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/* This is the FFT routine taken from PureData, a great piece of
software by Miller S. Puckette.
http://crca.ucsd.edu/~msp/software.html */
/*
** 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
*/
#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;
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;
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);
}