Add FS #10214. Initial commit of the original PDa code for the GSoC Pure Data plugin project of Wincent Balin. Stripped some non-sourcefiles and added a rockbox readme that needs a bit more info from Wincent. Is added to CATEGORIES and viewers, but not yet to SUBDIRS (ie doesn't build yet)

git-svn-id: svn://svn.rockbox.org/rockbox/trunk@21044 a1c6a512-1295-4272-9138-f99709370657

1 files changed, 838 insertions, 0 deletions

diff --git a/apps/plugins/pdbox/PDa/src/d_mayer_fft.c b/apps/plugins/pdbox/PDa/src/d_mayer_fft.c
new file mode 100644
index 0000000000..7c29c6e7c8
--- /dev/null
+++ b/apps/plugins/pdbox/PDa/src/d_mayer_fft.c
@@ -0,0 +1,838 @@
+/*
+** FFT and FHT routines
+**  Copyright 1988, 1993; Ron Mayer
+**  
+**  mayer_fht(fz,n);
+**      Does a hartley transform of "n" points in the array "fz".
+**  mayer_fft(n,real,imag)
+**      Does a fourier transform of "n" points of the "real" and
+**      "imag" arrays.
+**  mayer_ifft(n,real,imag)
+**      Does an inverse fourier transform of "n" points of the "real"
+**      and "imag" arrays.
+**  mayer_realfft(n,real)
+**      Does a real-valued fourier transform of "n" points of the
+**      "real" array.  The real part of the transform ends
+**      up in the first half of the array and the imaginary part of the
+**      transform ends up in the second half of the array.
+**  mayer_realifft(n,real)
+**      The inverse of the realfft() routine above.
+**      
+**      
+** NOTE: This routine uses at least 2 patented algorithms, and may be
+**       under the restrictions of a bunch of different organizations.
+**       Although I wrote it completely myself, it is kind of a derivative
+**       of a routine I once authored and released under the GPL, so it
+**       may fall under the free software foundation's restrictions;
+**       it was worked on as a Stanford Univ project, so they claim
+**       some rights to it; it was further optimized at work here, so
+**       I think this company claims parts of it.  The patents are
+**       held by R. Bracewell (the FHT algorithm) and O. Buneman (the
+**       trig generator), both at Stanford Univ.
+**       If it were up to me, I'd say go do whatever you want with it;
+**       but it would be polite to give credit to the following people
+**       if you use this anywhere:
+**           Euler     - probable inventor of the fourier transform.
+**           Gauss     - probable inventor of the FFT.
+**           Hartley   - probable inventor of the hartley transform.
+**           Buneman   - for a really cool trig generator
+**           Mayer(me) - for authoring this particular version and
+**                       including all the optimizations in one package.
+**       Thanks,
+**       Ron Mayer; mayer@acuson.com
+**
+*/
+
+/* This is a slightly modified version of Mayer's contribution; write
+* msp@ucsd.edu for the original code.  Kudos to Mayer for a fine piece
+* of work.  -msp
+*/
+
+#ifdef MSW
+#pragma warning( disable : 4305 )  /* uncast const double to float */
+#pragma warning( disable : 4244 )  /* uncast double to float */
+#pragma warning( disable : 4101 )  /* unused local variables */
+#endif
+
+#define REAL float
+#define GOOD_TRIG
+
+#ifdef GOOD_TRIG
+#else
+#define FAST_TRIG
+#endif
+
+#if defined(GOOD_TRIG)
+#define FHT_SWAP(a,b,t) {(t)=(a);(a)=(b);(b)=(t);}
+#define TRIG_VARS                                                \
+      int t_lam=0;
+#define TRIG_INIT(k,c,s)                                         \
+     {                                                           \
+      int i;                                                     \
+      for (i=2 ; i<=k ; i++)                                     \
+          {coswrk[i]=costab[i];sinwrk[i]=sintab[i];}             \
+      t_lam = 0;                                                 \
+      c = 1;                                                     \
+      s = 0;                                                     \
+     }
+#define TRIG_NEXT(k,c,s)                                         \
+     {                                                           \
+         int i,j;                                                \
+         (t_lam)++;                                              \
+         for (i=0 ; !((1<<i)&t_lam) ; i++);                      \
+         i = k-i;                                                \
+         s = sinwrk[i];                                          \
+         c = coswrk[i];                                          \
+         if (i>1)                                                \
+            {                                                    \
+             for (j=k-i+2 ; (1<<j)&t_lam ; j++);                 \
+             j         = k - j;                                  \
+             sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]);  \
+             coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]);  \
+            }                                                    \
+     }
+#define TRIG_RESET(k,c,s)
+#endif
+
+#if defined(FAST_TRIG)
+#define TRIG_VARS                                        \
+      REAL t_c,t_s;
+#define TRIG_INIT(k,c,s)                                 \
+    {                                                    \
+     t_c  = costab[k];                                   \
+     t_s  = sintab[k];                                   \
+     c    = 1;                                           \
+     s    = 0;                                           \
+    }
+#define TRIG_NEXT(k,c,s)                                 \
+    {                                                    \
+     REAL t = c;                                         \
+     c   = t*t_c - s*t_s;                                \
+     s   = t*t_s + s*t_c;                                \
+    }
+#define TRIG_RESET(k,c,s)
+#endif
+
+static REAL halsec[20]=
+    {
+     0,
+     0,
+     .54119610014619698439972320536638942006107206337801,
+     .50979557910415916894193980398784391368261849190893,
+     .50241928618815570551167011928012092247859337193963,
+     .50060299823519630134550410676638239611758632599591,
+     .50015063602065098821477101271097658495974913010340,
+     .50003765191554772296778139077905492847503165398345,
+     .50000941253588775676512870469186533538523133757983,
+     .50000235310628608051401267171204408939326297376426,
+     .50000058827484117879868526730916804925780637276181,
+     .50000014706860214875463798283871198206179118093251,
+     .50000003676714377807315864400643020315103490883972,
+     .50000000919178552207366560348853455333939112569380,
+     .50000000229794635411562887767906868558991922348920,
+     .50000000057448658687873302235147272458812263401372
+    };
+static REAL costab[20]=
+    {
+     .00000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768847,
+     .92387953251128675612818318939678828682241662586364,
+     .98078528040323044912618223613423903697393373089333,
+     .99518472667219688624483695310947992157547486872985,
+     .99879545620517239271477160475910069444320361470461,
+     .99969881869620422011576564966617219685006108125772,
+     .99992470183914454092164649119638322435060646880221,
+     .99998117528260114265699043772856771617391725094433,
+     .99999529380957617151158012570011989955298763362218,
+     .99999882345170190992902571017152601904826792288976,
+     .99999970586288221916022821773876567711626389934930,
+     .99999992646571785114473148070738785694820115568892,
+     .99999998161642929380834691540290971450507605124278,
+     .99999999540410731289097193313960614895889430318945,
+     .99999999885102682756267330779455410840053741619428
+    };
+static REAL sintab[20]=
+    {
+     1.0000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768846,
+     .38268343236508977172845998403039886676134456248561,
+     .19509032201612826784828486847702224092769161775195,
+     .09801714032956060199419556388864184586113667316749,
+     .04906767432741801425495497694268265831474536302574,
+     .02454122852291228803173452945928292506546611923944,
+     .01227153828571992607940826195100321214037231959176,
+     .00613588464915447535964023459037258091705788631738,
+     .00306795676296597627014536549091984251894461021344,
+     .00153398018628476561230369715026407907995486457522,
+     .00076699031874270452693856835794857664314091945205,
+     .00038349518757139558907246168118138126339502603495,
+     .00019174759731070330743990956198900093346887403385,
+     .00009587379909597734587051721097647635118706561284,
+     .00004793689960306688454900399049465887274686668768
+    };
+static REAL coswrk[20]=
+    {
+     .00000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768847,
+     .92387953251128675612818318939678828682241662586364,
+     .98078528040323044912618223613423903697393373089333,
+     .99518472667219688624483695310947992157547486872985,
+     .99879545620517239271477160475910069444320361470461,
+     .99969881869620422011576564966617219685006108125772,
+     .99992470183914454092164649119638322435060646880221,
+     .99998117528260114265699043772856771617391725094433,
+     .99999529380957617151158012570011989955298763362218,
+     .99999882345170190992902571017152601904826792288976,
+     .99999970586288221916022821773876567711626389934930,
+     .99999992646571785114473148070738785694820115568892,
+     .99999998161642929380834691540290971450507605124278,
+     .99999999540410731289097193313960614895889430318945,
+     .99999999885102682756267330779455410840053741619428
+    };
+static REAL sinwrk[20]=
+    {
+     1.0000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768846,
+     .38268343236508977172845998403039886676134456248561,
+     .19509032201612826784828486847702224092769161775195,
+     .09801714032956060199419556388864184586113667316749,
+     .04906767432741801425495497694268265831474536302574,
+     .02454122852291228803173452945928292506546611923944,
+     .01227153828571992607940826195100321214037231959176,
+     .00613588464915447535964023459037258091705788631738,
+     .00306795676296597627014536549091984251894461021344,
+     .00153398018628476561230369715026407907995486457522,
+     .00076699031874270452693856835794857664314091945205,
+     .00038349518757139558907246168118138126339502603495,
+     .00019174759731070330743990956198900093346887403385,
+     .00009587379909597734587051721097647635118706561284,
+     .00004793689960306688454900399049465887274686668768
+    };
+
+
+#define SQRT2_2   0.70710678118654752440084436210484
+#define SQRT2   2*0.70710678118654752440084436210484
+
+void mayer_fht(REAL *fz, int n)
+{
+/*  REAL a,b;
+REAL c1,s1,s2,c2,s3,c3,s4,c4;
+ REAL f0,g0,f1,g1,f2,g2,f3,g3; */
+ int  k,k1,k2,k3,k4,kx;
+ REAL *fi,*fn,*gi;
+ TRIG_VARS;
+
+ for (k1=1,k2=0;k1<n;k1++)
+    {
+     REAL aa;
+     for (k=n>>1; (!((k2^=k)&k)); k>>=1);
+     if (k1>k2)
+        {
+             aa=fz[k1];fz[k1]=fz[k2];fz[k2]=aa;
+        }
+    }
+ for ( k=0 ; (1<<k)<n ; k++ );
+ k  &= 1;
+ if (k==0)
+    {
+         for (fi=fz,fn=fz+n;fi<fn;fi+=4)
+            {
+             REAL f0,f1,f2,f3;
+             f1     = fi[0 ]-fi[1 ];
+             f0     = fi[0 ]+fi[1 ];
+             f3     = fi[2 ]-fi[3 ];
+             f2     = fi[2 ]+fi[3 ];
+             fi[2 ] = (f0-f2);  
+             fi[0 ] = (f0+f2);
+             fi[3 ] = (f1-f3);  
+             fi[1 ] = (f1+f3);
+            }
+    }
+ else
+    {
+         for (fi=fz,fn=fz+n,gi=fi+1;fi<fn;fi+=8,gi+=8)
+            {
+             REAL bs1,bc1,bs2,bc2,bs3,bc3,bs4,bc4,
+                bg0,bf0,bf1,bg1,bf2,bg2,bf3,bg3;
+             bc1     = fi[0 ] - gi[0 ];
+             bs1     = fi[0 ] + gi[0 ];
+             bc2     = fi[2 ] - gi[2 ];
+             bs2     = fi[2 ] + gi[2 ];
+             bc3     = fi[4 ] - gi[4 ];
+             bs3     = fi[4 ] + gi[4 ];
+             bc4     = fi[6 ] - gi[6 ];
+             bs4     = fi[6 ] + gi[6 ];
+             bf1     = (bs1 - bs2);     
+             bf0     = (bs1 + bs2);
+             bg1     = (bc1 - bc2);     
+             bg0     = (bc1 + bc2);
+             bf3     = (bs3 - bs4);     
+             bf2     = (bs3 + bs4);
+             bg3     = SQRT2*bc4;               
+             bg2     = SQRT2*bc3;
+             fi[4 ] = bf0 - bf2;
+             fi[0 ] = bf0 + bf2;
+             fi[6 ] = bf1 - bf3;
+             fi[2 ] = bf1 + bf3;
+             gi[4 ] = bg0 - bg2;
+             gi[0 ] = bg0 + bg2;
+             gi[6 ] = bg1 - bg3;
+             gi[2 ] = bg1 + bg3;
+            }
+    }
+ if (n<16) return;
+
+ do
+    {
+     REAL s1,c1;
+     int ii;
+     k  += 2;
+     k1  = 1  << k;
+     k2  = k1 << 1;
+     k4  = k2 << 1;
+     k3  = k2 + k1;
+     kx  = k1 >> 1;
+         fi  = fz;
+         gi  = fi + kx;
+         fn  = fz + n;
+         do
+            {
+             REAL g0,f0,f1,g1,f2,g2,f3,g3;
+             f1      = fi[0 ] - fi[k1];
+             f0      = fi[0 ] + fi[k1];
+             f3      = fi[k2] - fi[k3];
+             f2      = fi[k2] + fi[k3];
+             fi[k2]  = f0         - f2;
+             fi[0 ]  = f0         + f2;
+             fi[k3]  = f1         - f3;
+             fi[k1]  = f1         + f3;
+             g1      = gi[0 ] - gi[k1];
+             g0      = gi[0 ] + gi[k1];
+             g3      = SQRT2  * gi[k3];
+             g2      = SQRT2  * gi[k2];
+             gi[k2]  = g0         - g2;
+             gi[0 ]  = g0         + g2;
+             gi[k3]  = g1         - g3;
+             gi[k1]  = g1         + g3;
+             gi     += k4;
+             fi     += k4;
+            } while (fi<fn);
+     TRIG_INIT(k,c1,s1);
+     for (ii=1;ii<kx;ii++)
+        {
+         REAL c2,s2;
+         TRIG_NEXT(k,c1,s1);
+         c2 = c1*c1 - s1*s1;
+         s2 = 2*(c1*s1);
+             fn = fz + n;
+             fi = fz +ii;
+             gi = fz +k1-ii;
+             do
+                {
+                 REAL a,b,g0,f0,f1,g1,f2,g2,f3,g3;
+                 b       = s2*fi[k1] - c2*gi[k1];
+                 a       = c2*fi[k1] + s2*gi[k1];
+                 f1      = fi[0 ]    - a;
+                 f0      = fi[0 ]    + a;
+                 g1      = gi[0 ]    - b;
+                 g0      = gi[0 ]    + b;
+                 b       = s2*fi[k3] - c2*gi[k3];
+                 a       = c2*fi[k3] + s2*gi[k3];
+                 f3      = fi[k2]    - a;
+                 f2      = fi[k2]    + a;
+                 g3      = gi[k2]    - b;
+                 g2      = gi[k2]    + b;
+                 b       = s1*f2     - c1*g3;
+                 a       = c1*f2     + s1*g3;
+                 fi[k2]  = f0        - a;
+                 fi[0 ]  = f0        + a;
+                 gi[k3]  = g1        - b;
+                 gi[k1]  = g1        + b;
+                 b       = c1*g2     - s1*f3;
+                 a       = s1*g2     + c1*f3;
+                 gi[k2]  = g0        - a;
+                 gi[0 ]  = g0        + a;
+                 fi[k3]  = f1        - b;
+                 fi[k1]  = f1        + b;
+                 gi     += k4;
+                 fi     += k4;
+                } while (fi<fn);
+        }
+     TRIG_RESET(k,c1,s1);
+    } while (k4<n);
+}
+
+void mayer_fft(int n, REAL *real, REAL *imag)
+{
+ REAL a,b,c,d;
+ REAL q,r,s,t;
+ int i,j,k;
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i]; b = real[j];  q=a+b; r=a-b;
+  c = imag[i]; d = imag[j];  s=c+d; t=c-d;
+  real[i] = (q+t)*.5; real[j] = (q-t)*.5;
+  imag[i] = (s-r)*.5; imag[j] = (s+r)*.5;
+ }
+ mayer_fht(real,n);
+ mayer_fht(imag,n);
+}
+
+void mayer_ifft(int n, REAL *real, REAL *imag)
+{
+ REAL a,b,c,d;
+ REAL q,r,s,t;
+ int i,j,k;
+ mayer_fht(real,n);
+ mayer_fht(imag,n);
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i]; b = real[j];  q=a+b; r=a-b;
+  c = imag[i]; d = imag[j];  s=c+d; t=c-d;
+  imag[i] = (s+r)*0.5;  imag[j] = (s-r)*0.5;
+  real[i] = (q-t)*0.5;  real[j] = (q+t)*0.5;
+ }
+}
+
+void mayer_realfft(int n, REAL *real)
+{
+ REAL a,b,c,d;
+ int i,j,k;
+ mayer_fht(real,n);
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i];
+  b = real[j];
+  real[j] = (a-b)*0.5;
+  real[i] = (a+b)*0.5;
+ }
+}
+
+void mayer_realifft(int n, REAL *real)
+{
+ REAL a,b,c,d;
+ int i,j,k;
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i];
+  b = real[j];
+  real[j] = (a-b);
+  real[i] = (a+b);
+ }
+ mayer_fht(real,n);
+}
+/*
+** FFT and FHT routines
+**  Copyright 1988, 1993; Ron Mayer
+**  
+**  mayer_fht(fz,n);
+**      Does a hartley transform of "n" points in the array "fz".
+**  mayer_fft(n,real,imag)
+**      Does a fourier transform of "n" points of the "real" and
+**      "imag" arrays.
+**  mayer_ifft(n,real,imag)
+**      Does an inverse fourier transform of "n" points of the "real"
+**      and "imag" arrays.
+**  mayer_realfft(n,real)
+**      Does a real-valued fourier transform of "n" points of the
+**      "real" array.  The real part of the transform ends
+**      up in the first half of the array and the imaginary part of the
+**      transform ends up in the second half of the array.
+**  mayer_realifft(n,real)
+**      The inverse of the realfft() routine above.
+**      
+**      
+** NOTE: This routine uses at least 2 patented algorithms, and may be
+**       under the restrictions of a bunch of different organizations.
+**       Although I wrote it completely myself, it is kind of a derivative
+**       of a routine I once authored and released under the GPL, so it
+**       may fall under the free software foundation's restrictions;
+**       it was worked on as a Stanford Univ project, so they claim
+**       some rights to it; it was further optimized at work here, so
+**       I think this company claims parts of it.  The patents are
+**       held by R. Bracewell (the FHT algorithm) and O. Buneman (the
+**       trig generator), both at Stanford Univ.
+**       If it were up to me, I'd say go do whatever you want with it;
+**       but it would be polite to give credit to the following people
+**       if you use this anywhere:
+**           Euler     - probable inventor of the fourier transform.
+**           Gauss     - probable inventor of the FFT.
+**           Hartley   - probable inventor of the hartley transform.
+**           Buneman   - for a really cool trig generator
+**           Mayer(me) - for authoring this particular version and
+**                       including all the optimizations in one package.
+**       Thanks,
+**       Ron Mayer; mayer@acuson.com
+**
+*/
+
+/* This is a slightly modified version of Mayer's contribution; write
+* msp@ucsd.edu for the original code.  Kudos to Mayer for a fine piece
+* of work.  -msp
+*/
+
+#ifdef MSW
+#pragma warning( disable : 4305 )  /* uncast const double to float */
+#pragma warning( disable : 4244 )  /* uncast double to float */
+#pragma warning( disable : 4101 )  /* unused local variables */
+#endif
+
+#define REAL float
+#define GOOD_TRIG
+
+#ifdef GOOD_TRIG
+#else
+#define FAST_TRIG
+#endif
+
+#if defined(GOOD_TRIG)
+#define FHT_SWAP(a,b,t) {(t)=(a);(a)=(b);(b)=(t);}
+#define TRIG_VARS                                                \
+      int t_lam=0;
+#define TRIG_INIT(k,c,s)                                         \
+     {                                                           \
+      int i;                                                     \
+      for (i=2 ; i<=k ; i++)                                     \
+          {coswrk[i]=costab[i];sinwrk[i]=sintab[i];}             \
+      t_lam = 0;                                                 \
+      c = 1;                                                     \
+      s = 0;                                                     \
+     }
+#define TRIG_NEXT(k,c,s)                                         \
+     {                                                           \
+         int i,j;                                                \
+         (t_lam)++;                                              \
+         for (i=0 ; !((1<<i)&t_lam) ; i++);                      \
+         i = k-i;                                                \
+         s = sinwrk[i];                                          \
+         c = coswrk[i];                                          \
+         if (i>1)                                                \
+            {                                                    \
+             for (j=k-i+2 ; (1<<j)&t_lam ; j++);                 \
+             j         = k - j;                                  \
+             sinwrk[i] = halsec[i] * (sinwrk[i-1] + sinwrk[j]);  \
+             coswrk[i] = halsec[i] * (coswrk[i-1] + coswrk[j]);  \
+            }                                                    \
+     }
+#define TRIG_RESET(k,c,s)
+#endif
+
+#if defined(FAST_TRIG)
+#define TRIG_VARS                                        \
+      REAL t_c,t_s;
+#define TRIG_INIT(k,c,s)                                 \
+    {                                                    \
+     t_c  = costab[k];                                   \
+     t_s  = sintab[k];                                   \
+     c    = 1;                                           \
+     s    = 0;                                           \
+    }
+#define TRIG_NEXT(k,c,s)                                 \
+    {                                                    \
+     REAL t = c;                                         \
+     c   = t*t_c - s*t_s;                                \
+     s   = t*t_s + s*t_c;                                \
+    }
+#define TRIG_RESET(k,c,s)
+#endif
+
+static REAL halsec[20]=
+    {
+     0,
+     0,
+     .54119610014619698439972320536638942006107206337801,
+     .50979557910415916894193980398784391368261849190893,
+     .50241928618815570551167011928012092247859337193963,
+     .50060299823519630134550410676638239611758632599591,
+     .50015063602065098821477101271097658495974913010340,
+     .50003765191554772296778139077905492847503165398345,
+     .50000941253588775676512870469186533538523133757983,
+     .50000235310628608051401267171204408939326297376426,
+     .50000058827484117879868526730916804925780637276181,
+     .50000014706860214875463798283871198206179118093251,
+     .50000003676714377807315864400643020315103490883972,
+     .50000000919178552207366560348853455333939112569380,
+     .50000000229794635411562887767906868558991922348920,
+     .50000000057448658687873302235147272458812263401372
+    };
+static REAL costab[20]=
+    {
+     .00000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768847,
+     .92387953251128675612818318939678828682241662586364,
+     .98078528040323044912618223613423903697393373089333,
+     .99518472667219688624483695310947992157547486872985,
+     .99879545620517239271477160475910069444320361470461,
+     .99969881869620422011576564966617219685006108125772,
+     .99992470183914454092164649119638322435060646880221,
+     .99998117528260114265699043772856771617391725094433,
+     .99999529380957617151158012570011989955298763362218,
+     .99999882345170190992902571017152601904826792288976,
+     .99999970586288221916022821773876567711626389934930,
+     .99999992646571785114473148070738785694820115568892,
+     .99999998161642929380834691540290971450507605124278,
+     .99999999540410731289097193313960614895889430318945,
+     .99999999885102682756267330779455410840053741619428
+    };
+static REAL sintab[20]=
+    {
+     1.0000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768846,
+     .38268343236508977172845998403039886676134456248561,
+     .19509032201612826784828486847702224092769161775195,
+     .09801714032956060199419556388864184586113667316749,
+     .04906767432741801425495497694268265831474536302574,
+     .02454122852291228803173452945928292506546611923944,
+     .01227153828571992607940826195100321214037231959176,
+     .00613588464915447535964023459037258091705788631738,
+     .00306795676296597627014536549091984251894461021344,
+     .00153398018628476561230369715026407907995486457522,
+     .00076699031874270452693856835794857664314091945205,
+     .00038349518757139558907246168118138126339502603495,
+     .00019174759731070330743990956198900093346887403385,
+     .00009587379909597734587051721097647635118706561284,
+     .00004793689960306688454900399049465887274686668768
+    };
+static REAL coswrk[20]=
+    {
+     .00000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768847,
+     .92387953251128675612818318939678828682241662586364,
+     .98078528040323044912618223613423903697393373089333,
+     .99518472667219688624483695310947992157547486872985,
+     .99879545620517239271477160475910069444320361470461,
+     .99969881869620422011576564966617219685006108125772,
+     .99992470183914454092164649119638322435060646880221,
+     .99998117528260114265699043772856771617391725094433,
+     .99999529380957617151158012570011989955298763362218,
+     .99999882345170190992902571017152601904826792288976,
+     .99999970586288221916022821773876567711626389934930,
+     .99999992646571785114473148070738785694820115568892,
+     .99999998161642929380834691540290971450507605124278,
+     .99999999540410731289097193313960614895889430318945,
+     .99999999885102682756267330779455410840053741619428
+    };
+static REAL sinwrk[20]=
+    {
+     1.0000000000000000000000000000000000000000000000000,
+     .70710678118654752440084436210484903928483593768846,
+     .38268343236508977172845998403039886676134456248561,
+     .19509032201612826784828486847702224092769161775195,
+     .09801714032956060199419556388864184586113667316749,
+     .04906767432741801425495497694268265831474536302574,
+     .02454122852291228803173452945928292506546611923944,
+     .01227153828571992607940826195100321214037231959176,
+     .00613588464915447535964023459037258091705788631738,
+     .00306795676296597627014536549091984251894461021344,
+     .00153398018628476561230369715026407907995486457522,
+     .00076699031874270452693856835794857664314091945205,
+     .00038349518757139558907246168118138126339502603495,
+     .00019174759731070330743990956198900093346887403385,
+     .00009587379909597734587051721097647635118706561284,
+     .00004793689960306688454900399049465887274686668768
+    };
+
+
+#define SQRT2_2   0.70710678118654752440084436210484
+#define SQRT2   2*0.70710678118654752440084436210484
+
+void mayer_fht(REAL *fz, int n)
+{
+/*  REAL a,b;
+REAL c1,s1,s2,c2,s3,c3,s4,c4;
+ REAL f0,g0,f1,g1,f2,g2,f3,g3; */
+ int  k,k1,k2,k3,k4,kx;
+ REAL *fi,*fn,*gi;
+ TRIG_VARS;
+
+ for (k1=1,k2=0;k1<n;k1++)
+    {
+     REAL aa;
+     for (k=n>>1; (!((k2^=k)&k)); k>>=1);
+     if (k1>k2)
+        {
+             aa=fz[k1];fz[k1]=fz[k2];fz[k2]=aa;
+        }
+    }
+ for ( k=0 ; (1<<k)<n ; k++ );
+ k  &= 1;
+ if (k==0)
+    {
+         for (fi=fz,fn=fz+n;fi<fn;fi+=4)
+            {
+             REAL f0,f1,f2,f3;
+             f1     = fi[0 ]-fi[1 ];
+             f0     = fi[0 ]+fi[1 ];
+             f3     = fi[2 ]-fi[3 ];
+             f2     = fi[2 ]+fi[3 ];
+             fi[2 ] = (f0-f2);  
+             fi[0 ] = (f0+f2);
+             fi[3 ] = (f1-f3);  
+             fi[1 ] = (f1+f3);
+            }
+    }
+ else
+    {
+         for (fi=fz,fn=fz+n,gi=fi+1;fi<fn;fi+=8,gi+=8)
+            {
+             REAL bs1,bc1,bs2,bc2,bs3,bc3,bs4,bc4,
+                bg0,bf0,bf1,bg1,bf2,bg2,bf3,bg3;
+             bc1     = fi[0 ] - gi[0 ];
+             bs1     = fi[0 ] + gi[0 ];
+             bc2     = fi[2 ] - gi[2 ];
+             bs2     = fi[2 ] + gi[2 ];
+             bc3     = fi[4 ] - gi[4 ];
+             bs3     = fi[4 ] + gi[4 ];
+             bc4     = fi[6 ] - gi[6 ];
+             bs4     = fi[6 ] + gi[6 ];
+             bf1     = (bs1 - bs2);     
+             bf0     = (bs1 + bs2);
+             bg1     = (bc1 - bc2);     
+             bg0     = (bc1 + bc2);
+             bf3     = (bs3 - bs4);     
+             bf2     = (bs3 + bs4);
+             bg3     = SQRT2*bc4;               
+             bg2     = SQRT2*bc3;
+             fi[4 ] = bf0 - bf2;
+             fi[0 ] = bf0 + bf2;
+             fi[6 ] = bf1 - bf3;
+             fi[2 ] = bf1 + bf3;
+             gi[4 ] = bg0 - bg2;
+             gi[0 ] = bg0 + bg2;
+             gi[6 ] = bg1 - bg3;
+             gi[2 ] = bg1 + bg3;
+            }
+    }
+ if (n<16) return;
+
+ do
+    {
+     REAL s1,c1;
+     int ii;
+     k  += 2;
+     k1  = 1  << k;
+     k2  = k1 << 1;
+     k4  = k2 << 1;
+     k3  = k2 + k1;
+     kx  = k1 >> 1;
+         fi  = fz;
+         gi  = fi + kx;
+         fn  = fz + n;
+         do
+            {
+             REAL g0,f0,f1,g1,f2,g2,f3,g3;
+             f1      = fi[0 ] - fi[k1];
+             f0      = fi[0 ] + fi[k1];
+             f3      = fi[k2] - fi[k3];
+             f2      = fi[k2] + fi[k3];
+             fi[k2]  = f0         - f2;
+             fi[0 ]  = f0         + f2;
+             fi[k3]  = f1         - f3;
+             fi[k1]  = f1         + f3;
+             g1      = gi[0 ] - gi[k1];
+             g0      = gi[0 ] + gi[k1];
+             g3      = SQRT2  * gi[k3];
+             g2      = SQRT2  * gi[k2];
+             gi[k2]  = g0         - g2;
+             gi[0 ]  = g0         + g2;
+             gi[k3]  = g1         - g3;
+             gi[k1]  = g1         + g3;
+             gi     += k4;
+             fi     += k4;
+            } while (fi<fn);
+     TRIG_INIT(k,c1,s1);
+     for (ii=1;ii<kx;ii++)
+        {
+         REAL c2,s2;
+         TRIG_NEXT(k,c1,s1);
+         c2 = c1*c1 - s1*s1;
+         s2 = 2*(c1*s1);
+             fn = fz + n;
+             fi = fz +ii;
+             gi = fz +k1-ii;
+             do
+                {
+                 REAL a,b,g0,f0,f1,g1,f2,g2,f3,g3;
+                 b       = s2*fi[k1] - c2*gi[k1];
+                 a       = c2*fi[k1] + s2*gi[k1];
+                 f1      = fi[0 ]    - a;
+                 f0      = fi[0 ]    + a;
+                 g1      = gi[0 ]    - b;
+                 g0      = gi[0 ]    + b;
+                 b       = s2*fi[k3] - c2*gi[k3];
+                 a       = c2*fi[k3] + s2*gi[k3];
+                 f3      = fi[k2]    - a;
+                 f2      = fi[k2]    + a;
+                 g3      = gi[k2]    - b;
+                 g2      = gi[k2]    + b;
+                 b       = s1*f2     - c1*g3;
+                 a       = c1*f2     + s1*g3;
+                 fi[k2]  = f0        - a;
+                 fi[0 ]  = f0        + a;
+                 gi[k3]  = g1        - b;
+                 gi[k1]  = g1        + b;
+                 b       = c1*g2     - s1*f3;
+                 a       = s1*g2     + c1*f3;
+                 gi[k2]  = g0        - a;
+                 gi[0 ]  = g0        + a;
+                 fi[k3]  = f1        - b;
+                 fi[k1]  = f1        + b;
+                 gi     += k4;
+                 fi     += k4;
+                } while (fi<fn);
+        }
+     TRIG_RESET(k,c1,s1);
+    } while (k4<n);
+}
+
+void mayer_fft(int n, REAL *real, REAL *imag)
+{
+ REAL a,b,c,d;
+ REAL q,r,s,t;
+ int i,j,k;
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i]; b = real[j];  q=a+b; r=a-b;
+  c = imag[i]; d = imag[j];  s=c+d; t=c-d;
+  real[i] = (q+t)*.5; real[j] = (q-t)*.5;
+  imag[i] = (s-r)*.5; imag[j] = (s+r)*.5;
+ }
+ mayer_fht(real,n);
+ mayer_fht(imag,n);
+}
+
+void mayer_ifft(int n, REAL *real, REAL *imag)
+{
+ REAL a,b,c,d;
+ REAL q,r,s,t;
+ int i,j,k;
+ mayer_fht(real,n);
+ mayer_fht(imag,n);
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i]; b = real[j];  q=a+b; r=a-b;
+  c = imag[i]; d = imag[j];  s=c+d; t=c-d;
+  imag[i] = (s+r)*0.5;  imag[j] = (s-r)*0.5;
+  real[i] = (q-t)*0.5;  real[j] = (q+t)*0.5;
+ }
+}
+
+void mayer_realfft(int n, REAL *real)
+{
+ REAL a,b,c,d;
+ int i,j,k;
+ mayer_fht(real,n);
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i];
+  b = real[j];
+  real[j] = (a-b)*0.5;
+  real[i] = (a+b)*0.5;
+ }
+}
+
+void mayer_realifft(int n, REAL *real)
+{
+ REAL a,b,c,d;
+ int i,j,k;
+ for (i=1,j=n-1,k=n/2;i<k;i++,j--) {
+  a = real[i];
+  b = real[j];
+  real[j] = (a-b);
+  real[i] = (a+b);
+ }
+ mayer_fht(real,n);
+}