/*
* Copyright (c) 2015-2019 Sergey Bakhurin
* Digital Signal Processing Library [http://dsplib.org]
*
* This file is part of libdspl-2.0.
*
* is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* DSPL 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 Lesser General Public License
* along with Foobar. If not, see .
*/
#include
#include
#include
#include "dspl.h"
#include "dspl_internal.h"
/*******************************************************************************
2 points DFT
*******************************************************************************/
void dft2 (complex_t *x, complex_t* y)
{
RE(y[0]) = RE(x[0]) + RE(x[1]);
IM(y[0]) = IM(x[0]) + IM(x[1]);
RE(y[1]) = RE(x[0]) - RE(x[1]);
IM(y[1]) = IM(x[0]) - IM(x[1]);
}
/*******************************************************************************
3 points DFT (Winograd algorithm)
*******************************************************************************/
void dft3 (complex_t *x, complex_t* y)
{
double a, b, c, d;
a = RE(x[0]) - 0.5 * (RE(x[1]) + RE(x[2]));
b = DFT3_W * (IM(x[1]) - IM(x[2]));
c = IM(x[0]) - 0.5 * (IM(x[1]) + IM(x[2]));
d = DFT3_W * (RE(x[2]) - RE(x[1]));
RE(y[0]) = RE(x[0]) + RE(x[1]) + RE(x[2]);
IM(y[0]) = IM(x[0]) + IM(x[1]) + IM(x[2]);
RE(y[1]) = a + b;
IM(y[1]) = c + d;
RE(y[2]) = a - b;
IM(y[2]) = c - d;
}
/*******************************************************************************
4 points DFT (Winograd algorithm)
*******************************************************************************/
void dft4 (complex_t *x, complex_t* y)
{
double a0, b0, c0, d0, a1, b1, c1, d1;
a0 = RE(x[0]) + RE(x[2]);
b0 = RE(x[1]) + RE(x[3]);
c0 = IM(x[0]) + IM(x[2]);
d0 = IM(x[1]) + IM(x[3]);
a1 = RE(x[0]) - RE(x[2]);
b1 = RE(x[1]) - RE(x[3]);
c1 = IM(x[0]) - IM(x[2]);
d1 = IM(x[1]) - IM(x[3]);
RE(y[0]) = a0 + b0;
IM(y[0]) = c0 + d0;
RE(y[1]) = a1 + d1;
IM(y[1]) = c1 - b1;
RE(y[2]) = a0 - b0;
IM(y[2]) = c0 - d0;
RE(y[3]) = a1 - d1;
IM(y[3]) = c1 + b1;
}
/*******************************************************************************
5 points DFT (Winograd algorithm)
*******************************************************************************/
void dft5 (complex_t *x, complex_t* y)
{
complex_t sum[14];
complex_t mul[6];
RE(sum[1]) = RE(x[1]) + RE(x[4]);
IM(sum[1]) = IM(x[1]) + IM(x[4]);
RE(sum[2]) = RE(x[1]) - RE(x[4]);
IM(sum[2]) = IM(x[1]) - IM(x[4]);
RE(sum[3]) = RE(x[3]) + RE(x[2]);
IM(sum[3]) = IM(x[3]) + IM(x[2]);
RE(sum[4]) = RE(x[3]) - RE(x[2]);
IM(sum[4]) = IM(x[3]) - IM(x[2]);
RE(sum[5]) = RE(sum[1]) + RE(sum[3]);
IM(sum[5]) = IM(sum[1]) + IM(sum[3]);
RE(sum[6]) = RE(sum[1]) - RE(sum[3]);
IM(sum[6]) = IM(sum[1]) - IM(sum[3]);
RE(sum[7]) = RE(sum[2]) + RE(sum[4]);
IM(sum[7]) = IM(sum[2]) + IM(sum[4]);
RE(y[0]) = RE(sum[5]) + RE(x[0]);
IM(y[0]) = IM(sum[5]) + IM(x[0]);
RE(mul[1]) = RE(sum[5]) * DFT5_W1;
IM(mul[1]) = IM(sum[5]) * DFT5_W1;
RE(mul[2]) = RE(sum[6]) * DFT5_W2;
IM(mul[2]) = IM(sum[6]) * DFT5_W2;
RE(mul[3]) = -IM(sum[2]) * DFT5_W3;
IM(mul[3]) = RE(sum[2]) * DFT5_W3;
RE(mul[4]) = -IM(sum[7]) * DFT5_W4;
IM(mul[4]) = RE(sum[7]) * DFT5_W4;
RE(mul[5]) = -IM(sum[4]) * DFT5_W5;
IM(mul[5]) = RE(sum[4]) * DFT5_W5;
RE(sum[9]) = RE(y[0]) + RE(mul[1]);
IM(sum[9]) = IM(y[0]) + IM(mul[1]);
RE(sum[10]) = RE(sum[9]) + RE(mul[2]);
IM(sum[10]) = IM(sum[9]) + IM(mul[2]);
RE(sum[11]) = RE(sum[9]) - RE(mul[2]);
IM(sum[11]) = IM(sum[9]) - IM(mul[2]);
RE(sum[12]) = RE(mul[3]) - RE(mul[4]);
IM(sum[12]) = IM(mul[3]) - IM(mul[4]);
RE(sum[13]) = RE(mul[4]) + RE(mul[5]);
IM(sum[13]) = IM(mul[4]) + IM(mul[5]);
RE(y[4]) = RE(sum[10]) + RE(sum[12]);
IM(y[4]) = IM(sum[10]) + IM(sum[12]);
RE(y[3]) = RE(sum[11]) + RE(sum[13]);
IM(y[3]) = IM(sum[11]) + IM(sum[13]);
RE(y[2]) = RE(sum[11]) - RE(sum[13]);
IM(y[2]) = IM(sum[11]) - IM(sum[13]);
RE(y[1]) = RE(sum[10]) - RE(sum[12]);
IM(y[1]) = IM(sum[10]) - IM(sum[12]);
}
/*******************************************************************************
7 points DFT (Winograd algorithm)
*******************************************************************************/
void dft7 (complex_t *x, complex_t* y)
{
complex_t sum[31];
complex_t mul[9];
RE(sum[1]) = RE(x[1]) + RE(x[6]);
IM(sum[1]) = IM(x[1]) + IM(x[6]);
RE(sum[2]) = RE(x[1]) - RE(x[6]);
IM(sum[2]) = IM(x[1]) - IM(x[6]);
RE(sum[3]) = RE(x[4]) + RE(x[3]);
IM(sum[3]) = IM(x[4]) + IM(x[3]);
RE(sum[4]) = RE(x[4]) - RE(x[3]);
IM(sum[4]) = IM(x[4]) - IM(x[3]);
/* Winograd paper mistake?! */
RE(sum[5]) = RE(x[2]) + RE(x[5]);
IM(sum[5]) = IM(x[2]) + IM(x[5]);
/* Winograd paper mistake?! */
RE(sum[6]) = RE(x[2]) - RE(x[5]);
IM(sum[6]) = IM(x[2]) - IM(x[5]);
RE(sum[7]) = RE(sum[1]) + RE(sum[3]);
IM(sum[7]) = IM(sum[1]) + IM(sum[3]);
RE(sum[8]) = RE(sum[7]) + RE(sum[5]);
IM(sum[8]) = IM(sum[7]) + IM(sum[5]);
RE(y[0]) = RE(sum[9]) = RE(sum[8]) + RE(x[0]);
IM(y[0]) = IM(sum[9]) = IM(sum[8]) + IM(x[0]);
RE(sum[10]) = RE(sum[1]) - RE(sum[3]);
IM(sum[10]) = IM(sum[1]) - IM(sum[3]);
RE(sum[11]) = RE(sum[3]) - RE(sum[5]);
IM(sum[11]) = IM(sum[3]) - IM(sum[5]);
RE(sum[12]) = RE(sum[5]) - RE(sum[1]);
IM(sum[12]) = IM(sum[5]) - IM(sum[1]);
RE(sum[13]) = RE(sum[2]) + RE(sum[4]);
IM(sum[13]) = IM(sum[2]) + IM(sum[4]);
RE(sum[14]) = RE(sum[13]) + RE(sum[6]);
IM(sum[14]) = IM(sum[13]) + IM(sum[6]);
RE(sum[15]) = RE(sum[2]) - RE(sum[4]);
IM(sum[15]) = IM(sum[2]) - IM(sum[4]);
RE(sum[16]) = RE(sum[4]) - RE(sum[6]);
IM(sum[16]) = IM(sum[4]) - IM(sum[6]);
RE(sum[17]) = RE(sum[6]) - RE(sum[2]);
IM(sum[17]) = IM(sum[6]) - IM(sum[2]);
RE(mul[1]) = DFT7_W1 * RE(sum[8]);
IM(mul[1]) = DFT7_W1 * IM(sum[8]);
RE(mul[2]) = DFT7_W2 * RE(sum[10]);
IM(mul[2]) = DFT7_W2 * IM(sum[10]);
RE(mul[3]) = DFT7_W3 * RE(sum[11]);
IM(mul[3]) = DFT7_W3 * IM(sum[11]);
RE(mul[4]) = DFT7_W4 * RE(sum[12]);
IM(mul[4]) = DFT7_W4 * IM(sum[12]);
RE(mul[5]) = -DFT7_W5 * IM(sum[14]);
IM(mul[5]) = DFT7_W5 * RE(sum[14]);
RE(mul[6]) = -DFT7_W6 * IM(sum[15]);
IM(mul[6]) = DFT7_W6 * RE(sum[15]);
RE(mul[7]) = -DFT7_W7 * IM(sum[16]);
IM(mul[7]) = DFT7_W7 * RE(sum[16]);
RE(mul[8]) = -DFT7_W8 * IM(sum[17]);
IM(mul[8]) = DFT7_W8 * RE(sum[17]);
RE(sum[18]) = RE(y[0]) + RE(mul[1]);
IM(sum[18]) = IM(y[0]) + IM(mul[1]);
RE(sum[19]) = RE(sum[18]) + RE(mul[2]);
IM(sum[19]) = IM(sum[18]) + IM(mul[2]);
RE(sum[20]) = RE(sum[19]) + RE(mul[3]);
IM(sum[20]) = IM(sum[19]) + IM(mul[3]);
RE(sum[21]) = RE(sum[18]) - RE(mul[2]);
IM(sum[21]) = IM(sum[18]) - IM(mul[2]);
RE(sum[22]) = RE(sum[21]) - RE(mul[4]);
IM(sum[22]) = IM(sum[21]) - IM(mul[4]);
RE(sum[23]) = RE(sum[18]) - RE(mul[3]);
IM(sum[23]) = IM(sum[18]) - IM(mul[3]);
RE(sum[24]) = RE(sum[23]) + RE(mul[4]);
IM(sum[24]) = IM(sum[23]) + IM(mul[4]);
RE(sum[25]) = RE(mul[5]) + RE(mul[6]);
IM(sum[25]) = IM(mul[5]) + IM(mul[6]);
RE(sum[26]) = RE(sum[25]) + RE(mul[7]);
IM(sum[26]) = IM(sum[25]) + IM(mul[7]);
RE(sum[27]) = RE(mul[5]) - RE(mul[6]);
IM(sum[27]) = IM(mul[5]) - IM(mul[6]);
RE(sum[28]) = RE(sum[27]) - RE(mul[8]);
IM(sum[28]) = IM(sum[27]) - IM(mul[8]);
RE(sum[29]) = RE(mul[5]) - RE(mul[7]);
IM(sum[29]) = IM(mul[5]) - IM(mul[7]);
RE(sum[30]) = RE(sum[29]) + RE(mul[8]);
IM(sum[30]) = IM(sum[29]) + IM(mul[8]);
RE(y[1]) = RE(sum[20]) + RE(sum[26]);
IM(y[1]) = IM(sum[20]) + IM(sum[26]);
RE(y[2]) = RE(sum[22]) + RE(sum[28]);
IM(y[2]) = IM(sum[22]) + IM(sum[28]);
RE(y[3]) = RE(sum[24]) - RE(sum[30]);
IM(y[3]) = IM(sum[24]) - IM(sum[30]);
RE(y[4]) = RE(sum[24]) + RE(sum[30]);
IM(y[4]) = IM(sum[24]) + IM(sum[30]);
RE(y[5]) = RE(sum[22]) - RE(sum[28]);
IM(y[5]) = IM(sum[22]) - IM(sum[28]);
RE(y[6]) = RE(sum[20]) - RE(sum[26]);
IM(y[6]) = IM(sum[20]) - IM(sum[26]);
}
/*******************************************************************************
8 points DFT
*******************************************************************************/
void dft8 (complex_t *x, complex_t* y)
{
complex_t t0[8];
complex_t t1[8];
double tmp;
transpose2x4(x, t0);
dft4(t0, t1);
dft4(t0+4, t1+4);
/* 0.707106781186548 - 707106781186548i */
tmp = (RE(t1[5]) + IM(t1[5])) * DFT8_W;
IM(t1[5]) = (IM(t1[5]) - RE(t1[5])) * DFT8_W;
RE(t1[5]) = tmp;
/* 0.000000000000000 - 1.000000000000000i */
tmp = RE(t1[6]);
RE(t1[6]) = IM(t1[6]);
IM(t1[6]) = -tmp;
/* -0.707106781186548 - 707106781186548i */
tmp = (IM(t1[7]) - RE(t1[7])) * DFT8_W;
IM(t1[7]) = -(IM(t1[7]) + RE(t1[7])) * DFT8_W;
RE(t1[7]) = tmp;
transpose4x2(t1, t0);
RE(t1[0]) = RE(t0[0]) + RE(t0[1]);
IM(t1[0]) = IM(t0[0]) + IM(t0[1]);
RE(t1[1]) = RE(t0[0]) - RE(t0[1]);
IM(t1[1]) = IM(t0[0]) - IM(t0[1]);
RE(t1[2]) = RE(t0[2]) + RE(t0[3]);
IM(t1[2]) = IM(t0[2]) + IM(t0[3]);
RE(t1[3]) = RE(t0[2]) - RE(t0[3]);
IM(t1[3]) = IM(t0[2]) - IM(t0[3]);
RE(t1[4]) = RE(t0[4]) + RE(t0[5]);
IM(t1[4]) = IM(t0[4]) + IM(t0[5]);
RE(t1[5]) = RE(t0[4]) - RE(t0[5]);
IM(t1[5]) = IM(t0[4]) - IM(t0[5]);
RE(t1[6]) = RE(t0[6]) + RE(t0[7]);
IM(t1[6]) = IM(t0[6]) + IM(t0[7]);
RE(t1[7]) = RE(t0[6]) - RE(t0[7]);
IM(t1[7]) = IM(t0[6]) - IM(t0[7]);
transpose2x4(t1, y);
}
/*******************************************************************************
16 points DFT (Winograd algorithm)
*******************************************************************************/
void dft16(complex_t *x, complex_t* y)
{
complex_t t0[16];
complex_t t1[16];
double tmp;
transpose4x4(x, t0);
dft4(t0, t1);
dft4(t0+4, t1+4);
dft4(t0+8, t1+8);
dft4(t0+12, t1+12);
/* #define DFT16_W1 0.923879532511287 */
/* #define DFT16_W2 0.382683432365090 */
/* #define DFT16_W3 0.707106781186548 */
/* 0.923879532511287 - 0.382683432365090i */
tmp = RE(t1[5]) * DFT16_W1 + IM(t1[5]) * DFT16_W2;
IM(t1[5]) = -RE(t1[5]) * DFT16_W2 + IM(t1[5]) * DFT16_W1;
RE(t1[5]) = tmp;
/* 0.707106781186548 - 0.707106781186547i */
tmp = ( RE(t1[6]) + IM(t1[6])) * DFT16_W3;
IM(t1[6]) = (-RE(t1[6]) + IM(t1[6])) * DFT16_W3;
RE(t1[6]) = tmp;
/* 0.382683432365090 - 0.923879532511287i */
tmp = RE(t1[7]) * DFT16_W2 + IM(t1[7]) * DFT16_W1;
IM(t1[7]) = -RE(t1[7]) * DFT16_W1 + IM(t1[7]) * DFT16_W2;
RE(t1[7]) = tmp;
/* 0.707106781186548 - 0.707106781186547i */
tmp = ( RE(t1[9]) + IM(t1[9])) * DFT16_W3;
IM(t1[9]) = (-RE(t1[9]) + IM(t1[9])) * DFT16_W3;
RE(t1[9]) = tmp;
/* 0.000000000000000 - 1.000000000000000i */
tmp = RE(t1[10]);
RE(t1[10]) = IM(t1[10]);
IM(t1[10]) = -tmp;
/* -0.707106781186547 - 0.707106781186548i */
tmp = (-RE(t1[11]) + IM(t1[11])) * DFT16_W3;
IM(t1[11]) = (-RE(t1[11]) - IM(t1[11])) * DFT16_W3;
RE(t1[11]) = tmp;
/* 0.382683432365090 - 0.923879532511287i */
tmp = RE(t1[13]) * DFT16_W2 + IM(t1[13]) * DFT16_W1;
IM(t1[13]) = -RE(t1[13]) * DFT16_W1 + IM(t1[13]) * DFT16_W2;
RE(t1[13]) = tmp;
/* -0.707106781186547 - 0.707106781186548i */
tmp = (-RE(t1[14]) + IM(t1[14])) * DFT16_W3;
IM(t1[14]) = (-RE(t1[14]) - IM(t1[14])) * DFT16_W3;
RE(t1[14]) = tmp;
/* -0.923879532511287 + 0.382683432365090i */
tmp = -RE(t1[15]) * DFT16_W1 - IM(t1[15]) * DFT16_W2;
IM(t1[15]) = RE(t1[15]) * DFT16_W2 - IM(t1[15]) * DFT16_W1;
RE(t1[15]) = tmp;
transpose4x4(t1, t0);
dft4(t0, t1);
dft4(t0+4, t1+4);
dft4(t0+8, t1+8);
dft4(t0+12, t1+12);
transpose4x4(t1, y);
}
/*******************************************************************************
32 points DFT (Winograd algorithm)
*******************************************************************************/
void dft32(complex_t *x, complex_t* y, complex_t* w)
{
complex_t t0[32];
complex_t t1[32];
int i;
transpose4x8(x, t0);
dft8(t0, t1);
dft8(t0+8, t1+8);
dft8(t0+16, t1+16);
dft8(t0+24, t1+24);
for(i = 0; i < 32; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
transpose8x4(t0, t1);
for(i = 0; i < 8; i++)
dft4(t1 + i*4, t0 + i*4);
transpose4x8(t0, y);
}
/*******************************************************************************
64 points DFT (Winograd algorithm)
*******************************************************************************/
void dft64(complex_t *x, complex_t* y, complex_t* w)
{
complex_t t0[64];
complex_t t1[64];
int i;
transpose8x8(x, t0);
for(i = 0; i < 8; i++)
dft8(t0 + i*8, t1 + i*8);
for(i = 0; i < 64; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
transpose8x8(t0, t1);
for(i = 0; i < 8; i++)
dft8(t1 + i*8, t0 + i*8);
transpose8x8(t0, y);
}
/*******************************************************************************
256 points DFT (Winograd algorithm)
*******************************************************************************/
void dft128(complex_t *x, complex_t* y, complex_t* w)
{
complex_t t0[128];
complex_t t1[128];
int i;
matrix_transpose_cmplx(x,8,16,t0);
for(i = 0; i < 8; i++)
dft16(t0 + i*16, t1 + i*16);
for(i = 0; i < 128; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
matrix_transpose_cmplx(t0, 16, 8, t1);
for(i = 0; i < 16; i++)
dft8(t1 + i*8, t0 + i*8);
matrix_transpose_cmplx(t0, 8, 16, y);
}
/*******************************************************************************
256 points DFT (Winograd algorithm)
*******************************************************************************/
void dft256(complex_t *x, complex_t* y, complex_t* w)
{
complex_t t0[256];
complex_t t1[256];
int i;
transpose16x16(x, t0);
for(i = 0; i < 16; i++)
dft16(t0 + i*16, t1 + i*16);
for(i = 0; i < 256; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
transpose16x16(t0, t1);
for(i = 0; i < 16; i++)
dft16(t1 + i*16, t0 + i*16);
transpose16x16(t0, y);
}
/*******************************************************************************
512 points DFT (Winograd algorithm)
*******************************************************************************/
void dft512(complex_t *x, complex_t* y, complex_t* w, complex_t* w32)
{
complex_t t0[512];
complex_t t1[512];
int i;
matrix_transpose_cmplx(x,16,32,t0);
for(i = 0; i < 16; i++)
dft32(t0 + i*32, t1 + i*32, w32);
for(i = 0; i < 512; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
matrix_transpose_cmplx(t0, 32, 16, t1);
for(i = 0; i < 32; i++)
dft16(t1 + i*16, t0 + i*16);
matrix_transpose_cmplx(t0, 16, 32, y);
}
/*******************************************************************************
1024 points DFT (Winograd algorithm)
*******************************************************************************/
void dft1024(complex_t *x, complex_t* y, complex_t* w, complex_t* w32)
{
complex_t t0[1024];
complex_t t1[1024];
int i;
matrix_transpose_cmplx(x,32,32,t0);
for(i = 0; i < 32; i++)
dft32(t0 + i*32, t1 + i*32, w32);
for(i = 0; i < 1024; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
matrix_transpose_cmplx(t0, 32, 32, t1);
for(i = 0; i < 32; i++)
dft32(t1 + i*32, t0 + i*32, w32);
matrix_transpose_cmplx(t0, 32, 32, y);
}
/*******************************************************************************
2048 points DFT (Winograd algorithm)
*******************************************************************************/
void dft2048(complex_t *x, complex_t* y, complex_t* w,
complex_t* w32, complex_t* w64)
{
complex_t *t0 = NULL;
complex_t *t1 = NULL;
int i;
t0 = (complex_t*)malloc(2048*sizeof(complex_t));
t1 = (complex_t*)malloc(2048*sizeof(complex_t));
matrix_transpose_cmplx(x,32,64,t0);
for(i = 0; i < 32; i++)
dft64(t0 + i*64, t1 + i*64, w64);
for(i = 0; i < 2048; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
matrix_transpose_cmplx(t0, 64, 32, t1);
for(i = 0; i < 64; i++)
dft32(t1 + i*32, t0 + i*32, w32);
matrix_transpose_cmplx(t0, 32, 64, y);
free(t0);
free(t1);
}
/*******************************************************************************
4096 points DFT (Winograd algorithm)
*******************************************************************************/
void dft4096(complex_t *x, complex_t* y, complex_t* w, complex_t* w256)
{
complex_t *t0 = NULL;
complex_t *t1 = NULL;
int i;
t0 = (complex_t*)malloc(4096*sizeof(complex_t));
t1 = (complex_t*)malloc(4096*sizeof(complex_t));
matrix_transpose_cmplx(x,16,256,t0);
for(i = 0; i < 16; i++)
dft256(t0 + i*256, t1 + i*256, w256);
for(i = 0; i < 4096; i++)
{
RE(t0[i]) = CMRE(t1[i], w[i]);
IM(t0[i]) = CMIM(t1[i], w[i]);
}
matrix_transpose_cmplx(t0, 256, 16, t1);
for(i = 0; i < 256; i++)
dft16(t1 + i*16, t0 + i*16);
matrix_transpose_cmplx(t0, 16, 256, y);
free(t0);
free(t1);
}
/*******************************************************************************
4 x 2 matrix transpose
*******************************************************************************/
void transpose4x2(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 4]); IM(y[ 1]) = IM(x[ 4]);
RE(y[ 2]) = RE(x[ 1]); IM(y[ 2]) = IM(x[ 1]);
RE(y[ 3]) = RE(x[ 5]); IM(y[ 3]) = IM(x[ 5]);
RE(y[ 4]) = RE(x[ 2]); IM(y[ 4]) = IM(x[ 2]);
RE(y[ 5]) = RE(x[ 6]); IM(y[ 5]) = IM(x[ 6]);
RE(y[ 6]) = RE(x[ 3]); IM(y[ 6]) = IM(x[ 3]);
RE(y[ 7]) = RE(x[ 7]); IM(y[ 7]) = IM(x[ 7]);
}
/*******************************************************************************
2 x 4 matrix transpose
*******************************************************************************/
void transpose2x4(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 2]); IM(y[ 1]) = IM(x[ 2]);
RE(y[ 2]) = RE(x[ 4]); IM(y[ 2]) = IM(x[ 4]);
RE(y[ 3]) = RE(x[ 6]); IM(y[ 3]) = IM(x[ 6]);
RE(y[ 4]) = RE(x[ 1]); IM(y[ 4]) = IM(x[ 1]);
RE(y[ 5]) = RE(x[ 3]); IM(y[ 5]) = IM(x[ 3]);
RE(y[ 6]) = RE(x[ 5]); IM(y[ 6]) = IM(x[ 5]);
RE(y[ 7]) = RE(x[ 7]); IM(y[ 7]) = IM(x[ 7]);
}
/*******************************************************************************
4 x 4 matrix transpose
*******************************************************************************/
void transpose4x4(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 4]); IM(y[ 1]) = IM(x[ 4]);
RE(y[ 2]) = RE(x[ 8]); IM(y[ 2]) = IM(x[ 8]);
RE(y[ 3]) = RE(x[12]); IM(y[ 3]) = IM(x[12]);
RE(y[ 4]) = RE(x[ 1]); IM(y[ 4]) = IM(x[ 1]);
RE(y[ 5]) = RE(x[ 5]); IM(y[ 5]) = IM(x[ 5]);
RE(y[ 6]) = RE(x[ 9]); IM(y[ 6]) = IM(x[ 9]);
RE(y[ 7]) = RE(x[13]); IM(y[ 7]) = IM(x[13]);
RE(y[ 8]) = RE(x[ 2]); IM(y[ 8]) = IM(x[ 2]);
RE(y[ 9]) = RE(x[ 6]); IM(y[ 9]) = IM(x[ 6]);
RE(y[10]) = RE(x[10]); IM(y[10]) = IM(x[10]);
RE(y[11]) = RE(x[14]); IM(y[11]) = IM(x[14]);
RE(y[12]) = RE(x[ 3]); IM(y[12]) = IM(x[ 3]);
RE(y[13]) = RE(x[ 7]); IM(y[13]) = IM(x[ 7]);
RE(y[14]) = RE(x[11]); IM(y[14]) = IM(x[11]);
RE(y[15]) = RE(x[15]); IM(y[15]) = IM(x[15]);
}
/*******************************************************************************
8 x 4 matrix transpose
*******************************************************************************/
void transpose8x4(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 8]); IM(y[ 1]) = IM(x[ 8]);
RE(y[ 2]) = RE(x[ 16]); IM(y[ 2]) = IM(x[ 16]);
RE(y[ 3]) = RE(x[ 24]); IM(y[ 3]) = IM(x[ 24]);
RE(y[ 4]) = RE(x[ 1]); IM(y[ 4]) = IM(x[ 1]);
RE(y[ 5]) = RE(x[ 9]); IM(y[ 5]) = IM(x[ 9]);
RE(y[ 6]) = RE(x[ 17]); IM(y[ 6]) = IM(x[ 17]);
RE(y[ 7]) = RE(x[ 25]); IM(y[ 7]) = IM(x[ 25]);
RE(y[ 8]) = RE(x[ 2]); IM(y[ 8]) = IM(x[ 2]);
RE(y[ 9]) = RE(x[ 10]); IM(y[ 9]) = IM(x[ 10]);
RE(y[10]) = RE(x[ 18]); IM(y[10]) = IM(x[ 18]);
RE(y[11]) = RE(x[ 26]); IM(y[11]) = IM(x[ 26]);
RE(y[12]) = RE(x[ 3]); IM(y[12]) = IM(x[ 3]);
RE(y[13]) = RE(x[ 11]); IM(y[13]) = IM(x[ 11]);
RE(y[14]) = RE(x[ 19]); IM(y[14]) = IM(x[ 19]);
RE(y[15]) = RE(x[ 27]); IM(y[15]) = IM(x[ 27]);
RE(y[16]) = RE(x[ 4]); IM(y[16]) = IM(x[ 4]);
RE(y[17]) = RE(x[ 12]); IM(y[17]) = IM(x[ 12]);
RE(y[18]) = RE(x[ 20]); IM(y[18]) = IM(x[ 20]);
RE(y[19]) = RE(x[ 28]); IM(y[19]) = IM(x[ 28]);
RE(y[20]) = RE(x[ 5]); IM(y[20]) = IM(x[ 5]);
RE(y[21]) = RE(x[ 13]); IM(y[21]) = IM(x[ 13]);
RE(y[22]) = RE(x[ 21]); IM(y[22]) = IM(x[ 21]);
RE(y[23]) = RE(x[ 29]); IM(y[23]) = IM(x[ 29]);
RE(y[24]) = RE(x[ 6]); IM(y[24]) = IM(x[ 6]);
RE(y[25]) = RE(x[ 14]); IM(y[25]) = IM(x[ 14]);
RE(y[26]) = RE(x[ 22]); IM(y[26]) = IM(x[ 22]);
RE(y[27]) = RE(x[ 30]); IM(y[27]) = IM(x[ 30]);
RE(y[28]) = RE(x[ 7]); IM(y[28]) = IM(x[ 7]);
RE(y[29]) = RE(x[ 15]); IM(y[29]) = IM(x[ 15]);
RE(y[30]) = RE(x[ 23]); IM(y[30]) = IM(x[ 23]);
RE(y[31]) = RE(x[ 31]); IM(y[31]) = IM(x[ 31]);
}
/*******************************************************************************
4 x 8 matrix transpose
*******************************************************************************/
void transpose4x8(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 4]); IM(y[ 1]) = IM(x[ 4]);
RE(y[ 2]) = RE(x[ 8]); IM(y[ 2]) = IM(x[ 8]);
RE(y[ 3]) = RE(x[ 12]); IM(y[ 3]) = IM(x[ 12]);
RE(y[ 4]) = RE(x[ 16]); IM(y[ 4]) = IM(x[ 16]);
RE(y[ 5]) = RE(x[ 20]); IM(y[ 5]) = IM(x[ 20]);
RE(y[ 6]) = RE(x[ 24]); IM(y[ 6]) = IM(x[ 24]);
RE(y[ 7]) = RE(x[ 28]); IM(y[ 7]) = IM(x[ 28]);
RE(y[ 8]) = RE(x[ 1]); IM(y[ 8]) = IM(x[ 1]);
RE(y[ 9]) = RE(x[ 5]); IM(y[ 9]) = IM(x[ 5]);
RE(y[10]) = RE(x[ 9]); IM(y[10]) = IM(x[ 9]);
RE(y[11]) = RE(x[ 13]); IM(y[11]) = IM(x[ 13]);
RE(y[12]) = RE(x[ 17]); IM(y[12]) = IM(x[ 17]);
RE(y[13]) = RE(x[ 21]); IM(y[13]) = IM(x[ 21]);
RE(y[14]) = RE(x[ 25]); IM(y[14]) = IM(x[ 25]);
RE(y[15]) = RE(x[ 29]); IM(y[15]) = IM(x[ 29]);
RE(y[16]) = RE(x[ 2]); IM(y[16]) = IM(x[ 2]);
RE(y[17]) = RE(x[ 6]); IM(y[17]) = IM(x[ 6]);
RE(y[18]) = RE(x[ 10]); IM(y[18]) = IM(x[ 10]);
RE(y[19]) = RE(x[ 14]); IM(y[19]) = IM(x[ 14]);
RE(y[20]) = RE(x[ 18]); IM(y[20]) = IM(x[ 18]);
RE(y[21]) = RE(x[ 22]); IM(y[21]) = IM(x[ 22]);
RE(y[22]) = RE(x[ 26]); IM(y[22]) = IM(x[ 26]);
RE(y[23]) = RE(x[ 30]); IM(y[23]) = IM(x[ 30]);
RE(y[24]) = RE(x[ 3]); IM(y[24]) = IM(x[ 3]);
RE(y[25]) = RE(x[ 7]); IM(y[25]) = IM(x[ 7]);
RE(y[26]) = RE(x[ 11]); IM(y[26]) = IM(x[ 11]);
RE(y[27]) = RE(x[ 15]); IM(y[27]) = IM(x[ 15]);
RE(y[28]) = RE(x[ 19]); IM(y[28]) = IM(x[ 19]);
RE(y[29]) = RE(x[ 23]); IM(y[29]) = IM(x[ 23]);
RE(y[30]) = RE(x[ 27]); IM(y[30]) = IM(x[ 27]);
RE(y[31]) = RE(x[ 31]); IM(y[31]) = IM(x[ 31]);
}
/*******************************************************************************
4 x 8 matrix transpose
*******************************************************************************/
void transpose8x8(complex_t *x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 8]); IM(y[ 1]) = IM(x[ 8]);
RE(y[ 2]) = RE(x[16]); IM(y[ 2]) = IM(x[16]);
RE(y[ 3]) = RE(x[24]); IM(y[ 3]) = IM(x[24]);
RE(y[ 4]) = RE(x[32]); IM(y[ 4]) = IM(x[32]);
RE(y[ 5]) = RE(x[40]); IM(y[ 5]) = IM(x[40]);
RE(y[ 6]) = RE(x[48]); IM(y[ 6]) = IM(x[48]);
RE(y[ 7]) = RE(x[56]); IM(y[ 7]) = IM(x[56]);
RE(y[ 8]) = RE(x[ 1]); IM(y[ 8]) = IM(x[ 1]);
RE(y[ 9]) = RE(x[ 9]); IM(y[ 9]) = IM(x[ 9]);
RE(y[ 10]) = RE(x[17]); IM(y[ 10]) = IM(x[17]);
RE(y[ 11]) = RE(x[25]); IM(y[ 11]) = IM(x[25]);
RE(y[ 12]) = RE(x[33]); IM(y[ 12]) = IM(x[33]);
RE(y[ 13]) = RE(x[41]); IM(y[ 13]) = IM(x[41]);
RE(y[ 14]) = RE(x[49]); IM(y[ 14]) = IM(x[49]);
RE(y[ 15]) = RE(x[57]); IM(y[ 15]) = IM(x[57]);
RE(y[ 16]) = RE(x[ 2]); IM(y[ 16]) = IM(x[ 2]);
RE(y[ 17]) = RE(x[10]); IM(y[ 17]) = IM(x[10]);
RE(y[ 18]) = RE(x[18]); IM(y[ 18]) = IM(x[18]);
RE(y[ 19]) = RE(x[26]); IM(y[ 19]) = IM(x[26]);
RE(y[ 20]) = RE(x[34]); IM(y[ 20]) = IM(x[34]);
RE(y[ 21]) = RE(x[42]); IM(y[ 21]) = IM(x[42]);
RE(y[ 22]) = RE(x[50]); IM(y[ 22]) = IM(x[50]);
RE(y[ 23]) = RE(x[58]); IM(y[ 23]) = IM(x[58]);
RE(y[ 24]) = RE(x[ 3]); IM(y[ 24]) = IM(x[ 3]);
RE(y[ 25]) = RE(x[11]); IM(y[ 25]) = IM(x[11]);
RE(y[ 26]) = RE(x[19]); IM(y[ 26]) = IM(x[19]);
RE(y[ 27]) = RE(x[27]); IM(y[ 27]) = IM(x[27]);
RE(y[ 28]) = RE(x[35]); IM(y[ 28]) = IM(x[35]);
RE(y[ 29]) = RE(x[43]); IM(y[ 29]) = IM(x[43]);
RE(y[ 30]) = RE(x[51]); IM(y[ 30]) = IM(x[51]);
RE(y[ 31]) = RE(x[59]); IM(y[ 31]) = IM(x[59]);
RE(y[ 32]) = RE(x[ 4]); IM(y[ 32]) = IM(x[ 4]);
RE(y[ 33]) = RE(x[12]); IM(y[ 33]) = IM(x[12]);
RE(y[ 34]) = RE(x[20]); IM(y[ 34]) = IM(x[20]);
RE(y[ 35]) = RE(x[28]); IM(y[ 35]) = IM(x[28]);
RE(y[ 36]) = RE(x[36]); IM(y[ 36]) = IM(x[36]);
RE(y[ 37]) = RE(x[44]); IM(y[ 37]) = IM(x[44]);
RE(y[ 38]) = RE(x[52]); IM(y[ 38]) = IM(x[52]);
RE(y[ 39]) = RE(x[60]); IM(y[ 39]) = IM(x[60]);
RE(y[ 40]) = RE(x[ 5]); IM(y[ 40]) = IM(x[ 5]);
RE(y[ 41]) = RE(x[13]); IM(y[ 41]) = IM(x[13]);
RE(y[ 42]) = RE(x[21]); IM(y[ 42]) = IM(x[21]);
RE(y[ 43]) = RE(x[29]); IM(y[ 43]) = IM(x[29]);
RE(y[ 44]) = RE(x[37]); IM(y[ 44]) = IM(x[37]);
RE(y[ 45]) = RE(x[45]); IM(y[ 45]) = IM(x[45]);
RE(y[ 46]) = RE(x[53]); IM(y[ 46]) = IM(x[53]);
RE(y[ 47]) = RE(x[61]); IM(y[ 47]) = IM(x[61]);
RE(y[ 48]) = RE(x[ 6]); IM(y[ 48]) = IM(x[ 6]);
RE(y[ 49]) = RE(x[14]); IM(y[ 49]) = IM(x[14]);
RE(y[ 50]) = RE(x[22]); IM(y[ 50]) = IM(x[22]);
RE(y[ 51]) = RE(x[30]); IM(y[ 51]) = IM(x[30]);
RE(y[ 52]) = RE(x[38]); IM(y[ 52]) = IM(x[38]);
RE(y[ 53]) = RE(x[46]); IM(y[ 53]) = IM(x[46]);
RE(y[ 54]) = RE(x[54]); IM(y[ 54]) = IM(x[54]);
RE(y[ 55]) = RE(x[62]); IM(y[ 55]) = IM(x[62]);
RE(y[ 56]) = RE(x[ 7]); IM(y[ 56]) = IM(x[ 7]);
RE(y[ 57]) = RE(x[15]); IM(y[ 57]) = IM(x[15]);
RE(y[ 58]) = RE(x[23]); IM(y[ 58]) = IM(x[23]);
RE(y[ 59]) = RE(x[31]); IM(y[ 59]) = IM(x[31]);
RE(y[ 60]) = RE(x[39]); IM(y[ 60]) = IM(x[39]);
RE(y[ 61]) = RE(x[47]); IM(y[ 61]) = IM(x[47]);
RE(y[ 62]) = RE(x[55]); IM(y[ 62]) = IM(x[55]);
RE(y[ 63]) = RE(x[63]); IM(y[ 63]) = IM(x[63]);
}
/*******************************************************************************
16 x 16 matrix transpose
*******************************************************************************/
void transpose16x16(complex_t* x, complex_t* y)
{
RE(y[ 0]) = RE(x[ 0]); IM(y[ 0]) = IM(x[ 0]);
RE(y[ 1]) = RE(x[ 16]); IM(y[ 1]) = IM(x[ 16]);
RE(y[ 2]) = RE(x[ 32]); IM(y[ 2]) = IM(x[ 32]);
RE(y[ 3]) = RE(x[ 48]); IM(y[ 3]) = IM(x[ 48]);
RE(y[ 4]) = RE(x[ 64]); IM(y[ 4]) = IM(x[ 64]);
RE(y[ 5]) = RE(x[ 80]); IM(y[ 5]) = IM(x[ 80]);
RE(y[ 6]) = RE(x[ 96]); IM(y[ 6]) = IM(x[ 96]);
RE(y[ 7]) = RE(x[112]); IM(y[ 7]) = IM(x[112]);
RE(y[ 8]) = RE(x[128]); IM(y[ 8]) = IM(x[128]);
RE(y[ 9]) = RE(x[144]); IM(y[ 9]) = IM(x[144]);
RE(y[ 10]) = RE(x[160]); IM(y[ 10]) = IM(x[160]);
RE(y[ 11]) = RE(x[176]); IM(y[ 11]) = IM(x[176]);
RE(y[ 12]) = RE(x[192]); IM(y[ 12]) = IM(x[192]);
RE(y[ 13]) = RE(x[208]); IM(y[ 13]) = IM(x[208]);
RE(y[ 14]) = RE(x[224]); IM(y[ 14]) = IM(x[224]);
RE(y[ 15]) = RE(x[240]); IM(y[ 15]) = IM(x[240]);
RE(y[ 16]) = RE(x[ 1]); IM(y[ 16]) = IM(x[ 1]);
RE(y[ 17]) = RE(x[ 17]); IM(y[ 17]) = IM(x[ 17]);
RE(y[ 18]) = RE(x[ 33]); IM(y[ 18]) = IM(x[ 33]);
RE(y[ 19]) = RE(x[ 49]); IM(y[ 19]) = IM(x[ 49]);
RE(y[ 20]) = RE(x[ 65]); IM(y[ 20]) = IM(x[ 65]);
RE(y[ 21]) = RE(x[ 81]); IM(y[ 21]) = IM(x[ 81]);
RE(y[ 22]) = RE(x[ 97]); IM(y[ 22]) = IM(x[ 97]);
RE(y[ 23]) = RE(x[113]); IM(y[ 23]) = IM(x[113]);
RE(y[ 24]) = RE(x[129]); IM(y[ 24]) = IM(x[129]);
RE(y[ 25]) = RE(x[145]); IM(y[ 25]) = IM(x[145]);
RE(y[ 26]) = RE(x[161]); IM(y[ 26]) = IM(x[161]);
RE(y[ 27]) = RE(x[177]); IM(y[ 27]) = IM(x[177]);
RE(y[ 28]) = RE(x[193]); IM(y[ 28]) = IM(x[193]);
RE(y[ 29]) = RE(x[209]); IM(y[ 29]) = IM(x[209]);
RE(y[ 30]) = RE(x[225]); IM(y[ 30]) = IM(x[225]);
RE(y[ 31]) = RE(x[241]); IM(y[ 31]) = IM(x[241]);
RE(y[ 32]) = RE(x[ 2]); IM(y[ 32]) = IM(x[ 2]);
RE(y[ 33]) = RE(x[ 18]); IM(y[ 33]) = IM(x[ 18]);
RE(y[ 34]) = RE(x[ 34]); IM(y[ 34]) = IM(x[ 34]);
RE(y[ 35]) = RE(x[ 50]); IM(y[ 35]) = IM(x[ 50]);
RE(y[ 36]) = RE(x[ 66]); IM(y[ 36]) = IM(x[ 66]);
RE(y[ 37]) = RE(x[ 82]); IM(y[ 37]) = IM(x[ 82]);
RE(y[ 38]) = RE(x[ 98]); IM(y[ 38]) = IM(x[ 98]);
RE(y[ 39]) = RE(x[114]); IM(y[ 39]) = IM(x[114]);
RE(y[ 40]) = RE(x[130]); IM(y[ 40]) = IM(x[130]);
RE(y[ 41]) = RE(x[146]); IM(y[ 41]) = IM(x[146]);
RE(y[ 42]) = RE(x[162]); IM(y[ 42]) = IM(x[162]);
RE(y[ 43]) = RE(x[178]); IM(y[ 43]) = IM(x[178]);
RE(y[ 44]) = RE(x[194]); IM(y[ 44]) = IM(x[194]);
RE(y[ 45]) = RE(x[210]); IM(y[ 45]) = IM(x[210]);
RE(y[ 46]) = RE(x[226]); IM(y[ 46]) = IM(x[226]);
RE(y[ 47]) = RE(x[242]); IM(y[ 47]) = IM(x[242]);
RE(y[ 48]) = RE(x[ 3]); IM(y[ 48]) = IM(x[ 3]);
RE(y[ 49]) = RE(x[ 19]); IM(y[ 49]) = IM(x[ 19]);
RE(y[ 50]) = RE(x[ 35]); IM(y[ 50]) = IM(x[ 35]);
RE(y[ 51]) = RE(x[ 51]); IM(y[ 51]) = IM(x[ 51]);
RE(y[ 52]) = RE(x[ 67]); IM(y[ 52]) = IM(x[ 67]);
RE(y[ 53]) = RE(x[ 83]); IM(y[ 53]) = IM(x[ 83]);
RE(y[ 54]) = RE(x[ 99]); IM(y[ 54]) = IM(x[ 99]);
RE(y[ 55]) = RE(x[115]); IM(y[ 55]) = IM(x[115]);
RE(y[ 56]) = RE(x[131]); IM(y[ 56]) = IM(x[131]);
RE(y[ 57]) = RE(x[147]); IM(y[ 57]) = IM(x[147]);
RE(y[ 58]) = RE(x[163]); IM(y[ 58]) = IM(x[163]);
RE(y[ 59]) = RE(x[179]); IM(y[ 59]) = IM(x[179]);
RE(y[ 60]) = RE(x[195]); IM(y[ 60]) = IM(x[195]);
RE(y[ 61]) = RE(x[211]); IM(y[ 61]) = IM(x[211]);
RE(y[ 62]) = RE(x[227]); IM(y[ 62]) = IM(x[227]);
RE(y[ 63]) = RE(x[243]); IM(y[ 63]) = IM(x[243]);
RE(y[ 64]) = RE(x[ 4]); IM(y[ 64]) = IM(x[ 4]);
RE(y[ 65]) = RE(x[ 20]); IM(y[ 65]) = IM(x[ 20]);
RE(y[ 66]) = RE(x[ 36]); IM(y[ 66]) = IM(x[ 36]);
RE(y[ 67]) = RE(x[ 52]); IM(y[ 67]) = IM(x[ 52]);
RE(y[ 68]) = RE(x[ 68]); IM(y[ 68]) = IM(x[ 68]);
RE(y[ 69]) = RE(x[ 84]); IM(y[ 69]) = IM(x[ 84]);
RE(y[ 70]) = RE(x[100]); IM(y[ 70]) = IM(x[100]);
RE(y[ 71]) = RE(x[116]); IM(y[ 71]) = IM(x[116]);
RE(y[ 72]) = RE(x[132]); IM(y[ 72]) = IM(x[132]);
RE(y[ 73]) = RE(x[148]); IM(y[ 73]) = IM(x[148]);
RE(y[ 74]) = RE(x[164]); IM(y[ 74]) = IM(x[164]);
RE(y[ 75]) = RE(x[180]); IM(y[ 75]) = IM(x[180]);
RE(y[ 76]) = RE(x[196]); IM(y[ 76]) = IM(x[196]);
RE(y[ 77]) = RE(x[212]); IM(y[ 77]) = IM(x[212]);
RE(y[ 78]) = RE(x[228]); IM(y[ 78]) = IM(x[228]);
RE(y[ 79]) = RE(x[244]); IM(y[ 79]) = IM(x[244]);
RE(y[ 80]) = RE(x[ 5]); IM(y[ 80]) = IM(x[ 5]);
RE(y[ 81]) = RE(x[ 21]); IM(y[ 81]) = IM(x[ 21]);
RE(y[ 82]) = RE(x[ 37]); IM(y[ 82]) = IM(x[ 37]);
RE(y[ 83]) = RE(x[ 53]); IM(y[ 83]) = IM(x[ 53]);
RE(y[ 84]) = RE(x[ 69]); IM(y[ 84]) = IM(x[ 69]);
RE(y[ 85]) = RE(x[ 85]); IM(y[ 85]) = IM(x[ 85]);
RE(y[ 86]) = RE(x[101]); IM(y[ 86]) = IM(x[101]);
RE(y[ 87]) = RE(x[117]); IM(y[ 87]) = IM(x[117]);
RE(y[ 88]) = RE(x[133]); IM(y[ 88]) = IM(x[133]);
RE(y[ 89]) = RE(x[149]); IM(y[ 89]) = IM(x[149]);
RE(y[ 90]) = RE(x[165]); IM(y[ 90]) = IM(x[165]);
RE(y[ 91]) = RE(x[181]); IM(y[ 91]) = IM(x[181]);
RE(y[ 92]) = RE(x[197]); IM(y[ 92]) = IM(x[197]);
RE(y[ 93]) = RE(x[213]); IM(y[ 93]) = IM(x[213]);
RE(y[ 94]) = RE(x[229]); IM(y[ 94]) = IM(x[229]);
RE(y[ 95]) = RE(x[245]); IM(y[ 95]) = IM(x[245]);
RE(y[ 96]) = RE(x[ 6]); IM(y[ 96]) = IM(x[ 6]);
RE(y[ 97]) = RE(x[ 22]); IM(y[ 97]) = IM(x[ 22]);
RE(y[ 98]) = RE(x[ 38]); IM(y[ 98]) = IM(x[ 38]);
RE(y[ 99]) = RE(x[ 54]); IM(y[ 99]) = IM(x[ 54]);
RE(y[100]) = RE(x[ 70]); IM(y[100]) = IM(x[ 70]);
RE(y[101]) = RE(x[ 86]); IM(y[101]) = IM(x[ 86]);
RE(y[102]) = RE(x[102]); IM(y[102]) = IM(x[102]);
RE(y[103]) = RE(x[118]); IM(y[103]) = IM(x[118]);
RE(y[104]) = RE(x[134]); IM(y[104]) = IM(x[134]);
RE(y[105]) = RE(x[150]); IM(y[105]) = IM(x[150]);
RE(y[106]) = RE(x[166]); IM(y[106]) = IM(x[166]);
RE(y[107]) = RE(x[182]); IM(y[107]) = IM(x[182]);
RE(y[108]) = RE(x[198]); IM(y[108]) = IM(x[198]);
RE(y[109]) = RE(x[214]); IM(y[109]) = IM(x[214]);
RE(y[110]) = RE(x[230]); IM(y[110]) = IM(x[230]);
RE(y[111]) = RE(x[246]); IM(y[111]) = IM(x[246]);
RE(y[112]) = RE(x[ 7]); IM(y[112]) = IM(x[ 7]);
RE(y[113]) = RE(x[ 23]); IM(y[113]) = IM(x[ 23]);
RE(y[114]) = RE(x[ 39]); IM(y[114]) = IM(x[ 39]);
RE(y[115]) = RE(x[ 55]); IM(y[115]) = IM(x[ 55]);
RE(y[116]) = RE(x[ 71]); IM(y[116]) = IM(x[ 71]);
RE(y[117]) = RE(x[ 87]); IM(y[117]) = IM(x[ 87]);
RE(y[118]) = RE(x[103]); IM(y[118]) = IM(x[103]);
RE(y[119]) = RE(x[119]); IM(y[119]) = IM(x[119]);
RE(y[120]) = RE(x[135]); IM(y[120]) = IM(x[135]);
RE(y[121]) = RE(x[151]); IM(y[121]) = IM(x[151]);
RE(y[122]) = RE(x[167]); IM(y[122]) = IM(x[167]);
RE(y[123]) = RE(x[183]); IM(y[123]) = IM(x[183]);
RE(y[124]) = RE(x[199]); IM(y[124]) = IM(x[199]);
RE(y[125]) = RE(x[215]); IM(y[125]) = IM(x[215]);
RE(y[126]) = RE(x[231]); IM(y[126]) = IM(x[231]);
RE(y[127]) = RE(x[247]); IM(y[127]) = IM(x[247]);
RE(y[128]) = RE(x[ 8]); IM(y[128]) = IM(x[ 8]);
RE(y[129]) = RE(x[ 24]); IM(y[129]) = IM(x[ 24]);
RE(y[130]) = RE(x[ 40]); IM(y[130]) = IM(x[ 40]);
RE(y[131]) = RE(x[ 56]); IM(y[131]) = IM(x[ 56]);
RE(y[132]) = RE(x[ 72]); IM(y[132]) = IM(x[ 72]);
RE(y[133]) = RE(x[ 88]); IM(y[133]) = IM(x[ 88]);
RE(y[134]) = RE(x[104]); IM(y[134]) = IM(x[104]);
RE(y[135]) = RE(x[120]); IM(y[135]) = IM(x[120]);
RE(y[136]) = RE(x[136]); IM(y[136]) = IM(x[136]);
RE(y[137]) = RE(x[152]); IM(y[137]) = IM(x[152]);
RE(y[138]) = RE(x[168]); IM(y[138]) = IM(x[168]);
RE(y[139]) = RE(x[184]); IM(y[139]) = IM(x[184]);
RE(y[140]) = RE(x[200]); IM(y[140]) = IM(x[200]);
RE(y[141]) = RE(x[216]); IM(y[141]) = IM(x[216]);
RE(y[142]) = RE(x[232]); IM(y[142]) = IM(x[232]);
RE(y[143]) = RE(x[248]); IM(y[143]) = IM(x[248]);
RE(y[144]) = RE(x[ 9]); IM(y[144]) = IM(x[ 9]);
RE(y[145]) = RE(x[ 25]); IM(y[145]) = IM(x[ 25]);
RE(y[146]) = RE(x[ 41]); IM(y[146]) = IM(x[ 41]);
RE(y[147]) = RE(x[ 57]); IM(y[147]) = IM(x[ 57]);
RE(y[148]) = RE(x[ 73]); IM(y[148]) = IM(x[ 73]);
RE(y[149]) = RE(x[ 89]); IM(y[149]) = IM(x[ 89]);
RE(y[150]) = RE(x[105]); IM(y[150]) = IM(x[105]);
RE(y[151]) = RE(x[121]); IM(y[151]) = IM(x[121]);
RE(y[152]) = RE(x[137]); IM(y[152]) = IM(x[137]);
RE(y[153]) = RE(x[153]); IM(y[153]) = IM(x[153]);
RE(y[154]) = RE(x[169]); IM(y[154]) = IM(x[169]);
RE(y[155]) = RE(x[185]); IM(y[155]) = IM(x[185]);
RE(y[156]) = RE(x[201]); IM(y[156]) = IM(x[201]);
RE(y[157]) = RE(x[217]); IM(y[157]) = IM(x[217]);
RE(y[158]) = RE(x[233]); IM(y[158]) = IM(x[233]);
RE(y[159]) = RE(x[249]); IM(y[159]) = IM(x[249]);
RE(y[160]) = RE(x[ 10]); IM(y[160]) = IM(x[ 10]);
RE(y[161]) = RE(x[ 26]); IM(y[161]) = IM(x[ 26]);
RE(y[162]) = RE(x[ 42]); IM(y[162]) = IM(x[ 42]);
RE(y[163]) = RE(x[ 58]); IM(y[163]) = IM(x[ 58]);
RE(y[164]) = RE(x[ 74]); IM(y[164]) = IM(x[ 74]);
RE(y[165]) = RE(x[ 90]); IM(y[165]) = IM(x[ 90]);
RE(y[166]) = RE(x[106]); IM(y[166]) = IM(x[106]);
RE(y[167]) = RE(x[122]); IM(y[167]) = IM(x[122]);
RE(y[168]) = RE(x[138]); IM(y[168]) = IM(x[138]);
RE(y[169]) = RE(x[154]); IM(y[169]) = IM(x[154]);
RE(y[170]) = RE(x[170]); IM(y[170]) = IM(x[170]);
RE(y[171]) = RE(x[186]); IM(y[171]) = IM(x[186]);
RE(y[172]) = RE(x[202]); IM(y[172]) = IM(x[202]);
RE(y[173]) = RE(x[218]); IM(y[173]) = IM(x[218]);
RE(y[174]) = RE(x[234]); IM(y[174]) = IM(x[234]);
RE(y[175]) = RE(x[250]); IM(y[175]) = IM(x[250]);
RE(y[176]) = RE(x[ 11]); IM(y[176]) = IM(x[ 11]);
RE(y[177]) = RE(x[ 27]); IM(y[177]) = IM(x[ 27]);
RE(y[178]) = RE(x[ 43]); IM(y[178]) = IM(x[ 43]);
RE(y[179]) = RE(x[ 59]); IM(y[179]) = IM(x[ 59]);
RE(y[180]) = RE(x[ 75]); IM(y[180]) = IM(x[ 75]);
RE(y[181]) = RE(x[ 91]); IM(y[181]) = IM(x[ 91]);
RE(y[182]) = RE(x[107]); IM(y[182]) = IM(x[107]);
RE(y[183]) = RE(x[123]); IM(y[183]) = IM(x[123]);
RE(y[184]) = RE(x[139]); IM(y[184]) = IM(x[139]);
RE(y[185]) = RE(x[155]); IM(y[185]) = IM(x[155]);
RE(y[186]) = RE(x[171]); IM(y[186]) = IM(x[171]);
RE(y[187]) = RE(x[187]); IM(y[187]) = IM(x[187]);
RE(y[188]) = RE(x[203]); IM(y[188]) = IM(x[203]);
RE(y[189]) = RE(x[219]); IM(y[189]) = IM(x[219]);
RE(y[190]) = RE(x[235]); IM(y[190]) = IM(x[235]);
RE(y[191]) = RE(x[251]); IM(y[191]) = IM(x[251]);
RE(y[192]) = RE(x[ 12]); IM(y[192]) = IM(x[ 12]);
RE(y[193]) = RE(x[ 28]); IM(y[193]) = IM(x[ 28]);
RE(y[194]) = RE(x[ 44]); IM(y[194]) = IM(x[ 44]);
RE(y[195]) = RE(x[ 60]); IM(y[195]) = IM(x[ 60]);
RE(y[196]) = RE(x[ 76]); IM(y[196]) = IM(x[ 76]);
RE(y[197]) = RE(x[ 92]); IM(y[197]) = IM(x[ 92]);
RE(y[198]) = RE(x[108]); IM(y[198]) = IM(x[108]);
RE(y[199]) = RE(x[124]); IM(y[199]) = IM(x[124]);
RE(y[200]) = RE(x[140]); IM(y[200]) = IM(x[140]);
RE(y[201]) = RE(x[156]); IM(y[201]) = IM(x[156]);
RE(y[202]) = RE(x[172]); IM(y[202]) = IM(x[172]);
RE(y[203]) = RE(x[188]); IM(y[203]) = IM(x[188]);
RE(y[204]) = RE(x[204]); IM(y[204]) = IM(x[204]);
RE(y[205]) = RE(x[220]); IM(y[205]) = IM(x[220]);
RE(y[206]) = RE(x[236]); IM(y[206]) = IM(x[236]);
RE(y[207]) = RE(x[252]); IM(y[207]) = IM(x[252]);
RE(y[208]) = RE(x[ 13]); IM(y[208]) = IM(x[ 13]);
RE(y[209]) = RE(x[ 29]); IM(y[209]) = IM(x[ 29]);
RE(y[210]) = RE(x[ 45]); IM(y[210]) = IM(x[ 45]);
RE(y[211]) = RE(x[ 61]); IM(y[211]) = IM(x[ 61]);
RE(y[212]) = RE(x[ 77]); IM(y[212]) = IM(x[ 77]);
RE(y[213]) = RE(x[ 93]); IM(y[213]) = IM(x[ 93]);
RE(y[214]) = RE(x[109]); IM(y[214]) = IM(x[109]);
RE(y[215]) = RE(x[125]); IM(y[215]) = IM(x[125]);
RE(y[216]) = RE(x[141]); IM(y[216]) = IM(x[141]);
RE(y[217]) = RE(x[157]); IM(y[217]) = IM(x[157]);
RE(y[218]) = RE(x[173]); IM(y[218]) = IM(x[173]);
RE(y[219]) = RE(x[189]); IM(y[219]) = IM(x[189]);
RE(y[220]) = RE(x[205]); IM(y[220]) = IM(x[205]);
RE(y[221]) = RE(x[221]); IM(y[221]) = IM(x[221]);
RE(y[222]) = RE(x[237]); IM(y[222]) = IM(x[237]);
RE(y[223]) = RE(x[253]); IM(y[223]) = IM(x[253]);
RE(y[224]) = RE(x[ 14]); IM(y[224]) = IM(x[ 14]);
RE(y[225]) = RE(x[ 30]); IM(y[225]) = IM(x[ 30]);
RE(y[226]) = RE(x[ 46]); IM(y[226]) = IM(x[ 46]);
RE(y[227]) = RE(x[ 62]); IM(y[227]) = IM(x[ 62]);
RE(y[228]) = RE(x[ 78]); IM(y[228]) = IM(x[ 78]);
RE(y[229]) = RE(x[ 94]); IM(y[229]) = IM(x[ 94]);
RE(y[230]) = RE(x[110]); IM(y[230]) = IM(x[110]);
RE(y[231]) = RE(x[126]); IM(y[231]) = IM(x[126]);
RE(y[232]) = RE(x[142]); IM(y[232]) = IM(x[142]);
RE(y[233]) = RE(x[158]); IM(y[233]) = IM(x[158]);
RE(y[234]) = RE(x[174]); IM(y[234]) = IM(x[174]);
RE(y[235]) = RE(x[190]); IM(y[235]) = IM(x[190]);
RE(y[236]) = RE(x[206]); IM(y[236]) = IM(x[206]);
RE(y[237]) = RE(x[222]); IM(y[237]) = IM(x[222]);
RE(y[238]) = RE(x[238]); IM(y[238]) = IM(x[238]);
RE(y[239]) = RE(x[254]); IM(y[239]) = IM(x[254]);
RE(y[240]) = RE(x[ 15]); IM(y[240]) = IM(x[ 15]);
RE(y[241]) = RE(x[ 31]); IM(y[241]) = IM(x[ 31]);
RE(y[242]) = RE(x[ 47]); IM(y[242]) = IM(x[ 47]);
RE(y[243]) = RE(x[ 63]); IM(y[243]) = IM(x[ 63]);
RE(y[244]) = RE(x[ 79]); IM(y[244]) = IM(x[ 79]);
RE(y[245]) = RE(x[ 95]); IM(y[245]) = IM(x[ 95]);
RE(y[246]) = RE(x[111]); IM(y[246]) = IM(x[111]);
RE(y[247]) = RE(x[127]); IM(y[247]) = IM(x[127]);
RE(y[248]) = RE(x[143]); IM(y[248]) = IM(x[143]);
RE(y[249]) = RE(x[159]); IM(y[249]) = IM(x[159]);
RE(y[250]) = RE(x[175]); IM(y[250]) = IM(x[175]);
RE(y[251]) = RE(x[191]); IM(y[251]) = IM(x[191]);
RE(y[252]) = RE(x[207]); IM(y[252]) = IM(x[207]);
RE(y[253]) = RE(x[223]); IM(y[253]) = IM(x[223]);
RE(y[254]) = RE(x[239]); IM(y[254]) = IM(x[239]);
RE(y[255]) = RE(x[255]); IM(y[255]) = IM(x[255]);
}