text: /* fft/real_pass_5.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 void
  FUNCTION(fft_real,pass_5) (const BASE in[],
                             const size_t istride,
                             BASE out[],
                             const size_t ostride,
                             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[])
  {
    size_t k, k1;
  
    const size_t factor = 5;
    const size_t m = n / factor;
    const size_t q = n / product;
    const size_t product_1 = product / factor;
  
    const ATOMIC sina = sin (2.0 * M_PI / 5.0);
    const ATOMIC sinb = sin (2.0 * M_PI / 10.0);
  
    for (k1 = 0; k1 < q; k1++)
      {
        const size_t from0 = k1 * product_1;
        const size_t from1 = from0 + m;
        const size_t from2 = from1 + m;
        const size_t from3 = from2 + m;
        const size_t from4 = from3 + m;
        
        const ATOMIC z0_real = VECTOR(in,istride,from0);
        const ATOMIC z1_real = VECTOR(in,istride,from1);
        const ATOMIC z2_real = VECTOR(in,istride,from2);
        const ATOMIC z3_real = VECTOR(in,istride,from3);
        const ATOMIC z4_real = VECTOR(in,istride,from4);
        
        /* t1 = z1 + z4 */
        const ATOMIC t1_real = z1_real + z4_real;
  
        /* t2 = z2 + z3 */
        const ATOMIC t2_real = z2_real + z3_real;
  
        /* t3 = z1 - z4 */
        const ATOMIC t3_real = z1_real - z4_real;
  
        /* t4 = z2 - z3 */
        const ATOMIC t4_real = z2_real - z3_real;
  
        /* t5 = t1 + t2 */
        const ATOMIC t5_real = t1_real + t2_real;
  
        /* t6 = (sqrt(5)/4)(t1 - t2) */
        const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real);
  
        /* t7 = z0 - ((t5)/4) */
        const ATOMIC t7_real = z0_real - t5_real / 4.0;
  
        /* t8 = t7 + t6 */
        const ATOMIC t8_real = t7_real + t6_real;
  
        /* t9 = t7 - t6 */
        const ATOMIC t9_real = t7_real - t6_real;
  
        /* t10 = -(sin(2 pi/5) t3 + sin(2 pi/10) t4 ) */
        const ATOMIC t10_real = -sina * t3_real - sinb * t4_real;
  
        /* t11 = -(sin(2 pi/10) t3 - sin(2 pi/5) t4) */
        const ATOMIC t11_real = -sinb * t3_real + sina * t4_real;
  
        /* x0 = z0 + t5 */
        const ATOMIC x0_real = z0_real + t5_real;
  
        /* x1 = t8 + i t10 */
        const ATOMIC x1_real = t8_real;
        const ATOMIC x1_imag = t10_real;
  
        /* x2 = t9 + i t11 */
        const ATOMIC x2_real = t9_real;
        const ATOMIC x2_imag = t11_real;
  
        const size_t to0 = product * k1;
        const size_t to1 = to0 + 2 * product_1 - 1;
        const size_t to2 = to1 + 2 * product_1;
        
        VECTOR(out,ostride,to0) = x0_real;
        VECTOR(out,ostride,to1) = x1_real;
        VECTOR(out,ostride,to1 + 1) = x1_imag;
        VECTOR(out,ostride,to2) = x2_real;
        VECTOR(out,ostride,to2 + 1) = x2_imag;
      }
  
    if (product_1 == 1)
      return;
  
    for (k = 1; k < (product_1 + 1) / 2; k++)
      {
        const ATOMIC w1_real = GSL_REAL(twiddle1[k - 1]);
        const ATOMIC w1_imag = -GSL_IMAG(twiddle1[k - 1]);
        const ATOMIC w2_real = GSL_REAL(twiddle2[k - 1]);
        const ATOMIC w2_imag = -GSL_IMAG(twiddle2[k - 1]);
        const ATOMIC w3_real = GSL_REAL(twiddle3[k - 1]);
        const ATOMIC w3_imag = -GSL_IMAG(twiddle3[k - 1]);
        const ATOMIC w4_real = GSL_REAL(twiddle4[k - 1]);
        const ATOMIC w4_imag = -GSL_IMAG(twiddle4[k - 1]);
  
        for (k1 = 0; k1 < q; k1++)
          {
            const size_t from0 = k1 * product_1 + 2 * k - 1;
            const size_t from1 = from0 + m;
            const size_t from2 = from1 + m;
            const size_t from3 = from2 + m;
            const size_t from4 = from3 + m;
            
            const ATOMIC f0_real = VECTOR(in,istride,from0);
            const ATOMIC f0_imag = VECTOR(in,istride,from0 + 1);
            const ATOMIC f1_real = VECTOR(in,istride,from1);
            const ATOMIC f1_imag = VECTOR(in,istride,from1 + 1);
            const ATOMIC f2_real = VECTOR(in,istride,from2);
            const ATOMIC f2_imag = VECTOR(in,istride,from2 + 1);
            const ATOMIC f3_real = VECTOR(in,istride,from3);
            const ATOMIC f3_imag = VECTOR(in,istride,from3 + 1);
            const ATOMIC f4_real = VECTOR(in,istride,from4);
            const ATOMIC f4_imag = VECTOR(in,istride,from4 + 1);
            
            const ATOMIC z0_real = f0_real;
            const ATOMIC z0_imag = f0_imag;
            const ATOMIC z1_real = w1_real * f1_real - w1_imag * f1_imag;
            const ATOMIC z1_imag = w1_real * f1_imag + w1_imag * f1_real;
            const ATOMIC z2_real = w2_real * f2_real - w2_imag * f2_imag;
            const ATOMIC z2_imag = w2_real * f2_imag + w2_imag * f2_real;
            const ATOMIC z3_real = w3_real * f3_real - w3_imag * f3_imag;
            const ATOMIC z3_imag = w3_real * f3_imag + w3_imag * f3_real;
            const ATOMIC z4_real = w4_real * f4_real - w4_imag * f4_imag;
            const ATOMIC z4_imag = w4_real * f4_imag + w4_imag * f4_real;
            
            /* compute x = W(5) z */
            
            /* t1 = z1 + z4 */
            const ATOMIC t1_real = z1_real + z4_real;
            const ATOMIC t1_imag = z1_imag + z4_imag;
            
            /* t2 = z2 + z3 */
            const ATOMIC t2_real = z2_real + z3_real;
            const ATOMIC t2_imag = z2_imag + z3_imag;
            
            /* t3 = z1 - z4 */
            const ATOMIC t3_real = z1_real - z4_real;
            const ATOMIC t3_imag = z1_imag - z4_imag;
            
            /* t4 = z2 - z3 */
            const ATOMIC t4_real = z2_real - z3_real;
            const ATOMIC t4_imag = z2_imag - z3_imag;
            
            /* t5 = t1 + t2 */
            const ATOMIC t5_real = t1_real + t2_real;
            const ATOMIC t5_imag = t1_imag + t2_imag;
            
            /* t6 = (sqrt(5)/4)(t1 - t2) */
            const ATOMIC t6_real = (sqrt (5.0) / 4.0) * (t1_real - t2_real);
            const ATOMIC t6_imag = (sqrt (5.0) / 4.0) * (t1_imag - t2_imag);
            
            /* t7 = z0 - ((t5)/4) */
            const ATOMIC t7_real = z0_real - t5_real / 4.0;
            const ATOMIC t7_imag = z0_imag - t5_imag / 4.0;
            
            /* t8 = t7 + t6 */
            const ATOMIC t8_real = t7_real + t6_real;
            const ATOMIC t8_imag = t7_imag + t6_imag;
            
            /* t9 = t7 - t6 */
            const ATOMIC t9_real = t7_real - t6_real;
            const ATOMIC t9_imag = t7_imag - t6_imag;
            
            /* t10 = - (sin(2 pi/5) t3 + sin(2 pi/10) t4) */
            const ATOMIC t10_real = -sina * t3_real - sinb * t4_real;
            const ATOMIC t10_imag = -sina * t3_imag - sinb * t4_imag;
            
            /* t11 = -(sin(2 pi/10) t3 - sin(2 pi/5) t4) */
            const ATOMIC t11_real = -sinb * t3_real + sina * t4_real;
            const ATOMIC t11_imag = -sinb * t3_imag + sina * t4_imag;
  
            /* x0 = z0 + t5 */
            const ATOMIC x0_real = z0_real + t5_real;
            const ATOMIC x0_imag = z0_imag + t5_imag;
  
            /* x1 = t8 + i t10 */
            const ATOMIC x1_real = t8_real - t10_imag;
            const ATOMIC x1_imag = t8_imag + t10_real;
  
            /* x2 = t9 + i t11 */
            const ATOMIC x2_real = t9_real - t11_imag;
            const ATOMIC x2_imag = t9_imag + t11_real;
            
            /* x3 = t9 - i t11 */
            const ATOMIC x3_real = t9_real + t11_imag;
            const ATOMIC x3_imag = t9_imag - t11_real;
  
            /* x4 = t8 - i t10 */
            const ATOMIC x4_real = t8_real + t10_imag;
            const ATOMIC x4_imag = t8_imag - t10_real;
  
            const size_t to0 = k1 * product + 2 * k - 1;
            const size_t to1 = to0 + 2 * product_1;
            const size_t to2 = to1 + 2 * product_1;
            const size_t to3 = 2 * product_1 - 2 * k + k1 * product - 1;
            const size_t to4 = to3 + 2 * product_1;
            
            VECTOR(out,ostride,to0) = x0_real;
            VECTOR(out,ostride,to0 + 1) = x0_imag;
            
            VECTOR(out,ostride,to1) = x1_real;
            VECTOR(out,ostride,to1 + 1) = x1_imag;
            
            VECTOR(out,ostride,to2) = x2_real;
            VECTOR(out,ostride,to2 + 1) = x2_imag;
            
            VECTOR(out,ostride,to3) = x4_real;
            VECTOR(out,ostride,to3 + 1) = -x4_imag;
            
            VECTOR(out,ostride,to4) = x3_real;
            VECTOR(out,ostride,to4 + 1) = -x3_imag;
          }
      }
  
    if (product_1 % 2 == 1)
      return;
  
    for (k1 = 0; k1 < q; k1++)
      {
        const size_t from0 = k1 * product_1 + product_1 - 1;
        const size_t from1 = from0 + m;
        const size_t from2 = from1 + m;
        const size_t from3 = from2 + m;
        const size_t from4 = from3 + m;
        
        const ATOMIC z0_real = VECTOR(in,istride,from0);
        const ATOMIC z1_real = VECTOR(in,istride,from1);
        const ATOMIC z2_real = VECTOR(in,istride,from2);
        const ATOMIC z3_real = VECTOR(in,istride,from3);
        const ATOMIC z4_real = VECTOR(in,istride,from4);
        
        const ATOMIC t1 = z1_real - z4_real;
        const ATOMIC t2 = z1_real + z4_real;
        const ATOMIC t3 = z2_real - z3_real;
        const ATOMIC t4 = z2_real + z3_real;
        const ATOMIC t5 = t1 - t3;
        const ATOMIC t6 = z0_real + t5 / 4.0;
        const ATOMIC t7 = (sqrt (5.0) / 4.0) * (t1 + t3);
  
        const size_t to0 = k1 * product + product_1 - 1;
        const size_t to1 = to0 + 2 * product_1;
        const size_t to2 = to1 + 2 * product_1;
        
        VECTOR(out,ostride,to0) = t6 + t7;
        VECTOR(out,ostride,to0 + 1) = -sinb * t2 - sina * t4;
        
        VECTOR(out,ostride,to1) = t6 - t7;
        VECTOR(out,ostride,to1 + 1) = -sina * t2 + sinb * t4;
        
        VECTOR(out,ostride,to2) = z0_real - t5;
      }
  
    return;
  }
  