package com.isti.traceview.jnt.FFT;
import org.apache.log4j.Logger;
/**
* Computes FFT's of complex, single precision data of arbitrary length n. This
* class uses the Mixed Radix method; it has special methods to handle factors
* 2, 3, 4, 5, 6 and 7, as well as a general factor.
* <P>
* This method appears to be faster than the Radix2 method, when both methods
* apply, but requires extra storage (which ComplexDoubleFFT_Mixed manages
* itself).
*
* <P>
* See {@link ComplexFloatFFT ComplexFloatFFT} for details of data layout.
*
* @author Bruce R. Miller bruce.miller@nist.gov
* Contribution of the National Institute of Standards and Technology,
* not subject to copyright.
* Derived from GSL (Gnu Scientific Library)
* GSL's FFT Code by Brian Gough bjg@vvv.lanl.gov
* Since GSL is released under
* <a href="http://www.gnu.org/copyleft/gpl.html">GPL</a>,
* this package must also be.
*/
public class ComplexFloatFFT_Mixed extends ComplexFloatFFT {
private static final Logger logger = Logger.getLogger(ComplexFloatFFT_Mixed.class);
static final double PI = (float) Math.PI;
static final int FORWARD = -1;
static final int BACKWARD = +1;
public ComplexFloatFFT_Mixed(int n) {
super(n);
try {
setup_wavetable(n);
} catch (Error e) {
logger.error("Error:", e);
}
}
public void transform(float data[], int i0, int stride) {
try {
checkData(data, i0, stride);
transform_internal(data, i0, stride, FORWARD);
} catch (IllegalArgumentException e) {
logger.error("IllegalArgumentException:", e);
}
}
public void backtransform(float data[], int i0, int stride) {
try {
checkData(data, i0, stride);
transform_internal(data, i0, stride, BACKWARD);
} catch (IllegalArgumentException e) {
logger.error("IllegalArgumentException:", e);
}
}
/*
* ______________________________________________________________________
* Setting up the Wavetable
*/
private int factors[];
// Reversed the last 2 levels of the twiddle array compared to what the C
// version had.
private float twiddle[][][];
private int available_factors[] = { 7, 6, 5, 4, 3, 2 };
void setup_wavetable(int n) {
if (n <= 0)
throw new Error("length must be positive integer : " + n);
this.n = n;
try {
factors = Factorize.factor(n, available_factors);
} catch (Error e) {
logger.error("Error:", e);
}
double d_theta = -2.0 * PI / ((double) n);
int product = 1;
twiddle = new float[factors.length][][];
for (int i = 0; i < factors.length; i++) {
int factor = factors[i];
int product_1 = product; /* product_1 = p_(i-1) */
product *= factor;
int q = n / product;
twiddle[i] = new float[q + 1][2 * (factor - 1)];
float twid[][] = twiddle[i];
for (int j = 1; j < factor; j++) {
twid[0][2 * (j - 1)] = 1.0f;
twid[0][2 * (j - 1) + 1] = 0.0f;
}
for (int k = 1; k <= q; k++) {
int m = 0;
for (int j = 1; j < factor; j++) {
// int m = (k*j*product_1) % n;
m += k * product_1;
m %= n;
double theta = d_theta * m; /* d_theta*j*k*p_(i-1) */
twid[k][2 * (j - 1)] = (float) Math.cos(theta);
twid[k][2 * (j - 1) + 1] = (float) Math.sin(theta);
}
}
}
}
/*
* ______________________________________________________________________
* The main transformation driver
*/
void transform_internal(float data[], int i0, int stride, int sign) {
if (n == 1)
return; /* FFT of 1 data point is the identity */
float scratch[] = new float[2 * n];
int product = 1;
int state = 0;
float in[], out[];
int istride, ostride;
int in0, out0;
for (int i = 0; i < factors.length; i++) {
int factor = factors[i];
product *= factor;
if (state == 0) {
in = data;
in0 = i0;
istride = stride;
out = scratch;
out0 = 0;
ostride = 2;
state = 1;
} else {
in = scratch;
in0 = 0;
istride = 2;
out = data;
out0 = i0;
ostride = stride;
state = 0;
}
switch (factor) {
case 2:
pass_2(i, in, in0, istride, out, out0, ostride, sign, product);
break;
case 3:
pass_3(i, in, in0, istride, out, out0, ostride, sign, product);
break;
case 4:
pass_4(i, in, in0, istride, out, out0, ostride, sign, product);
break;
case 5:
pass_5(i, in, in0, istride, out, out0, ostride, sign, product);
break;
case 6:
pass_6(i, in, in0, istride, out, out0, ostride, sign, product);
break;
case 7:
pass_7(i, in, in0, istride, out, out0, ostride, sign, product);
break;
default:
pass_n(i, in, in0, istride, out, out0, ostride, sign, factor,
product);
}
}
if (state == 1) { /* copy results back from scratch to data */
for (int i = 0; i < n; i++) {
data[i0 + stride * i] = scratch[2 * i];
data[i0 + stride * i + 1] = scratch[2 * i + 1];
}
}
}
/* ______________________________________________________________________ */
void pass_2(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 2;
int m = n / factor;
int q = n / product;
int product_1 = product / factor;
int di = istride * m;
int dj = ostride * product_1;
int i = in0, j = out0;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w_real = twids[0];
float w_imag = -sign * twids[1];
for (k1 = 0; k1 < product_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
i += istride;
/* compute x = W(2) z */
/* apply twiddle factors */
/* out0 = 1 * (z0 + z1) */
out[j] = z0_real + z1_real;
out[j + 1] = z0_imag + z1_imag;
/* out1 = w * (z0 - z1) */
x_real = z0_real - z1_real;
x_imag = z0_imag - z1_imag;
out[j + dj] = w_real * x_real - w_imag * x_imag;
out[j + dj + 1] = w_real * x_imag + w_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_3(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 3;
int m = n / factor;
int q = n / product;
int product_1 = product / factor;
//int jump = (factor - 1) * product_1;
float tau = (float) (sign * Math.sqrt(3.0) / 2.0);
int di = istride * m;
int dj = ostride * product_1;
int i = in0, j = out0;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w1_real = twids[0];
float w1_imag = -sign * twids[1];
float w2_real = twids[2];
float w2_imag = -sign * twids[3];
for (k1 = 0; k1 < product_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
float z2_real = in[i + 2 * di];
float z2_imag = in[i + 2 * di + 1];
i += istride;
/* compute x = W(3) z */
/* t1 = z1 + z2 */
float t1_real = z1_real + z2_real;
float t1_imag = z1_imag + z2_imag;
/* t2 = z0 - t1/2 */
float t2_real = z0_real - t1_real / 2.0f;
float t2_imag = z0_imag - t1_imag / 2.0f;
/* t3 = (+/-) sin(pi/3)*(z1 - z2) */
float t3_real = tau * (z1_real - z2_real);
float t3_imag = tau * (z1_imag - z2_imag);
/* apply twiddle factors */
/* out0 = 1 * (z0 + t1) */
out[j] = z0_real + t1_real;
out[j + 1] = z0_imag + t1_imag;
/* out1 = w1 * (t2 + i t3) */
x_real = t2_real - t3_imag;
x_imag = t2_imag + t3_real;
out[j + dj] = w1_real * x_real - w1_imag * x_imag;
out[j + dj + 1] = w1_real * x_imag + w1_imag * x_real;
/* out2 = w2 * (t2 - i t3) */
x_real = t2_real + t3_imag;
x_imag = t2_imag - t3_real;
out[j + 2 * dj] = w2_real * x_real - w2_imag * x_imag;
out[j + 2 * dj + 1] = w2_real * x_imag + w2_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_4(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 4;
int m = n / factor;
int q = n / product;
int p_1 = product / factor;
//int jump = (factor - 1) * p_1;
int i = in0, j = out0;
int di = istride * m;
int dj = ostride * p_1;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w1_real = twids[0];
float w1_imag = -sign * twids[1];
float w2_real = twids[2];
float w2_imag = -sign * twids[3];
float w3_real = twids[4];
float w3_imag = -sign * twids[5];
for (k1 = 0; k1 < p_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
float z2_real = in[i + 2 * di];
float z2_imag = in[i + 2 * di + 1];
float z3_real = in[i + 3 * di];
float z3_imag = in[i + 3 * di + 1];
i += istride;
/* compute x = W(4) z */
/* t1 = z0 + z2 */
float t1_real = z0_real + z2_real;
float t1_imag = z0_imag + z2_imag;
/* t2 = z1 + z3 */
float t2_real = z1_real + z3_real;
float t2_imag = z1_imag + z3_imag;
/* t3 = z0 - z2 */
float t3_real = z0_real - z2_real;
float t3_imag = z0_imag - z2_imag;
/* t4 = (+/-) (z1 - z3) */
float t4_real = sign * (z1_real - z3_real);
float t4_imag = sign * (z1_imag - z3_imag);
/* apply twiddle factors */
/* out0 = 1 * (t1 + t2) */
out[j] = t1_real + t2_real;
out[j + 1] = t1_imag + t2_imag;
/* out1 = w1 * (t3 + i t4) */
x_real = t3_real - t4_imag;
x_imag = t3_imag + t4_real;
out[j + dj] = w1_real * x_real - w1_imag * x_imag;
out[j + dj + 1] = w1_real * x_imag + w1_imag * x_real;
/* out2 = w2 * (t1 - t2) */
x_real = t1_real - t2_real;
x_imag = t1_imag - t2_imag;
out[j + 2 * dj] = w2_real * x_real - w2_imag * x_imag;
out[j + 2 * dj + 1] = w2_real * x_imag + w2_imag * x_real;
/* out3 = w3 * (t3 - i t4) */
x_real = t3_real + t4_imag;
x_imag = t3_imag - t4_real;
out[j + 3 * dj] = w3_real * x_real - w3_imag * x_imag;
out[j + 3 * dj + 1] = w3_real * x_imag + w3_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_5(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 5;
int m = n / factor;
int q = n / product;
int p_1 = product / factor;
//int jump = (factor - 1) * p_1;
float tau = (float) (Math.sqrt(5.0) / 4.0);
float sin_2pi_by_5 = (float) (sign * Math.sin(2.0 * PI / 5.0));
float sin_2pi_by_10 = (float) (sign * Math.sin(2.0 * PI / 10.0));
int i = in0, j = out0;
int di = istride * m;
int dj = ostride * p_1;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w1_real = twids[0];
float w1_imag = -sign * twids[1];
float w2_real = twids[2];
float w2_imag = -sign * twids[3];
float w3_real = twids[4];
float w3_imag = -sign * twids[5];
float w4_real = twids[6];
float w4_imag = -sign * twids[7];
for (k1 = 0; k1 < p_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
float z2_real = in[i + 2 * di];
float z2_imag = in[i + 2 * di + 1];
float z3_real = in[i + 3 * di];
float z3_imag = in[i + 3 * di + 1];
float z4_real = in[i + 4 * di];
float z4_imag = in[i + 4 * di + 1];
i += istride;
/* compute x = W(5) z */
/* t1 = z1 + z4 */
float t1_real = z1_real + z4_real;
float t1_imag = z1_imag + z4_imag;
/* t2 = z2 + z3 */
float t2_real = z2_real + z3_real;
float t2_imag = z2_imag + z3_imag;
/* t3 = z1 - z4 */
float t3_real = z1_real - z4_real;
float t3_imag = z1_imag - z4_imag;
/* t4 = z2 - z3 */
float t4_real = z2_real - z3_real;
float t4_imag = z2_imag - z3_imag;
/* t5 = t1 + t2 */
float t5_real = t1_real + t2_real;
float t5_imag = t1_imag + t2_imag;
/* t6 = (sqrt(5)/4)(t1 - t2) */
float t6_real = tau * (t1_real - t2_real);
float t6_imag = tau * (t1_imag - t2_imag);
/* t7 = z0 - ((t5)/4) */
float t7_real = z0_real - t5_real / 4.0f;
float t7_imag = z0_imag - t5_imag / 4.0f;
/* t8 = t7 + t6 */
float t8_real = t7_real + t6_real;
float t8_imag = t7_imag + t6_imag;
/* t9 = t7 - t6 */
float t9_real = t7_real - t6_real;
float t9_imag = t7_imag - t6_imag;
/* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */
float t10_real = sin_2pi_by_5 * t3_real + sin_2pi_by_10
* t4_real;
float t10_imag = sin_2pi_by_5 * t3_imag + sin_2pi_by_10
* t4_imag;
/* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */
float t11_real = sin_2pi_by_10 * t3_real - sin_2pi_by_5
* t4_real;
float t11_imag = sin_2pi_by_10 * t3_imag - sin_2pi_by_5
* t4_imag;
/* apply twiddle factors */
/* out0 = 1 * (z0 + t5) */
out[j] = z0_real + t5_real;
out[j + 1] = z0_imag + t5_imag;
/* out1 = w1 * (t8 + i t10) */
x_real = t8_real - t10_imag;
x_imag = t8_imag + t10_real;
out[j + dj] = w1_real * x_real - w1_imag * x_imag;
out[j + dj + 1] = w1_real * x_imag + w1_imag * x_real;
/* out2 = w2 * (t9 + i t11) */
x_real = t9_real - t11_imag;
x_imag = t9_imag + t11_real;
out[j + 2 * dj] = w2_real * x_real - w2_imag * x_imag;
out[j + 2 * dj + 1] = w2_real * x_imag + w2_imag * x_real;
/* out3 = w3 * (t9 - i t11) */
x_real = t9_real + t11_imag;
x_imag = t9_imag - t11_real;
out[j + 3 * dj] = w3_real * x_real - w3_imag * x_imag;
out[j + 3 * dj + 1] = w3_real * x_imag + w3_imag * x_real;
/* out4 = w4 * (t8 - i t10) */
x_real = t8_real + t10_imag;
x_imag = t8_imag - t10_real;
out[j + 4 * dj] = w4_real * x_real - w4_imag * x_imag;
out[j + 4 * dj + 1] = w4_real * x_imag + w4_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_6(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 6;
int m = n / factor;
int q = n / product;
int p_1 = product / factor;
//int jump = (factor - 1) * p_1;
float tau = (float) (sign * Math.sqrt(3.0) / 2.0);
int i = in0, j = out0;
int di = istride * m;
int dj = ostride * p_1;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w1_real = twids[0];
float w1_imag = -sign * twids[1];
float w2_real = twids[2];
float w2_imag = -sign * twids[3];
float w3_real = twids[4];
float w3_imag = -sign * twids[5];
float w4_real = twids[6];
float w4_imag = -sign * twids[7];
float w5_real = twids[8];
float w5_imag = -sign * twids[9];
for (k1 = 0; k1 < p_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
float z2_real = in[i + 2 * di];
float z2_imag = in[i + 2 * di + 1];
float z3_real = in[i + 3 * di];
float z3_imag = in[i + 3 * di + 1];
float z4_real = in[i + 4 * di];
float z4_imag = in[i + 4 * di + 1];
float z5_real = in[i + 5 * di];
float z5_imag = in[i + 5 * di + 1];
i += istride;
/* compute x = W(6) z */
/*
* W(6) is a combination of sums and differences of W(3) acting
* on the even and odd elements of z
*/
/* ta1 = z2 + z4 */
float ta1_real = z2_real + z4_real;
float ta1_imag = z2_imag + z4_imag;
/* ta2 = z0 - ta1/2 */
float ta2_real = z0_real - ta1_real / 2;
float ta2_imag = z0_imag - ta1_imag / 2;
/* ta3 = (+/-) sin(pi/3)*(z2 - z4) */
float ta3_real = tau * (z2_real - z4_real);
float ta3_imag = tau * (z2_imag - z4_imag);
/* a0 = z0 + ta1 */
float a0_real = z0_real + ta1_real;
float a0_imag = z0_imag + ta1_imag;
/* a1 = ta2 + i ta3 */
float a1_real = ta2_real - ta3_imag;
float a1_imag = ta2_imag + ta3_real;
/* a2 = ta2 - i ta3 */
float a2_real = ta2_real + ta3_imag;
float a2_imag = ta2_imag - ta3_real;
/* tb1 = z5 + z1 */
float tb1_real = z5_real + z1_real;
float tb1_imag = z5_imag + z1_imag;
/* tb2 = z3 - tb1/2 */
float tb2_real = z3_real - tb1_real / 2;
float tb2_imag = z3_imag - tb1_imag / 2;
/* tb3 = (+/-) sin(pi/3)*(z5 - z1) */
float tb3_real = tau * (z5_real - z1_real);
float tb3_imag = tau * (z5_imag - z1_imag);
/* b0 = z3 + tb1 */
float b0_real = z3_real + tb1_real;
float b0_imag = z3_imag + tb1_imag;
/* b1 = tb2 + i tb3 */
float b1_real = tb2_real - tb3_imag;
float b1_imag = tb2_imag + tb3_real;
/* b2 = tb2 - i tb3 */
float b2_real = tb2_real + tb3_imag;
float b2_imag = tb2_imag - tb3_real;
/* apply twiddle factors */
/* out0 = 1 * (a0 + b0) */
out[j] = a0_real + b0_real;
out[j + 1] = a0_imag + b0_imag;
/* out1 = w1 * (a1 - b1) */
x_real = a1_real - b1_real;
x_imag = a1_imag - b1_imag;
out[j + dj] = w1_real * x_real - w1_imag * x_imag;
out[j + dj + 1] = w1_real * x_imag + w1_imag * x_real;
/* out2 = w2 * (a2 + b2) */
x_real = a2_real + b2_real;
x_imag = a2_imag + b2_imag;
out[j + 2 * dj] = w2_real * x_real - w2_imag * x_imag;
out[j + 2 * dj + 1] = w2_real * x_imag + w2_imag * x_real;
/* out3 = w3 * (a0 - b0) */
x_real = a0_real - b0_real;
x_imag = a0_imag - b0_imag;
out[j + 3 * dj] = w3_real * x_real - w3_imag * x_imag;
out[j + 3 * dj + 1] = w3_real * x_imag + w3_imag * x_real;
/* out4 = w4 * (a1 + b1) */
x_real = a1_real + b1_real;
x_imag = a1_imag + b1_imag;
out[j + 4 * dj] = w4_real * x_real - w4_imag * x_imag;
out[j + 4 * dj + 1] = w4_real * x_imag + w4_imag * x_real;
/* out5 = w5 * (a2 - b2) */
x_real = a2_real - b2_real;
x_imag = a2_imag - b2_imag;
out[j + 5 * dj] = w5_real * x_real - w5_imag * x_imag;
out[j + 5 * dj + 1] = w5_real * x_imag + w5_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_7(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int product) {
int k, k1;
int factor = 7;
int m = n / factor;
int q = n / product;
int p_1 = product / factor;
//int jump = (factor - 1) * p_1;
float c1 = (float) Math.cos(1.0 * 2.0 * PI / 7.0);
float c2 = (float) Math.cos(2.0 * 2.0 * PI / 7.0);
float c3 = (float) Math.cos(3.0 * 2.0 * PI / 7.0);
float s1 = (float) ((-sign) * Math.sin(1.0 * 2.0 * PI / 7.0));
float s2 = (float) ((-sign) * Math.sin(2.0 * 2.0 * PI / 7.0));
float s3 = (float) ((-sign) * Math.sin(3.0 * 2.0 * PI / 7.0));
int i = in0, j = out0;
int di = istride * m;
int dj = ostride * p_1;
float x_real, x_imag;
for (k = 0; k < q; k++) {
float twids[] = twiddle[fi][k];
float w1_real = twids[0];
float w1_imag = -sign * twids[1];
float w2_real = twids[2];
float w2_imag = -sign * twids[3];
float w3_real = twids[4];
float w3_imag = -sign * twids[5];
float w4_real = twids[6];
float w4_imag = -sign * twids[7];
float w5_real = twids[8];
float w5_imag = -sign * twids[9];
float w6_real = twids[10];
float w6_imag = -sign * twids[11];
for (k1 = 0; k1 < p_1; k1++) {
float z0_real = in[i];
float z0_imag = in[i + 1];
float z1_real = in[i + di];
float z1_imag = in[i + di + 1];
float z2_real = in[i + 2 * di];
float z2_imag = in[i + 2 * di + 1];
float z3_real = in[i + 3 * di];
float z3_imag = in[i + 3 * di + 1];
float z4_real = in[i + 4 * di];
float z4_imag = in[i + 4 * di + 1];
float z5_real = in[i + 5 * di];
float z5_imag = in[i + 5 * di + 1];
float z6_real = in[i + 6 * di];
float z6_imag = in[i + 6 * di + 1];
i += istride;
/* compute x = W(7) z */
/* t0 = z1 + z6 */
float t0_real = z1_real + z6_real;
float t0_imag = z1_imag + z6_imag;
/* t1 = z1 - z6 */
float t1_real = z1_real - z6_real;
float t1_imag = z1_imag - z6_imag;
/* t2 = z2 + z5 */
float t2_real = z2_real + z5_real;
float t2_imag = z2_imag + z5_imag;
/* t3 = z2 - z5 */
float t3_real = z2_real - z5_real;
float t3_imag = z2_imag - z5_imag;
/* t4 = z4 + z3 */
float t4_real = z4_real + z3_real;
float t4_imag = z4_imag + z3_imag;
/* t5 = z4 - z3 */
float t5_real = z4_real - z3_real;
float t5_imag = z4_imag - z3_imag;
/* t6 = t2 + t0 */
float t6_real = t2_real + t0_real;
float t6_imag = t2_imag + t0_imag;
/* t7 = t5 + t3 */
float t7_real = t5_real + t3_real;
float t7_imag = t5_imag + t3_imag;
/* b0 = z0 + t6 + t4 */
float b0_real = z0_real + t6_real + t4_real;
float b0_imag = z0_imag + t6_imag + t4_imag;
/* b1 = ((cos(2pi/7) + cos(4pi/7) + cos(6pi/7))/3-1) (t6 + t4) */
float b1_real = (((c1 + c2 + c3) / 3.0f - 1.0f) * (t6_real + t4_real));
float b1_imag = (((c1 + c2 + c3) / 3.0f - 1.0f) * (t6_imag + t4_imag));
/* b2 = ((2*cos(2pi/7) - cos(4pi/7) - cos(6pi/7))/3) (t0 - t4) */
float b2_real = (((2.0f * c1 - c2 - c3) / 3.0f) * (t0_real - t4_real));
float b2_imag = (((2.0f * c1 - c2 - c3) / 3.0f) * (t0_imag - t4_imag));
/* b3 = ((cos(2pi/7) - 2*cos(4pi/7) + cos(6pi/7))/3) (t4 - t2) */
float b3_real = (((c1 - 2.0f * c2 + c3) / 3.0f) * (t4_real - t2_real));
float b3_imag = (((c1 - 2.0f * c2 + c3) / 3.0f) * (t4_imag - t2_imag));
/* b4 = ((cos(2pi/7) + cos(4pi/7) - 2*cos(6pi/7))/3) (t2 - t0) */
float b4_real = (((c1 + c2 - 2.0f * c3) / 3.0f) * (t2_real - t0_real));
float b4_imag = (((c1 + c2 - 2.0f * c3) / 3.0f) * (t2_imag - t0_imag));
/*
* b5 = sign * ((sin(2pi/7) + sin(4pi/7) - sin(6pi/7))/3) (t7 +
* t1)
*/
float b5_real = ((s1 + s2 - s3) / 3.0f) * (t7_real + t1_real);
float b5_imag = ((s1 + s2 - s3) / 3.0f) * (t7_imag + t1_imag);
/*
* b6 = sign * ((2sin(2pi/7) - sin(4pi/7) + sin(6pi/7))/3) (t1 -
* t5)
*/
float b6_real = ((2.0f * s1 - s2 + s3) / 3.0f)
* (t1_real - t5_real);
float b6_imag = ((2.0f * s1 - s2 + s3) / 3.0f)
* (t1_imag - t5_imag);
/*
* b7 = sign * ((sin(2pi/7) - 2sin(4pi/7) - sin(6pi/7))/3) (t5 -
* t3)
*/
float b7_real = ((s1 - 2.0f * s2 - s3) / 3.0f)
* (t5_real - t3_real);
float b7_imag = ((s1 - 2.0f * s2 - s3) / 3.0f)
* (t5_imag - t3_imag);
/*
* b8 = sign * ((sin(2pi/7) + sin(4pi/7) + 2sin(6pi/7))/3) (t3 -
* t1)
*/
float b8_real = ((s1 + s2 + 2.0f * s3) / 3.0f)
* (t3_real - t1_real);
float b8_imag = ((s1 + s2 + 2.0f * s3) / 3.0f)
* (t3_imag - t1_imag);
/* T0 = b0 + b1 */
float T0_real = b0_real + b1_real;
float T0_imag = b0_imag + b1_imag;
/* T1 = b2 + b3 */
float T1_real = b2_real + b3_real;
float T1_imag = b2_imag + b3_imag;
/* T2 = b4 - b3 */
float T2_real = b4_real - b3_real;
float T2_imag = b4_imag - b3_imag;
/* T3 = -b2 - b4 */
float T3_real = -b2_real - b4_real;
float T3_imag = -b2_imag - b4_imag;
/* T4 = b6 + b7 */
float T4_real = b6_real + b7_real;
float T4_imag = b6_imag + b7_imag;
/* T5 = b8 - b7 */
float T5_real = b8_real - b7_real;
float T5_imag = b8_imag - b7_imag;
/* T6 = -b8 - b6 */
float T6_real = -b8_real - b6_real;
float T6_imag = -b8_imag - b6_imag;
/* T7 = T0 + T1 */
float T7_real = T0_real + T1_real;
float T7_imag = T0_imag + T1_imag;
/* T8 = T0 + T2 */
float T8_real = T0_real + T2_real;
float T8_imag = T0_imag + T2_imag;
/* T9 = T0 + T3 */
float T9_real = T0_real + T3_real;
float T9_imag = T0_imag + T3_imag;
/* T10 = T4 + b5 */
float T10_real = T4_real + b5_real;
float T10_imag = T4_imag + b5_imag;
/* T11 = T5 + b5 */
float T11_real = T5_real + b5_real;
float T11_imag = T5_imag + b5_imag;
/* T12 = T6 + b5 */
float T12_real = T6_real + b5_real;
float T12_imag = T6_imag + b5_imag;
/* apply twiddle factors */
/* out0 = 1 * b0 */
out[j] = b0_real;
out[j + 1] = b0_imag;
/* out1 = w1 * (T7 - i T10) */
x_real = T7_real + T10_imag;
x_imag = T7_imag - T10_real;
out[j + dj] = w1_real * x_real - w1_imag * x_imag;
out[j + dj + 1] = w1_real * x_imag + w1_imag * x_real;
/* out2 = w2 * (T9 - i T12) */
x_real = T9_real + T12_imag;
x_imag = T9_imag - T12_real;
out[j + 2 * dj] = w2_real * x_real - w2_imag * x_imag;
out[j + 2 * dj + 1] = w2_real * x_imag + w2_imag * x_real;
/* out3 = w3 * (T8 + i T11) */
x_real = T8_real - T11_imag;
x_imag = T8_imag + T11_real;
out[j + 3 * dj] = w3_real * x_real - w3_imag * x_imag;
out[j + 3 * dj + 1] = w3_real * x_imag + w3_imag * x_real;
/* out4 = w4 * (T8 - i T11) */
x_real = T8_real + T11_imag;
x_imag = T8_imag - T11_real;
out[j + 4 * dj] = w4_real * x_real - w4_imag * x_imag;
out[j + 4 * dj + 1] = w4_real * x_imag + w4_imag * x_real;
/* out5 = w5 * (T9 + i T12) */
x_real = T9_real - T12_imag;
x_imag = T9_imag + T12_real;
out[j + 5 * dj] = w5_real * x_real - w5_imag * x_imag;
out[j + 5 * dj + 1] = w5_real * x_imag + w5_imag * x_real;
/* out6 = w6 * (T7 + i T10) */
x_real = T7_real - T10_imag;
x_imag = T7_imag + T10_real;
out[j + 6 * dj] = w6_real * x_real - w6_imag * x_imag;
out[j + 6 * dj + 1] = w6_real * x_imag + w6_imag * x_real;
j += ostride;
}
j += (factor - 1) * dj;
}
}
/* ______________________________________________________________________ */
void pass_n(int fi, float in[], int in0, int istride, float out[],
int out0, int ostride, int sign, int factor, int product) {
int i = 0, j = 0;
int k, k1;
int m = n / factor;
int q = n / product;
int p_1 = product / factor;
int jump = (factor - 1) * p_1;
int e, e1;
for (i = 0; i < m; i++) {
out[out0 + ostride * i] = in[in0 + istride * i];
out[out0 + ostride * i + 1] = in[in0 + istride * i + 1];
}
for (e = 1; e < (factor - 1) / 2 + 1; e++) {
for (i = 0; i < m; i++) {
int idx = i + e * m;
int idxc = i + (factor - e) * m;
out[out0 + ostride * idx] = in[in0 + istride * idx]
+ in[in0 + istride * idxc];
out[out0 + ostride * idx + 1] = in[in0 + istride * idx + 1]
+ in[in0 + istride * idxc + 1];
out[out0 + ostride * idxc] = in[in0 + istride * idx]
- in[in0 + istride * idxc];
out[out0 + ostride * idxc + 1] = in[in0 + istride * idx + 1]
- in[in0 + istride * idxc + 1];
}
}
/* e = 0 */
for (i = 0; i < m; i++) {
in[in0 + istride * i] = out[out0 + ostride * i];
in[in0 + istride * i + 1] = out[out0 + ostride * i + 1];
}
for (e1 = 1; e1 < (factor - 1) / 2 + 1; e1++) {
for (i = 0; i < m; i++) {
in[in0 + istride * i] += out[out0 + ostride * (i + e1 * m)];
in[in0 + istride * i + 1] += out[out0 + ostride * (i + e1 * m)
+ 1];
}
}
float twiddl[] = twiddle[fi][q];
for (e = 1; e < (factor - 1) / 2 + 1; e++) {
int idx = e;
float w_real, w_imag;
int em = e * m;
int ecm = (factor - e) * m;
for (i = 0; i < m; i++) {
in[in0 + istride * (i + em)] = out[out0 + ostride * i];
in[in0 + istride * (i + em) + 1] = out[out0 + ostride * i + 1];
in[in0 + istride * (i + ecm)] = out[out0 + ostride * i];
in[in0 + istride * (i + ecm) + 1] = out[out0 + ostride * i + 1];
}
for (e1 = 1; e1 < (factor - 1) / 2 + 1; e1++) {
if (idx == 0) {
w_real = 1;
w_imag = 0;
} else {
w_real = twiddl[2 * (idx - 1)];
w_imag = -sign * twiddl[2 * (idx - 1) + 1];
}
for (i = 0; i < m; i++) {
float ap = w_real * out[out0 + ostride * (i + e1 * m)];
float am = w_imag
* out[out0 + ostride * (i + (factor - e1) * m) + 1];
float bp = w_real * out[out0 + ostride * (i + e1 * m) + 1];
float bm = w_imag
* out[out0 + ostride * (i + (factor - e1) * m)];
in[in0 + istride * (i + em)] += (ap - am);
in[in0 + istride * (i + em) + 1] += (bp + bm);
in[in0 + istride * (i + ecm)] += (ap + am);
in[in0 + istride * (i + ecm) + 1] += (bp - bm);
}
idx += e;
idx %= factor;
}
}
i = 0;
j = 0;
/* k = 0 */
for (k1 = 0; k1 < p_1; k1++) {
out[out0 + ostride * k1] = in[in0 + istride * k1];
out[out0 + ostride * k1 + 1] = in[in0 + istride * k1 + 1];
}
for (e1 = 1; e1 < factor; e1++) {
for (k1 = 0; k1 < p_1; k1++) {
out[out0 + ostride * (k1 + e1 * p_1)] = in[in0 + istride
* (k1 + e1 * m)];
out[out0 + ostride * (k1 + e1 * p_1) + 1] = in[in0 + istride
* (k1 + e1 * m) + 1];
}
}
i = p_1;
j = product;
for (k = 1; k < q; k++) {
for (k1 = 0; k1 < p_1; k1++) {
out[out0 + ostride * j] = in[in0 + istride * i];
out[out0 + ostride * j + 1] = in[in0 + istride * i + 1];
i++;
j++;
}
j += jump;
}
i = p_1;
j = product;
for (k = 1; k < q; k++) {
twiddl = twiddle[fi][k];
for (k1 = 0; k1 < p_1; k1++) {
for (e1 = 1; e1 < factor; e1++) {
float x_real = in[in0 + istride * (i + e1 * m)];
float x_imag = in[in0 + istride * (i + e1 * m) + 1];
float w_real = twiddl[2 * (e1 - 1)];
float w_imag = -sign * twiddl[2 * (e1 - 1) + 1];
out[out0 + ostride * (j + e1 * p_1)] = w_real * x_real
- w_imag * x_imag;
out[out0 + ostride * (j + e1 * p_1) + 1] = w_real * x_imag
+ w_imag * x_real;
}
i++;
j++;
}
j += jump;
}
}
}