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authorGravatar Alexey Yakovenko <wakeroid@gmail.com>2010-03-20 13:58:08 +0100
committerGravatar Alexey Yakovenko <wakeroid@gmail.com>2010-03-20 13:58:08 +0100
commit074097b6c41d1dd6d01a4fa7e257bafb310f5692 (patch)
tree197c2739b3b4971fd27993ad2693cdc45a643d27 /plugins/supereq
parenta723a88e649bba5b8187bee0a7156beca31a1c8c (diff)
supereq plugin prototype
Diffstat (limited to 'plugins/supereq')
-rw-r--r--plugins/supereq/Equ.cpp647
-rw-r--r--plugins/supereq/Fftsg_fl.cpp2673
-rw-r--r--plugins/supereq/Makefile.am8
-rw-r--r--plugins/supereq/paramlist.hpp120
-rw-r--r--plugins/supereq/supereq.c105
-rw-r--r--plugins/supereq/supereq.h29
6 files changed, 3582 insertions, 0 deletions
diff --git a/plugins/supereq/Equ.cpp b/plugins/supereq/Equ.cpp
new file mode 100644
index 00000000..42fdcc13
--- /dev/null
+++ b/plugins/supereq/Equ.cpp
@@ -0,0 +1,647 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <assert.h>
+#include "paramlist.hpp"
+
+typedef float REAL;
+void rfft(int n,int isign,REAL x[]);
+
+#define M 15
+
+#define PI 3.1415926535897932384626433832795
+
+#define RINT(x) ((x) >= 0 ? ((int)((x) + 0.5)) : ((int)((x) - 0.5)))
+
+#define DITHERLEN 65536
+
+// play -c 2 -r 44100 -fs -sw
+
+static REAL fact[M+1];
+static REAL aa = 96;
+static REAL iza;
+static REAL *lires,*lires1,*lires2,*rires,*rires1,*rires2,*irest;
+static REAL *fsamples;
+static REAL *ditherbuf;
+static int ditherptr = 0;
+static volatile int chg_ires,cur_ires;
+static int winlen,winlenbit,tabsize,nbufsamples;
+static short *inbuf;
+static REAL *outbuf;
+static int maxamp;
+int enable = 1, dither = 0;
+
+#define NCH 2
+
+#define NBANDS 17
+static REAL bands[] = {
+ 65.406392,92.498606,130.81278,184.99721,261.62557,369.99442,523.25113,
+ 739.9884 ,1046.5023,1479.9768,2093.0045,2959.9536,4186.0091,5919.9072,
+ 8372.0181,11839.814,16744.036
+};
+
+static REAL alpha(REAL a)
+{
+ if (a <= 21) return 0;
+ if (a <= 50) return 0.5842*pow(a-21,0.4)+0.07886*(a-21);
+ return 0.1102*(a-8.7);
+}
+
+static REAL izero(REAL x)
+{
+ REAL ret = 1;
+ int m;
+
+ for(m=1;m<=M;m++)
+ {
+ REAL t;
+ t = pow(x/2,m)/fact[m];
+ ret += t*t;
+ }
+
+ return ret;
+}
+
+extern "C" void equ_init(int wb)
+{
+ int i,j;
+
+ if (lires1 != NULL) free(lires1);
+ if (lires2 != NULL) free(lires2);
+ if (rires1 != NULL) free(rires1);
+ if (rires2 != NULL) free(rires2);
+ if (irest != NULL) free(irest);
+ if (fsamples != NULL) free(fsamples);
+ if (inbuf != NULL) free(inbuf);
+ if (outbuf != NULL) free(outbuf);
+ if (ditherbuf != NULL) free(ditherbuf);
+
+ winlen = (1 << (wb-1))-1;
+ winlenbit = wb;
+ tabsize = 1 << wb;
+
+ lires1 = (REAL *)malloc(sizeof(REAL)*tabsize);
+ lires2 = (REAL *)malloc(sizeof(REAL)*tabsize);
+ rires1 = (REAL *)malloc(sizeof(REAL)*tabsize);
+ rires2 = (REAL *)malloc(sizeof(REAL)*tabsize);
+ irest = (REAL *)malloc(sizeof(REAL)*tabsize);
+ fsamples = (REAL *)malloc(sizeof(REAL)*tabsize);
+ inbuf = (short *)calloc(winlen*NCH,sizeof(int));
+ outbuf = (REAL *)calloc(tabsize*NCH,sizeof(REAL));
+ ditherbuf = (REAL *)malloc(sizeof(REAL)*DITHERLEN);
+
+ lires = lires1;
+ rires = rires1;
+ cur_ires = 1;
+ chg_ires = 1;
+
+ for(i=0;i<DITHERLEN;i++)
+ ditherbuf[i] = (float(rand())/RAND_MAX-0.5);
+
+ for(i=0;i<=M;i++)
+ {
+ fact[i] = 1;
+ for(j=1;j<=i;j++) fact[i] *= j;
+ }
+
+ iza = izero(alpha(aa));
+}
+
+// -(N-1)/2 <= n <= (N-1)/2
+static REAL win(REAL n,int N)
+{
+ return izero(alpha(aa)*sqrt(1-4*n*n/((N-1)*(N-1))))/iza;
+}
+
+static REAL sinc(REAL x)
+{
+ return x == 0 ? 1 : sin(x)/x;
+}
+
+static REAL hn_lpf(int n,REAL f,REAL fs)
+{
+ REAL t = 1/fs;
+ REAL omega = 2*PI*f;
+ return 2*f*t*sinc(n*omega*t);
+}
+
+static REAL hn_imp(int n)
+{
+ return n == 0 ? 1.0 : 0.0;
+}
+
+static REAL hn(int n,paramlist &param2,REAL fs)
+{
+ paramlistelm *e;
+ REAL ret,lhn;
+
+ lhn = hn_lpf(n,param2.elm->upper,fs);
+ ret = param2.elm->gain*lhn;
+
+ for(e=param2.elm->next;e->next != NULL && e->upper < fs/2;e = e->next)
+ {
+ REAL lhn2 = hn_lpf(n,e->upper,fs);
+ ret += e->gain*(lhn2-lhn);
+ lhn = lhn2;
+ }
+
+ ret += e->gain*(hn_imp(n)-lhn);
+
+ return ret;
+}
+
+void process_param(REAL *bc,paramlist *param,paramlist &param2,REAL fs,int ch)
+{
+ paramlistelm **pp,*p,*e,*e2;
+ int i;
+
+ delete param2.elm;
+ param2.elm = NULL;
+
+ for(i=0,pp=&param2.elm;i<=NBANDS;i++,pp = &(*pp)->next)
+ {
+ (*pp) = new paramlistelm;
+ (*pp)->lower = i == 0 ? 0 : bands[i-1];
+ (*pp)->upper = i == NBANDS-1 ? fs : bands[i ];
+ (*pp)->gain = bc[i];
+ }
+
+ for(e = param->elm;e != NULL;e = e->next)
+ {
+ if ((ch == 0 && !e->left) || (ch == 1 && !e->right)) continue;
+ if (e->lower >= e->upper) continue;
+
+ for(p=param2.elm;p != NULL;p = p->next)
+ if (p->upper > e->lower) break;
+
+ while(p != NULL && p->lower < e->upper)
+ {
+ if (e->lower <= p->lower && p->upper <= e->upper) {
+ p->gain *= pow(10,e->gain/20);
+ p = p->next;
+ continue;
+ }
+ if (p->lower < e->lower && e->upper < p->upper) {
+ e2 = new paramlistelm;
+ e2->lower = e->upper;
+ e2->upper = p->upper;
+ e2->gain = p->gain;
+ e2->next = p->next;
+ p->next = e2;
+
+ e2 = new paramlistelm;
+ e2->lower = e->lower;
+ e2->upper = e->upper;
+ e2->gain = p->gain * pow(10,e->gain/20);
+ e2->next = p->next;
+ p->next = e2;
+
+ p->upper = e->lower;
+
+ p = p->next->next->next;
+ continue;
+ }
+ if (p->lower < e->lower) {
+ e2 = new paramlistelm;
+ e2->lower = e->lower;
+ e2->upper = p->upper;
+ e2->gain = p->gain * pow(10,e->gain/20);
+ e2->next = p->next;
+ p->next = e2;
+
+ p->upper = e->lower;
+ p = p->next->next;
+ continue;
+ }
+ if (e->upper < p->upper) {
+ e2 = new paramlistelm;
+ e2->lower = e->upper;
+ e2->upper = p->upper;
+ e2->gain = p->gain;
+ e2->next = p->next;
+ p->next = e2;
+
+ p->upper = e->upper;
+ p->gain = p->gain * pow(10,e->gain/20);
+ p = p->next->next;
+ continue;
+ }
+ abort();
+ }
+ }
+}
+
+extern "C" void equ_makeTable(REAL *lbc,REAL *rbc,paramlist *param,REAL fs)
+{
+ int i,cires = cur_ires;
+ REAL *nires;
+
+ if (fs <= 0) return;
+
+ paramlist param2;
+
+ // L
+
+ process_param(lbc,param,param2,fs,0);
+
+ for(i=0;i<winlen;i++)
+ irest[i] = hn(i-winlen/2,param2,fs)*win(i-winlen/2,winlen);
+
+ for(;i<tabsize;i++)
+ irest[i] = 0;
+
+ rfft(tabsize,1,irest);
+
+ nires = cires == 1 ? lires2 : lires1;
+
+ for(i=0;i<tabsize;i++)
+ nires[i] = irest[i];
+
+ process_param(rbc,param,param2,fs,1);
+
+ // R
+
+ for(i=0;i<winlen;i++)
+ irest[i] = hn(i-winlen/2,param2,fs)*win(i-winlen/2,winlen);
+
+ for(;i<tabsize;i++)
+ irest[i] = 0;
+
+ rfft(tabsize,1,irest);
+
+ nires = cires == 1 ? rires2 : rires1;
+
+ for(i=0;i<tabsize;i++)
+ nires[i] = irest[i];
+
+ //
+
+ chg_ires = cires == 1 ? 2 : 1;
+}
+
+extern "C" void equ_quit(void)
+{
+ free(lires1);
+ free(lires2);
+ free(rires1);
+ free(rires2);
+ free(irest);
+ free(fsamples);
+ free(inbuf);
+ free(outbuf);
+
+ lires1 = NULL;
+ lires2 = NULL;
+ rires1 = NULL;
+ rires2 = NULL;
+ irest = NULL;
+ fsamples = NULL;
+ inbuf = NULL;
+ outbuf = NULL;
+
+ rfft(0,0,NULL);
+}
+
+extern "C" void equ_clearbuf(int bps,int srate)
+{
+ int i;
+
+ nbufsamples = 0;
+ for(i=0;i<tabsize*NCH;i++) outbuf[i] = 0;
+}
+
+extern "C" int equ_modifySamples(char *buf,int nsamples,int nch,int bps)
+{
+ int i,p,ch;
+ REAL *ires;
+ int amax = (1 << (bps-1))-1;
+ int amin = -(1 << (bps-1));
+ static float hm1 = 0, hm2 = 0;
+
+ if (chg_ires) {
+ cur_ires = chg_ires;
+ lires = cur_ires == 1 ? lires1 : lires2;
+ rires = cur_ires == 1 ? rires1 : rires2;
+ chg_ires = 0;
+ }
+
+ p = 0;
+
+ while(nbufsamples+nsamples >= winlen)
+ {
+ switch(bps)
+ {
+ case 8:
+ for(i=0;i<(winlen-nbufsamples)*nch;i++)
+ {
+ inbuf[nbufsamples*nch+i] = ((unsigned char *)buf)[i+p*nch] - 0x80;
+ float s = outbuf[nbufsamples*nch+i];
+ if (dither) {
+ float u;
+ s -= hm1;
+ u = s;
+ s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ s = RINT(s);
+ hm1 = s - u;
+ ((unsigned char *)buf)[i+p*nch] = s + 0x80;
+ } else {
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ ((unsigned char *)buf)[i+p*nch] = RINT(s) + 0x80;
+ }
+ }
+ for(i=winlen*nch;i<tabsize*nch;i++)
+ outbuf[i-winlen*nch] = outbuf[i];
+
+ break;
+
+ case 16:
+ for(i=0;i<(winlen-nbufsamples)*nch;i++)
+ {
+ inbuf[nbufsamples*nch+i] = ((short *)buf)[i+p*nch];
+ float s = outbuf[nbufsamples*nch+i];
+ if (dither) {
+ float u;
+ s -= hm1;
+ u = s;
+ s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ s = RINT(s);
+ hm1 = s - u;
+ ((short *)buf)[i+p*nch] = s;
+ } else {
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ ((short *)buf)[i+p*nch] = RINT(s);
+ }
+ }
+ for(i=winlen*nch;i<tabsize*nch;i++)
+ outbuf[i-winlen*nch] = outbuf[i];
+
+ break;
+
+ case 24:
+ for(i=0;i<(winlen-nbufsamples)*nch;i++)
+ {
+ ((int *)inbuf)[nbufsamples*nch+i] =
+ (((unsigned char *)buf)[(i+p*nch)*3 ] ) +
+ (((unsigned char *)buf)[(i+p*nch)*3+1] << 8) +
+ ((( signed char *)buf)[(i+p*nch)*3+2] << 16) ;
+
+ float s = outbuf[nbufsamples*nch+i];
+ //if (dither) s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ int s2 = RINT(s);
+ ((signed char *)buf)[(i+p*nch)*3 ] = s2 & 255; s2 >>= 8;
+ ((signed char *)buf)[(i+p*nch)*3+1] = s2 & 255; s2 >>= 8;
+ ((signed char *)buf)[(i+p*nch)*3+2] = s2 & 255;
+ }
+ for(i=winlen*nch;i<tabsize*nch;i++)
+ outbuf[i-winlen*nch] = outbuf[i];
+
+ break;
+
+ default:
+ assert(0);
+ }
+
+ p += winlen-nbufsamples;
+ nsamples -= winlen-nbufsamples;
+ nbufsamples = 0;
+
+ for(ch=0;ch<nch;ch++)
+ {
+ ires = ch == 0 ? lires : rires;
+
+ if (bps == 24) {
+ for(i=0;i<winlen;i++)
+ fsamples[i] = ((int *)inbuf)[nch*i+ch];
+ } else {
+ for(i=0;i<winlen;i++)
+ fsamples[i] = inbuf[nch*i+ch];
+ }
+
+ for(i=winlen;i<tabsize;i++)
+ fsamples[i] = 0;
+
+ if (enable) {
+ rfft(tabsize,1,fsamples);
+
+ fsamples[0] = ires[0]*fsamples[0];
+ fsamples[1] = ires[1]*fsamples[1];
+
+ for(i=1;i<tabsize/2;i++)
+ {
+ REAL re,im;
+
+ re = ires[i*2 ]*fsamples[i*2] - ires[i*2+1]*fsamples[i*2+1];
+ im = ires[i*2+1]*fsamples[i*2] + ires[i*2 ]*fsamples[i*2+1];
+
+ fsamples[i*2 ] = re;
+ fsamples[i*2+1] = im;
+ }
+
+ rfft(tabsize,-1,fsamples);
+ } else {
+ for(i=winlen-1+winlen/2;i>=winlen/2;i--) fsamples[i] = fsamples[i-winlen/2]*tabsize/2;
+ for(;i>=0;i--) fsamples[i] = 0;
+ }
+
+ for(i=0;i<winlen;i++) outbuf[i*nch+ch] += fsamples[i]/tabsize*2;
+
+ for(i=winlen;i<tabsize;i++) outbuf[i*nch+ch] = fsamples[i]/tabsize*2;
+ }
+ }
+
+ switch(bps)
+ {
+ case 8:
+ for(i=0;i<nsamples*nch;i++)
+ {
+ inbuf[nbufsamples*nch+i] = ((unsigned char *)buf)[i+p*nch] - 0x80;
+ float s = outbuf[nbufsamples*nch+i];
+ if (dither) {
+ float u;
+ s -= hm1;
+ u = s;
+ s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ s = RINT(s);
+ hm1 = s - u;
+ ((unsigned char *)buf)[i+p*nch] = s + 0x80;
+ } else {
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ ((unsigned char *)buf)[i+p*nch] = RINT(s) + 0x80;
+ }
+ }
+ break;
+
+ case 16:
+ for(i=0;i<nsamples*nch;i++)
+ {
+ inbuf[nbufsamples*nch+i] = ((short *)buf)[i+p*nch];
+ float s = outbuf[nbufsamples*nch+i];
+ if (dither) {
+ float u;
+ s -= hm1;
+ u = s;
+ s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ s = RINT(s);
+ hm1 = s - u;
+ ((short *)buf)[i+p*nch] = s;
+ } else {
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ ((short *)buf)[i+p*nch] = RINT(s);
+ }
+ }
+ break;
+
+ case 24:
+ for(i=0;i<nsamples*nch;i++)
+ {
+ ((int *)inbuf)[nbufsamples*nch+i] =
+ (((unsigned char *)buf)[(i+p*nch)*3 ] ) +
+ (((unsigned char *)buf)[(i+p*nch)*3+1] << 8) +
+ ((( signed char *)buf)[(i+p*nch)*3+2] << 16) ;
+
+ float s = outbuf[nbufsamples*nch+i];
+ //if (dither) s += ditherbuf[(ditherptr++) & (DITHERLEN-1)];
+ if (s < amin) s = amin;
+ if (amax < s) s = amax;
+ int s2 = RINT(s);
+ ((signed char *)buf)[(i+p*nch)*3 ] = s2 & 255; s2 >>= 8;
+ ((signed char *)buf)[(i+p*nch)*3+1] = s2 & 255; s2 >>= 8;
+ ((signed char *)buf)[(i+p*nch)*3+2] = s2 & 255;
+ }
+ break;
+
+ default:
+ assert(0);
+ }
+
+ p += nsamples;
+ nbufsamples += nsamples;
+
+ return p;
+}
+
+#if 0
+void usage(void)
+{
+ fprintf(stderr,"Ouch!\n");
+}
+
+int main(int argc,char **argv)
+{
+ FILE *fpi,*fpo;
+ char buf[576*2*2];
+
+ static REAL bc[] =
+ {1.0, 0,1.0, 0,1.0, 0,1.0, 0,1.0, 0,1.0, 0,1.0, 0,1.0, 0,1.0, 0};
+
+ init(14);
+ makeTable(bc,44100);
+
+ if (argc != 3 && argc != 4) exit(-1);
+
+ fpi = fopen(argv[1],"r");
+ fpo = fopen(argv[2],"w");
+
+ if (!fpi || !fpo) exit(-1);
+
+ /* generate wav header */
+
+ {
+ short word;
+ int dword;
+
+ fwrite("RIFF",4,1,fpo);
+ dword = 0;
+ fwrite(&dword,4,1,fpo);
+
+ fwrite("WAVEfmt ",8,1,fpo);
+ dword = 16;
+ fwrite(&dword,4,1,fpo);
+ word = 1;
+ fwrite(&word,2,1,fpo); /* format category, PCM */
+ word = 2;
+ fwrite(&word,2,1,fpo); /* channels */
+ dword = 44100;
+ fwrite(&dword,4,1,fpo); /* sampling rate */
+ dword = 44100*2*2;
+ fwrite(&dword,4,1,fpo); /* bytes per sec */
+ word = 4;
+ fwrite(&word,2,1,fpo); /* block alignment */
+ word = 16;
+ fwrite(&word,2,1,fpo); /* ??? */
+
+ fwrite("data",4,1,fpo);
+ dword = 0;
+ fwrite(&dword,4,1,fpo);
+ }
+
+ preamp = 65536;
+ maxamp = 0;
+
+ if (argc == 4) {
+ preamp = 32767*65536/atoi(argv[3]);
+ fprintf(stderr,"preamp = %d\n",preamp);
+ }
+
+ for(;;)
+ {
+ int n,m;
+
+ n = fread(buf,1,576*2*2,fpi);
+ if (n <= 0) break;
+ m = modifySamples((short *)buf,n/4,2);
+ fwrite(buf,4,m,fpo);
+ }
+
+#if 0
+ for(;;)
+ {
+ int n = flushbuf((short *)buf,576);
+ if (n == 0) break;
+ fwrite(buf,4,n,fpo);
+ }
+#endif
+
+ {
+ short word;
+ int dword;
+ int len = ftell(fpo);
+
+ fseek(fpo,4,SEEK_SET);
+ dword = len-8;
+ fwrite(&dword,4,1,fpo);
+
+ fseek(fpo,40,SEEK_SET);
+ dword = len-44;
+ fwrite(&dword,4,1,fpo);
+ }
+
+ if (maxamp != 0) {
+ fprintf(stderr,"maxamp = %d\n",maxamp);
+ }
+
+ quit();
+}
+#endif
+
+extern "C" void *paramlist_alloc (void) {
+ return (void *)(new paramlist);
+}
+extern "C" void paramlist_free (void *pl) {
+ delete ((paramlist *)pl);
+}
+
diff --git a/plugins/supereq/Fftsg_fl.cpp b/plugins/supereq/Fftsg_fl.cpp
new file mode 100644
index 00000000..ff6fc42a
--- /dev/null
+++ b/plugins/supereq/Fftsg_fl.cpp
@@ -0,0 +1,2673 @@
+#include <stdlib.h>
+
+typedef float REAL;
+
+/*
+Fast Fourier/Cosine/Sine Transform
+ dimension :one
+ data length :power of 2
+ decimation :frequency
+ radix :split-radix
+ data :inplace
+ table :use
+functions
+ cdft: Complex Discrete Fourier Transform
+ rdft: Real Discrete Fourier Transform
+ ddct: Discrete Cosine Transform
+ ddst: Discrete Sine Transform
+ dfct: Cosine Transform of RDFT (Real Symmetric DFT)
+ dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
+function prototypes
+ void cdft(int, int, REAL *, int *, REAL *);
+ void rdft(int, int, REAL *, int *, REAL *);
+ void ddct(int, int, REAL *, int *, REAL *);
+ void ddst(int, int, REAL *, int *, REAL *);
+ void dfct(int, REAL *, REAL *, int *, REAL *);
+ void dfst(int, REAL *, REAL *, int *, REAL *);
+
+
+-------- Complex DFT (Discrete Fourier Transform) --------
+ [definition]
+ <case1>
+ X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
+ <case2>
+ X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
+ (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ cdft(2*n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ cdft(2*n, -1, a, ip, w);
+ [parameters]
+ 2*n :data length (int)
+ n >= 1, n = power of 2
+ a[0...2*n-1] :input/output data (REAL *)
+ input data
+ a[2*j] = Re(x[j]),
+ a[2*j+1] = Im(x[j]), 0<=j<n
+ output data
+ a[2*k] = Re(X[k]),
+ a[2*k+1] = Im(X[k]), 0<=k<n
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n/2-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ cdft(2*n, -1, a, ip, w);
+ is
+ cdft(2*n, 1, a, ip, w);
+ for (j = 0; j <= 2 * n - 1; j++) {
+ a[j] *= 1.0 / n;
+ }
+ .
+
+
+-------- Real DFT / Inverse of Real DFT --------
+ [definition]
+ <case1> RDFT
+ R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
+ I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
+ <case2> IRDFT (excluding scale)
+ a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
+ sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
+ sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ rdft(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ rdft(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (REAL *)
+ <case1>
+ output data
+ a[2*k] = R[k], 0<=k<n/2
+ a[2*k+1] = I[k], 0<k<n/2
+ a[1] = R[n/2]
+ <case2>
+ input data
+ a[2*j] = R[j], 0<=j<n/2
+ a[2*j+1] = I[j], 0<j<n/2
+ a[1] = R[n/2]
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n/2-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ rdft(n, 1, a, ip, w);
+ is
+ rdft(n, -1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
+ [definition]
+ <case1> IDCT (excluding scale)
+ C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
+ <case2> DCT
+ C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ ddct(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ ddct(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (REAL *)
+ output data
+ a[k] = C[k], 0<=k<n
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/4-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ ddct(n, -1, a, ip, w);
+ is
+ a[0] *= 0.5;
+ ddct(n, 1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+-------- DST (Discrete Sine Transform) / Inverse of DST --------
+ [definition]
+ <case1> IDST (excluding scale)
+ S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
+ <case2> DST
+ S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
+ [usage]
+ <case1>
+ ip[0] = 0; // first time only
+ ddst(n, 1, a, ip, w);
+ <case2>
+ ip[0] = 0; // first time only
+ ddst(n, -1, a, ip, w);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (REAL *)
+ <case1>
+ input data
+ a[j] = A[j], 0<j<n
+ a[0] = A[n]
+ output data
+ a[k] = S[k], 0<=k<n
+ <case2>
+ output data
+ a[k] = S[k], 0<k<n
+ a[0] = S[n]
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/2)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/4-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ ddst(n, -1, a, ip, w);
+ is
+ a[0] *= 0.5;
+ ddst(n, 1, a, ip, w);
+ for (j = 0; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
+ [definition]
+ C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
+ [usage]
+ ip[0] = 0; // first time only
+ dfct(n, a, t, ip, w);
+ [parameters]
+ n :data length - 1 (int)
+ n >= 2, n = power of 2
+ a[0...n] :input/output data (REAL *)
+ output data
+ a[k] = C[k], 0<=k<=n
+ t[0...n/2] :work area (REAL *)
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/4)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/8-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a, t, ip, w);
+ is
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a, t, ip, w);
+ for (j = 0; j <= n; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
+ [definition]
+ S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
+ [usage]
+ ip[0] = 0; // first time only
+ dfst(n, a, t, ip, w);
+ [parameters]
+ n :data length + 1 (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (REAL *)
+ output data
+ a[k] = S[k], 0<k<n
+ (a[0] is used for work area)
+ t[0...n/2-1] :work area (REAL *)
+ ip[0...*] :work area for bit reversal (int *)
+ length of ip >= 2+sqrt(n/4)
+ strictly,
+ length of ip >=
+ 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+ ip[0],ip[1] are pointers of the cos/sin table.
+ w[0...n*5/8-1] :cos/sin table (REAL *)
+ w[],ip[] are initialized if ip[0] == 0.
+ [remark]
+ Inverse of
+ dfst(n, a, t, ip, w);
+ is
+ dfst(n, a, t, ip, w);
+ for (j = 1; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+
+
+Appendix :
+ The cos/sin table is recalculated when the larger table required.
+ w[] and ip[] are compatible with all routines.
+*/
+
+
+void cdft(int n, int isgn, REAL *a, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ int nw;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ if (isgn >= 0) {
+ cftfsub(n, a, ip + 2, nw, w);
+ } else {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+}
+
+
+void rdft(int n, int isgn, REAL *a, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void makect(int nc, int *ip, REAL *c);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void rftfsub(int n, REAL *a, int nc, REAL *c);
+ void rftbsub(int n, REAL *a, int nc, REAL *c);
+ int nw, nc;
+ REAL xi;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > (nc << 2)) {
+ nc = n >> 2;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ }
+ xi = a[0] - a[1];
+ a[0] += a[1];
+ a[1] = xi;
+ } else {
+ a[1] = 0.5 * (a[0] - a[1]);
+ a[0] -= a[1];
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+}
+
+
+void ddct(int n, int isgn, REAL *a, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void makect(int nc, int *ip, REAL *c);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void rftfsub(int n, REAL *a, int nc, REAL *c);
+ void rftbsub(int n, REAL *a, int nc, REAL *c);
+ void dctsub(int n, REAL *a, int nc, REAL *c);
+ int j, nw, nc;
+ REAL xr;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > nc) {
+ nc = n;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn < 0) {
+ xr = a[n - 1];
+ for (j = n - 2; j >= 2; j -= 2) {
+ a[j + 1] = a[j] - a[j - 1];
+ a[j] += a[j - 1];
+ }
+ a[1] = a[0] - xr;
+ a[0] += xr;
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+ dctsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ }
+ xr = a[0] - a[1];
+ a[0] += a[1];
+ for (j = 2; j < n; j += 2) {
+ a[j - 1] = a[j] - a[j + 1];
+ a[j] += a[j + 1];
+ }
+ a[n - 1] = xr;
+ }
+}
+
+
+void ddst(int n, int isgn, REAL *a, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void makect(int nc, int *ip, REAL *c);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void rftfsub(int n, REAL *a, int nc, REAL *c);
+ void rftbsub(int n, REAL *a, int nc, REAL *c);
+ void dstsub(int n, REAL *a, int nc, REAL *c);
+ int j, nw, nc;
+ REAL xr;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > nc) {
+ nc = n;
+ makect(nc, ip, w + nw);
+ }
+ if (isgn < 0) {
+ xr = a[n - 1];
+ for (j = n - 2; j >= 2; j -= 2) {
+ a[j + 1] = -a[j] - a[j - 1];
+ a[j] -= a[j - 1];
+ }
+ a[1] = a[0] + xr;
+ a[0] -= xr;
+ if (n > 4) {
+ rftbsub(n, a, nc, w + nw);
+ cftbsub(n, a, ip + 2, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip + 2, nw, w);
+ }
+ }
+ dstsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip + 2, nw, w);
+ }
+ xr = a[0] - a[1];
+ a[0] += a[1];
+ for (j = 2; j < n; j += 2) {
+ a[j - 1] = -a[j] - a[j + 1];
+ a[j] -= a[j + 1];
+ }
+ a[n - 1] = -xr;
+ }
+}
+
+
+void dfct(int n, REAL *a, REAL *t, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void makect(int nc, int *ip, REAL *c);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void rftfsub(int n, REAL *a, int nc, REAL *c);
+ void dctsub(int n, REAL *a, int nc, REAL *c);
+ int j, k, l, m, mh, nw, nc;
+ REAL xr, xi, yr, yi;
+
+ nw = ip[0];
+ if (n > (nw << 3)) {
+ nw = n >> 3;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > (nc << 1)) {
+ nc = n >> 1;
+ makect(nc, ip, w + nw);
+ }
+ m = n >> 1;
+ yi = a[m];
+ xi = a[0] + a[n];
+ a[0] -= a[n];
+ t[0] = xi - yi;
+ t[m] = xi + yi;
+ if (n > 2) {
+ mh = m >> 1;
+ for (j = 1; j < mh; j++) {
+ k = m - j;
+ xr = a[j] - a[n - j];
+ xi = a[j] + a[n - j];
+ yr = a[k] - a[n - k];
+ yi = a[k] + a[n - k];
+ a[j] = xr;
+ a[k] = yr;
+ t[j] = xi - yi;
+ t[k] = xi + yi;
+ }
+ t[mh] = a[mh] + a[n - mh];
+ a[mh] -= a[n - mh];
+ dctsub(m, a, nc, w + nw);
+ if (m > 4) {
+ cftfsub(m, a, ip + 2, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip + 2, nw, w);
+ }
+ a[n - 1] = a[0] - a[1];
+ a[1] = a[0] + a[1];
+ for (j = m - 2; j >= 2; j -= 2) {
+ a[2 * j + 1] = a[j] + a[j + 1];
+ a[2 * j - 1] = a[j] - a[j + 1];
+ }
+ l = 2;
+ m = mh;
+ while (m >= 2) {
+ dctsub(m, t, nc, w + nw);
+ if (m > 4) {
+ cftfsub(m, t, ip + 2, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip + 2, nw, w);
+ }
+ a[n - l] = t[0] - t[1];
+ a[l] = t[0] + t[1];
+ k = 0;
+ for (j = 2; j < m; j += 2) {
+ k += l << 2;
+ a[k - l] = t[j] - t[j + 1];
+ a[k + l] = t[j] + t[j + 1];
+ }
+ l <<= 1;
+ mh = m >> 1;
+ for (j = 0; j < mh; j++) {
+ k = m - j;
+ t[j] = t[m + k] - t[m + j];
+ t[k] = t[m + k] + t[m + j];
+ }
+ t[mh] = t[m + mh];
+ m = mh;
+ }
+ a[l] = t[0];
+ a[n] = t[2] - t[1];
+ a[0] = t[2] + t[1];
+ } else {
+ a[1] = a[0];
+ a[2] = t[0];
+ a[0] = t[1];
+ }
+}
+
+
+void dfst(int n, REAL *a, REAL *t, int *ip, REAL *w)
+{
+ void makewt(int nw, int *ip, REAL *w);
+ void makect(int nc, int *ip, REAL *c);
+ void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w);
+ void rftfsub(int n, REAL *a, int nc, REAL *c);
+ void dstsub(int n, REAL *a, int nc, REAL *c);
+ int j, k, l, m, mh, nw, nc;
+ REAL xr, xi, yr, yi;
+
+ nw = ip[0];
+ if (n > (nw << 3)) {
+ nw = n >> 3;
+ makewt(nw, ip, w);
+ }
+ nc = ip[1];
+ if (n > (nc << 1)) {
+ nc = n >> 1;
+ makect(nc, ip, w + nw);
+ }
+ if (n > 2) {
+ m = n >> 1;
+ mh = m >> 1;
+ for (j = 1; j < mh; j++) {
+ k = m - j;
+ xr = a[j] + a[n - j];
+ xi = a[j] - a[n - j];
+ yr = a[k] + a[n - k];
+ yi = a[k] - a[n - k];
+ a[j] = xr;
+ a[k] = yr;
+ t[j] = xi + yi;
+ t[k] = xi - yi;
+ }
+ t[0] = a[mh] - a[n - mh];
+ a[mh] += a[n - mh];
+ a[0] = a[m];
+ dstsub(m, a, nc, w + nw);
+ if (m > 4) {
+ cftfsub(m, a, ip + 2, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip + 2, nw, w);
+ }
+ a[n - 1] = a[1] - a[0];
+ a[1] = a[0] + a[1];
+ for (j = m - 2; j >= 2; j -= 2) {
+ a[2 * j + 1] = a[j] - a[j + 1];
+ a[2 * j - 1] = -a[j] - a[j + 1];
+ }
+ l = 2;
+ m = mh;
+ while (m >= 2) {
+ dstsub(m, t, nc, w + nw);
+ if (m > 4) {
+ cftfsub(m, t, ip + 2, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip + 2, nw, w);
+ }
+ a[n - l] = t[1] - t[0];
+ a[l] = t[0] + t[1];
+ k = 0;
+ for (j = 2; j < m; j += 2) {
+ k += l << 2;
+ a[k - l] = -t[j] - t[j + 1];
+ a[k + l] = t[j] - t[j + 1];
+ }
+ l <<= 1;
+ mh = m >> 1;
+ for (j = 1; j < mh; j++) {
+ k = m - j;
+ t[j] = t[m + k] + t[m + j];
+ t[k] = t[m + k] - t[m + j];
+ }
+ t[0] = t[m + mh];
+ m = mh;
+ }
+ a[l] = t[0];
+ }
+ a[0] = 0;
+}
+
+
+/* -------- initializing routines -------- */
+
+
+#include <math.h>
+
+void makewt(int nw, int *ip, REAL *w)
+{
+ int j, nwh, nw0, nw1;
+ REAL delta, wn4r, wk1r, wk1i, wk3r, wk3i;
+
+ ip[0] = nw;
+ ip[1] = 1;
+ if (nw > 2) {
+ nwh = nw >> 1;
+ delta = atan(1.0) / nwh;
+ wn4r = cos(delta * nwh);
+ w[0] = 1;
+ w[1] = wn4r;
+ if (nwh >= 4) {
+ w[2] = 0.5 / cos(delta * 2);
+ w[3] = 0.5 / cos(delta * 6);
+ }
+ for (j = 4; j < nwh; j += 4) {
+ w[j] = cos(delta * j);
+ w[j + 1] = sin(delta * j);
+ w[j + 2] = cos(3 * delta * j);
+ w[j + 3] = sin(3 * delta * j);
+ }
+ nw0 = 0;
+ while (nwh > 2) {
+ nw1 = nw0 + nwh;
+ nwh >>= 1;
+ w[nw1] = 1;
+ w[nw1 + 1] = wn4r;
+ if (nwh >= 4) {
+ wk1r = w[nw0 + 4];
+ wk3r = w[nw0 + 6];
+ w[nw1 + 2] = 0.5 / wk1r;
+ w[nw1 + 3] = 0.5 / wk3r;
+ }
+ for (j = 4; j < nwh; j += 4) {
+ wk1r = w[nw0 + 2 * j];
+ wk1i = w[nw0 + 2 * j + 1];
+ wk3r = w[nw0 + 2 * j + 2];
+ wk3i = w[nw0 + 2 * j + 3];
+ w[nw1 + j] = wk1r;
+ w[nw1 + j + 1] = wk1i;
+ w[nw1 + j + 2] = wk3r;
+ w[nw1 + j + 3] = wk3i;
+ }
+ nw0 = nw1;
+ }
+ }
+}
+
+
+void makect(int nc, int *ip, REAL *c)
+{
+ int j, nch;
+ REAL delta;
+
+ ip[1] = nc;
+ if (nc > 1) {
+ nch = nc >> 1;
+ delta = atan(1.0) / nch;
+ c[0] = cos(delta * nch);
+ c[nch] = 0.5 * c[0];
+ for (j = 1; j < nch; j++) {
+ c[j] = 0.5 * cos(delta * j);
+ c[nc - j] = 0.5 * sin(delta * j);
+ }
+ }
+}
+
+
+/* -------- child routines -------- */
+
+
+#ifndef CDFT_RECURSIVE_N /* length of the recursive FFT mode */
+#define CDFT_RECURSIVE_N 512 /* <= (L1 cache size) / 16 */
+#endif
+
+
+void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w)
+{
+ void bitrv2(int n, int *ip, REAL *a);
+ void bitrv216(REAL *a);
+ void bitrv208(REAL *a);
+ void cftf1st(int n, REAL *a, REAL *w);
+ void cftrec1(int n, REAL *a, int nw, REAL *w);
+ void cftrec2(int n, REAL *a, int nw, REAL *w);
+ void cftexp1(int n, REAL *a, int nw, REAL *w);
+ void cftfx41(int n, REAL *a, int nw, REAL *w);
+ void cftf161(REAL *a, REAL *w);
+ void cftf081(REAL *a, REAL *w);
+ void cftf040(REAL *a);
+ void cftx020(REAL *a);
+ int m;
+
+ if (n > 32) {
+ m = n >> 2;
+ cftf1st(n, a, &w[nw - m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else if (m > 32) {
+ cftexp1(n, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2(n, ip, a);
+ } else if (n > 8) {
+ if (n == 32) {
+ cftf161(a, &w[nw - 8]);
+ bitrv216(a);
+ } else {
+ cftf081(a, w);
+ bitrv208(a);
+ }
+ } else if (n == 8) {
+ cftf040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+}
+
+
+void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w)
+{
+ void bitrv2conj(int n, int *ip, REAL *a);
+ void bitrv216neg(REAL *a);
+ void bitrv208neg(REAL *a);
+ void cftb1st(int n, REAL *a, REAL *w);
+ void cftrec1(int n, REAL *a, int nw, REAL *w);
+ void cftrec2(int n, REAL *a, int nw, REAL *w);
+ void cftexp1(int n, REAL *a, int nw, REAL *w);
+ void cftfx41(int n, REAL *a, int nw, REAL *w);
+ void cftf161(REAL *a, REAL *w);
+ void cftf081(REAL *a, REAL *w);
+ void cftb040(REAL *a);
+ void cftx020(REAL *a);
+ int m;
+
+ if (n > 32) {
+ m = n >> 2;
+ cftb1st(n, a, &w[nw - m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else if (m > 32) {
+ cftexp1(n, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2conj(n, ip, a);
+ } else if (n > 8) {
+ if (n == 32) {
+ cftf161(a, &w[nw - 8]);
+ bitrv216neg(a);
+ } else {
+ cftf081(a, w);
+ bitrv208neg(a);
+ }
+ } else if (n == 8) {
+ cftb040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+}
+
+
+void bitrv2(int n, int *ip, REAL *a)
+{
+ int j, j1, k, k1, l, m, m2;
+ REAL xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ j1 = 2 * k + m2 + ip[k];
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ } else {
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = a[j1 + 1];
+ yr = a[k1];
+ yi = a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ }
+ }
+}
+
+
+void bitrv2conj(int n, int *ip, REAL *a)
+{
+ int j, j1, k, k1, l, m, m2;
+ REAL xr, xi, yr, yi;
+
+ ip[0] = 0;
+ l = n;
+ m = 1;
+ while ((m << 3) < l) {
+ l >>= 1;
+ for (j = 0; j < m; j++) {
+ ip[m + j] = ip[j] + l;
+ }
+ m <<= 1;
+ }
+ m2 = 2 * m;
+ if ((m << 3) == l) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 -= m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += 2 * m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ j1 = k1 + m2;
+ k1 = j1 + m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ k1 += m2;
+ a[k1 + 1] = -a[k1 + 1];
+ }
+ } else {
+ a[1] = -a[1];
+ a[m2 + 1] = -a[m2 + 1];
+ for (k = 1; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 2 * j + ip[k];
+ k1 = 2 * k + ip[j];
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ j1 += m2;
+ k1 += m2;
+ xr = a[j1];
+ xi = -a[j1 + 1];
+ yr = a[k1];
+ yi = -a[k1 + 1];
+ a[j1] = yr;
+ a[j1 + 1] = yi;
+ a[k1] = xr;
+ a[k1 + 1] = xi;
+ }
+ k1 = 2 * k + ip[k];
+ a[k1 + 1] = -a[k1 + 1];
+ a[k1 + m2 + 1] = -a[k1 + m2 + 1];
+ }
+ }
+}
+
+
+void bitrv216(REAL *a)
+{
+ REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
+ x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i,
+ x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
+
+ x1r = a[2];
+ x1i = a[3];
+ x2r = a[4];
+ x2i = a[5];
+ x3r = a[6];
+ x3i = a[7];
+ x4r = a[8];
+ x4i = a[9];
+ x5r = a[10];
+ x5i = a[11];
+ x7r = a[14];
+ x7i = a[15];
+ x8r = a[16];
+ x8i = a[17];
+ x10r = a[20];
+ x10i = a[21];
+ x11r = a[22];
+ x11i = a[23];
+ x12r = a[24];
+ x12i = a[25];
+ x13r = a[26];
+ x13i = a[27];
+ x14r = a[28];
+ x14i = a[29];
+ a[2] = x8r;
+ a[3] = x8i;
+ a[4] = x4r;
+ a[5] = x4i;
+ a[6] = x12r;
+ a[7] = x12i;
+ a[8] = x2r;
+ a[9] = x2i;
+ a[10] = x10r;
+ a[11] = x10i;
+ a[14] = x14r;
+ a[15] = x14i;
+ a[16] = x1r;
+ a[17] = x1i;
+ a[20] = x5r;
+ a[21] = x5i;
+ a[22] = x13r;
+ a[23] = x13i;
+ a[24] = x3r;
+ a[25] = x3i;
+ a[26] = x11r;
+ a[27] = x11i;
+ a[28] = x7r;
+ a[29] = x7i;
+}
+
+
+void bitrv216neg(REAL *a)
+{
+ REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
+ x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i,
+ x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i,
+ x13r, x13i, x14r, x14i, x15r, x15i;
+
+ x1r = a[2];
+ x1i = a[3];
+ x2r = a[4];
+ x2i = a[5];
+ x3r = a[6];
+ x3i = a[7];
+ x4r = a[8];
+ x4i = a[9];
+ x5r = a[10];
+ x5i = a[11];
+ x6r = a[12];
+ x6i = a[13];
+ x7r = a[14];
+ x7i = a[15];
+ x8r = a[16];
+ x8i = a[17];
+ x9r = a[18];
+ x9i = a[19];
+ x10r = a[20];
+ x10i = a[21];
+ x11r = a[22];
+ x11i = a[23];
+ x12r = a[24];
+ x12i = a[25];
+ x13r = a[26];
+ x13i = a[27];
+ x14r = a[28];
+ x14i = a[29];
+ x15r = a[30];
+ x15i = a[31];
+ a[2] = x15r;
+ a[3] = x15i;
+ a[4] = x7r;
+ a[5] = x7i;
+ a[6] = x11r;
+ a[7] = x11i;
+ a[8] = x3r;
+ a[9] = x3i;
+ a[10] = x13r;
+ a[11] = x13i;
+ a[12] = x5r;
+ a[13] = x5i;
+ a[14] = x9r;
+ a[15] = x9i;
+ a[16] = x1r;
+ a[17] = x1i;
+ a[18] = x14r;
+ a[19] = x14i;
+ a[20] = x6r;
+ a[21] = x6i;
+ a[22] = x10r;
+ a[23] = x10i;
+ a[24] = x2r;
+ a[25] = x2i;
+ a[26] = x12r;
+ a[27] = x12i;
+ a[28] = x4r;
+ a[29] = x4i;
+ a[30] = x8r;
+ a[31] = x8i;
+}
+
+
+void bitrv208(REAL *a)
+{
+ REAL x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;
+
+ x1r = a[2];
+ x1i = a[3];
+ x3r = a[6];
+ x3i = a[7];
+ x4r = a[8];
+ x4i = a[9];
+ x6r = a[12];
+ x6i = a[13];
+ a[2] = x4r;
+ a[3] = x4i;
+ a[6] = x6r;
+ a[7] = x6i;
+ a[8] = x1r;
+ a[9] = x1i;
+ a[12] = x3r;
+ a[13] = x3i;
+}
+
+
+void bitrv208neg(REAL *a)
+{
+ REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
+ x5r, x5i, x6r, x6i, x7r, x7i;
+
+ x1r = a[2];
+ x1i = a[3];
+ x2r = a[4];
+ x2i = a[5];
+ x3r = a[6];
+ x3i = a[7];
+ x4r = a[8];
+ x4i = a[9];
+ x5r = a[10];
+ x5i = a[11];
+ x6r = a[12];
+ x6i = a[13];
+ x7r = a[14];
+ x7i = a[15];
+ a[2] = x7r;
+ a[3] = x7i;
+ a[4] = x3r;
+ a[5] = x3i;
+ a[6] = x5r;
+ a[7] = x5i;
+ a[8] = x1r;
+ a[9] = x1i;
+ a[10] = x6r;
+ a[11] = x6i;
+ a[12] = x2r;
+ a[13] = x2i;
+ a[14] = x4r;
+ a[15] = x4i;
+}
+
+
+void cftf1st(int n, REAL *a, REAL *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ REAL wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ j1 = m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[0] + a[j2];
+ x0i = a[1] + a[j2 + 1];
+ x1r = a[0] - a[j2];
+ x1i = a[1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j2] = x1r - x3i;
+ a[j2 + 1] = x1i + x3r;
+ a[j3] = x1r + x3i;
+ a[j3 + 1] = x1i - x3r;
+ wn4r = w[1];
+ csc1 = w[2];
+ csc3 = w[3];
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ k = 0;
+ for (j = 2; j < mh - 2; j += 4) {
+ k += 4;
+ wk1r = csc1 * (wd1r + w[k]);
+ wk1i = csc1 * (wd1i + w[k + 1]);
+ wk3r = csc3 * (wd3r + w[k + 2]);
+ wk3i = csc3 * (wd3i - w[k + 3]);
+ wd1r = w[k];
+ wd1i = w[k + 1];
+ wd3r = w[k + 2];
+ wd3i = -w[k + 3];
+ j1 = j + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j] + a[j2];
+ x0i = a[j + 1] + a[j2 + 1];
+ x1r = a[j] - a[j2];
+ x1i = a[j + 1] - a[j2 + 1];
+ y0r = a[j + 2] + a[j2 + 2];
+ y0i = a[j + 3] + a[j2 + 3];
+ y1r = a[j + 2] - a[j2 + 2];
+ y1i = a[j + 3] - a[j2 + 3];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 + 2] + a[j3 + 2];
+ y2i = a[j1 + 3] + a[j3 + 3];
+ y3r = a[j1 + 2] - a[j3 + 2];
+ y3i = a[j1 + 3] - a[j3 + 3];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j + 2] = y0r + y2r;
+ a[j + 3] = y0i + y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i - y2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1r * x0r - wk1i * x0i;
+ a[j2 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i + y3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r + wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i - wk3i * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i - y3r;
+ a[j3 + 2] = wd3r * x0r + wd3i * x0i;
+ a[j3 + 3] = wd3r * x0i - wd3i * x0r;
+ j0 = m - j;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] + a[j2];
+ x0i = a[j0 + 1] + a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = a[j0 + 1] - a[j2 + 1];
+ y0r = a[j0 - 2] + a[j2 - 2];
+ y0i = a[j0 - 1] + a[j2 - 1];
+ y1r = a[j0 - 2] - a[j2 - 2];
+ y1i = a[j0 - 1] - a[j2 - 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 - 2] + a[j3 - 2];
+ y2i = a[j1 - 1] + a[j3 - 1];
+ y3r = a[j1 - 2] - a[j3 - 2];
+ y3i = a[j1 - 1] - a[j3 - 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i + x2i;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i + y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j1 - 2] = y0r - y2r;
+ a[j1 - 1] = y0i - y2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 1] = wk1i * x0i + wk1r * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i + y3r;
+ a[j2 - 2] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 1] = wk3i * x0i - wk3r * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i - y3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ }
+ wk1r = csc1 * (wd1r + wn4r);
+ wk1i = csc1 * (wd1i + wn4r);
+ wk3r = csc3 * (wd3r - wn4r);
+ wk3i = csc3 * (wd3i - wn4r);
+ j0 = mh;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0 - 2] + a[j2 - 2];
+ x0i = a[j0 - 1] + a[j2 - 1];
+ x1r = a[j0 - 2] - a[j2 - 2];
+ x1i = a[j0 - 1] - a[j2 - 1];
+ x2r = a[j1 - 2] + a[j3 - 2];
+ x2i = a[j1 - 1] + a[j3 - 1];
+ x3r = a[j1 - 2] - a[j3 - 2];
+ x3i = a[j1 - 1] - a[j3 - 1];
+ a[j0 - 2] = x0r + x2r;
+ a[j0 - 1] = x0i + x2i;
+ a[j1 - 2] = x0r - x2r;
+ a[j1 - 1] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2 - 2] = wk1r * x0r - wk1i * x0i;
+ a[j2 - 1] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3 - 2] = wk3r * x0r + wk3i * x0i;
+ a[j3 - 1] = wk3r * x0i - wk3i * x0r;
+ x0r = a[j0] + a[j2];
+ x0i = a[j0 + 1] + a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = a[j0 + 1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (x0i - x0r);
+ x0r = a[j0 + 2] + a[j2 + 2];
+ x0i = a[j0 + 3] + a[j2 + 3];
+ x1r = a[j0 + 2] - a[j2 + 2];
+ x1i = a[j0 + 3] - a[j2 + 3];
+ x2r = a[j1 + 2] + a[j3 + 2];
+ x2i = a[j1 + 3] + a[j3 + 3];
+ x3r = a[j1 + 2] - a[j3 + 2];
+ x3i = a[j1 + 3] - a[j3 + 3];
+ a[j0 + 2] = x0r + x2r;
+ a[j0 + 3] = x0i + x2i;
+ a[j1 + 2] = x0r - x2r;
+ a[j1 + 3] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2 + 2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 3] = wk1i * x0i + wk1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3 + 2] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 3] = wk3i * x0i - wk3r * x0r;
+}
+
+
+void cftb1st(int n, REAL *a, REAL *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ REAL wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ j1 = m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[0] + a[j2];
+ x0i = -a[1] - a[j2 + 1];
+ x1r = a[0] - a[j2];
+ x1i = -a[1] + a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[0] = x0r + x2r;
+ a[1] = x0i - x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ a[j2] = x1r + x3i;
+ a[j2 + 1] = x1i + x3r;
+ a[j3] = x1r - x3i;
+ a[j3 + 1] = x1i - x3r;
+ wn4r = w[1];
+ csc1 = w[2];
+ csc3 = w[3];
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ k = 0;
+ for (j = 2; j < mh - 2; j += 4) {
+ k += 4;
+ wk1r = csc1 * (wd1r + w[k]);
+ wk1i = csc1 * (wd1i + w[k + 1]);
+ wk3r = csc3 * (wd3r + w[k + 2]);
+ wk3i = csc3 * (wd3i - w[k + 3]);
+ wd1r = w[k];
+ wd1i = w[k + 1];
+ wd3r = w[k + 2];
+ wd3i = -w[k + 3];
+ j1 = j + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j] + a[j2];
+ x0i = -a[j + 1] - a[j2 + 1];
+ x1r = a[j] - a[j2];
+ x1i = -a[j + 1] + a[j2 + 1];
+ y0r = a[j + 2] + a[j2 + 2];
+ y0i = -a[j + 3] - a[j2 + 3];
+ y1r = a[j + 2] - a[j2 + 2];
+ y1i = -a[j + 3] + a[j2 + 3];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 + 2] + a[j3 + 2];
+ y2i = a[j1 + 3] + a[j3 + 3];
+ y3r = a[j1 + 2] - a[j3 + 2];
+ y3i = a[j1 + 3] - a[j3 + 3];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i - x2i;
+ a[j + 2] = y0r + y2r;
+ a[j + 3] = y0i - y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i + y2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1r * x0r - wk1i * x0i;
+ a[j2 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i + y3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r + wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i - wk3i * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i - y3r;
+ a[j3 + 2] = wd3r * x0r + wd3i * x0i;
+ a[j3 + 3] = wd3r * x0i - wd3i * x0r;
+ j0 = m - j;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] + a[j2];
+ x0i = -a[j0 + 1] - a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = -a[j0 + 1] + a[j2 + 1];
+ y0r = a[j0 - 2] + a[j2 - 2];
+ y0i = -a[j0 - 1] - a[j2 - 1];
+ y1r = a[j0 - 2] - a[j2 - 2];
+ y1i = -a[j0 - 1] + a[j2 - 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ y2r = a[j1 - 2] + a[j3 - 2];
+ y2i = a[j1 - 1] + a[j3 - 1];
+ y3r = a[j1 - 2] - a[j3 - 2];
+ y3i = a[j1 - 1] - a[j3 - 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i - x2i;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i - y2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ a[j1 - 2] = y0r - y2r;
+ a[j1 - 1] = y0i + y2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 1] = wk1i * x0i + wk1r * x0r;
+ x0r = y1r + y3i;
+ x0i = y1i + y3r;
+ a[j2 - 2] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 1] = wk3i * x0i - wk3r * x0r;
+ x0r = y1r - y3i;
+ x0i = y1i - y3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ }
+ wk1r = csc1 * (wd1r + wn4r);
+ wk1i = csc1 * (wd1i + wn4r);
+ wk3r = csc3 * (wd3r - wn4r);
+ wk3i = csc3 * (wd3i - wn4r);
+ j0 = mh;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0 - 2] + a[j2 - 2];
+ x0i = -a[j0 - 1] - a[j2 - 1];
+ x1r = a[j0 - 2] - a[j2 - 2];
+ x1i = -a[j0 - 1] + a[j2 - 1];
+ x2r = a[j1 - 2] + a[j3 - 2];
+ x2i = a[j1 - 1] + a[j3 - 1];
+ x3r = a[j1 - 2] - a[j3 - 2];
+ x3i = a[j1 - 1] - a[j3 - 1];
+ a[j0 - 2] = x0r + x2r;
+ a[j0 - 1] = x0i - x2i;
+ a[j1 - 2] = x0r - x2r;
+ a[j1 - 1] = x0i + x2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2 - 2] = wk1r * x0r - wk1i * x0i;
+ a[j2 - 1] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3 - 2] = wk3r * x0r + wk3i * x0i;
+ a[j3 - 1] = wk3r * x0i - wk3i * x0r;
+ x0r = a[j0] + a[j2];
+ x0i = -a[j0 + 1] - a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = -a[j0 + 1] + a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i - x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i + x2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (x0i - x0r);
+ x0r = a[j0 + 2] + a[j2 + 2];
+ x0i = -a[j0 + 3] - a[j2 + 3];
+ x1r = a[j0 + 2] - a[j2 + 2];
+ x1i = -a[j0 + 3] + a[j2 + 3];
+ x2r = a[j1 + 2] + a[j3 + 2];
+ x2i = a[j1 + 3] + a[j3 + 3];
+ x3r = a[j1 + 2] - a[j3 + 2];
+ x3i = a[j1 + 3] - a[j3 + 3];
+ a[j0 + 2] = x0r + x2r;
+ a[j0 + 3] = x0i - x2i;
+ a[j1 + 2] = x0r - x2r;
+ a[j1 + 3] = x0i + x2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2 + 2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 3] = wk1i * x0i + wk1r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3 + 2] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 3] = wk3i * x0i - wk3r * x0r;
+}
+
+
+void cftrec1(int n, REAL *a, int nw, REAL *w)
+{
+ void cftrec1(int n, REAL *a, int nw, REAL *w);
+ void cftrec2(int n, REAL *a, int nw, REAL *w);
+ void cftmdl1(int n, REAL *a, REAL *w);
+ void cftexp1(int n, REAL *a, int nw, REAL *w);
+ int m;
+
+ m = n >> 2;
+ cftmdl1(n, a, &w[nw - 2 * m]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec1(m, &a[3 * m], nw, w);
+ } else {
+ cftexp1(n, a, nw, w);
+ }
+}
+
+
+void cftrec2(int n, REAL *a, int nw, REAL *w)
+{
+ void cftrec1(int n, REAL *a, int nw, REAL *w);
+ void cftrec2(int n, REAL *a, int nw, REAL *w);
+ void cftmdl2(int n, REAL *a, REAL *w);
+ void cftexp2(int n, REAL *a, int nw, REAL *w);
+ int m;
+
+ m = n >> 2;
+ cftmdl2(n, a, &w[nw - n]);
+ if (n > CDFT_RECURSIVE_N) {
+ cftrec1(m, a, nw, w);
+ cftrec2(m, &a[m], nw, w);
+ cftrec1(m, &a[2 * m], nw, w);
+ cftrec2(m, &a[3 * m], nw, w);
+ } else {
+ cftexp2(n, a, nw, w);
+ }
+}
+
+
+void cftexp1(int n, REAL *a, int nw, REAL *w)
+{
+ void cftmdl1(int n, REAL *a, REAL *w);
+ void cftmdl2(int n, REAL *a, REAL *w);
+ void cftfx41(int n, REAL *a, int nw, REAL *w);
+ void cftfx42(int n, REAL *a, int nw, REAL *w);
+ int j, k, l;
+
+ l = n >> 2;
+ while (l > 128) {
+ for (k = l; k < n; k <<= 2) {
+ for (j = k - l; j < n; j += 4 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftmdl2(l, &a[k + j], &w[nw - l]);
+ cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
+ }
+ }
+ cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
+ l >>= 2;
+ }
+ for (k = l; k < n; k <<= 2) {
+ for (j = k - l; j < n; j += 4 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[j], nw, w);
+ cftmdl2(l, &a[k + j], &w[nw - l]);
+ cftfx42(l, &a[k + j], nw, w);
+ cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[2 * k + j], nw, w);
+ }
+ }
+ cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[n - l], nw, w);
+}
+
+
+void cftexp2(int n, REAL *a, int nw, REAL *w)
+{
+ void cftmdl1(int n, REAL *a, REAL *w);
+ void cftmdl2(int n, REAL *a, REAL *w);
+ void cftfx41(int n, REAL *a, int nw, REAL *w);
+ void cftfx42(int n, REAL *a, int nw, REAL *w);
+ int j, k, l, m;
+
+ m = n >> 1;
+ l = n >> 2;
+ while (l > 128) {
+ for (k = l; k < m; k <<= 2) {
+ for (j = k - l; j < m; j += 2 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
+ }
+ for (j = 2 * k - l; j < m; j += 4 * k) {
+ cftmdl2(l, &a[j], &w[nw - l]);
+ cftmdl2(l, &a[m + j], &w[nw - l]);
+ }
+ }
+ l >>= 2;
+ }
+ for (k = l; k < m; k <<= 2) {
+ for (j = k - l; j < m; j += 2 * k) {
+ cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[j], nw, w);
+ cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
+ cftfx41(l, &a[m + j], nw, w);
+ }
+ for (j = 2 * k - l; j < m; j += 4 * k) {
+ cftmdl2(l, &a[j], &w[nw - l]);
+ cftfx42(l, &a[j], nw, w);
+ cftmdl2(l, &a[m + j], &w[nw - l]);
+ cftfx42(l, &a[m + j], nw, w);
+ }
+ }
+}
+
+
+void cftmdl1(int n, REAL *a, REAL *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ REAL wn4r, wk1r, wk1i, wk3r, wk3i;
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ j1 = m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[0] + a[j2];
+ x0i = a[1] + a[j2 + 1];
+ x1r = a[0] - a[j2];
+ x1i = a[1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ a[j2] = x1r - x3i;
+ a[j2 + 1] = x1i + x3r;
+ a[j3] = x1r + x3i;
+ a[j3 + 1] = x1i - x3r;
+ wn4r = w[1];
+ k = 0;
+ for (j = 2; j < mh; j += 2) {
+ k += 4;
+ wk1r = w[k];
+ wk1i = w[k + 1];
+ wk3r = w[k + 2];
+ wk3i = -w[k + 3];
+ j1 = j + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j] + a[j2];
+ x0i = a[j + 1] + a[j2 + 1];
+ x1r = a[j] - a[j2];
+ x1i = a[j + 1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[j] = x0r + x2r;
+ a[j + 1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1r * x0r - wk1i * x0i;
+ a[j2 + 1] = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3r * x0r + wk3i * x0i;
+ a[j3 + 1] = wk3r * x0i - wk3i * x0r;
+ j0 = m - j;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] + a[j2];
+ x0i = a[j0 + 1] + a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = a[j0 + 1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wk1i * x0r - wk1r * x0i;
+ a[j2 + 1] = wk1i * x0i + wk1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = wk3i * x0r + wk3r * x0i;
+ a[j3 + 1] = wk3i * x0i - wk3r * x0r;
+ }
+ j0 = mh;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] + a[j2];
+ x0i = a[j0 + 1] + a[j2 + 1];
+ x1r = a[j0] - a[j2];
+ x1i = a[j0 + 1] - a[j2 + 1];
+ x2r = a[j1] + a[j3];
+ x2i = a[j1 + 1] + a[j3 + 1];
+ x3r = a[j1] - a[j3];
+ x3i = a[j1 + 1] - a[j3 + 1];
+ a[j0] = x0r + x2r;
+ a[j0 + 1] = x0i + x2i;
+ a[j1] = x0r - x2r;
+ a[j1 + 1] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2] = wn4r * (x0r - x0i);
+ a[j2 + 1] = wn4r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wn4r * (x0r + x0i);
+ a[j3 + 1] = -wn4r * (x0i - x0r);
+}
+
+
+void cftmdl2(int n, REAL *a, REAL *w)
+{
+ int j, j0, j1, j2, j3, k, kr, m, mh;
+ REAL wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ wn4r = w[1];
+ j1 = m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[0] - a[j2 + 1];
+ x0i = a[1] + a[j2];
+ x1r = a[0] + a[j2 + 1];
+ x1i = a[1] - a[j2];
+ x2r = a[j1] - a[j3 + 1];
+ x2i = a[j1 + 1] + a[j3];
+ x3r = a[j1] + a[j3 + 1];
+ x3i = a[j1 + 1] - a[j3];
+ y0r = wn4r * (x2r - x2i);
+ y0i = wn4r * (x2i + x2r);
+ a[0] = x0r + y0r;
+ a[1] = x0i + y0i;
+ a[j1] = x0r - y0r;
+ a[j1 + 1] = x0i - y0i;
+ y0r = wn4r * (x3r - x3i);
+ y0i = wn4r * (x3i + x3r);
+ a[j2] = x1r - y0i;
+ a[j2 + 1] = x1i + y0r;
+ a[j3] = x1r + y0i;
+ a[j3 + 1] = x1i - y0r;
+ k = 0;
+ kr = 2 * m;
+ for (j = 2; j < mh; j += 2) {
+ k += 4;
+ wk1r = w[k];
+ wk1i = w[k + 1];
+ wk3r = w[k + 2];
+ wk3i = -w[k + 3];
+ kr -= 4;
+ wd1i = w[kr];
+ wd1r = w[kr + 1];
+ wd3i = w[kr + 2];
+ wd3r = -w[kr + 3];
+ j1 = j + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j] - a[j2 + 1];
+ x0i = a[j + 1] + a[j2];
+ x1r = a[j] + a[j2 + 1];
+ x1i = a[j + 1] - a[j2];
+ x2r = a[j1] - a[j3 + 1];
+ x2i = a[j1 + 1] + a[j3];
+ x3r = a[j1] + a[j3 + 1];
+ x3i = a[j1 + 1] - a[j3];
+ y0r = wk1r * x0r - wk1i * x0i;
+ y0i = wk1r * x0i + wk1i * x0r;
+ y2r = wd1r * x2r - wd1i * x2i;
+ y2i = wd1r * x2i + wd1i * x2r;
+ a[j] = y0r + y2r;
+ a[j + 1] = y0i + y2i;
+ a[j1] = y0r - y2r;
+ a[j1 + 1] = y0i - y2i;
+ y0r = wk3r * x1r + wk3i * x1i;
+ y0i = wk3r * x1i - wk3i * x1r;
+ y2r = wd3r * x3r + wd3i * x3i;
+ y2i = wd3r * x3i - wd3i * x3r;
+ a[j2] = y0r + y2r;
+ a[j2 + 1] = y0i + y2i;
+ a[j3] = y0r - y2r;
+ a[j3 + 1] = y0i - y2i;
+ j0 = m - j;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] - a[j2 + 1];
+ x0i = a[j0 + 1] + a[j2];
+ x1r = a[j0] + a[j2 + 1];
+ x1i = a[j0 + 1] - a[j2];
+ x2r = a[j1] - a[j3 + 1];
+ x2i = a[j1 + 1] + a[j3];
+ x3r = a[j1] + a[j3 + 1];
+ x3i = a[j1 + 1] - a[j3];
+ y0r = wd1i * x0r - wd1r * x0i;
+ y0i = wd1i * x0i + wd1r * x0r;
+ y2r = wk1i * x2r - wk1r * x2i;
+ y2i = wk1i * x2i + wk1r * x2r;
+ a[j0] = y0r + y2r;
+ a[j0 + 1] = y0i + y2i;
+ a[j1] = y0r - y2r;
+ a[j1 + 1] = y0i - y2i;
+ y0r = wd3i * x1r + wd3r * x1i;
+ y0i = wd3i * x1i - wd3r * x1r;
+ y2r = wk3i * x3r + wk3r * x3i;
+ y2i = wk3i * x3i - wk3r * x3r;
+ a[j2] = y0r + y2r;
+ a[j2 + 1] = y0i + y2i;
+ a[j3] = y0r - y2r;
+ a[j3 + 1] = y0i - y2i;
+ }
+ wk1r = w[m];
+ wk1i = w[m + 1];
+ j0 = mh;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0] - a[j2 + 1];
+ x0i = a[j0 + 1] + a[j2];
+ x1r = a[j0] + a[j2 + 1];
+ x1i = a[j0 + 1] - a[j2];
+ x2r = a[j1] - a[j3 + 1];
+ x2i = a[j1 + 1] + a[j3];
+ x3r = a[j1] + a[j3 + 1];
+ x3i = a[j1 + 1] - a[j3];
+ y0r = wk1r * x0r - wk1i * x0i;
+ y0i = wk1r * x0i + wk1i * x0r;
+ y2r = wk1i * x2r - wk1r * x2i;
+ y2i = wk1i * x2i + wk1r * x2r;
+ a[j0] = y0r + y2r;
+ a[j0 + 1] = y0i + y2i;
+ a[j1] = y0r - y2r;
+ a[j1 + 1] = y0i - y2i;
+ y0r = wk1i * x1r - wk1r * x1i;
+ y0i = wk1i * x1i + wk1r * x1r;
+ y2r = wk1r * x3r - wk1i * x3i;
+ y2i = wk1r * x3i + wk1i * x3r;
+ a[j2] = y0r - y2r;
+ a[j2 + 1] = y0i - y2i;
+ a[j3] = y0r + y2r;
+ a[j3 + 1] = y0i + y2i;
+}
+
+
+void cftfx41(int n, REAL *a, int nw, REAL *w)
+{
+ void cftf161(REAL *a, REAL *w);
+ void cftf162(REAL *a, REAL *w);
+ void cftf081(REAL *a, REAL *w);
+ void cftf082(REAL *a, REAL *w);
+
+ if (n == 128) {
+ cftf161(a, &w[nw - 8]);
+ cftf162(&a[32], &w[nw - 32]);
+ cftf161(&a[64], &w[nw - 8]);
+ cftf161(&a[96], &w[nw - 8]);
+ } else {
+ cftf081(a, &w[nw - 16]);
+ cftf082(&a[16], &w[nw - 16]);
+ cftf081(&a[32], &w[nw - 16]);
+ cftf081(&a[48], &w[nw - 16]);
+ }
+}
+
+
+void cftfx42(int n, REAL *a, int nw, REAL *w)
+{
+ void cftf161(REAL *a, REAL *w);
+ void cftf162(REAL *a, REAL *w);
+ void cftf081(REAL *a, REAL *w);
+ void cftf082(REAL *a, REAL *w);
+
+ if (n == 128) {
+ cftf161(a, &w[nw - 8]);
+ cftf162(&a[32], &w[nw - 32]);
+ cftf161(&a[64], &w[nw - 8]);
+ cftf162(&a[96], &w[nw - 32]);
+ } else {
+ cftf081(a, &w[nw - 16]);
+ cftf082(&a[16], &w[nw - 16]);
+ cftf081(&a[32], &w[nw - 16]);
+ cftf082(&a[48], &w[nw - 16]);
+ }
+}
+
+
+void cftf161(REAL *a, REAL *w)
+{
+ REAL wn4r, wk1r, wk1i,
+ x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
+ y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
+ y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
+ y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
+
+ wn4r = w[1];
+ wk1i = wn4r * w[2];
+ wk1r = wk1i + w[2];
+ x0r = a[0] + a[16];
+ x0i = a[1] + a[17];
+ x1r = a[0] - a[16];
+ x1i = a[1] - a[17];
+ x2r = a[8] + a[24];
+ x2i = a[9] + a[25];
+ x3r = a[8] - a[24];
+ x3i = a[9] - a[25];
+ y0r = x0r + x2r;
+ y0i = x0i + x2i;
+ y4r = x0r - x2r;
+ y4i = x0i - x2i;
+ y8r = x1r - x3i;
+ y8i = x1i + x3r;
+ y12r = x1r + x3i;
+ y12i = x1i - x3r;
+ x0r = a[2] + a[18];
+ x0i = a[3] + a[19];
+ x1r = a[2] - a[18];
+ x1i = a[3] - a[19];
+ x2r = a[10] + a[26];
+ x2i = a[11] + a[27];
+ x3r = a[10] - a[26];
+ x3i = a[11] - a[27];
+ y1r = x0r + x2r;
+ y1i = x0i + x2i;
+ y5r = x0r - x2r;
+ y5i = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ y9r = wk1r * x0r - wk1i * x0i;
+ y9i = wk1r * x0i + wk1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ y13r = wk1i * x0r - wk1r * x0i;
+ y13i = wk1i * x0i + wk1r * x0r;
+ x0r = a[4] + a[20];
+ x0i = a[5] + a[21];
+ x1r = a[4] - a[20];
+ x1i = a[5] - a[21];
+ x2r = a[12] + a[28];
+ x2i = a[13] + a[29];
+ x3r = a[12] - a[28];
+ x3i = a[13] - a[29];
+ y2r = x0r + x2r;
+ y2i = x0i + x2i;
+ y6r = x0r - x2r;
+ y6i = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ y10r = wn4r * (x0r - x0i);
+ y10i = wn4r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ y14r = wn4r * (x0r + x0i);
+ y14i = wn4r * (x0i - x0r);
+ x0r = a[6] + a[22];
+ x0i = a[7] + a[23];
+ x1r = a[6] - a[22];
+ x1i = a[7] - a[23];
+ x2r = a[14] + a[30];
+ x2i = a[15] + a[31];
+ x3r = a[14] - a[30];
+ x3i = a[15] - a[31];
+ y3r = x0r + x2r;
+ y3i = x0i + x2i;
+ y7r = x0r - x2r;
+ y7i = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ y11r = wk1i * x0r - wk1r * x0i;
+ y11i = wk1i * x0i + wk1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ y15r = wk1r * x0r - wk1i * x0i;
+ y15i = wk1r * x0i + wk1i * x0r;
+ x0r = y12r - y14r;
+ x0i = y12i - y14i;
+ x1r = y12r + y14r;
+ x1i = y12i + y14i;
+ x2r = y13r - y15r;
+ x2i = y13i - y15i;
+ x3r = y13r + y15r;
+ x3i = y13i + y15i;
+ a[24] = x0r + x2r;
+ a[25] = x0i + x2i;
+ a[26] = x0r - x2r;
+ a[27] = x0i - x2i;
+ a[28] = x1r - x3i;
+ a[29] = x1i + x3r;
+ a[30] = x1r + x3i;
+ a[31] = x1i - x3r;
+ x0r = y8r + y10r;
+ x0i = y8i + y10i;
+ x1r = y8r - y10r;
+ x1i = y8i - y10i;
+ x2r = y9r + y11r;
+ x2i = y9i + y11i;
+ x3r = y9r - y11r;
+ x3i = y9i - y11i;
+ a[16] = x0r + x2r;
+ a[17] = x0i + x2i;
+ a[18] = x0r - x2r;
+ a[19] = x0i - x2i;
+ a[20] = x1r - x3i;
+ a[21] = x1i + x3r;
+ a[22] = x1r + x3i;
+ a[23] = x1i - x3r;
+ x0r = y5r - y7i;
+ x0i = y5i + y7r;
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ x0r = y5r + y7i;
+ x0i = y5i - y7r;
+ x3r = wn4r * (x0r - x0i);
+ x3i = wn4r * (x0i + x0r);
+ x0r = y4r - y6i;
+ x0i = y4i + y6r;
+ x1r = y4r + y6i;
+ x1i = y4i - y6r;
+ a[8] = x0r + x2r;
+ a[9] = x0i + x2i;
+ a[10] = x0r - x2r;
+ a[11] = x0i - x2i;
+ a[12] = x1r - x3i;
+ a[13] = x1i + x3r;
+ a[14] = x1r + x3i;
+ a[15] = x1i - x3r;
+ x0r = y0r + y2r;
+ x0i = y0i + y2i;
+ x1r = y0r - y2r;
+ x1i = y0i - y2i;
+ x2r = y1r + y3r;
+ x2i = y1i + y3i;
+ x3r = y1r - y3r;
+ x3i = y1i - y3i;
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[2] = x0r - x2r;
+ a[3] = x0i - x2i;
+ a[4] = x1r - x3i;
+ a[5] = x1i + x3r;
+ a[6] = x1r + x3i;
+ a[7] = x1i - x3r;
+}
+
+
+void cftf162(REAL *a, REAL *w)
+{
+ REAL wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
+ x0r, x0i, x1r, x1i, x2r, x2i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
+ y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
+ y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
+ y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
+
+ wn4r = w[1];
+ wk1r = w[4];
+ wk1i = w[5];
+ wk3r = w[6];
+ wk3i = w[7];
+ wk2r = w[8];
+ wk2i = w[9];
+ x1r = a[0] - a[17];
+ x1i = a[1] + a[16];
+ x0r = a[8] - a[25];
+ x0i = a[9] + a[24];
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ y0r = x1r + x2r;
+ y0i = x1i + x2i;
+ y4r = x1r - x2r;
+ y4i = x1i - x2i;
+ x1r = a[0] + a[17];
+ x1i = a[1] - a[16];
+ x0r = a[8] + a[25];
+ x0i = a[9] - a[24];
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ y8r = x1r - x2i;
+ y8i = x1i + x2r;
+ y12r = x1r + x2i;
+ y12i = x1i - x2r;
+ x0r = a[2] - a[19];
+ x0i = a[3] + a[18];
+ x1r = wk1r * x0r - wk1i * x0i;
+ x1i = wk1r * x0i + wk1i * x0r;
+ x0r = a[10] - a[27];
+ x0i = a[11] + a[26];
+ x2r = wk3i * x0r - wk3r * x0i;
+ x2i = wk3i * x0i + wk3r * x0r;
+ y1r = x1r + x2r;
+ y1i = x1i + x2i;
+ y5r = x1r - x2r;
+ y5i = x1i - x2i;
+ x0r = a[2] + a[19];
+ x0i = a[3] - a[18];
+ x1r = wk3r * x0r - wk3i * x0i;
+ x1i = wk3r * x0i + wk3i * x0r;
+ x0r = a[10] + a[27];
+ x0i = a[11] - a[26];
+ x2r = wk1r * x0r + wk1i * x0i;
+ x2i = wk1r * x0i - wk1i * x0r;
+ y9r = x1r - x2r;
+ y9i = x1i - x2i;
+ y13r = x1r + x2r;
+ y13i = x1i + x2i;
+ x0r = a[4] - a[21];
+ x0i = a[5] + a[20];
+ x1r = wk2r * x0r - wk2i * x0i;
+ x1i = wk2r * x0i + wk2i * x0r;
+ x0r = a[12] - a[29];
+ x0i = a[13] + a[28];
+ x2r = wk2i * x0r - wk2r * x0i;
+ x2i = wk2i * x0i + wk2r * x0r;
+ y2r = x1r + x2r;
+ y2i = x1i + x2i;
+ y6r = x1r - x2r;
+ y6i = x1i - x2i;
+ x0r = a[4] + a[21];
+ x0i = a[5] - a[20];
+ x1r = wk2i * x0r - wk2r * x0i;
+ x1i = wk2i * x0i + wk2r * x0r;
+ x0r = a[12] + a[29];
+ x0i = a[13] - a[28];
+ x2r = wk2r * x0r - wk2i * x0i;
+ x2i = wk2r * x0i + wk2i * x0r;
+ y10r = x1r - x2r;
+ y10i = x1i - x2i;
+ y14r = x1r + x2r;
+ y14i = x1i + x2i;
+ x0r = a[6] - a[23];
+ x0i = a[7] + a[22];
+ x1r = wk3r * x0r - wk3i * x0i;
+ x1i = wk3r * x0i + wk3i * x0r;
+ x0r = a[14] - a[31];
+ x0i = a[15] + a[30];
+ x2r = wk1i * x0r - wk1r * x0i;
+ x2i = wk1i * x0i + wk1r * x0r;
+ y3r = x1r + x2r;
+ y3i = x1i + x2i;
+ y7r = x1r - x2r;
+ y7i = x1i - x2i;
+ x0r = a[6] + a[23];
+ x0i = a[7] - a[22];
+ x1r = wk1i * x0r + wk1r * x0i;
+ x1i = wk1i * x0i - wk1r * x0r;
+ x0r = a[14] + a[31];
+ x0i = a[15] - a[30];
+ x2r = wk3i * x0r - wk3r * x0i;
+ x2i = wk3i * x0i + wk3r * x0r;
+ y11r = x1r + x2r;
+ y11i = x1i + x2i;
+ y15r = x1r - x2r;
+ y15i = x1i - x2i;
+ x1r = y0r + y2r;
+ x1i = y0i + y2i;
+ x2r = y1r + y3r;
+ x2i = y1i + y3i;
+ a[0] = x1r + x2r;
+ a[1] = x1i + x2i;
+ a[2] = x1r - x2r;
+ a[3] = x1i - x2i;
+ x1r = y0r - y2r;
+ x1i = y0i - y2i;
+ x2r = y1r - y3r;
+ x2i = y1i - y3i;
+ a[4] = x1r - x2i;
+ a[5] = x1i + x2r;
+ a[6] = x1r + x2i;
+ a[7] = x1i - x2r;
+ x1r = y4r - y6i;
+ x1i = y4i + y6r;
+ x0r = y5r - y7i;
+ x0i = y5i + y7r;
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ a[8] = x1r + x2r;
+ a[9] = x1i + x2i;
+ a[10] = x1r - x2r;
+ a[11] = x1i - x2i;
+ x1r = y4r + y6i;
+ x1i = y4i - y6r;
+ x0r = y5r + y7i;
+ x0i = y5i - y7r;
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ a[12] = x1r - x2i;
+ a[13] = x1i + x2r;
+ a[14] = x1r + x2i;
+ a[15] = x1i - x2r;
+ x1r = y8r + y10r;
+ x1i = y8i + y10i;
+ x2r = y9r - y11r;
+ x2i = y9i - y11i;
+ a[16] = x1r + x2r;
+ a[17] = x1i + x2i;
+ a[18] = x1r - x2r;
+ a[19] = x1i - x2i;
+ x1r = y8r - y10r;
+ x1i = y8i - y10i;
+ x2r = y9r + y11r;
+ x2i = y9i + y11i;
+ a[20] = x1r - x2i;
+ a[21] = x1i + x2r;
+ a[22] = x1r + x2i;
+ a[23] = x1i - x2r;
+ x1r = y12r - y14i;
+ x1i = y12i + y14r;
+ x0r = y13r + y15i;
+ x0i = y13i - y15r;
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ a[24] = x1r + x2r;
+ a[25] = x1i + x2i;
+ a[26] = x1r - x2r;
+ a[27] = x1i - x2i;
+ x1r = y12r + y14i;
+ x1i = y12i - y14r;
+ x0r = y13r - y15i;
+ x0i = y13i + y15r;
+ x2r = wn4r * (x0r - x0i);
+ x2i = wn4r * (x0i + x0r);
+ a[28] = x1r - x2i;
+ a[29] = x1i + x2r;
+ a[30] = x1r + x2i;
+ a[31] = x1i - x2r;
+}
+
+
+void cftf081(REAL *a, REAL *w)
+{
+ REAL wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
+ y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
+
+ wn4r = w[1];
+ x0r = a[0] + a[8];
+ x0i = a[1] + a[9];
+ x1r = a[0] - a[8];
+ x1i = a[1] - a[9];
+ x2r = a[4] + a[12];
+ x2i = a[5] + a[13];
+ x3r = a[4] - a[12];
+ x3i = a[5] - a[13];
+ y0r = x0r + x2r;
+ y0i = x0i + x2i;
+ y2r = x0r - x2r;
+ y2i = x0i - x2i;
+ y1r = x1r - x3i;
+ y1i = x1i + x3r;
+ y3r = x1r + x3i;
+ y3i = x1i - x3r;
+ x0r = a[2] + a[10];
+ x0i = a[3] + a[11];
+ x1r = a[2] - a[10];
+ x1i = a[3] - a[11];
+ x2r = a[6] + a[14];
+ x2i = a[7] + a[15];
+ x3r = a[6] - a[14];
+ x3i = a[7] - a[15];
+ y4r = x0r + x2r;
+ y4i = x0i + x2i;
+ y6r = x0r - x2r;
+ y6i = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ x2r = x1r + x3i;
+ x2i = x1i - x3r;
+ y5r = wn4r * (x0r - x0i);
+ y5i = wn4r * (x0r + x0i);
+ y7r = wn4r * (x2r - x2i);
+ y7i = wn4r * (x2r + x2i);
+ a[8] = y1r + y5r;
+ a[9] = y1i + y5i;
+ a[10] = y1r - y5r;
+ a[11] = y1i - y5i;
+ a[12] = y3r - y7i;
+ a[13] = y3i + y7r;
+ a[14] = y3r + y7i;
+ a[15] = y3i - y7r;
+ a[0] = y0r + y4r;
+ a[1] = y0i + y4i;
+ a[2] = y0r - y4r;
+ a[3] = y0i - y4i;
+ a[4] = y2r - y6i;
+ a[5] = y2i + y6r;
+ a[6] = y2r + y6i;
+ a[7] = y2i - y6r;
+}
+
+
+void cftf082(REAL *a, REAL *w)
+{
+ REAL wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
+ y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
+
+ wn4r = w[1];
+ wk1r = w[4];
+ wk1i = w[5];
+ y0r = a[0] - a[9];
+ y0i = a[1] + a[8];
+ y1r = a[0] + a[9];
+ y1i = a[1] - a[8];
+ x0r = a[4] - a[13];
+ x0i = a[5] + a[12];
+ y2r = wn4r * (x0r - x0i);
+ y2i = wn4r * (x0i + x0r);
+ x0r = a[4] + a[13];
+ x0i = a[5] - a[12];
+ y3r = wn4r * (x0r - x0i);
+ y3i = wn4r * (x0i + x0r);
+ x0r = a[2] - a[11];
+ x0i = a[3] + a[10];
+ y4r = wk1r * x0r - wk1i * x0i;
+ y4i = wk1r * x0i + wk1i * x0r;
+ x0r = a[2] + a[11];
+ x0i = a[3] - a[10];
+ y5r = wk1i * x0r - wk1r * x0i;
+ y5i = wk1i * x0i + wk1r * x0r;
+ x0r = a[6] - a[15];
+ x0i = a[7] + a[14];
+ y6r = wk1i * x0r - wk1r * x0i;
+ y6i = wk1i * x0i + wk1r * x0r;
+ x0r = a[6] + a[15];
+ x0i = a[7] - a[14];
+ y7r = wk1r * x0r - wk1i * x0i;
+ y7i = wk1r * x0i + wk1i * x0r;
+ x0r = y0r + y2r;
+ x0i = y0i + y2i;
+ x1r = y4r + y6r;
+ x1i = y4i + y6i;
+ a[0] = x0r + x1r;
+ a[1] = x0i + x1i;
+ a[2] = x0r - x1r;
+ a[3] = x0i - x1i;
+ x0r = y0r - y2r;
+ x0i = y0i - y2i;
+ x1r = y4r - y6r;
+ x1i = y4i - y6i;
+ a[4] = x0r - x1i;
+ a[5] = x0i + x1r;
+ a[6] = x0r + x1i;
+ a[7] = x0i - x1r;
+ x0r = y1r - y3i;
+ x0i = y1i + y3r;
+ x1r = y5r - y7r;
+ x1i = y5i - y7i;
+ a[8] = x0r + x1r;
+ a[9] = x0i + x1i;
+ a[10] = x0r - x1r;
+ a[11] = x0i - x1i;
+ x0r = y1r + y3i;
+ x0i = y1i - y3r;
+ x1r = y5r + y7r;
+ x1i = y5i + y7i;
+ a[12] = x0r - x1i;
+ a[13] = x0i + x1r;
+ a[14] = x0r + x1i;
+ a[15] = x0i - x1r;
+}
+
+
+void cftf040(REAL *a)
+{
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ x0r = a[0] + a[4];
+ x0i = a[1] + a[5];
+ x1r = a[0] - a[4];
+ x1i = a[1] - a[5];
+ x2r = a[2] + a[6];
+ x2i = a[3] + a[7];
+ x3r = a[2] - a[6];
+ x3i = a[3] - a[7];
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[2] = x1r - x3i;
+ a[3] = x1i + x3r;
+ a[6] = x1r + x3i;
+ a[7] = x1i - x3r;
+}
+
+
+void cftb040(REAL *a)
+{
+ REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+ x0r = a[0] + a[4];
+ x0i = a[1] + a[5];
+ x1r = a[0] - a[4];
+ x1i = a[1] - a[5];
+ x2r = a[2] + a[6];
+ x2i = a[3] + a[7];
+ x3r = a[2] - a[6];
+ x3i = a[3] - a[7];
+ a[0] = x0r + x2r;
+ a[1] = x0i + x2i;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[2] = x1r + x3i;
+ a[3] = x1i - x3r;
+ a[6] = x1r - x3i;
+ a[7] = x1i + x3r;
+}
+
+
+void cftx020(REAL *a)
+{
+ REAL x0r, x0i;
+
+ x0r = a[0] - a[2];
+ x0i = a[1] - a[3];
+ a[0] += a[2];
+ a[1] += a[3];
+ a[2] = x0r;
+ a[3] = x0i;
+}
+
+
+void rftfsub(int n, REAL *a, int nc, REAL *c)
+{
+ int j, k, kk, ks, m;
+ REAL wkr, wki, xr, xi, yr, yi;
+
+ m = n >> 1;
+ ks = 2 * nc / m;
+ kk = 0;
+ for (j = 2; j < m; j += 2) {
+ k = n - j;
+ kk += ks;
+ wkr = 0.5 - c[nc - kk];
+ wki = c[kk];
+ xr = a[j] - a[k];
+ xi = a[j + 1] + a[k + 1];
+ yr = wkr * xr - wki * xi;
+ yi = wkr * xi + wki * xr;
+ a[j] -= yr;
+ a[j + 1] -= yi;
+ a[k] += yr;
+ a[k + 1] -= yi;
+ }
+}
+
+
+void rftbsub(int n, REAL *a, int nc, REAL *c)
+{
+ int j, k, kk, ks, m;
+ REAL wkr, wki, xr, xi, yr, yi;
+
+ m = n >> 1;
+ ks = 2 * nc / m;
+ kk = 0;
+ for (j = 2; j < m; j += 2) {
+ k = n - j;
+ kk += ks;
+ wkr = 0.5 - c[nc - kk];
+ wki = c[kk];
+ xr = a[j] - a[k];
+ xi = a[j + 1] + a[k + 1];
+ yr = wkr * xr + wki * xi;
+ yi = wkr * xi - wki * xr;
+ a[j] -= yr;
+ a[j + 1] -= yi;
+ a[k] += yr;
+ a[k + 1] -= yi;
+ }
+}
+
+
+void dctsub(int n, REAL *a, int nc, REAL *c)
+{
+ int j, k, kk, ks, m;
+ REAL wkr, wki, xr;
+
+ m = n >> 1;
+ ks = nc / n;
+ kk = 0;
+ for (j = 1; j < m; j++) {
+ k = n - j;
+ kk += ks;
+ wkr = c[kk] - c[nc - kk];
+ wki = c[kk] + c[nc - kk];
+ xr = wki * a[j] - wkr * a[k];
+ a[j] = wkr * a[j] + wki * a[k];
+ a[k] = xr;
+ }
+ a[m] *= c[0];
+}
+
+
+void dstsub(int n, REAL *a, int nc, REAL *c)
+{
+ int j, k, kk, ks, m;
+ REAL wkr, wki, xr;
+
+ m = n >> 1;
+ ks = nc / n;
+ kk = 0;
+ for (j = 1; j < m; j++) {
+ k = n - j;
+ kk += ks;
+ wkr = c[kk] - c[nc - kk];
+ wki = c[kk] + c[nc - kk];
+ xr = wki * a[k] - wkr * a[j];
+ a[k] = wkr * a[k] + wki * a[j];
+ a[j] = xr;
+ }
+ a[m] *= c[0];
+}
+
+void rfft(int n,int isign,REAL x[])
+{
+ static int ipsize = 0,wsize=0;
+ static int *ip = NULL;
+ static REAL *w = NULL;
+ int newipsize,newwsize;
+
+ if (n == 0) {
+ free(ip); ip = NULL; ipsize = 0;
+ free(w); w = NULL; wsize = 0;
+ return;
+ }
+
+ newipsize = 2+sqrt(n/2);
+ if (newipsize > ipsize) {
+ ipsize = newipsize;
+ ip = (int *)realloc(ip,sizeof(int)*ipsize);
+ ip[0] = 0;
+ }
+
+ newwsize = n/2;
+ if (newwsize > wsize) {
+ wsize = newwsize;
+ w = (REAL *)realloc(w,sizeof(REAL)*wsize);
+ }
+
+ rdft(n,isign,x,ip,w);
+}
diff --git a/plugins/supereq/Makefile.am b/plugins/supereq/Makefile.am
new file mode 100644
index 00000000..f86c3e06
--- /dev/null
+++ b/plugins/supereq/Makefile.am
@@ -0,0 +1,8 @@
+supereqdir = $(libdir)/$(PACKAGE)
+pkglib_LTLIBRARIES = supereq.la
+supereq_la_SOURCES = supereq.c Equ.cpp Fftsg_fl.cpp paramlist.hpp
+
+supereq_la_LDFLAGS = -module
+
+supereq_la_LIBADD = $(LDADD)
+AM_CFLAGS = -std=c99
diff --git a/plugins/supereq/paramlist.hpp b/plugins/supereq/paramlist.hpp
new file mode 100644
index 00000000..0c513b78
--- /dev/null
+++ b/plugins/supereq/paramlist.hpp
@@ -0,0 +1,120 @@
+//#include <iostream.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+class paramlistelm {
+public:
+ class paramlistelm *next;
+
+ char left,right;
+ float lower,upper,gain,gain2;
+ int sortindex;
+
+ paramlistelm(void) {
+ left = right = 1;
+ lower = upper = gain = 0;
+ next = NULL;
+ };
+
+ ~paramlistelm() {
+ delete next;
+ next = NULL;
+ };
+
+ char *getString(void) {
+ static char str[64];
+ sprintf(str,"%gHz to %gHz, %gdB %c%c",
+ (double)lower,(double)upper,(double)gain,left?'L':' ',right?'R':' ');
+ return str;
+ }
+};
+
+class paramlist {
+public:
+ class paramlistelm *elm;
+
+ paramlist(void) {
+ elm = NULL;
+ }
+
+ ~paramlist() {
+ delete elm;
+ elm = NULL;
+ }
+
+ void copy(paramlist &src)
+ {
+ delete elm;
+ elm = NULL;
+
+ paramlistelm **p,*q;
+ for(p=&elm,q=src.elm;q != NULL;q = q->next,p = &(*p)->next)
+ {
+ *p = new paramlistelm;
+ (*p)->left = q->left;
+ (*p)->right = q->right;
+ (*p)->lower = q->lower;
+ (*p)->upper = q->upper;
+ (*p)->gain = q->gain;
+ }
+ }
+
+ paramlistelm *newelm(void)
+ {
+ paramlistelm **e;
+ for(e = &elm;*e != NULL;e = &(*e)->next) ;
+ *e = new paramlistelm;
+
+ return *e;
+ }
+
+ int getnelm(void)
+ {
+ int i;
+ paramlistelm *e;
+
+ for(e = elm,i = 0;e != NULL;e = e->next,i++) ;
+
+ return i;
+ }
+
+ void delelm(paramlistelm *p)
+ {
+ paramlistelm **e;
+ for(e = &elm;*e != NULL && p != *e;e = &(*e)->next) ;
+ if (*e == NULL) return;
+ *e = (*e)->next;
+ p->next = NULL;
+ delete p;
+ }
+
+ void sortelm(void)
+ {
+ int i=0;
+
+ if (elm == NULL) return;
+
+ for(paramlistelm *r = elm;r != NULL;r = r->next) r->sortindex = i++;
+
+ paramlistelm **p,**q;
+
+ for(p=&elm->next;*p != NULL;)
+ {
+ for(q=&elm;*q != *p;q = &(*q)->next)
+ if ((*p)->lower < (*q)->lower ||
+ ((*p)->lower == (*q)->lower && (*p)->sortindex < (*q)->sortindex)) break;
+
+ if (p == q) {p = &(*p)->next; continue;}
+
+ paramlistelm **pn = p;
+ paramlistelm *pp = *p;
+ *p = (*p)->next;
+ pp->next = *q;
+ *q = pp;
+
+ p = pn;
+ }
+ }
+};
+
diff --git a/plugins/supereq/supereq.c b/plugins/supereq/supereq.c
new file mode 100644
index 00000000..d3509312
--- /dev/null
+++ b/plugins/supereq/supereq.c
@@ -0,0 +1,105 @@
+/*
+ DeaDBeeF - ultimate music player for GNU/Linux systems with X11
+ Copyright (C) 2009-2010 Alexey Yakovenko <waker@users.sourceforge.net>
+
+ This program is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public License
+ as published by the Free Software Foundation; either version 2
+ of the License, or (at your option) any later version.
+
+ This program 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 General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+*/
+#include "../../deadbeef.h"
+#include "supereq.h"
+
+static DB_functions_t *deadbeef;
+
+void *paramlist_alloc (void);
+void paramlist_free (void *);
+void equ_makeTable(float *lbc,float *rbc,void *param,float fs);
+int equ_modifySamples(char *buf,int nsamples,int nch,int bps);
+void equ_clearbuf(int bps,int srate);
+void equ_init(int wb);
+void equ_quit(void);
+
+float last_srate = 0;
+int last_nch = 0, last_bps = 0;
+float lbands[18] = {1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0};
+float rbands[18] = {1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0};
+void *paramsroot;
+
+int
+supereq_plugin_start (void) {
+ equ_init (14);
+ paramsroot = paramlist_alloc ();
+ return 0;
+}
+
+int
+supereq_plugin_stop (void) {
+ equ_quit ();
+ paramlist_free (paramsroot);
+ return 0;
+}
+
+
+int
+supereq_process_int16 (int16_t *samples, int nsamples, int nch, int bps, int srate) {
+ if ((nch != 1 && nch != 2) || (bps != 8 && bps != 16 && bps != 24)) return nsamples;
+ if (last_srate != srate) {
+ equ_makeTable (lbands, rbands, paramsroot, srate);
+ last_srate = srate;
+ last_nch = nch;
+ last_bps = bps;
+ equ_clearbuf(bps,srate);
+ }
+ else if (last_nch != nch || last_bps != bps) {
+ last_nch = nch;
+ last_bps = bps;
+ equ_clearbuf(bps,srate);
+ }
+ equ_modifySamples((char *)samples,nsamples,nch,bps);
+ return nsamples;
+}
+
+float
+supereq_get_band (int band) {
+ return lbands[band];
+}
+
+void
+supereq_set_band (int band, float value) {
+ last_srate = 0;
+ lbands[band] = rbands[band] = value;
+}
+
+static DB_supereq_dsp_t plugin = {
+ .dsp.plugin.api_vmajor = DB_API_VERSION_MAJOR,
+ .dsp.plugin.api_vminor = DB_API_VERSION_MINOR,
+ .dsp.plugin.type = DB_PLUGIN_DSP,
+ .dsp.plugin.id = "supereq",
+ .dsp.plugin.name = "SuperEQ",
+ .dsp.plugin.descr = "equalizer plugin using SuperEQ library by Naoki Shibata",
+ .dsp.plugin.author = "Alexey Yakovenko",
+ .dsp.plugin.email = "waker@users.sourceforge.net",
+ .dsp.plugin.website = "http://deadbeef.sf.net",
+ .dsp.plugin.start = supereq_plugin_start,
+ .dsp.plugin.stop = supereq_plugin_stop,
+// .dsp.plugin.configdialog = settings_dlg,
+ .dsp.process_int16 = supereq_process_int16,
+ .get_band = supereq_get_band,
+ .set_band = supereq_set_band,
+};
+
+DB_plugin_t *
+supereq_load (DB_functions_t *api) {
+ deadbeef = api;
+ return DB_PLUGIN (&plugin);
+}
diff --git a/plugins/supereq/supereq.h b/plugins/supereq/supereq.h
new file mode 100644
index 00000000..65fa5905
--- /dev/null
+++ b/plugins/supereq/supereq.h
@@ -0,0 +1,29 @@
+/*
+ DeaDBeeF - ultimate music player for GNU/Linux systems with X11
+ Copyright (C) 2009-2010 Alexey Yakovenko <waker@users.sourceforge.net>
+
+ This program is free software; you can redistribute it and/or
+ modify it under the terms of the GNU General Public License
+ as published by the Free Software Foundation; either version 2
+ of the License, or (at your option) any later version.
+
+ This program 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 General Public License
+ along with this program; if not, write to the Free Software
+ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+*/
+
+#ifndef __SUPEREQ_H
+#define __SUPEREQ_H
+
+typedef struct DB_supereq_dsp_s {
+ DB_dsp_t dsp;
+ float (*get_band) (int band);
+ void (*set_band) (int band, float value);
+} DB_supereq_dsp_t;
+
+#endif
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-18 14:04:54 +0000