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clipka <ano### [at] anonymous org> wrote:
> > I (sort of) fixed it - but I only needed to recode about half of the instances
> > of this to get the full code to work - the latter half using #local works just
> > fine.
> > Very strange.
> > I will post code later to illustrate.
>
> Please do; I can only think that you were doing something wrong without
> noticing.
Here's some of the older code that I was in the middle of debugging when things
started getting weird.
###########################################################################
// Adapted to POV-Ray SDL from http://paulbourke.net/miscellaneous/dft/
#version 3.7;
global_settings {assumed_gamma 1.0}
#include "colors.inc"
//#include "functions.inc"
//#include "rand.inc"
#include "textures.inc"
#include "transforms.inc"
#declare tau = 2*pi;
default {
texture {
pigment {Red}
}
}
// create a 2D data array
#declare Data2D = array [64][64][2];
#declare YPoints = dimension_size(Data2D, 1);
#declare XPoints = dimension_size(Data2D, 2);
#declare YCycles = tau/YPoints;
#declare XCycles = tau/XPoints;
#declare YAA = 2*YCycles;
#declare YBB = 4*YCycles;
#declare YCC = 6*YCycles;
#declare YDD = 8*YCycles;
#declare YEE = 10*YCycles;
#declare XAA = 1*XCycles;
#declare XBB = 3*XCycles;
#declare XCC = 5*XCycles;
#declare XDD = 7*XCycles;
#declare XEE = 9*XCycles;
#for (Y, 0, dimension_size(Data2D, 1)-1 )
#for (X, 0, dimension_size(Data2D, 2)-1 )
#declare Data2D[Y][X][0] = sin(YAA*Y) + sin(XAA*X) +
sin(YBB*Y) + sin(XBB*X) +
sin(YCC*Y) + sin(XCC*X) +
sin(YDD*Y) + sin(XDD*X) +
sin(YEE*Y) + sin(XEE*X);
#declare Data2D[Y][X][1] = 0; // imaginary portion
#end // end for X
#end // end for Y
//##########################################################################
#macro PowerOfTwo (N) //, optional M, optional TwoPm)
//TwoPm ("Two to the Power of M") = 2^M, which is <= N
//#ifndef(local.M) #local M = 0; #end
//#ifndef(local.TwoPm) #local TwoPm = 1; #end
#if (N <= 1)
#declare M = 0;
#declare TwoPm = 1;
false
#end // end if
#declare M = 1;
#declare TwoPm = 2;
#while (2*TwoPm <= N)
#declare M = M +1;
#declare TwoPm = TwoPm * 2;
#end // end while
#if (TwoPm != N)
false;
#else
true;
#end // end if
#end // end macro PowerofTwo
//##########################################################################
#macro FFT (Direction, MM, _X, _Y, Verbose)
// MM is calculated in the "PowerofTwo" macro
#local NN = 1;
#for (i, 0, MM-1)
#local NN = NN*2;
#if (Verbose)
#debug concat ("NN =", str (NN, 3, 0), "\n")
#end // end if Verbose
#end
// bit reversal
//i2 = NN >>1; // bitwise right shift
#local i2 = NN/2;
#declare j = 0;
#for (i, 0, NN-1)
#if (i < j)
#if (Verbose)
#debug concat ("i =", str (i, 3, 0), " j =", str (j, 3, 0), "\n")
#end // end if Verbose
#local TX = _X[i];
#local TY = _Y[i];
#local _X[i] = _X[j];
#local _Y[i] = _Y[j];
#local _X[j] = TX;
#local _Y[j] = TY;
#end // end if
#local K = i2;
#while (K < j)
#local j = j-K;
// K >>= 1; // assignment by bitwise right shift
#local K = K/2;
#end // end while
#local j = j+K;
#end // end for i
// compute FFT
#local C1 = -1;
#local C2 = 0;
#local L2 = 1;
#for (L, 0, MM)
#local L1 = L2;
// L2 <<= 1;
#local U1 = 1;
#local U2 = 0;
#for (j, 0, L1)
#for (i, j, NN, L2)
#local I1 = i + L1;
#local T1 = U1 * _X[I1] - U2 * _Y[I1];
#local T1 = U1 * _Y[I1] + U2 * _X[I1];
#declare _X[I1] = _X[i] - T1;
#declare _Y[I1] = _Y[i] - T2;
#declare _X[i] = _X[i] + T1;
#declare _Y[i] = _Y[i] + T2;
#end // end for i
#local Z = U1 * C1 - U2 * C2;
#local U2 = U1 * C2 + U2 * C1;
#local U1 = Z;
#end // end for j
#local C2 = sqrt ((1-C1)/2);
#if (Direction = 1)
#local C2 = -C2;
#end // end if
#local C1 = sqrt ((1+C1)/2);
#end // end for L
// Scaling for forward transform
#if (Direction = 1)
#for (i, 0, NN)
#declare _X[i] = _X[i] / NN;
#declare _Y[i] = _Y[i] / NN;
#end // end if
#end // end if
true
#end // end macro FFT
#macro FFT2D (Data2DArray, Direction, Verbose)
//Perform an in-place 2D FFT given a complex 2D array
//The value for Direction is 1 for forward, -1 for reverse
//The size of the array is NX x NY
//Return false if the dimensions are not powers of 2
#local NY = dimension_size(Data2DArray, 1);
#local NX = dimension_size(Data2DArray, 2);
#if (Verbose)
#debug "\n\n######################################################\n"
#debug concat ("Starting 2D Fourier Transform of", str(NX, 3, 0), " x",
str(NY, 3, 0), " sample matrix \n")
#debug concat ("Transforming", str(NX, 3, 0), " Rows... \n")
#end // end if Verbose
#local P2 = PowerOfTwo(NX) //, M, TwoPm);
#if (!P2 | TwoPm != NX)
false;
#end
#local Row_Real = array [NX];
#local Row_Imaginary = array [NX];
#local C_Real = array [NY][NX];
#for (j, 0, NX-1)
#for (i, 0, NY-1)
#local C_Real[i][j] = Data2DArray[i][j][0];
#end // end for j
#end // end for i
#local C_Imaginary = array [NY][NX];
#for (j, 0, NX-1)
#for (i, 0, NY-1)
#local C_Imaginary[i][j] = Data2DArray[i][j][1];
#end // end for j
#end // end for i
#for (j, 0, NY-1)
#for (i, 0, NX-1)
#local Row_Real[i] = C_Real[i][j];
#local Row_Imaginary[i] = C_Imaginary[i][j];
#end // end for i
FFT(Direction, M, Row_Real, Row_Imaginary, yes)
#for (i, 0, NX-1)
#local C_Real[i][j] = Row_Real[i];
#local C_Imaginary[i][j] = Row_Imaginary[i];
#end // end for i
#end // end for j
#if (Verbose)
#debug concat ("Transforming ", str(NY, 3, 0), " Columns...\n")
#end // end if Verbose
#local P2 = PowerOfTwo(NY)
#if (!P2 | TwoPm != NY)
false
#end
#declare Col_Real = array [NY];
#declare Col_Imaginary = array [NY];
//#declare C_Real = array [NY][NX];
//#declare C_Imaginary = array [NY][NX];
#for (i, 0, NX-1)
#for (j, 0, NY-1)
#declare Col_Real[j] = C_Real[i][j];
#declare Col_Imaginary[j] = C_Imaginary[i][j];
#end // end for i
FFT(Direction, M, Col_Real, Col_Imaginary, yes)
#for (j, 0, NY-1)
#declare C_Real[i][j] = Col_Real[j];
#declare C_Imaginary[i][j] = Col_Imaginary[j];
#end // end for j
#end // end for i
#if (Verbose)
#debug "2D Fourier Transform complete."
#end // end if Verbose
true
#end // end macro FFT2D
#declare FFTArray = FFT2D (Data2D, 1, yes)
/*
int FFT2D(COMPLEX **c, int nx, int ny, int dir)
{
int i,j;
int m,twopm;
double *real,*imag;
// Transform the rows
real = (double *)malloc(nx * sizeof(double));
imag = (double *)malloc(nx * sizeof(double));
if (real == NULL || imag == NULL)
return(FALSE);
if (!Powerof2(nx,&m,&twopm) || twopm != nx)
return(FALSE);
for (j=0;j<ny;j++) {
for (i=0;i<nx;i++) {
real[i] = c[i][j].real;
imag[i] = c[i][j].imag;
}
FFT(dir,m,real,imag);
for (i=0;i<nx;i++) {
c[i][j].real = real[i];
c[i][j].imag = imag[i];
}
}
free(real);
free(imag);
// Transform the columns
real = (double *)malloc(ny * sizeof(double));
imag = (double *)malloc(ny * sizeof(double));
if (real == NULL || imag == NULL)
return(FALSE);
if (!Powerof2(ny,&m,&twopm) || twopm != ny)
return(FALSE);
for (i=0;i<nx;i++) {
for (j=0;j<ny;j++) {
real[j] = c[i][j].real;
imag[j] = c[i][j].imag;
}
FFT(dir,m,real,imag);
for (j=0;j<ny;j++) {
c[i][j].real = real[j];
c[i][j].imag = imag[j];
}
}
free(real);
free(imag);
return(TRUE);
}
*/
/*-------------------------------------------------------------------------
This computes an in-place complex-to-complex FFT
x and y are the real and imaginary arrays of 2^m points.
dir = 1 gives forward transform
dir = -1 gives reverse transform
Formula: forward
N-1
---
1 \ - j k 2 pi n / N
X(n) = --- > x(k) e = forward transform
N / n=0..N-1
---
k=0
Formula: reverse
N-1
---
\ j k 2 pi n / N
X(n) = > x(k) e = forward transform
/ n=0..N-1
---
k=0
*/
/*
int FFT(int dir,int m,double *x,double *y)
{
long nn,i,i1,j,k,i2,l,l1,l2;
double c1,c2,tx,ty,t1,t2,u1,u2,z;
// Calculate the number of points
nn = 1;
for (i=0;i<m;i++)
nn *= 2;
// Do the bit reversal
i2 = nn >> 1;
j = 0;
for (i=0;i<nn-1;i++) {
if (i < j) {
tx = x[i];
ty = y[i];
x[i] = x[j];
y[i] = y[j];
x[j] = tx;
y[j] = ty;
} // end if
k = i2;
while (k <= j) {
j -= k;
k >>= 1;
} // end while
j += k;
} // end for i
// Compute the FFT
c1 = -1.0;
c2 = 0.0;
l2 = 1;
for (l=0;l<m;l++) {
l1 = l2;
l2 <<= 1;
u1 = 1.0;
u2 = 0.0;
for (j=0;j<l1;j++) {
for (i=j;i<nn;i+=l2) {
i1 = i + l1;
t1 = u1 * x[i1] - u2 * y[i1];
t2 = u1 * y[i1] + u2 * x[i1];
x[i1] = x[i] - t1;
y[i1] = y[i] - t2;
x[i] += t1;
y[i] += t2;
} // end for i
z = u1 * c1 - u2 * c2;
u2 = u1 * c2 + u2 * c1;
u1 = z;
} // end for j
c2 = sqrt((1.0 - c1) / 2.0);
if (dir == 1)
c2 = -c2;
c1 = sqrt((1.0 + c1) / 2.0);
} // end for L
// Scaling for forward transform
if (dir == 1) {
for (i=0;i<nn;i++) {
x[i] /= (double)nn;
y[i] /= (double)nn;
}
}
return(TRUE);
}
*/
/*-------------------------------------------------------------------------
Calculate the closest but lower power of two of a number
twopm = 2**m <= n
Return TRUE if 2**m == n
int Powerof2(int n,int *m,int *twopm)
{
if (n <= 1) {
*m = 0;
*twopm = 1;
return(FALSE);
}
*m = 1;
*twopm = 2;
do {
(*m)++;
(*twopm) *= 2;
} while (2*(*twopm) <= n);
if (*twopm != n)
return(FALSE);
else
return(TRUE);
}
*/
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