1992 | if = if - iink |
---|
1993 | jbase = jbase + jump |
---|
1994 | ENDDO |
---|
1995 | |
---|
1996 | IF ( ic > id ) RETURN |
---|
1997 | |
---|
1998 | ENDIF |
---|
1999 | |
---|
2000 | ibase = 0 |
---|
2001 | DO l = 1, la |
---|
2002 | i = ibase |
---|
2003 | j = jbase |
---|
2004 | !DIR$ IVDEP |
---|
2005 | !CDIR NODEP |
---|
2006 | !OCL NOVREC |
---|
2007 | DO ijk = 1, lot |
---|
2008 | c(ja+j) = a(ib+i) + (a(ia+i)+a(ic+i)) |
---|
2009 | c(jd+j) = b(ib+i) - (b(ia+i)+b(ic+i)) |
---|
2010 | c(jb+j) = (sin60*(a(ia+i)-a(ic+i))) - (0.5_wp*(b(ia+i)+b(ic+i))+b(ib+i)) |
---|
2011 | c(jf+j) = -(sin60*(a(ia+i)-a(ic+i))) - (0.5_wp*(b(ia+i)+b(ic+i))+b(ib+i)) |
---|
2012 | c(jc+j) = sin60*(b(ic+i)-b(ia+i)) + (0.5_wp*(a(ia+i)+a(ic+i))-a(ib+i)) |
---|
2013 | c(je+j) = sin60*(b(ic+i)-b(ia+i)) - (0.5_wp*(a(ia+i)+a(ic+i))-a(ib+i)) |
---|
2014 | i = i + inc3 |
---|
2015 | j = j + inc4 |
---|
2016 | ENDDO |
---|
2017 | ibase = ibase + inc1 |
---|
2018 | jbase = jbase + inc2 |
---|
2019 | ENDDO |
---|
2020 | |
---|
2021 | ELSE |
---|
2022 | |
---|
2023 | ssin60 = 2.0_wp * sin60 |
---|
2024 | DO l = 1, la |
---|
2025 | i = ibase |
---|
2026 | j = jbase |
---|
2027 | !DIR$ IVDEP |
---|
2028 | !CDIR NODEP |
---|
2029 | !OCL NOVREC |
---|
2030 | DO ijk = 1, lot |
---|
2031 | c(ja+j) = (2.0_wp*(a(ia+i)+a(id+i))) + (2.0_wp*(a(ib+i)+a(ic+i))) |
---|
2032 | c(jd+j) = (2.0_wp*(a(ia+i)-a(id+i))) - (2.0_wp*(a(ib+i)-a(ic+i))) |
---|
2033 | c(jb+j) = (2.0_wp*(a(ia+i)-a(id+i))+(a(ib+i)-a(ic+i))) - (ssin60*(b(ib+i)+b(ic+i))) |
---|
2034 | c(jf+j) = (2.0_wp*(a(ia+i)-a(id+i))+(a(ib+i)-a(ic+i))) + (ssin60*(b(ib+i)+b(ic+i))) |
---|
2035 | c(jc+j) = (2.0_wp*(a(ia+i)+a(id+i))-(a(ib+i)+a(ic+i))) - (ssin60*(b(ib+i)-b(ic+i))) |
---|
2036 | c(je+j) = (2.0_wp*(a(ia+i)+a(id+i))-(a(ib+i)+a(ic+i))) + (ssin60*(b(ib+i)-b(ic+i))) |
---|
2037 | i = i + inc3 |
---|
2038 | j = j + inc4 |
---|
2039 | ENDDO |
---|
2040 | ibase = ibase + inc1 |
---|
2041 | jbase = jbase + inc2 |
---|
2042 | ENDDO |
---|
2043 | |
---|
2044 | ENDIF |
---|
2045 | |
---|
2046 | ! |
---|
2047 | !-- Coding for factor 8 |
---|
2048 | CASE ( 6 ) |
---|
2049 | |
---|
2050 | IF ( la /= m ) THEN |
---|
2051 | ierr = 3 |
---|
2052 | RETURN |
---|
2053 | ENDIF |
---|
2054 | |
---|
2055 | ia = 1 |
---|
2056 | ib = ia + la*inc1 |
---|
2057 | ic = ib + 2*la*inc1 |
---|
2058 | id = ic + 2*la*inc1 |
---|
2059 | ie = id + 2*la*inc1 |
---|
2060 | ja = 1 |
---|
2061 | jb = ja + jink |
---|
2062 | jc = jb + jink |
---|
2063 | jd = jc + jink |
---|
2064 | je = jd + jink |
---|
2065 | jf = je + jink |
---|
2066 | jg = jf + jink |
---|
2067 | jh = jg + jink |
---|
2068 | ssin45 = SQRT( 2.0_wp ) |
---|
2069 | |
---|
2070 | DO l = 1, la |
---|
2071 | i = ibase |
---|
2072 | j = jbase |
---|
2073 | !DIR$ IVDEP |
---|
2074 | !CDIR NODEP |
---|
2075 | !OCL NOVREC |
---|
2076 | DO ijk = 1, lot |
---|
2077 | c(ja+j) = 2.0_wp*(((a(ia+i)+a(ie+i))+a(ic+i))+(a(ib+i)+a(id+i))) |
---|
2078 | c(je+j) = 2.0_wp*(((a(ia+i)+a(ie+i))+a(ic+i))-(a(ib+i)+a(id+i))) |
---|
2079 | c(jc+j) = 2.0_wp*(((a(ia+i)+a(ie+i))-a(ic+i))-(b(ib+i)-b(id+i))) |
---|
2080 | c(jg+j) = 2.0_wp*(((a(ia+i)+a(ie+i))-a(ic+i))+(b(ib+i)-b(id+i))) |
---|
2081 | c(jb+j) = 2.0_wp*((a(ia+i)-a(ie+i))-b(ic+i)) + ssin45*((a(ib+i)-a(id+i))-(b(ib+i)+b(id+i))) |
---|
2082 | c(jf+j) = 2.0_wp*((a(ia+i)-a(ie+i))-b(ic+i)) - ssin45*((a(ib+i)-a(id+i))-(b(ib+i)+b(id+i))) |
---|
2083 | c(jd+j) = 2.0_wp*((a(ia+i)-a(ie+i))+b(ic+i)) - ssin45*((a(ib+i)-a(id+i))+(b(ib+i)+b(id+i))) |
---|
2084 | c(jh+j) = 2.0_wp*((a(ia+i)-a(ie+i))+b(ic+i)) + ssin45*((a(ib+i)-a(id+i))+(b(ib+i)+b(id+i))) |
---|
2085 | i = i + inc3 |
---|
2086 | j = j + inc4 |
---|
2087 | ENDDO |
---|
2088 | ibase = ibase + inc1 |
---|
2089 | jbase = jbase + inc2 |
---|
2090 | ENDDO |
---|
2091 | |
---|
2092 | END SELECT |
---|
2093 | |
---|
2094 | END SUBROUTINE rpassm |
---|
2095 | |
---|
2096 | !------------------------------------------------------------------------------! |
---|
2097 | ! Description: |
---|
2098 | ! ------------ |
---|
2099 | !> Computes factors of n & trigonometric functins required by fft99 & fft991cy |
---|
2100 | !> Method: Dimension trigs(n),ifax(1),jfax(10),lfax(7) |
---|
2101 | !> subroutine 'set99' - computes factors of n & trigonometric |
---|
2102 | !> functins required by fft99 & fft991cy |
---|
2103 | !------------------------------------------------------------------------------! |
---|
2104 | SUBROUTINE set99( trigs, ifax, n ) |
---|
2105 | |
---|
2106 | |
---|
2107 | USE control_parameters, & |
---|
2108 | ONLY: message_string |
---|
2109 | |
---|
2110 | USE kinds |
---|
2111 | |
---|
2112 | IMPLICIT NONE |
---|
2113 | |
---|
2114 | INTEGER(iwp) :: n !< |
---|
2115 | |
---|
2116 | INTEGER(iwp) :: ifax(*) !< |
---|
2117 | REAL(wp) :: trigs(*) !< |
---|
2118 | |
---|
2119 | |
---|
2120 | REAL(wp) :: angle !< |
---|
2121 | REAL(wp) :: del !< |
---|
2122 | INTEGER(iwp) :: i !< |
---|
2123 | INTEGER(iwp) :: ifac !< |
---|
2124 | INTEGER(iwp) :: ixxx !< |
---|
2125 | INTEGER(iwp) :: k !< |
---|
2126 | INTEGER(iwp) :: l !< |
---|
2127 | INTEGER(iwp) :: nfax !< |
---|
2128 | INTEGER(iwp) :: nhl !< |
---|
2129 | INTEGER(iwp) :: nil !< |
---|
2130 | INTEGER(iwp) :: nu !< |
---|
2131 | |
---|
2132 | INTEGER(iwp) :: jfax(10) !< |
---|
2133 | INTEGER(iwp) :: lfax(7) !< |
---|
2134 | |
---|
2135 | DATA lfax / 6, 8, 5, 4, 3, 2, 1 / |
---|
2136 | |
---|
2137 | |
---|
2138 | ixxx = 1 |
---|
2139 | |
---|
2140 | del = 4.0_wp * ASIN( 1.0_wp ) / REAL( n, KIND=wp ) |
---|
2141 | nil = 0 |
---|
2142 | nhl = (n/2) - 1 |
---|
2143 | DO k = nil, nhl |
---|
2144 | angle = REAL( k, KIND=wp ) * del |
---|
2145 | trigs(2*k+1) = COS( angle ) |
---|
2146 | trigs(2*k+2) = SIN( angle ) |
---|
2147 | ENDDO |
---|
2148 | |
---|
2149 | ! |
---|
2150 | !-- Find factors of n (8,6,5,4,3,2; only one 8 allowed). |
---|
2151 | !-- Look for sixes first, store factors in descending order. |
---|
2152 | nu = n |
---|
2153 | ifac = 6 |
---|
2154 | k = 0 |
---|
2155 | l = 1 |
---|
2156 | |
---|
2157 | DO |
---|
2158 | |
---|
2159 | IF ( MOD( nu, ifac ) == 0 ) THEN |
---|
2160 | k = k + 1 |
---|
2161 | jfax(k) = ifac |
---|
2162 | IF ( ifac == 8 .AND. k /= 1 ) THEN |
---|
2163 | jfax(1) = 8 |
---|
2164 | jfax(k) = 6 |
---|
2165 | ENDIF |
---|
2166 | nu = nu/ifac |
---|
2167 | IF ( nu == 1 ) EXIT |
---|
2168 | IF ( ifac /= 8 ) CYCLE |
---|
2169 | ENDIF |
---|
2170 | |
---|
2171 | l = l + 1 |
---|
2172 | ifac = lfax(l) |
---|
2173 | IF (ifac < 2 ) THEN |
---|
2174 | message_string = 'number of gridpoints along x or/and y ' // & |
---|
2175 | 'contain illegal factors' // & |
---|
2176 | '&only factors 2, 3, 5 are allowed' |
---|
2177 | CALL message( 'temperton_fft', 'PA0311', 1, 2, 0, 6, 0 ) |
---|
2178 | RETURN |
---|
2179 | ENDIF |
---|
2180 | |
---|
2181 | ENDDO |
---|
2182 | ! |
---|
2183 | !-- Now reverse order of factors |
---|
2184 | nfax = k |
---|
2185 | ifax(1) = nfax |
---|
2186 | DO i = 1, nfax |
---|
2187 | ifax(nfax+2-i) = jfax(i) |
---|
2188 | ENDDO |
---|
2189 | ifax(10) = n |
---|
2190 | |
---|
2191 | END SUBROUTINE set99 |
---|
2192 | |
---|
2193 | END MODULE temperton_fft |
---|