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c_pass_7.c

/* fft/c_pass_7.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */

static int
FUNCTION(fft_complex,pass_7) (const BASE in[],
                              const size_t istride,
                              BASE out[],
                              const size_t ostride,
                              const gsl_fft_direction sign,
                              const size_t product,
                              const size_t n,
                              const TYPE(gsl_complex) twiddle1[],
                              const TYPE(gsl_complex) twiddle2[],
                              const TYPE(gsl_complex) twiddle3[],
                              const TYPE(gsl_complex) twiddle4[],
                              const TYPE(gsl_complex) twiddle5[],
                              const TYPE(gsl_complex) twiddle6[])
{
  size_t i = 0, j = 0;
  size_t k, k1;

  const size_t factor = 7;
  const size_t m = n / factor;
  const size_t q = n / product;
  const size_t p_1 = product / factor;
  const size_t jump = (factor - 1) * p_1;

  const ATOMIC c1 = cos(1.0 * 2.0 * M_PI / 7.0) ;
  const ATOMIC c2 = cos(2.0 * 2.0 * M_PI / 7.0) ;
  const ATOMIC c3 = cos(3.0 * 2.0 * M_PI / 7.0) ;

  const ATOMIC s1 = sin(1.0 * 2.0 * M_PI / 7.0) ;
  const ATOMIC s2 = sin(2.0 * 2.0 * M_PI / 7.0) ;
  const ATOMIC s3 = sin(3.0 * 2.0 * M_PI / 7.0) ;

  for (k = 0; k < q; k++)
    {
      ATOMIC w1_real, w1_imag, w2_real, w2_imag, w3_real, w3_imag, w4_real,
        w4_imag, w5_real, w5_imag, w6_real, w6_imag;

      if (k == 0)
        {
          w1_real = 1.0;
          w1_imag = 0.0;
          w2_real = 1.0;
          w2_imag = 0.0;
          w3_real = 1.0;
          w3_imag = 0.0;
          w4_real = 1.0;
          w4_imag = 0.0;
          w5_real = 1.0;
          w5_imag = 0.0;
          w6_real = 1.0;
          w6_imag = 0.0;
        }
      else
        {
          if (sign == gsl_fft_forward)
            {
              /* forward tranform */
              w1_real = GSL_REAL(twiddle1[k - 1]);
              w1_imag = GSL_IMAG(twiddle1[k - 1]);
              w2_real = GSL_REAL(twiddle2[k - 1]);
              w2_imag = GSL_IMAG(twiddle2[k - 1]);
              w3_real = GSL_REAL(twiddle3[k - 1]);
              w3_imag = GSL_IMAG(twiddle3[k - 1]);
              w4_real = GSL_REAL(twiddle4[k - 1]);
              w4_imag = GSL_IMAG(twiddle4[k - 1]);
              w5_real = GSL_REAL(twiddle5[k - 1]);
              w5_imag = GSL_IMAG(twiddle5[k - 1]);
              w6_real = GSL_REAL(twiddle6[k - 1]);
              w6_imag = GSL_IMAG(twiddle6[k - 1]);
            }
          else
            {
              /* backward tranform: w -> conjugate(w) */
              w1_real = GSL_REAL(twiddle1[k - 1]);
              w1_imag = -GSL_IMAG(twiddle1[k - 1]);
              w2_real = GSL_REAL(twiddle2[k - 1]);
              w2_imag = -GSL_IMAG(twiddle2[k - 1]);
              w3_real = GSL_REAL(twiddle3[k - 1]);
              w3_imag = -GSL_IMAG(twiddle3[k - 1]);
              w4_real = GSL_REAL(twiddle4[k - 1]);
              w4_imag = -GSL_IMAG(twiddle4[k - 1]);
              w5_real = GSL_REAL(twiddle5[k - 1]);
              w5_imag = -GSL_IMAG(twiddle5[k - 1]);
              w6_real = GSL_REAL(twiddle6[k - 1]);
              w6_imag = -GSL_IMAG(twiddle6[k - 1]);
            }
        }

      for (k1 = 0; k1 < p_1; k1++)
        {
          const ATOMIC z0_real = REAL(in,istride,i);
          const ATOMIC z0_imag = IMAG(in,istride,i);
          const ATOMIC z1_real = REAL(in,istride,i+m);
          const ATOMIC z1_imag = IMAG(in,istride,i+m);
          const ATOMIC z2_real = REAL(in,istride,i+2*m);
          const ATOMIC z2_imag = IMAG(in,istride,i+2*m);
          const ATOMIC z3_real = REAL(in,istride,i+3*m);
          const ATOMIC z3_imag = IMAG(in,istride,i+3*m);
          const ATOMIC z4_real = REAL(in,istride,i+4*m);
          const ATOMIC z4_imag = IMAG(in,istride,i+4*m);
          const ATOMIC z5_real = REAL(in,istride,i+5*m);
          const ATOMIC z5_imag = IMAG(in,istride,i+5*m);
          const ATOMIC z6_real = REAL(in,istride,i+6*m);
          const ATOMIC z6_imag = IMAG(in,istride,i+6*m);

          /* compute x = W(7) z */
          
          /* t0 = z1 + z6 */
          const ATOMIC t0_real = z1_real + z6_real ;
          const ATOMIC t0_imag = z1_imag + z6_imag ; 
          
          /* t1 = z1 - z6 */
          const ATOMIC t1_real = z1_real - z6_real ;
          const ATOMIC t1_imag = z1_imag - z6_imag ; 
          
          /* t2 = z2 + z5 */
          const ATOMIC t2_real = z2_real + z5_real ;
          const ATOMIC t2_imag = z2_imag + z5_imag ; 
          
          /* t3 = z2 - z5 */
          const ATOMIC t3_real = z2_real - z5_real ;
          const ATOMIC t3_imag = z2_imag - z5_imag ; 
          
          /* t4 = z4 + z3 */
          const ATOMIC t4_real = z4_real + z3_real ;
          const ATOMIC t4_imag = z4_imag + z3_imag ; 
          
          /* t5 = z4 - z3 */
          const ATOMIC t5_real = z4_real - z3_real ;
          const ATOMIC t5_imag = z4_imag - z3_imag ; 
          
          /* t6 = t2 + t0 */
          const ATOMIC t6_real = t2_real + t0_real ;
          const ATOMIC t6_imag = t2_imag + t0_imag ;
          
          /* t7 = t5 + t3 */
          const ATOMIC t7_real = t5_real + t3_real ;
          const ATOMIC t7_imag = t5_imag + t3_imag ;
          
          /* b0 = z0 + t6 + t4 */
          const ATOMIC b0_real = z0_real + t6_real + t4_real ;
          const ATOMIC b0_imag = z0_imag + t6_imag + t4_imag ;
          
          /* b1 = ((cos(2pi/7) + cos(4pi/7) + cos(6pi/7))/3-1) (t6 + t4) */
          const ATOMIC b1_real = (((c1 + c2 + c3)/3.0 - 1.0) * (t6_real + t4_real));
          const ATOMIC b1_imag = (((c1 + c2 + c3)/3.0 - 1.0) * (t6_imag + t4_imag));
          
          /* b2 = ((2*cos(2pi/7) - cos(4pi/7) - cos(6pi/7))/3) (t0 - t4) */
          const ATOMIC b2_real = (((2.0 * c1 - c2 - c3)/3.0) * (t0_real - t4_real));
          const ATOMIC b2_imag = (((2.0 * c1 - c2 - c3)/3.0) * (t0_imag - t4_imag));
          
          /* b3 = ((cos(2pi/7) - 2*cos(4pi/7) + cos(6pi/7))/3) (t4 - t2) */
          const ATOMIC b3_real = (((c1 - 2.0*c2 + c3)/3.0) * (t4_real - t2_real));
          const ATOMIC b3_imag = (((c1 - 2.0*c2 + c3)/3.0) * (t4_imag - t2_imag));
          
          /* b4 = ((cos(2pi/7) + cos(4pi/7) - 2*cos(6pi/7))/3) (t2 - t0) */
          const ATOMIC b4_real = (((c1 + c2 - 2.0 * c3)/3.0) * (t2_real - t0_real));
          const ATOMIC b4_imag = (((c1 + c2 - 2.0 * c3)/3.0) * (t2_imag - t0_imag));
          
          /* b5 = sign * ((sin(2pi/7) + sin(4pi/7) - sin(6pi/7))/3) (t7 + t1) */
          const ATOMIC b5_real = (-(int)sign) * ((s1 + s2 - s3)/3.0) * (t7_real + t1_real) ;
          const ATOMIC b5_imag = (-(int)sign) * ((s1 + s2 - s3)/3.0) * (t7_imag + t1_imag) ;
          
          /* b6 = sign * ((2sin(2pi/7) - sin(4pi/7) + sin(6pi/7))/3) (t1 - t5) */
          const ATOMIC b6_real = (-(int)sign) * ((2.0 * s1 - s2 + s3)/3.0) * (t1_real - t5_real) ;
          const ATOMIC b6_imag = (-(int)sign) * ((2.0 * s1 - s2 + s3)/3.0) * (t1_imag - t5_imag) ;
          
          /* b7 = sign * ((sin(2pi/7) - 2sin(4pi/7) - sin(6pi/7))/3) (t5 - t3) */
          const ATOMIC b7_real = (-(int)sign) * ((s1 - 2.0 * s2 - s3)/3.0) * (t5_real - t3_real) ;
          const ATOMIC b7_imag = (-(int)sign) * ((s1 - 2.0 * s2 - s3)/3.0) * (t5_imag - t3_imag) ;
          
          /* b8 = sign * ((sin(2pi/7) + sin(4pi/7) + 2sin(6pi/7))/3) (t3 - t1) */
          const ATOMIC b8_real = (-(int)sign) * ((s1 + s2 + 2.0 * s3)/3.0) * (t3_real - t1_real) ;
          const ATOMIC b8_imag = (-(int)sign) * ((s1 + s2 + 2.0 * s3)/3.0) * (t3_imag - t1_imag) ;
          
          
          /* T0 = b0 + b1 */
          const ATOMIC T0_real = b0_real + b1_real ;
          const ATOMIC T0_imag = b0_imag + b1_imag ;
          
          /* T1 = b2 + b3 */
          const ATOMIC T1_real = b2_real + b3_real ;
          const ATOMIC T1_imag = b2_imag + b3_imag ;
          
          /* T2 = b4 - b3 */
          const ATOMIC T2_real = b4_real - b3_real ;
          const ATOMIC T2_imag = b4_imag - b3_imag ;
          
          /* T3 = -b2 - b4 */
          const ATOMIC T3_real = -b2_real - b4_real ;
          const ATOMIC T3_imag = -b2_imag - b4_imag ;
          
          /* T4 = b6 + b7 */
          const ATOMIC T4_real = b6_real + b7_real ;
          const ATOMIC T4_imag = b6_imag + b7_imag ;
          
          /* T5 = b8 - b7 */
          const ATOMIC T5_real = b8_real - b7_real ;
          const ATOMIC T5_imag = b8_imag - b7_imag ;
          
          /* T6 = -b8 - b6 */
          const ATOMIC T6_real = -b8_real - b6_real ;
          const ATOMIC T6_imag = -b8_imag - b6_imag ;
          
          /* T7 = T0 + T1 */
          const ATOMIC T7_real = T0_real + T1_real ;
          const ATOMIC T7_imag = T0_imag + T1_imag ;
          
          /* T8 = T0 + T2 */
          const ATOMIC T8_real = T0_real + T2_real ;
          const ATOMIC T8_imag = T0_imag + T2_imag ;
          
          /* T9 = T0 + T3 */
          const ATOMIC T9_real = T0_real + T3_real ;
          const ATOMIC T9_imag = T0_imag + T3_imag ;
          
          /* T10 = T4 + b5 */
          const ATOMIC T10_real = T4_real + b5_real ;
          const ATOMIC T10_imag = T4_imag + b5_imag ;
          
          /* T11 = T5 + b5 */
          const ATOMIC T11_real = T5_real + b5_real ;
          const ATOMIC T11_imag = T5_imag + b5_imag ;
          
          /* T12 = T6 + b5 */
          const ATOMIC T12_real = T6_real + b5_real ;
          const ATOMIC T12_imag = T6_imag + b5_imag ;
          
          
          /* x0 = b0 */
          const ATOMIC x0_real = b0_real ;
          const ATOMIC x0_imag = b0_imag ;
          
          /* x1 = T7 - i T10 */
          const ATOMIC x1_real = T7_real + T10_imag ;
          const ATOMIC x1_imag = T7_imag - T10_real ;
          
          /* x2 = T9 - i T12 */
          const ATOMIC x2_real = T9_real + T12_imag ;
          const ATOMIC x2_imag = T9_imag - T12_real ;
          
          /* x3 = T8 + i T11 */
          const ATOMIC x3_real = T8_real - T11_imag ;
          const ATOMIC x3_imag = T8_imag + T11_real ;
          
          /* x4 = T8 - i T11 */
          const ATOMIC x4_real = T8_real + T11_imag ;
          const ATOMIC x4_imag = T8_imag - T11_real ;
          
          /* x5 = T9 + i T12 */
          const ATOMIC x5_real = T9_real - T12_imag ;
          const ATOMIC x5_imag = T9_imag + T12_real ;
          
          /* x6 = T7 + i T10 */
          const ATOMIC x6_real = T7_real - T10_imag ;
          const ATOMIC x6_imag = T7_imag + T10_real ;
          
          /* apply twiddle factors */
          
          /* to0 = 1 * x0 */
          REAL(out,ostride,j) = x0_real;
          IMAG(out,ostride,j) = x0_imag;
          
          /* to1 = w1 * x1 */
          REAL(out,ostride,j+p_1) = w1_real * x1_real - w1_imag * x1_imag;
          IMAG(out,ostride,j+p_1) = w1_real * x1_imag + w1_imag * x1_real;

          /* to2 = w2 * x2 */
          REAL(out,ostride,j+2*p_1) = w2_real * x2_real - w2_imag * x2_imag;
          IMAG(out,ostride,j+2*p_1) = w2_real * x2_imag + w2_imag * x2_real;

          /* to3 = w3 * x3 */
          REAL(out,ostride,j+3*p_1) = w3_real * x3_real - w3_imag * x3_imag;
          IMAG(out,ostride,j+3*p_1) = w3_real * x3_imag + w3_imag * x3_real;

          /* to4 = w4 * x4 */
          REAL(out,ostride,j+4*p_1) = w4_real * x4_real - w4_imag * x4_imag;
          IMAG(out,ostride,j+4*p_1) = w4_real * x4_imag + w4_imag * x4_real;

          /* to5 = w5 * x5 */
          REAL(out,ostride,j+5*p_1) = w5_real * x5_real - w5_imag * x5_imag;
          IMAG(out,ostride,j+5*p_1) = w5_real * x5_imag + w5_imag * x5_real;
          
          /* to6 = w6 * x6 */
          REAL(out,ostride,j+6*p_1) = w6_real * x6_real - w6_imag * x6_imag;
          IMAG(out,ostride,j+6*p_1) = w6_real * x6_imag + w6_imag * x6_real;
          
          i++; j++;
        }
      j += jump;
    }
  return 0;
}

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