mirror of
https://github.com/mborgerding/kissfft.git
synced 2025-05-27 13:10:26 -04:00
Dog slow, but does mixed radix!
'make test' output : ### testing SNR for 1024 point FFTs #### DOUBLE snr_t2f = 295.52 snr_f2t = 307.98 #### FLOAT snr_t2f = 144.62 snr_f2t = 143.23 #### SHORT snr_t2f = -31.515 snr_f2t = -60.836 #### timing 10000 x 1024 point FFTs #### DOUBLE Elapsed:0:44.17 user:35.11 sys:0.27 #### FLOAT Elapsed:0:24.22 user:19.66 sys:0.16 #### SHORT Elapsed:0:30.39 user:25.07 sys:0.09
This commit is contained in:
Mark Borgerding
parent
08be1d86b4
commit
30c4ee30f5
6
fft.py
6
fft.py
@ -15,18 +15,22 @@ def fft(f):
|
||||
else:
|
||||
raise Exception('%s not factorable ' % n)
|
||||
|
||||
print 'n=%d,p=%d' % (n,p)
|
||||
print f,' << fin'
|
||||
m = n/p
|
||||
Fout=[]
|
||||
for q in range(p): # 0,1
|
||||
fp = f[q::p]
|
||||
print fp,'<< fp'
|
||||
Fp = fft( fp )
|
||||
Fout.extend( Fp )
|
||||
|
||||
for u in range(m):
|
||||
scratch = Fout[u::m] # u to end in strides of m
|
||||
print scratch
|
||||
for q1 in range(p):
|
||||
k = q1*m + u # indices to Fout above that became scratch
|
||||
Fout[ k ] = scratch[0]
|
||||
Fout[ k ] = scratch[0] # cuz e**0==1 in loop below
|
||||
for q in range(1,p):
|
||||
t = e ** ( j*2*pi*k*q/n )
|
||||
Fout[ k ] += scratch[q] * t
|
||||
|
||||
294
kiss_fft.c
294
kiss_fft.c
@ -27,66 +27,21 @@ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
* }kiss_fft_cpx;
|
||||
*/
|
||||
|
||||
typedef struct {
|
||||
int nr; // N remaining
|
||||
int radix; // radix of the stage
|
||||
kiss_fft_cpx * twiddle;
|
||||
}kiss_fft_stage;
|
||||
|
||||
const double pi=3.14159265358979323846264338327;
|
||||
|
||||
|
||||
#define MAX_STAGES 20
|
||||
typedef struct {
|
||||
int nfft;
|
||||
int nstages;
|
||||
int allocsize;
|
||||
kiss_fft_stage stages[MAX_STAGES];
|
||||
int * unscramble_indices;
|
||||
kiss_fft_cpx * buf1;
|
||||
int inverse;
|
||||
}kiss_fft_state;
|
||||
|
||||
|
||||
|
||||
#ifdef FIXED_POINT
|
||||
|
||||
# define TWIDDLE_RANGE ( (1<<FIXED_POINT_FRAC_BITS) - 1 )
|
||||
|
||||
/* The fixed point versions of C_ADD and C_SUB divide by two
|
||||
* after the add/sub.
|
||||
* This is to prevent overflow.
|
||||
* The cumulative effect is to multiply the sequence by 1/Nfft.
|
||||
* */
|
||||
# define C_ADD(x,a,b) \
|
||||
do{ (x).r = ( ( (a).r+(b).r +1) >> 1 );\
|
||||
(x).i = ( ( (a).i+(b).i +1) >> 1 ); }while(0)
|
||||
# define C_SUB(x,a,b) \
|
||||
do{ (x).r = ( ( (a).r-(b).r +1) >> 1 );\
|
||||
(x).i = ( ( (a).i-(b).i +1) >> 1 ); }while(0)
|
||||
|
||||
/* We don't have to worry about overflow from multiplying by twiddle factors since they
|
||||
* all have unity magnitude. Still need to shift away fractional bits after adding 1/2 for
|
||||
* rounding.
|
||||
* */
|
||||
# define C_MUL(m,a,b) \
|
||||
do{ (m).r = ( ( (a).r*(b).r - (a).i*(b).i) + (TWIDDLE_RANGE>>1) ) >> FIXED_POINT_FRAC_BITS;\
|
||||
(m).i = ( ( (a).r*(b).i + (a).i*(b).r) + (TWIDDLE_RANGE>>1) ) >> FIXED_POINT_FRAC_BITS;\
|
||||
}while(0)
|
||||
#else // not FIXED_POINT
|
||||
|
||||
#define C_ADD(x,a,b) \
|
||||
do{ (x).r = (a).r+(b).r;\
|
||||
(x).i = (a).i+(b).i;}while(0)
|
||||
#define C_SUB(x,a,b) \
|
||||
do{ (x).r = (a).r-(b).r;\
|
||||
(x).i = (a).i-(b).i;}while(0)
|
||||
#define C_MUL(m,a,b) \
|
||||
do{ (m).r = (a).r*(b).r - (a).i*(b).i;\
|
||||
(m).i = (a).r*(b).i + (a).i*(b).r; }while(0)
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
static
|
||||
kiss_fft_cpx cexp(double phase)
|
||||
{
|
||||
@ -96,69 +51,6 @@ kiss_fft_cpx cexp(double phase)
|
||||
return x;
|
||||
}
|
||||
|
||||
// create the twiddle factors
|
||||
static
|
||||
void make_twiddles(kiss_fft_cpx * twiddle,int ntwid,int symmetry,int inverse_fft)
|
||||
{
|
||||
int n;
|
||||
int denom = ntwid*symmetry;
|
||||
|
||||
for (n=0;n<ntwid;++n) {
|
||||
twiddle[n] = cexp( 2*pi*n/denom );
|
||||
//twiddle[n].r = cos(2*pi*n/denom);
|
||||
//twiddle[n].i = -sin(2*pi*n/denom);
|
||||
// inverse fft uses complex conjugate twiddle factors
|
||||
if (inverse_fft)
|
||||
twiddle[n].i *= -1;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// reverse the bits for numbers from 0 to N-1
|
||||
static
|
||||
int bit_reverse(int i,int N)
|
||||
{
|
||||
int rev=0;
|
||||
while ( N >>= 1 ) {
|
||||
rev = rev*2 + (i&1);
|
||||
i>>=1;
|
||||
}
|
||||
return rev;
|
||||
}
|
||||
|
||||
// make a list of index swaps that need to be done for bit-reversed addressing
|
||||
static
|
||||
int make_bit_reverse_indices(int *swap_indices ,int nfft)
|
||||
{
|
||||
int n,nswap;
|
||||
nswap=0;
|
||||
// set up swap indices to unwrap bit-reversed addressing
|
||||
for ( n=0; n<nfft; ++n ) {
|
||||
swap_indices[nswap*2] = bit_reverse(n,nfft);
|
||||
if ( n < swap_indices[nswap*2] ) {
|
||||
swap_indices[nswap*2+1] = n;
|
||||
++nswap;
|
||||
}
|
||||
}
|
||||
return nswap;
|
||||
}
|
||||
|
||||
static
|
||||
void undo_bit_rev( kiss_fft_cpx * f, const int * swap_indices,int nswap)
|
||||
{
|
||||
int i,i0,i1;
|
||||
kiss_fft_cpx tmp;
|
||||
|
||||
// unwrap bit-reverse indexing
|
||||
for ( i=0 ; i<nswap ; ++i ) {
|
||||
i0= *swap_indices++;
|
||||
i1= *swap_indices++;
|
||||
tmp = f[i0];
|
||||
f[i0] = f[i1];
|
||||
f[i1] = tmp;
|
||||
}
|
||||
}
|
||||
|
||||
static kiss_fft_cpx cadd(kiss_fft_cpx a,kiss_fft_cpx b)
|
||||
{
|
||||
kiss_fft_cpx c;
|
||||
@ -173,84 +65,94 @@ static kiss_fft_cpx cmul(kiss_fft_cpx a,kiss_fft_cpx b)
|
||||
return c;
|
||||
}
|
||||
|
||||
|
||||
|
||||
// the heart of the fft
|
||||
static
|
||||
void fft_work( kiss_fft_cpx * h,kiss_fft_cpx * h2,const kiss_fft_stage * stage , int nstages )
|
||||
void fft_work(
|
||||
kiss_fft_cpx * Fout,
|
||||
const kiss_fft_cpx * f,
|
||||
int fstride,
|
||||
int n,
|
||||
int inverse,
|
||||
kiss_fft_cpx * scratch
|
||||
)
|
||||
{
|
||||
int n;
|
||||
{ // declare automatic variables in here to reduce stack usage
|
||||
int nx,ny,Nx,Ny;
|
||||
kiss_fft_cpx twid;
|
||||
double inc1 = -2*pi/(stage->radix * stage->nr);
|
||||
Ny = stage->nr;
|
||||
Nx = stage->radix;
|
||||
int m,p=0,q,q1,u,k;
|
||||
kiss_fft_cpx t;
|
||||
double two_pi_divN;
|
||||
|
||||
for (ny=0;ny<Ny; ++ny) {
|
||||
for ( nx=0 ; nx<Nx ; ++nx ) {
|
||||
h2[ny] = h[ny];
|
||||
|
||||
h2[ny] = cadd( h2[ny] , cmul( twid ,h[ nx * nr + ny ] ) );
|
||||
}
|
||||
|
||||
twid = cexp();
|
||||
cmul(h2[ny]);
|
||||
}
|
||||
/*
|
||||
h2[n] = h[n] + h[n+N/2]
|
||||
h2[n+N/2] = ( h[n] - h[n+N/2] ) * exp ( n * j*2*pi/N)
|
||||
|
||||
for ( n = 0 ; n < stage->nr ; ++n )
|
||||
{
|
||||
C_ADD( csum, *f1 , *f2 );
|
||||
C_SUB( cdiff, *f1 , *f2 );
|
||||
C_MUL(*f2, cdiff, *twid);
|
||||
*f1++ = csum;
|
||||
++f2;
|
||||
++twid;
|
||||
}
|
||||
*/
|
||||
}
|
||||
if ( nstages == 1 )
|
||||
if (n==1) {
|
||||
*Fout = *f;
|
||||
return;
|
||||
}
|
||||
|
||||
for (n=0;n<stage->radix;++n) {
|
||||
int offset = n * stage->nr;
|
||||
fft_work( h2 + offset , h + offset ,stage+1,nstages-1);
|
||||
two_pi_divN = 2*pi/n;
|
||||
if (inverse)
|
||||
two_pi_divN *= -1;
|
||||
|
||||
if (n%2 == 0) p=2;
|
||||
else if(n%3 == 0) p=3;
|
||||
else if(n%5 == 0) p=5;
|
||||
else if(n%7 == 0) p=7;
|
||||
else {
|
||||
fprintf(stderr,"%d is not divisible by %d\n",n,p);
|
||||
p=n;
|
||||
exit(1);
|
||||
}
|
||||
m = n/p;
|
||||
/* n = stage->n; m = stage->m; p = stage->p; */
|
||||
|
||||
#ifdef LOUD
|
||||
printf("n=%d,p=%d\n",n,p);
|
||||
for (k=0;k<n;++k) {
|
||||
t=f[k*fstride];
|
||||
printf("(%.3f,%.3f) ",t.r,t.i);
|
||||
}
|
||||
printf(" <<< fin \n");
|
||||
#endif
|
||||
|
||||
for (q=0;q<p;++q) {
|
||||
#ifdef LOUD
|
||||
for (k=0;k<m;++k) {
|
||||
t = (f+q*fstride)[fstride*p*k];
|
||||
printf("(%.3f,%.3f) ",t.r,t.i);
|
||||
}
|
||||
printf(" <<< f[fstride*k+q] \n");
|
||||
#endif
|
||||
fft_work( Fout + m*q, f+q*fstride, fstride*p, m,inverse, scratch );
|
||||
}
|
||||
|
||||
#ifdef LOUD
|
||||
printf("twiddling n=%d,p=%d\n",n,p);
|
||||
#endif
|
||||
|
||||
for ( u=0; u<m; ++u ) {
|
||||
for ( q1=0 ; q1<p ; ++q1 ) {
|
||||
scratch[q1] = Fout[ u+q1*m ];
|
||||
#ifdef LOUD
|
||||
printf("(%.3f,%.3f) ",scratch[q1].r,scratch[q1].i);
|
||||
#endif
|
||||
}
|
||||
#ifdef LOUD
|
||||
printf(" <<< scratch \n");
|
||||
#endif
|
||||
|
||||
for ( q1=0 ; q1<p ; ++q1 ) {
|
||||
k=q1*m+u;
|
||||
Fout[ k ] = scratch[0];
|
||||
for (q=1;q<p;++q ) {
|
||||
//t = e ** ( j*2*pi*k*q/n );
|
||||
t = cexp( two_pi_divN * k * q );
|
||||
Fout[ k ] = cadd( Fout[ k ] ,
|
||||
cmul( scratch[q] , t ) );
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static
|
||||
kiss_fft_state * decompose( kiss_fft_state * st, int * pnfft,int radix,int inverse_fft)
|
||||
{
|
||||
int nfft = *pnfft;
|
||||
|
||||
while (nfft>1 && (nfft%radix)==0) {
|
||||
int newsize;
|
||||
int nstages=st->nstages;
|
||||
nfft /= radix;
|
||||
fprintf(stderr,"%d ",radix);
|
||||
|
||||
newsize = st->allocsize + nfft * sizeof(kiss_fft_cpx);
|
||||
|
||||
st=(kiss_fft_state*)realloc(st,newsize);
|
||||
|
||||
st->stages[nstages].radix=radix;
|
||||
st->stages[nstages].nr=nfft;
|
||||
st->stages[nstages].twiddle = (kiss_fft_cpx*)((char*)st + st->allocsize);
|
||||
|
||||
make_twiddles( st->stages[nstages].twiddle,nfft,radix,inverse_fft );
|
||||
st->allocsize = newsize;
|
||||
st->nstages = nstages+1;
|
||||
}
|
||||
*pnfft = nfft;
|
||||
return st;
|
||||
}
|
||||
|
||||
/*
|
||||
/*
|
||||
* void * kiss_fft_alloc(int nfft,int inverse_fft)
|
||||
*
|
||||
*
|
||||
* User-callable function to allocate all necessary scratch space for the fft.
|
||||
*
|
||||
* The return value is a contiguous block of memory, allocated with malloc. As such,
|
||||
@ -259,41 +161,23 @@ kiss_fft_state * decompose( kiss_fft_state * st, int * pnfft,int radix,int inver
|
||||
void * kiss_fft_alloc(int nfft,int inverse_fft)
|
||||
{
|
||||
kiss_fft_state * st=NULL;
|
||||
int tmp;
|
||||
int i;
|
||||
int allocsize=sizeof(kiss_fft_state) + nfft*( sizeof(int) + sizeof(kiss_fft_cpx) );
|
||||
|
||||
st = ( kiss_fft_state *)malloc( allocsize );
|
||||
st = ( kiss_fft_state *)malloc( sizeof(kiss_fft_state) );
|
||||
st->nfft=nfft;
|
||||
st->nstages=0;
|
||||
st->allocsize=allocsize;
|
||||
st->unscramble_indices = (int*)(st+1);// just past end of buffer
|
||||
st->buf1 = (kiss_fft_cpx*)( st->unscramble_indices + nfft);
|
||||
|
||||
for (i=0;i<nfft;++i)
|
||||
st->unscramble_indices[i] = i;
|
||||
|
||||
fprintf(stderr,"factoring %d: ",nfft);
|
||||
|
||||
tmp=nfft;
|
||||
st = decompose( st,&tmp,2,inverse_fft);
|
||||
fprintf(stderr,"\n");
|
||||
|
||||
// TODO factor 3,5,7,11 ???
|
||||
if ( tmp > 1 ) {
|
||||
fprintf(stderr,"%d not factorable by 2,3 (%d remaining)\n",nfft,tmp);
|
||||
free(st);
|
||||
return NULL;
|
||||
}
|
||||
st->inverse = inverse_fft;
|
||||
|
||||
return st;
|
||||
}
|
||||
|
||||
void kiss_fft(const void * cfg,kiss_fft_cpx *f)
|
||||
{
|
||||
int i,n;
|
||||
const kiss_fft_state * st = cfg;
|
||||
fft_work( f,st->buf1, st->stages , st->nstages );
|
||||
if (st->nstages&1) {
|
||||
memcpy( st->buf1 , f,sizeof(kiss_fft_cpx) * st->nfft );
|
||||
}
|
||||
kiss_fft_cpx tmpbuf[1024];
|
||||
kiss_fft_cpx scratch[1024];
|
||||
n = st->nfft;
|
||||
|
||||
for (i=0;i<n;++i)
|
||||
tmpbuf[i] = f[i];
|
||||
|
||||
fft_work( f, tmpbuf, 1, n, st->inverse, scratch );
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user