mirror of https://github.com/saitohirga/WSJT-X.git
185 lines
5.1 KiB
Fortran
185 lines
5.1 KiB
Fortran
SUBROUTINE xfft2(DATA,NB)
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c
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c the cooley-tukey fast fourier transform in usasi basic fortran
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c
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C .. Scalar Arguments ..
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INTEGER NB
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C ..
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C .. Array Arguments ..
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REAL DATA(NB+2)
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C ..
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C .. Local Scalars ..
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REAL DIFI,DIFR,RTHLF,SUMI,SUMR,T2I,T2R,T3I,T3R,T4I,
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+ T4R,TEMPI,TEMPR,THETA,TWOPI,U1I,U1R,U2I,U2R,U3I,U3R,
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+ U4I,U4R,W2I,W2R,W3I,W3R,WI,WR,WSTPI,WSTPR
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INTEGER I,I2,IPAR,J,K1,K2,K3,K4,KDIF,KMIN,
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+ KSTEP,L,LMAX,M,MMAX,NH
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C ..
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C .. Intrinsic Functions ..
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INTRINSIC COS,MAX0,REAL,SIN
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C ..
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C .. Data statements ..
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DATA TWOPI/6.2831853071796/,RTHLF/0.70710678118655/
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c
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c 1. real transform for the 1st dimension, n even. method--
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c transform a complex array of length n/2 whose real parts
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c are the even numbered real values and whose imaginary parts
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c are the odd numbered real values. separate and supply
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c the second half by conjugate symmetry.
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c
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NH = NB/2
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c
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c shuffle data by bit reversal, since n=2**k.
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c
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J = 1
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DO 131 I2 = 1,NB,2
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IF (J-I2) 124,127,127
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124 TEMPR = DATA(I2)
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TEMPI = DATA(I2+1)
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DATA(I2) = DATA(J)
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DATA(I2+1) = DATA(J+1)
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DATA(J) = TEMPR
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DATA(J+1) = TEMPI
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127 M = NH
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128 IF (J-M) 130,130,129
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129 J = J - M
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M = M/2
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IF (M-2) 130,128,128
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130 J = J + M
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131 CONTINUE
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c
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c main loop for factors of two. perform fourier transforms of
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c length four, with one of length two if needed. the twiddle factor
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c w=exp(-2*pi*sqrt(-1)*m/(4*mmax)). check for w=-sqrt(-1)
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c and repeat for w=w*(1-sqrt(-1))/sqrt(2).
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c
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IF (NB-2) 174,174,143
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143 IPAR = NH
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144 IF (IPAR-2) 149,146,145
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145 IPAR = IPAR/4
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GO TO 144
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146 DO 147 K1 = 1,NB,4
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K2 = K1 + 2
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TEMPR = DATA(K2)
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TEMPI = DATA(K2+1)
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DATA(K2) = DATA(K1) - TEMPR
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DATA(K2+1) = DATA(K1+1) - TEMPI
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DATA(K1) = DATA(K1) + TEMPR
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DATA(K1+1) = DATA(K1+1) + TEMPI
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147 CONTINUE
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149 MMAX = 2
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150 IF (MMAX-NH) 151,174,174
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151 LMAX = MAX0(4,MMAX/2)
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DO 173 L = 2,LMAX,4
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M = L
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IF (MMAX-2) 156,156,152
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152 THETA = -TWOPI*REAL(L)/REAL(4*MMAX)
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WR = COS(THETA)
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WI = SIN(THETA)
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155 W2R = WR*WR - WI*WI
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W2I = 2.*WR*WI
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W3R = W2R*WR - W2I*WI
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W3I = W2R*WI + W2I*WR
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156 KMIN = 1 + IPAR*M
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IF (MMAX-2) 157,157,158
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157 KMIN = 1
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158 KDIF = IPAR*MMAX
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159 KSTEP = 4*KDIF
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IF (KSTEP-NB) 160,160,169
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160 DO 168 K1 = KMIN,NB,KSTEP
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K2 = K1 + KDIF
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K3 = K2 + KDIF
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K4 = K3 + KDIF
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IF (MMAX-2) 161,161,164
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161 U1R = DATA(K1) + DATA(K2)
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U1I = DATA(K1+1) + DATA(K2+1)
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U2R = DATA(K3) + DATA(K4)
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U2I = DATA(K3+1) + DATA(K4+1)
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U3R = DATA(K1) - DATA(K2)
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U3I = DATA(K1+1) - DATA(K2+1)
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U4R = DATA(K3+1) - DATA(K4+1)
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U4I = DATA(K4) - DATA(K3)
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GO TO 167
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164 T2R = W2R*DATA(K2) - W2I*DATA(K2+1)
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T2I = W2R*DATA(K2+1) + W2I*DATA(K2)
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T3R = WR*DATA(K3) - WI*DATA(K3+1)
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T3I = WR*DATA(K3+1) + WI*DATA(K3)
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T4R = W3R*DATA(K4) - W3I*DATA(K4+1)
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T4I = W3R*DATA(K4+1) + W3I*DATA(K4)
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U1R = DATA(K1) + T2R
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U1I = DATA(K1+1) + T2I
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U2R = T3R + T4R
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U2I = T3I + T4I
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U3R = DATA(K1) - T2R
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U3I = DATA(K1+1) - T2I
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U4R = T3I - T4I
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U4I = T4R - T3R
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167 DATA(K1) = U1R + U2R
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DATA(K1+1) = U1I + U2I
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DATA(K2) = U3R + U4R
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DATA(K2+1) = U3I + U4I
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DATA(K3) = U1R - U2R
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DATA(K3+1) = U1I - U2I
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DATA(K4) = U3R - U4R
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DATA(K4+1) = U3I - U4I
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168 CONTINUE
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KDIF = KSTEP
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KMIN = 4*KMIN - 3
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GO TO 159
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169 M = M + LMAX
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IF (M-MMAX) 170,170,173
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170 TEMPR = WR
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WR = (WR+WI)*RTHLF
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WI = (WI-TEMPR)*RTHLF
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GO TO 155
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173 CONTINUE
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IPAR = 3 - IPAR
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MMAX = MMAX + MMAX
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GO TO 150
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c
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c complete a real transform in the 1st dimension, n even, by con-
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c jugate symmetries.
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c
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174 THETA = -TWOPI/REAL(NB)
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WSTPR = COS(THETA)
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WSTPI = SIN(THETA)
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WR = WSTPR
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WI = WSTPI
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I = 3
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J = NB - 1
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GO TO 207
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205 SUMR = (DATA(I)+DATA(J))/2.
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SUMI = (DATA(I+1)+DATA(J+1))/2.
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DIFR = (DATA(I)-DATA(J))/2.
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DIFI = (DATA(I+1)-DATA(J+1))/2.
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TEMPR = WR*SUMI + WI*DIFR
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TEMPI = WI*SUMI - WR*DIFR
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DATA(I) = SUMR + TEMPR
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DATA(I+1) = DIFI + TEMPI
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DATA(J) = SUMR - TEMPR
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DATA(J+1) = -DIFI + TEMPI
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I = I + 2
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J = J - 2
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TEMPR = WR
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WR = WR*WSTPR - WI*WSTPI
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WI = TEMPR*WSTPI + WI*WSTPR
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207 IF (I-J) 205,208,211
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208 DATA(I+1) = -DATA(I+1)
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211 DATA(NB+1) = DATA(1) - DATA(2)
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DATA(NB+2) = 0.
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DATA(1) = DATA(1) + DATA(2)
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DATA(2) = 0.
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RETURN
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END
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