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Fixed point works (in the loosest sense of the word "works")

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Fixed point sums are divided by 2 each stage.  This will never overflow for radix 2 ffts.
For mixed radix, it may overflow, but will usually give better SNR.

'make test' output:

### testing SNR for  1024 point FFTs
#### DOUBLE
snr_t2f = 295.30
snr_f2t = 308.25
#### FLOAT
snr_t2f = 146.92
snr_f2t = 143.25
#### SHORT
snr_t2f = 54.645
snr_f2t = 24.677

#### timing 10000 x 1024 point FFTs
#### DOUBLE
Elapsed:0:25.96 user:19.77 sys:0.22
#### FLOAT
Elapsed:0:06.62 user:5.48 sys:0.11
#### SHORT
Elapsed:0:06.01 user:4.75 sys:0.12
This commit is contained in:
Mark Borgerding 2003-10-11 14:34:01 +00:00
parent 61571342a5
commit 7ec9402d5b
1 changed files with 62 additions and 64 deletions
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126
kiss_fft.c
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@ -33,9 +33,31 @@ const double pi=3.14159265358979323846264338327;
typedef struct { typedef struct {
int nfft; int nfft;
int inverse; int inverse;
int *factors;
kiss_fft_cpx * twiddles; kiss_fft_cpx * twiddles;
kiss_fft_cpx * tmpbuf;
kiss_fft_cpx * scratch;
}kiss_fft_state; }kiss_fft_state;
#ifdef 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)
/* 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) + (1<<14) ) >> 15;\
(m).i = ( ( (a).r*(b).i + (a).i*(b).r) + (1<<14) ) >> 15;\
}while(0)
#else // not FIXED_POINT
#define C_ADD(x,a,b) \ #define C_ADD(x,a,b) \
do{ (x).r = (a).r+(b).r;\ do{ (x).r = (a).r+(b).r;\
(x).i = (a).i+(b).i;}while(0) (x).i = (a).i+(b).i;}while(0)
@ -45,13 +67,19 @@ typedef struct {
#define C_MUL(m,a,b) \ #define C_MUL(m,a,b) \
do{ (m).r = (a).r*(b).r - (a).i*(b).i;\ do{ (m).r = (a).r*(b).r - (a).i*(b).i;\
(m).i = (a).r*(b).i + (a).i*(b).r; }while(0) (m).i = (a).r*(b).i + (a).i*(b).r; }while(0)
#endif
static static
kiss_fft_cpx cexp(double phase) kiss_fft_cpx cexp(double phase)
{ {
kiss_fft_cpx x; kiss_fft_cpx x;
#ifdef FIXED_POINT
x.r = (kiss_fft_scalar) ( 32767*cos(phase) );
x.i = (kiss_fft_scalar) ( -32767*sin(phase) );
#else
x.r = cos(phase); x.r = cos(phase);
x.i = -sin(phase); x.i = -sin(phase);
#endif
return x; return x;
} }
@ -85,7 +113,8 @@ void fft_work(
int Norig, int Norig,
int inverse, int inverse,
kiss_fft_cpx * scratch, kiss_fft_cpx * scratch,
kiss_fft_cpx * twiddles kiss_fft_cpx * twiddles,
int * factors
) )
{ {
int m,p=0,q,q1,u,k; int m,p=0,q,q1,u,k;
@ -95,58 +124,22 @@ void fft_work(
*Fout = *f; *Fout = *f;
return; return;
} }
/* p=*factors++;
double two_pi_divN; m=*factors++;//m = n/p;
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) { for (q=0;q<p;++q) {
#ifdef LOUD fft_work( Fout + m*q, f+q*fstride, fstride*p, m,Norig,inverse, scratch ,twiddles,factors);
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,Norig,inverse, scratch ,twiddles);
} }
#ifdef LOUD
printf("twiddling n=%d,p=%d\n",n,p);
#endif
for ( u=0; u<m; ++u ) { for ( u=0; u<m; ++u ) {
for ( q1=0 ; q1<p ; ++q1 ) { for ( q1=0 ; q1<p ; ++q1 ) {
#ifdef FIXED_POINT
scratch[q1].r = Fout[ u+q1*m ].r>>1;
scratch[q1].i = Fout[ u+q1*m ].i>>1;
#else
scratch[q1] = Fout[ u+q1*m ]; scratch[q1] = Fout[ u+q1*m ];
#ifdef LOUD #endif
printf("(%.3f,%.3f) ",scratch[q1].r,scratch[q1].i);
#endif
} }
#ifdef LOUD
printf(" <<< scratch \n");
#endif
for ( q1=0 ; q1<p ; ++q1 ) { for ( q1=0 ; q1<p ; ++q1 ) {
int twidx=0; int twidx=0;
@ -157,21 +150,6 @@ void fft_work(
if (twidx>=Norig) if (twidx>=Norig)
twidx-=Norig; twidx-=Norig;
t = twiddles[twidx]; t = twiddles[twidx];
/*
kiss_fft_cpx diff,tref;
tref = cexp( two_pi_divN * k * q );
diff = csub(t,tref);
if (
diff.r * diff.r + diff.i*diff.i * 100
>
tref.r * tref.r + tref.i*tref.i)
{
printf("twiddling n=%d,p=%d\n",n,p);
printf("t=(%.3f,%.3f) ",t.r,t.i);
printf("tref=(%.3f,%.3f) ",tref.r,tref.i);
printf("diff=(%.3f,%.3f) \n",diff.r,diff.i);
}
*/
Fout[ k ] = cadd( Fout[ k ] , Fout[ k ] = cadd( Fout[ k ] ,
cmul( scratch[q] , t ) ); cmul( scratch[q] , t ) );
} }
@ -189,6 +167,7 @@ void fft_work(
* */ * */
void * kiss_fft_alloc(int nfft,int inverse_fft) void * kiss_fft_alloc(int nfft,int inverse_fft)
{ {
int nstages=0;
int i; int i;
kiss_fft_state * st=NULL; kiss_fft_state * st=NULL;
st = ( kiss_fft_state *)malloc( sizeof(kiss_fft_state) ); st = ( kiss_fft_state *)malloc( sizeof(kiss_fft_state) );
@ -196,6 +175,10 @@ void * kiss_fft_alloc(int nfft,int inverse_fft)
st->inverse = inverse_fft; st->inverse = inverse_fft;
st->twiddles = (kiss_fft_cpx*)malloc( sizeof(kiss_fft_cpx)*nfft ); st->twiddles = (kiss_fft_cpx*)malloc( sizeof(kiss_fft_cpx)*nfft );
st->tmpbuf = (kiss_fft_cpx*)malloc( sizeof(kiss_fft_cpx)*nfft );
st->scratch = (kiss_fft_cpx*)malloc( sizeof(kiss_fft_cpx)*nfft );
st->factors = (int*)malloc( sizeof(int)*nfft );
for (i=0;i<nfft;++i) { for (i=0;i<nfft;++i) {
double phase = ( 2*pi /nfft ) * i; double phase = ( 2*pi /nfft ) * i;
@ -204,6 +187,22 @@ void * kiss_fft_alloc(int nfft,int inverse_fft)
st->twiddles[i] = cexp( phase ); st->twiddles[i] = cexp( phase );
} }
while (nfft>1) {
const int primes[] = {2,3,5,7,11,13,17,-1};
int p=nfft;
i=0;
while ( primes[i] != -1 ) {
if ( nfft % primes[i] == 0){
p = primes[i];
break;
}
}
st->factors[2*nstages] = p;
nfft /= p;
st->factors[2*nstages+1] = nfft;
++nstages;
}
return st; return st;
} }
@ -211,12 +210,11 @@ void kiss_fft(const void * cfg,kiss_fft_cpx *f)
{ {
int i,n; int i,n;
const kiss_fft_state * st = cfg; const kiss_fft_state * st = cfg;
kiss_fft_cpx tmpbuf[1024];
kiss_fft_cpx scratch[1024];
n = st->nfft; n = st->nfft;
for (i=0;i<n;++i) for (i=0;i<n;++i)
tmpbuf[i] = f[i]; st->tmpbuf[i] = f[i];
fft_work( f, tmpbuf, 1, n,n, st->inverse, scratch ,st->twiddles); fft_work( f, st->tmpbuf, 1, n,n, st->inverse, st->scratch ,st->twiddles,st->factors);
} }