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authorMiller Puckette <millerpuckette@users.sourceforge.net>2007-07-29 20:17:07 +0000
committerMiller Puckette <millerpuckette@users.sourceforge.net>2007-07-29 20:17:07 +0000
commit818a869255441dd5deffcb1bd82626ee6f8a6bab (patch)
tree438ea14c9be6bc16ffa3dfc017d1cdc2f4e9324e /pd
parent5e1af062fc473cfb998d2b00e761c655dec88f2c (diff)
add files that didn't seem to be uploaded
svn path=/trunk/; revision=8254
Diffstat (limited to 'pd')
-rw-r--r--pd/doc/3.audio.examples/A07.fusion.pd76
-rw-r--r--pd/doc/3.audio.examples/A08.beating.pd41
-rw-r--r--pd/doc/3.audio.examples/A09.frequency.mod.pd54
-rw-r--r--pd/doc/3.audio.examples/A10.review.pd37
-rw-r--r--pd/src/d_fft_fftsg.c3462
-rw-r--r--pd/src/d_fft_fftw.c93
-rw-r--r--pd/src/d_fftsg_h.c3447
7 files changed, 7210 insertions, 0 deletions
diff --git a/pd/doc/3.audio.examples/A07.fusion.pd b/pd/doc/3.audio.examples/A07.fusion.pd
new file mode 100644
index 00000000..e391099c
--- /dev/null
+++ b/pd/doc/3.audio.examples/A07.fusion.pd
@@ -0,0 +1,76 @@
+#N canvas 18 14 650 653 12;
+#X floatatom 32 60 0 0 0 0 - - -;
+#X obj 32 86 mtof;
+#X obj 32 323 output~;
+#X msg 32 34 60;
+#X text 67 63 <-- choose a pitch;
+#X text 68 34 <-- reset to middle C;
+#X obj 32 154 osc~;
+#X obj 73 130 * 2;
+#X obj 73 154 osc~;
+#X obj 137 154 osc~;
+#X obj 137 130 * 3;
+#X obj 201 155 osc~;
+#X obj 201 131 * 4;
+#X obj 137 179 *~ 0.2;
+#X obj 33 289 +~;
+#X obj 74 259 *~;
+#X obj 109 260 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0
+1;
+#X obj 74 210 +~;
+#X obj 74 234 +~;
+#X text 133 7 Adding sinusoids to make a complex tone;
+#N canvas 0 0 450 300 graph1 0;
+#X array tab.01.07 882 float 0;
+#X coords 0 1.02 881 -1.02 200 130 1;
+#X restore 426 222 graph;
+#X msg 116 295 bang;
+#X text 165 294 <-- click to graph;
+#X text 260 129 frequencies of harmonics;
+#X text 260 155 four oscillators;
+#X text 264 181 adjust amplitudes;
+#X text 109 233 add the three overtones together;
+#X obj 116 324 tabwrite~ tab.01.07;
+#X text 381 632 updated for Pd version 0.40.;
+#X text 429 360 ---- 0.02 seconds ----;
+#X obj 73 179 *~ 0.1;
+#X obj 201 179 *~ 0.5;
+#X text 129 259 <-- overtones ON/OFF;
+#X text 29 580 To hear the output \, choose a pitch (at top) \, optionally
+click the "overtones" control \, and mouse up the output volume. Click
+the "bang" message to graph it.;
+#X text 31 392 A simple way to build non-sinusoidal \, periodic musical
+tones is to sum a series of harmonically tuned sinusoids. Here the
+four oscillators have frequencies in a 1:2:3:4 ratio (the three "*"
+objects compute the second \, third \, and fourth one). The amplitudes
+are adjusted by the "*~ 0.1" \, etc. \, objects. Note that \, since
+the frequency (from the "mtof") is a message \, a "*" box suffices
+to operate on it \, but the oscillator's output \, being an audio signal
+\, needs "*~" instead. The control marked "overtones ON/OFF" is a toggle
+switch. Click to turn it on and off. Of the overtones are "off" you
+hear only a sinusoid from the forst oscillator. If on \, you hear all
+four.;
+#X connect 0 0 1 0;
+#X connect 1 0 6 0;
+#X connect 1 0 7 0;
+#X connect 1 0 10 0;
+#X connect 1 0 12 0;
+#X connect 3 0 0 0;
+#X connect 6 0 14 0;
+#X connect 7 0 8 0;
+#X connect 8 0 30 0;
+#X connect 9 0 13 0;
+#X connect 10 0 9 0;
+#X connect 11 0 31 0;
+#X connect 12 0 11 0;
+#X connect 13 0 17 1;
+#X connect 14 0 2 0;
+#X connect 14 0 2 1;
+#X connect 14 0 27 0;
+#X connect 15 0 14 1;
+#X connect 16 0 15 1;
+#X connect 17 0 18 0;
+#X connect 18 0 15 0;
+#X connect 21 0 27 0;
+#X connect 30 0 17 0;
+#X connect 31 0 18 1;
diff --git a/pd/doc/3.audio.examples/A08.beating.pd b/pd/doc/3.audio.examples/A08.beating.pd
new file mode 100644
index 00000000..e7657450
--- /dev/null
+++ b/pd/doc/3.audio.examples/A08.beating.pd
@@ -0,0 +1,41 @@
+#N canvas 53 63 581 571 12;
+#X obj 31 212 output~;
+#X obj 32 178 +~;
+#X text 320 537 updated for Pd version 0.40.;
+#X obj 32 110 +~;
+#X obj 187 105 +~;
+#X obj 187 52 osc~ 440;
+#X obj 32 57 osc~ 330;
+#X obj 53 81 osc~ 330.2;
+#X obj 208 75 osc~ 440.33;
+#X obj 342 102 +~;
+#X obj 343 52 osc~ 587;
+#X obj 364 75 osc~ 587.25;
+#X obj 33 147 +~;
+#X text 133 7 Beating between closely tuned sinusoids;
+#X text 33 280 In each of the three pairs of oscillators above \, the
+two frequencies are within 1/3 Hz or closer (for example \, the leftmost
+ones are close to 330 Hz but separated by 1/5 Hz.) The result is a
+gradual change in amplitude as the phases of the two slip against each
+other. This is called beating. More complex beating pattenrs may be
+made by using three or more oscillators. Also their amplitudes need
+not be equal (as they are here).;
+#X text 31 407 They are all summed using "+~" boxes. They could have
+been summed in any order ("+~" is commutative for practical purposes)
+but here they are added in pairs to emphasize the relationships between
+them.;
+#X text 30 474 In contrast to the previous example \, the oscillators
+are not tuned to the overtone series (ratios 1:2:3:4...) and so the
+frequencies 330 \, 440 \, and 587 are heard separately.;
+#X connect 1 0 0 0;
+#X connect 1 0 0 1;
+#X connect 3 0 12 0;
+#X connect 4 0 12 1;
+#X connect 5 0 4 0;
+#X connect 6 0 3 0;
+#X connect 7 0 3 1;
+#X connect 8 0 4 1;
+#X connect 9 0 1 1;
+#X connect 10 0 9 0;
+#X connect 11 0 9 1;
+#X connect 12 0 1 0;
diff --git a/pd/doc/3.audio.examples/A09.frequency.mod.pd b/pd/doc/3.audio.examples/A09.frequency.mod.pd
new file mode 100644
index 00000000..aedb1cc1
--- /dev/null
+++ b/pd/doc/3.audio.examples/A09.frequency.mod.pd
@@ -0,0 +1,54 @@
+#N canvas 92 96 760 640 12;
+#X obj 259 168 *~;
+#X floatatom 259 83 0 0 0 0 - - -;
+#X floatatom 169 118 0 0 0 0 - - -;
+#X obj 169 188 +~;
+#N canvas 0 0 450 300 graph1 0;
+#X array fm-output 441 float 0;
+#X coords 0 1.02 440 -1.02 200 130 1;
+#X restore 527 40 graph;
+#X msg 244 228 bang;
+#X text 286 228 <-- click to graph;
+#X obj 244 252 tabwrite~ fm-output;
+#X floatatom 281 138 0 0 0 0 - - -;
+#X text 166 75 carrier;
+#X text 165 93 frequency;
+#X text 244 59 frequency;
+#X text 245 42 modulation;
+#X text 33 8 FREQUENCY MODULATION ("FM") USING TWO OSCILLATORS;
+#X obj 168 232 osc~;
+#X text 52 214 "carrier";
+#X text 34 232 oscillator -->;
+#X text 47 149 add modulator;
+#X text 46 167 to carrier;
+#X text 44 186 frequency -->;
+#X text 320 150 index;
+#X text 322 131 modulation;
+#X obj 259 108 osc~;
+#X text 531 172 --- 0.01 seconds ----;
+#X text 53 443 To get the FM sound \, set all three of carrier frequency
+\, modulation frequency \, and modulation index in the hundreds. Note
+that you get a timbral change as you sweep modulation index \, because
+this changes the amplitudes of the components of the output sound but
+not their frequencies.;
+#X obj 167 270 output~;
+#X text 489 613 updated for Pd version 0.37;
+#X text 54 332 This patch shows the classical FM synthesis technique
+developed by John Chowning. It's nothing but an oscillator with vibrato
+controlled by another "modulation" oscillator. First \, to understand
+the patch \, set carrier frequency to 400 or so \, modulation frequency
+between 5 and 10 \, and try modulation index values between 0 and 400
+\, say. You'll hear a sine wave with vibrato.;
+#X text 55 526 The component frequencies are equal to the carrier frequency
+\, plus or minus multiples of the modulator frequency. A more complete
+discussion of FM occurs in part 5 of this series.;
+#X connect 0 0 3 1;
+#X connect 1 0 22 0;
+#X connect 2 0 3 0;
+#X connect 3 0 14 0;
+#X connect 5 0 7 0;
+#X connect 8 0 0 1;
+#X connect 14 0 7 0;
+#X connect 14 0 25 0;
+#X connect 14 0 25 1;
+#X connect 22 0 0 0;
diff --git a/pd/doc/3.audio.examples/A10.review.pd b/pd/doc/3.audio.examples/A10.review.pd
new file mode 100644
index 00000000..fbaaee43
--- /dev/null
+++ b/pd/doc/3.audio.examples/A10.review.pd
@@ -0,0 +1,37 @@
+#N canvas 36 68 652 461 12;
+#X text 157 10 PART 1 REVIEW;
+#X obj 67 113 tabwrite~;
+#X obj 67 87 line~;
+#X obj 71 220 +;
+#X obj 67 61 +~;
+#X obj 67 139 osc~;
+#X obj 72 319 r;
+#X obj 72 295 s;
+#X obj 71 269 inlet;
+#X obj 114 245 mtof;
+#X obj 71 244 ftom;
+#X obj 122 269 outlet;
+#X obj 67 164 dac~;
+#X text 27 34 So far we've seen these audio ("tilde") objects:;
+#X text 124 86 -- ramp generator;
+#X text 158 113 -- sampler (which we've only used for graphing so far)
+;
+#X text 113 165 -- audio output ("digital/analog converter" -- a misnomer)
+;
+#X text 34 193 ... and these "control" objects:;
+#X text 162 243 -- frequency to pitch conversion;
+#X text 184 270 -- input and output to a subpatch;
+#X text 108 296 ("send") -- wireless message sending;
+#X text 109 321 ("receive") ... and receiving;
+#X text 107 60 (etc.) -- arithmetic on audio signals;
+#X text 109 218 (etc.) -- arithmetic;
+#X text 385 426 updated for Pd version 0.40.;
+#X text 112 139 -- sinusoidal oscillator;
+#X obj 74 418 tgl 15 0 empty empty empty 0 -6 0 8 -262144 -1 -1 0 1
+;
+#X text 97 416 -- toggle switch;
+#X floatatom 74 395 0 0 0 0 - - -;
+#X text 109 394 -- number box;
+#X msg 74 372;
+#X text 111 372 -- message box;
+#X text 43 346 ... and these other (non-object) boxes:;
diff --git a/pd/src/d_fft_fftsg.c b/pd/src/d_fft_fftsg.c
new file mode 100644
index 00000000..4d89ef7b
--- /dev/null
+++ b/pd/src/d_fft_fftsg.c
@@ -0,0 +1,3462 @@
+/****************** begin Pd-specific prologue ***********************/
+
+/*
+This is the file, "fftsg.c" from the OOURA FFT package. The copyright notice
+from Ooura's README is:
+
+Copyright:
+ Copyright(C) 1996-2001 Takuya OOURA
+ email: ooura@mmm.t.u-tokyo.ac.jp
+ download: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html
+ You may use, copy, modify this code for any purpose and
+ without fee. You may distribute this ORIGINAL package.
+
+After the following prologue, the code is exactly Ooura's original, which I
+believe the above notice permits me to redistribute. See Ooura's website
+for another, more permissive-sounding copyright notice. -MSP
+*/
+
+/* ---------- Pd interface to OOURA FFT; imitate Mayer API ---------- */
+#include "m_pd.h"
+#ifdef MSW
+#include <malloc.h>
+#else
+#include <alloca.h>
+#endif
+
+#define FFTFLT double
+void cdft(int, int, double *, int *, double *);
+void rdft(int, int, double *, int *, double *);
+
+int ilog2(int n);
+
+static int ooura_maxn;
+static int *ooura_bitrev;
+static int ooura_bitrevsize;
+static FFTFLT *ooura_costab;
+
+static int ooura_init( int n)
+{
+ n = (1 << ilog2(n));
+ if (n < 64)
+ return (0);
+ if (n > ooura_maxn)
+ {
+ post("init");
+ if (ooura_maxn)
+ {
+ t_freebytes(ooura_bitrev, ooura_bitrevsize);
+ t_freebytes(ooura_costab, ooura_maxn * sizeof(FFTFLT) / 2);
+ }
+ ooura_bitrevsize = sizeof(int *) * (2 + (1 << (ilog2(n)/2)));
+ ooura_bitrev = (int *)t_getbytes(ooura_bitrevsize);
+ ooura_bitrev[0] = 0;
+ if (!ooura_bitrev)
+ {
+ error("out of memory allocating FFT buffer");
+ ooura_maxn = 0;
+ return (0);
+ }
+ ooura_costab = (FFTFLT *)t_getbytes(n * sizeof(FFTFLT)/2);
+ if (!ooura_costab)
+ {
+ error("out of memory allocating FFT buffer");
+ t_freebytes(ooura_bitrev, ooura_bitrevsize);
+ ooura_maxn = 0;
+ return (0);
+ }
+ ooura_maxn = n;
+ ooura_bitrev[0] = 0;
+ }
+ return (1);
+}
+
+EXTERN void mayer_fht(float *fz, int n)
+{
+ post("FHT: not yet implemented");
+}
+
+EXTERN void mayer_dofft(float *fz1, float *fz2, int n, int sgn)
+{
+ FFTFLT *buf, *fp3;
+ int i;
+ float *fp1, *fp2;
+ buf = alloca(n * (2 * sizeof(FFTFLT)));
+ if (!ooura_init(n))
+ return;
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
+ {
+ fp3[0] = *fp1++;
+ fp3[1] = *fp2++;
+ fp3 += 2;
+ }
+ cdft(2*n, sgn, buf, ooura_bitrev, ooura_costab);
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = buf; i < n; i++)
+ {
+ *fp1++ = fp3[0];
+ *fp2++ = fp3[1];
+ fp3 += 2;
+ }
+}
+
+EXTERN void mayer_fft(int n, float *fz1, float *fz2)
+{
+ mayer_dofft(fz1, fz2, n, -1);
+}
+
+EXTERN void mayer_ifft(int n, float *fz1, float *fz2)
+{
+ mayer_dofft(fz1, fz2, n, 1);
+}
+
+EXTERN void mayer_realfft(int n, float *fz)
+{
+ FFTFLT *buf, *fp3;
+ int i, nover2 = n/2;
+ float *fp1, *fp2;
+ buf = alloca(n * sizeof(FFTFLT));
+ if (!ooura_init(n))
+ return;
+ for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
+ buf[i] = fz[i];
+ rdft(n, 1, buf, ooura_bitrev, ooura_costab);
+ fz[0] = buf[0];
+ fz[nover2] = buf[1];
+ for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
+ i++, fp1++, fp2--, fp3 += 2)
+ *fp1 = fp3[0], *fp2 = fp3[1];
+}
+
+EXTERN void mayer_realifft(int n, float *fz)
+{
+ FFTFLT *buf, *fp3;
+ int i, nover2 = n/2;
+ float *fp1, *fp2;
+ buf = alloca(n * sizeof(FFTFLT));
+ if (!ooura_init(n))
+ return;
+ buf[0] = fz[0];
+ buf[1] = fz[nover2];
+ for (i = 1, fp1 = fz+1, fp2 = fz+(n-1), fp3 = buf+2; i < nover2;
+ i++, fp1++, fp2--, fp3 += 2)
+ fp3[0] = *fp1, fp3[1] = *fp2;
+ rdft(n, -1, buf, ooura_bitrev, ooura_costab);
+ for (i = 0, fp1 = fz, fp3 = buf; i < n; i++, fp1++, fp3++)
+ fz[i] = 2*buf[i];
+}
+
+/****************** end Pd-specific prologue ***********************/
+/*
+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, double *, int *, double *);
+ void rdft(int, int, double *, int *, double *);
+ void ddct(int, int, double *, int *, double *);
+ void ddst(int, int, double *, int *, double *);
+ void dfct(int, double *, double *, int *, double *);
+ void dfst(int, double *, double *, int *, double *);
+macro definitions
+ USE_CDFT_PTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
+ USE_CDFT_WINTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
+
+
+-------- 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 (double *)
+ 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 (double *)
+ 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 (double *)
+ <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 (double *)
+ 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 (double *)
+ 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 (double *)
+ 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 (double *)
+ <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 (double *)
+ 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 (double *)
+ output data
+ a[k] = C[k], 0<=k<=n
+ t[0...n/2] :work area (double *)
+ 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 (double *)
+ 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 (double *)
+ output data
+ a[k] = S[k], 0<k<n
+ (a[0] is used for work area)
+ t[0...n/2-1] :work area (double *)
+ 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 (double *)
+ 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, double *a, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ int nw;
+
+ nw = ip[0];
+ if (n > (nw << 2)) {
+ nw = n >> 2;
+ makewt(nw, ip, w);
+ }
+ if (isgn >= 0) {
+ cftfsub(n, a, ip, nw, w);
+ } else {
+ cftbsub(n, a, ip, nw, w);
+ }
+}
+
+
+void rdft(int n, int isgn, double *a, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ int nw, nc;
+ double 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, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip, 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, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip, nw, w);
+ }
+ }
+}
+
+
+void ddct(int n, int isgn, double *a, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ void dctsub(int n, double *a, int nc, double *c);
+ int j, nw, nc;
+ double 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, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip, nw, w);
+ }
+ }
+ dctsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip, 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, double *a, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void cftbsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void rftbsub(int n, double *a, int nc, double *c);
+ void dstsub(int n, double *a, int nc, double *c);
+ int j, nw, nc;
+ double 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, nw, w);
+ } else if (n == 4) {
+ cftbsub(n, a, ip, nw, w);
+ }
+ }
+ dstsub(n, a, nc, w + nw);
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a, ip, nw, w);
+ rftfsub(n, a, nc, w + nw);
+ } else if (n == 4) {
+ cftfsub(n, a, ip, 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, double *a, double *t, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void dctsub(int n, double *a, int nc, double *c);
+ int j, k, l, m, mh, nw, nc;
+ double 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, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip, 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, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip, 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, double *a, double *t, int *ip, double *w)
+{
+ void makewt(int nw, int *ip, double *w);
+ void makect(int nc, int *ip, double *c);
+ void cftfsub(int n, double *a, int *ip, int nw, double *w);
+ void rftfsub(int n, double *a, int nc, double *c);
+ void dstsub(int n, double *a, int nc, double *c);
+ int j, k, l, m, mh, nw, nc;
+ double 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, nw, w);
+ rftfsub(m, a, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, a, ip, 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, nw, w);
+ rftfsub(m, t, nc, w + nw);
+ } else if (m == 4) {
+ cftfsub(m, t, ip, 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, double *w)
+{
+ void makeipt(int nw, int *ip);
+ int j, nwh, nw0, nw1;
+ double 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] = cos(delta * 2);
+ w[3] = sin(delta * 2);
+ } else if (nwh > 4) {
+ makeipt(nw, ip);
+ 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];
+ wk1i = w[nw0 + 5];
+ w[nw1 + 2] = wk1r;
+ w[nw1 + 3] = wk1i;
+ } else 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 makeipt(int nw, int *ip)
+{
+ int j, l, m, m2, p, q;
+
+ ip[2] = 0;
+ ip[3] = 16;
+ m = 2;
+ for (l = nw; l > 32; l >>= 2) {
+ m2 = m << 1;
+ q = m2 << 3;
+ for (j = m; j < m2; j++) {
+ p = ip[j] << 2;
+ ip[m + j] = p;
+ ip[m2 + j] = p + q;
+ }
+ m = m2;
+ }
+}
+
+
+void makect(int nc, int *ip, double *c)
+{
+ int j, nch;
+ double 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 -------- */
+
+
+#ifdef USE_CDFT_PTHREADS
+#define USE_CDFT_THREADS
+#ifndef CDFT_THREADS_BEGIN_N
+#define CDFT_THREADS_BEGIN_N 8192
+#endif
+#ifndef CDFT_4THREADS_BEGIN_N
+#define CDFT_4THREADS_BEGIN_N 65536
+#endif
+#include <pthread.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define cdft_thread_t pthread_t
+#define cdft_thread_create(thp,func,argp) { \
+ if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#define cdft_thread_wait(th) { \
+ if (pthread_join(th, NULL) != 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#endif /* USE_CDFT_PTHREADS */
+
+
+#ifdef USE_CDFT_WINTHREADS
+#define USE_CDFT_THREADS
+#ifndef CDFT_THREADS_BEGIN_N
+#define CDFT_THREADS_BEGIN_N 32768
+#endif
+#ifndef CDFT_4THREADS_BEGIN_N
+#define CDFT_4THREADS_BEGIN_N 524288
+#endif
+#include <windows.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define cdft_thread_t HANDLE
+#define cdft_thread_create(thp,func,argp) { \
+ DWORD thid; \
+ *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
+ if (*(thp) == 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#define cdft_thread_wait(th) { \
+ WaitForSingleObject(th, INFINITE); \
+ CloseHandle(th); \
+}
+#endif /* USE_CDFT_WINTHREADS */
+
+
+void cftfsub(int n, double *a, int *ip, int nw, double *w)
+{
+ void bitrv2(int n, int *ip, double *a);
+ void bitrv216(double *a);
+ void bitrv208(double *a);
+ void cftf1st(int n, double *a, double *w);
+ void cftrec4(int n, double *a, int nw, double *w);
+ void cftleaf(int n, int isplt, double *a, int nw, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftf161(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf040(double *a);
+ void cftx020(double *a);
+#ifdef USE_CDFT_THREADS
+ void cftrec4_th(int n, double *a, int nw, double *w);
+#endif /* USE_CDFT_THREADS */
+
+ if (n > 8) {
+ if (n > 32) {
+ cftf1st(n, a, &w[nw - (n >> 2)]);
+#ifdef USE_CDFT_THREADS
+ if (n > CDFT_THREADS_BEGIN_N) {
+ cftrec4_th(n, a, nw, w);
+ } else
+#endif /* USE_CDFT_THREADS */
+ if (n > 512) {
+ cftrec4(n, a, nw, w);
+ } else if (n > 128) {
+ cftleaf(n, 1, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2(n, ip, a);
+ } else 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, double *a, int *ip, int nw, double *w)
+{
+ void bitrv2conj(int n, int *ip, double *a);
+ void bitrv216neg(double *a);
+ void bitrv208neg(double *a);
+ void cftb1st(int n, double *a, double *w);
+ void cftrec4(int n, double *a, int nw, double *w);
+ void cftleaf(int n, int isplt, double *a, int nw, double *w);
+ void cftfx41(int n, double *a, int nw, double *w);
+ void cftf161(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftb040(double *a);
+ void cftx020(double *a);
+#ifdef USE_CDFT_THREADS
+ void cftrec4_th(int n, double *a, int nw, double *w);
+#endif /* USE_CDFT_THREADS */
+
+ if (n > 8) {
+ if (n > 32) {
+ cftb1st(n, a, &w[nw - (n >> 2)]);
+#ifdef USE_CDFT_THREADS
+ if (n > CDFT_THREADS_BEGIN_N) {
+ cftrec4_th(n, a, nw, w);
+ } else
+#endif /* USE_CDFT_THREADS */
+ if (n > 512) {
+ cftrec4(n, a, nw, w);
+ } else if (n > 128) {
+ cftleaf(n, 1, a, nw, w);
+ } else {
+ cftfx41(n, a, nw, w);
+ }
+ bitrv2conj(n, ip, a);
+ } else 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, double *a)
+{
+ int j, j1, k, k1, l, m, nh, nm;
+ double xr, xi, yr, yi;
+
+ m = 1;
+ for (l = n >> 2; l > 8; l >>= 2) {
+ m <<= 1;
+ }
+ nh = n >> 1;
+ nm = 4 * m;
+ if (l == 8) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 4 * j + 2 * ip[m + k];
+ k1 = 4 * k + 2 * ip[m + 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 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 += nh;
+ k1 += 2;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 -= nm;
+ k1 += nm;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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;
+ k1 += nh;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 -= nm;
+ k1 += nm;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 = 4 * k + 2 * ip[m + k];
+ j1 = k1 + 2;
+ k1 += nh;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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;
+ k1 -= nh;
+ 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 += nh + 2;
+ k1 += nh + 2;
+ 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 -= nh - nm;
+ k1 += 2 * nm - 2;
+ 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 = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 4 * j + ip[m + k];
+ k1 = 4 * k + ip[m + 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 += nm;
+ k1 += nm;
+ 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 += nh;
+ k1 += 2;
+ 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 -= nm;
+ k1 -= nm;
+ 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;
+ k1 += nh;
+ 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 += nm;
+ k1 += nm;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= nm;
+ k1 -= nm;
+ 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 = 4 * k + ip[m + k];
+ j1 = k1 + 2;
+ k1 += nh;
+ 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 += nm;
+ k1 += nm;
+ 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, double *a)
+{
+ int j, j1, k, k1, l, m, nh, nm;
+ double xr, xi, yr, yi;
+
+ m = 1;
+ for (l = n >> 2; l > 8; l >>= 2) {
+ m <<= 1;
+ }
+ nh = n >> 1;
+ nm = 4 * m;
+ if (l == 8) {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 4 * j + 2 * ip[m + k];
+ k1 = 4 * k + 2 * ip[m + 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 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 += nh;
+ k1 += 2;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 -= nm;
+ k1 += nm;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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;
+ k1 += nh;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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 += nm;
+ k1 += 2 * nm;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 -= nm;
+ k1 += nm;
+ 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 -= nm;
+ k1 -= 2 * nm;
+ 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 = 4 * k + 2 * ip[m + k];
+ j1 = k1 + 2;
+ k1 += nh;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ j1 += nm;
+ k1 += 2 * nm;
+ 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 += nm;
+ k1 -= nm;
+ 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;
+ k1 -= nh;
+ 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 += nh + 2;
+ k1 += nh + 2;
+ 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 -= nh - nm;
+ k1 += 2 * nm - 2;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ }
+ } else {
+ for (k = 0; k < m; k++) {
+ for (j = 0; j < k; j++) {
+ j1 = 4 * j + ip[m + k];
+ k1 = 4 * k + ip[m + 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 += nm;
+ k1 += nm;
+ 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 += nh;
+ k1 += 2;
+ 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 -= nm;
+ k1 -= nm;
+ 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;
+ k1 += nh;
+ 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 += nm;
+ k1 += nm;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= nm;
+ k1 -= nm;
+ 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 = 4 * k + ip[m + k];
+ j1 = k1 + 2;
+ k1 += nh;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ j1 += nm;
+ k1 += nm;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ }
+ }
+}
+
+
+void bitrv216(double *a)
+{
+ double 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(double *a)
+{
+ double 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(double *a)
+{
+ double 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(double *a)
+{
+ double 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, double *a, double *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ double 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, double *a, double *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i;
+ double 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;
+}
+
+
+#ifdef USE_CDFT_THREADS
+struct cdft_arg_st {
+ int n0;
+ int n;
+ double *a;
+ int nw;
+ double *w;
+};
+typedef struct cdft_arg_st cdft_arg_t;
+
+
+void cftrec4_th(int n, double *a, int nw, double *w)
+{
+ void *cftrec1_th(void *p);
+ void *cftrec2_th(void *p);
+ int i, idiv4, m, nthread;
+ cdft_thread_t th[4];
+ cdft_arg_t ag[4];
+
+ nthread = 2;
+ idiv4 = 0;
+ m = n >> 1;
+ if (n > CDFT_4THREADS_BEGIN_N) {
+ nthread = 4;
+ idiv4 = 1;
+ m >>= 1;
+ }
+ for (i = 0; i < nthread; i++) {
+ ag[i].n0 = n;
+ ag[i].n = m;
+ ag[i].a = &a[i * m];
+ ag[i].nw = nw;
+ ag[i].w = w;
+ if (i != idiv4) {
+ cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
+ } else {
+ cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
+ }
+ }
+ for (i = 0; i < nthread; i++) {
+ cdft_thread_wait(th[i]);
+ }
+}
+
+
+void *cftrec1_th(void *p)
+{
+ int cfttree(int n, int j, int k, double *a, int nw, double *w);
+ void cftleaf(int n, int isplt, double *a, int nw, double *w);
+ void cftmdl1(int n, double *a, double *w);
+ int isplt, j, k, m, n, n0, nw;
+ double *a, *w;
+
+ n0 = ((cdft_arg_t *) p)->n0;
+ n = ((cdft_arg_t *) p)->n;
+ a = ((cdft_arg_t *) p)->a;
+ nw = ((cdft_arg_t *) p)->nw;
+ w = ((cdft_arg_t *) p)->w;
+ m = n0;
+ while (m > 512) {
+ m >>= 2;
+ cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
+ }
+ cftleaf(m, 1, &a[n - m], nw, w);
+ k = 0;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a, nw, w);
+ cftleaf(m, isplt, &a[j - m], nw, w);
+ }
+ return (void *) 0;
+}
+
+
+void *cftrec2_th(void *p)
+{
+ int cfttree(int n, int j, int k, double *a, int nw, double *w);
+ void cftleaf(int n, int isplt, double *a, int nw, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ int isplt, j, k, m, n, n0, nw;
+ double *a, *w;
+
+ n0 = ((cdft_arg_t *) p)->n0;
+ n = ((cdft_arg_t *) p)->n;
+ a = ((cdft_arg_t *) p)->a;
+ nw = ((cdft_arg_t *) p)->nw;
+ w = ((cdft_arg_t *) p)->w;
+ k = 1;
+ m = n0;
+ while (m > 512) {
+ m >>= 2;
+ k <<= 2;
+ cftmdl2(m, &a[n - m], &w[nw - m]);
+ }
+ cftleaf(m, 0, &a[n - m], nw, w);
+ k >>= 1;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a, nw, w);
+ cftleaf(m, isplt, &a[j - m], nw, w);
+ }
+ return (void *) 0;
+}
+#endif /* USE_CDFT_THREADS */
+
+
+void cftrec4(int n, double *a, int nw, double *w)
+{
+ int cfttree(int n, int j, int k, double *a, int nw, double *w);
+ void cftleaf(int n, int isplt, double *a, int nw, double *w);
+ void cftmdl1(int n, double *a, double *w);
+ int isplt, j, k, m;
+
+ m = n;
+ while (m > 512) {
+ m >>= 2;
+ cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
+ }
+ cftleaf(m, 1, &a[n - m], nw, w);
+ k = 0;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a, nw, w);
+ cftleaf(m, isplt, &a[j - m], nw, w);
+ }
+}
+
+
+int cfttree(int n, int j, int k, double *a, int nw, double *w)
+{
+ void cftmdl1(int n, double *a, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ int i, isplt, m;
+
+ if ((k & 3) != 0) {
+ isplt = k & 1;
+ if (isplt != 0) {
+ cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]);
+ } else {
+ cftmdl2(n, &a[j - n], &w[nw - n]);
+ }
+ } else {
+ m = n;
+ for (i = k; (i & 3) == 0; i >>= 2) {
+ m <<= 2;
+ }
+ isplt = i & 1;
+ if (isplt != 0) {
+ while (m > 128) {
+ cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]);
+ m >>= 2;
+ }
+ } else {
+ while (m > 128) {
+ cftmdl2(m, &a[j - m], &w[nw - m]);
+ m >>= 2;
+ }
+ }
+ }
+ return isplt;
+}
+
+
+void cftleaf(int n, int isplt, double *a, int nw, double *w)
+{
+ void cftmdl1(int n, double *a, double *w);
+ void cftmdl2(int n, double *a, double *w);
+ void cftf161(double *a, double *w);
+ void cftf162(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf082(double *a, double *w);
+
+ if (n == 512) {
+ cftmdl1(128, a, &w[nw - 64]);
+ cftf161(a, &w[nw - 8]);
+ cftf162(&a[32], &w[nw - 32]);
+ cftf161(&a[64], &w[nw - 8]);
+ cftf161(&a[96], &w[nw - 8]);
+ cftmdl2(128, &a[128], &w[nw - 128]);
+ cftf161(&a[128], &w[nw - 8]);
+ cftf162(&a[160], &w[nw - 32]);
+ cftf161(&a[192], &w[nw - 8]);
+ cftf162(&a[224], &w[nw - 32]);
+ cftmdl1(128, &a[256], &w[nw - 64]);
+ cftf161(&a[256], &w[nw - 8]);
+ cftf162(&a[288], &w[nw - 32]);
+ cftf161(&a[320], &w[nw - 8]);
+ cftf161(&a[352], &w[nw - 8]);
+ if (isplt != 0) {
+ cftmdl1(128, &a[384], &w[nw - 64]);
+ cftf161(&a[480], &w[nw - 8]);
+ } else {
+ cftmdl2(128, &a[384], &w[nw - 128]);
+ cftf162(&a[480], &w[nw - 32]);
+ }
+ cftf161(&a[384], &w[nw - 8]);
+ cftf162(&a[416], &w[nw - 32]);
+ cftf161(&a[448], &w[nw - 8]);
+ } else {
+ cftmdl1(64, a, &w[nw - 32]);
+ cftf081(a, &w[nw - 8]);
+ cftf082(&a[16], &w[nw - 8]);
+ cftf081(&a[32], &w[nw - 8]);
+ cftf081(&a[48], &w[nw - 8]);
+ cftmdl2(64, &a[64], &w[nw - 64]);
+ cftf081(&a[64], &w[nw - 8]);
+ cftf082(&a[80], &w[nw - 8]);
+ cftf081(&a[96], &w[nw - 8]);
+ cftf082(&a[112], &w[nw - 8]);
+ cftmdl1(64, &a[128], &w[nw - 32]);
+ cftf081(&a[128], &w[nw - 8]);
+ cftf082(&a[144], &w[nw - 8]);
+ cftf081(&a[160], &w[nw - 8]);
+ cftf081(&a[176], &w[nw - 8]);
+ if (isplt != 0) {
+ cftmdl1(64, &a[192], &w[nw - 32]);
+ cftf081(&a[240], &w[nw - 8]);
+ } else {
+ cftmdl2(64, &a[192], &w[nw - 64]);
+ cftf082(&a[240], &w[nw - 8]);
+ }
+ cftf081(&a[192], &w[nw - 8]);
+ cftf082(&a[208], &w[nw - 8]);
+ cftf081(&a[224], &w[nw - 8]);
+ }
+}
+
+
+void cftmdl1(int n, double *a, double *w)
+{
+ int j, j0, j1, j2, j3, k, m, mh;
+ double wn4r, wk1r, wk1i, wk3r, wk3i;
+ double 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, double *a, double *w)
+{
+ int j, j0, j1, j2, j3, k, kr, m, mh;
+ double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
+ double 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, double *a, int nw, double *w)
+{
+ void cftf161(double *a, double *w);
+ void cftf162(double *a, double *w);
+ void cftf081(double *a, double *w);
+ void cftf082(double *a, double *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 - 8]);
+ cftf082(&a[16], &w[nw - 8]);
+ cftf081(&a[32], &w[nw - 8]);
+ cftf081(&a[48], &w[nw - 8]);
+ }
+}
+
+
+void cftf161(double *a, double *w)
+{
+ double 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];
+ wk1r = w[2];
+ wk1i = w[3];
+ 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(double *a, double *w)
+{
+ double 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(double *a, double *w)
+{
+ double 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(double *a, double *w)
+{
+ double 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[2];
+ wk1i = w[3];
+ 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(double *a)
+{
+ double 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[2] = x1r - x3i;
+ a[3] = x1i + x3r;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[6] = x1r + x3i;
+ a[7] = x1i - x3r;
+}
+
+
+void cftb040(double *a)
+{
+ double 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[2] = x1r + x3i;
+ a[3] = x1i - x3r;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[6] = x1r - x3i;
+ a[7] = x1i + x3r;
+}
+
+
+void cftx020(double *a)
+{
+ double 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, double *a, int nc, double *c)
+{
+ int j, k, kk, ks, m;
+ double 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, double *a, int nc, double *c)
+{
+ int j, k, kk, ks, m;
+ double 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, double *a, int nc, double *c)
+{
+ int j, k, kk, ks, m;
+ double 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, double *a, int nc, double *c)
+{
+ int j, k, kk, ks, m;
+ double 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];
+}
+
diff --git a/pd/src/d_fft_fftw.c b/pd/src/d_fft_fftw.c
new file mode 100644
index 00000000..0ead62be
--- /dev/null
+++ b/pd/src/d_fft_fftw.c
@@ -0,0 +1,93 @@
+/* Copyright (c) 1997- Miller Puckette and others.
+* For information on usage and redistribution, and for a DISCLAIMER OF ALL
+* WARRANTIES, see the file, "LICENSE.txt," in this distribution. */
+
+/* --------- Pd interface to FFTW library; imitate Mayer API ---------- */
+
+#include "m_pd.h"
+#ifdef MSW
+#include <malloc.h>
+#else
+#include <alloca.h>
+#endif
+
+#error oops -- I'm talking to the old fftw. Apparently it's still changing.
+
+#include <fftw.h>
+
+int ilog2(int n);
+
+#define MINFFT 5
+#define MAXFFT 30
+
+/* from the FFTW website:
+ fftw_complex in[N], out[N];
+ fftw_plan p;
+ ...
+ p = fftw_create_plan(N, FFTW_FORWARD, FFTW_ESTIMATE);
+ ...
+ fftw_one(p, in, out);
+ ...
+ fftw_destroy_plan(p);
+
+FFTW_FORWARD or FFTW_BACKWARD, and indicates the direction of the transform you
+are interested in. Alternatively, you can use the sign of the exponent in the
+transform, -1 or +1, which corresponds to FFTW_FORWARD or FFTW_BACKWARD
+respectively. The flags argument is either FFTW_MEASURE
+
+*/
+
+static fftw_plan fftw_pvec[2 * (MAXFFT+1 - MINFFT)];
+
+static fftw_plan fftw_getplan(int n, int dir)
+{
+ logn = ilog2(n);
+ if (logn < MINFFT || logn > MAXFFT)
+ return (0);
+ int indx = 2*(logn-MINFFT) + inverse);
+ if (!fftw_pvec[indx]
+ fftw_pvec[indx] = fftw_create_plan(N, dir, FFTW_MEASURE);
+ return (fftw_pvec[indx]);
+}
+
+EXTERN void mayer_fht(float *fz, int n)
+{
+ post("FHT: not yet implemented");
+}
+
+static void mayer_dofft(int n, float *fz1, float *fz2, int dir)
+{
+ float *inbuf, *outbuf, *fp1, *fp2, *fp3;
+ int i;
+ fftw_plan p = fftw_getplan(n, dir);
+ inbuf = alloca(n * (4 * sizeof(float)));
+ outbuf = inbuf + 2*n;
+ if (!p)
+ return;
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = inbuf; i < n; i++)
+ fp3[0] = *fp1++, fp3[1] = *fp2++, fp3 += 2;
+ fftw_one(p, inbuf, outbuf);
+ for (i = 0, fp1 = fz1, fp2 = fz2, fp3 = outbuf; i < n; i++)
+ *fp1++ = fp3[0], *fp2++ = fp3[1], fp3 += 2;
+}
+
+EXTERN void mayer_fft(int n, float *fz1, float *fz2)
+{
+ mayer_dofft(n, fz1, fz2, FFTW_FORWARD);
+}
+
+EXTERN void mayer_ifft(int n, float *fz1, float *fz2)
+{
+ mayer_dofft(n, fz1, fz2, FFTW_BACKWARD);
+}
+
+EXTERN void mayer_realfft(int n, float *fz)
+{
+ post("rfft: not yet implemented");
+}
+
+EXTERN void mayer_realifft(int n, float *fz)
+{
+ post("rifft: not yet implemented");
+}
+
diff --git a/pd/src/d_fftsg_h.c b/pd/src/d_fftsg_h.c
new file mode 100644
index 00000000..e4c47c2a
--- /dev/null
+++ b/pd/src/d_fftsg_h.c
@@ -0,0 +1,3447 @@
+/*
+Fast Fourier/Cosine/Sine Transform
+ dimension :one
+ data length :power of 2
+ decimation :frequency
+ radix :split-radix
+ data :inplace
+ table :not 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, double *);
+ void rdft(int, int, double *);
+ void ddct(int, int, double *);
+ void ddst(int, int, double *);
+ void dfct(int, double *);
+ void dfst(int, double *);
+macro definitions
+ USE_CDFT_PTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
+ USE_CDFT_WINTHREADS : default=not defined
+ CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
+ CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
+
+
+-------- 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>
+ cdft(2*n, 1, a);
+ <case2>
+ cdft(2*n, -1, a);
+ [parameters]
+ 2*n :data length (int)
+ n >= 1, n = power of 2
+ a[0...2*n-1] :input/output data (double *)
+ 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
+ [remark]
+ Inverse of
+ cdft(2*n, -1, a);
+ is
+ cdft(2*n, 1, a);
+ 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>
+ rdft(n, 1, a);
+ <case2>
+ rdft(n, -1, a);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ <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]
+ [remark]
+ Inverse of
+ rdft(n, 1, a);
+ is
+ rdft(n, -1, a);
+ 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>
+ ddct(n, 1, a);
+ <case2>
+ ddct(n, -1, a);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ output data
+ a[k] = C[k], 0<=k<n
+ [remark]
+ Inverse of
+ ddct(n, -1, a);
+ is
+ a[0] *= 0.5;
+ ddct(n, 1, a);
+ 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>
+ ddst(n, 1, a);
+ <case2>
+ ddst(n, -1, a);
+ [parameters]
+ n :data length (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ <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]
+ [remark]
+ Inverse of
+ ddst(n, -1, a);
+ is
+ a[0] *= 0.5;
+ ddst(n, 1, a);
+ 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]
+ dfct(n, a);
+ [parameters]
+ n :data length - 1 (int)
+ n >= 2, n = power of 2
+ a[0...n] :input/output data (double *)
+ output data
+ a[k] = C[k], 0<=k<=n
+ [remark]
+ Inverse of
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a);
+ is
+ a[0] *= 0.5;
+ a[n] *= 0.5;
+ dfct(n, a);
+ 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]
+ dfst(n, a);
+ [parameters]
+ n :data length + 1 (int)
+ n >= 2, n = power of 2
+ a[0...n-1] :input/output data (double *)
+ output data
+ a[k] = S[k], 0<k<n
+ (a[0] is used for work area)
+ [remark]
+ Inverse of
+ dfst(n, a);
+ is
+ dfst(n, a);
+ for (j = 1; j <= n - 1; j++) {
+ a[j] *= 2.0 / n;
+ }
+ .
+*/
+
+
+void cdft(int n, int isgn, double *a)
+{
+ void cftfsub(int n, double *a);
+ void cftbsub(int n, double *a);
+
+ if (isgn >= 0) {
+ cftfsub(n, a);
+ } else {
+ cftbsub(n, a);
+ }
+}
+
+
+void rdft(int n, int isgn, double *a)
+{
+ void cftfsub(int n, double *a);
+ void cftbsub(int n, double *a);
+ void rftfsub(int n, double *a);
+ void rftbsub(int n, double *a);
+ double xi;
+
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a);
+ rftfsub(n, a);
+ } else if (n == 4) {
+ cftfsub(n, a);
+ }
+ 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);
+ cftbsub(n, a);
+ } else if (n == 4) {
+ cftbsub(n, a);
+ }
+ }
+}
+
+
+void ddct(int n, int isgn, double *a)
+{
+ void cftfsub(int n, double *a);
+ void cftbsub(int n, double *a);
+ void rftfsub(int n, double *a);
+ void rftbsub(int n, double *a);
+ void dctsub(int n, double *a);
+ void dctsub4(int n, double *a);
+ int j;
+ double xr;
+
+ 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);
+ cftbsub(n, a);
+ } else if (n == 4) {
+ cftbsub(n, a);
+ }
+ }
+ if (n > 4) {
+ dctsub(n, a);
+ } else {
+ dctsub4(n, a);
+ }
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a);
+ rftfsub(n, a);
+ } else if (n == 4) {
+ cftfsub(n, a);
+ }
+ 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, double *a)
+{
+ void cftfsub(int n, double *a);
+ void cftbsub(int n, double *a);
+ void rftfsub(int n, double *a);
+ void rftbsub(int n, double *a);
+ void dstsub(int n, double *a);
+ void dstsub4(int n, double *a);
+ int j;
+ double xr;
+
+ 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);
+ cftbsub(n, a);
+ } else if (n == 4) {
+ cftbsub(n, a);
+ }
+ }
+ if (n > 4) {
+ dstsub(n, a);
+ } else {
+ dstsub4(n, a);
+ }
+ if (isgn >= 0) {
+ if (n > 4) {
+ cftfsub(n, a);
+ rftfsub(n, a);
+ } else if (n == 4) {
+ cftfsub(n, a);
+ }
+ 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, double *a)
+{
+ void ddct(int n, int isgn, double *a);
+ void bitrv1(int n, double *a);
+ int j, k, m, mh;
+ double xr, xi, yr, yi, an;
+
+ m = n >> 1;
+ for (j = 0; j < m; j++) {
+ k = n - j;
+ xr = a[j] + a[k];
+ a[j] -= a[k];
+ a[k] = xr;
+ }
+ an = a[n];
+ while (m >= 2) {
+ ddct(m, 1, a);
+ if (m > 2) {
+ bitrv1(m, a);
+ }
+ mh = m >> 1;
+ xi = a[m];
+ a[m] = a[0];
+ a[0] = an - xi;
+ an += xi;
+ for (j = 1; j < mh; j++) {
+ k = m - j;
+ xr = a[m + k];
+ xi = a[m + j];
+ yr = a[j];
+ yi = a[k];
+ a[m + j] = yr;
+ a[m + k] = yi;
+ a[j] = xr - xi;
+ a[k] = xr + xi;
+ }
+ xr = a[mh];
+ a[mh] = a[m + mh];
+ a[m + mh] = xr;
+ m = mh;
+ }
+ xi = a[1];
+ a[1] = a[0];
+ a[0] = an + xi;
+ a[n] = an - xi;
+ if (n > 2) {
+ bitrv1(n, a);
+ }
+}
+
+
+void dfst(int n, double *a)
+{
+ void ddst(int n, int isgn, double *a);
+ void bitrv1(int n, double *a);
+ int j, k, m, mh;
+ double xr, xi, yr, yi;
+
+ m = n >> 1;
+ for (j = 1; j < m; j++) {
+ k = n - j;
+ xr = a[j] - a[k];
+ a[j] += a[k];
+ a[k] = xr;
+ }
+ a[0] = a[m];
+ while (m >= 2) {
+ ddst(m, 1, a);
+ if (m > 2) {
+ bitrv1(m, a);
+ }
+ mh = m >> 1;
+ for (j = 1; j < mh; j++) {
+ k = m - j;
+ xr = a[m + k];
+ xi = a[m + j];
+ yr = a[j];
+ yi = a[k];
+ a[m + j] = yr;
+ a[m + k] = yi;
+ a[j] = xr + xi;
+ a[k] = xr - xi;
+ }
+ a[m] = a[0];
+ a[0] = a[m + mh];
+ a[m + mh] = a[mh];
+ m = mh;
+ }
+ a[1] = a[0];
+ a[0] = 0;
+ if (n > 2) {
+ bitrv1(n, a);
+ }
+}
+
+
+/* -------- child routines -------- */
+
+
+#include <math.h>
+#ifndef M_PI_2
+#define M_PI_2 1.570796326794896619231321691639751442098584699687
+#endif
+#ifndef WR5000 /* cos(M_PI_2*0.5000) */
+#define WR5000 0.707106781186547524400844362104849039284835937688
+#endif
+#ifndef WR2500 /* cos(M_PI_2*0.2500) */
+#define WR2500 0.923879532511286756128183189396788286822416625863
+#endif
+#ifndef WI2500 /* sin(M_PI_2*0.2500) */
+#define WI2500 0.382683432365089771728459984030398866761344562485
+#endif
+#ifndef WR1250 /* cos(M_PI_2*0.1250) */
+#define WR1250 0.980785280403230449126182236134239036973933730893
+#endif
+#ifndef WI1250 /* sin(M_PI_2*0.1250) */
+#define WI1250 0.195090322016128267848284868477022240927691617751
+#endif
+#ifndef WR3750 /* cos(M_PI_2*0.3750) */
+#define WR3750 0.831469612302545237078788377617905756738560811987
+#endif
+#ifndef WI3750 /* sin(M_PI_2*0.3750) */
+#define WI3750 0.555570233019602224742830813948532874374937190754
+#endif
+
+
+#ifdef USE_CDFT_PTHREADS
+#define USE_CDFT_THREADS
+#ifndef CDFT_THREADS_BEGIN_N
+#define CDFT_THREADS_BEGIN_N 8192
+#endif
+#ifndef CDFT_4THREADS_BEGIN_N
+#define CDFT_4THREADS_BEGIN_N 65536
+#endif
+#include <pthread.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define cdft_thread_t pthread_t
+#define cdft_thread_create(thp,func,argp) { \
+ if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#define cdft_thread_wait(th) { \
+ if (pthread_join(th, NULL) != 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#endif /* USE_CDFT_PTHREADS */
+
+
+#ifdef USE_CDFT_WINTHREADS
+#define USE_CDFT_THREADS
+#ifndef CDFT_THREADS_BEGIN_N
+#define CDFT_THREADS_BEGIN_N 32768
+#endif
+#ifndef CDFT_4THREADS_BEGIN_N
+#define CDFT_4THREADS_BEGIN_N 524288
+#endif
+#include <windows.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define cdft_thread_t HANDLE
+#define cdft_thread_create(thp,func,argp) { \
+ DWORD thid; \
+ *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
+ if (*(thp) == 0) { \
+ fprintf(stderr, "cdft thread error\n"); \
+ exit(1); \
+ } \
+}
+#define cdft_thread_wait(th) { \
+ WaitForSingleObject(th, INFINITE); \
+ CloseHandle(th); \
+}
+#endif /* USE_CDFT_WINTHREADS */
+
+
+#ifndef CDFT_LOOP_DIV /* control of the CDFT's speed & tolerance */
+#define CDFT_LOOP_DIV 32
+#endif
+
+#ifndef RDFT_LOOP_DIV /* control of the RDFT's speed & tolerance */
+#define RDFT_LOOP_DIV 64
+#endif
+
+#ifndef DCST_LOOP_DIV /* control of the DCT,DST's speed & tolerance */
+#define DCST_LOOP_DIV 64
+#endif
+
+
+void cftfsub(int n, double *a)
+{
+ void bitrv2(int n, double *a);
+ void bitrv216(double *a);
+ void bitrv208(double *a);
+ void cftmdl1(int n, double *a);
+ void cftrec4(int n, double *a);
+ void cftleaf(int n, int isplt, double *a);
+ void cftfx41(int n, double *a);
+ void cftf161(double *a);
+ void cftf081(double *a);
+ void cftf040(double *a);
+ void cftx020(double *a);
+#ifdef USE_CDFT_THREADS
+ void cftrec4_th(int n, double *a);
+#endif /* USE_CDFT_THREADS */
+
+ if (n > 8) {
+ if (n > 32) {
+ cftmdl1(n, a);
+#ifdef USE_CDFT_THREADS
+ if (n > CDFT_THREADS_BEGIN_N) {
+ cftrec4_th(n, a);
+ } else
+#endif /* USE_CDFT_THREADS */
+ if (n > 512) {
+ cftrec4(n, a);
+ } else if (n > 128) {
+ cftleaf(n, 1, a);
+ } else {
+ cftfx41(n, a);
+ }
+ bitrv2(n, a);
+ } else if (n == 32) {
+ cftf161(a);
+ bitrv216(a);
+ } else {
+ cftf081(a);
+ bitrv208(a);
+ }
+ } else if (n == 8) {
+ cftf040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+}
+
+
+void cftbsub(int n, double *a)
+{
+ void bitrv2conj(int n, double *a);
+ void bitrv216neg(double *a);
+ void bitrv208neg(double *a);
+ void cftb1st(int n, double *a);
+ void cftrec4(int n, double *a);
+ void cftleaf(int n, int isplt, double *a);
+ void cftfx41(int n, double *a);
+ void cftf161(double *a);
+ void cftf081(double *a);
+ void cftb040(double *a);
+ void cftx020(double *a);
+#ifdef USE_CDFT_THREADS
+ void cftrec4_th(int n, double *a);
+#endif /* USE_CDFT_THREADS */
+
+ if (n > 8) {
+ if (n > 32) {
+ cftb1st(n, a);
+#ifdef USE_CDFT_THREADS
+ if (n > CDFT_THREADS_BEGIN_N) {
+ cftrec4_th(n, a);
+ } else
+#endif /* USE_CDFT_THREADS */
+ if (n > 512) {
+ cftrec4(n, a);
+ } else if (n > 128) {
+ cftleaf(n, 1, a);
+ } else {
+ cftfx41(n, a);
+ }
+ bitrv2conj(n, a);
+ } else if (n == 32) {
+ cftf161(a);
+ bitrv216neg(a);
+ } else {
+ cftf081(a);
+ bitrv208neg(a);
+ }
+ } else if (n == 8) {
+ cftb040(a);
+ } else if (n == 4) {
+ cftx020(a);
+ }
+}
+
+
+void bitrv2(int n, double *a)
+{
+ int j0, k0, j1, k1, l, m, i, j, k, nh;
+ double xr, xi, yr, yi;
+
+ m = 4;
+ for (l = n >> 2; l > 8; l >>= 2) {
+ m <<= 1;
+ }
+ nh = n >> 1;
+ if (l == 8) {
+ j0 = 0;
+ for (k0 = 0; k0 < m; k0 += 4) {
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 4) {
+ xr = a[j];
+ xi = a[j + 1];
+ yr = a[k];
+ yi = a[k + 1];
+ a[j] = yr;
+ a[j + 1] = yi;
+ a[k] = xr;
+ a[k + 1] = xi;
+ j1 = j + m;
+ k1 = k + 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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 += m;
+ k1 += 2 * m;
+ 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 += nh;
+ k1 += 2;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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 -= m;
+ k1 += m;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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;
+ k1 += nh;
+ 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 += m;
+ k1 += 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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 += m;
+ k1 += 2 * m;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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 -= m;
+ k1 += m;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 2;
+ k1 += nh;
+ 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 += m;
+ k1 += 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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;
+ k1 -= nh;
+ 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 += nh + 2;
+ k1 += nh + 2;
+ 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 -= nh - m;
+ k1 += 2 * m - 2;
+ 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;
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ }
+ } else {
+ j0 = 0;
+ for (k0 = 0; k0 < m; k0 += 4) {
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 4) {
+ xr = a[j];
+ xi = a[j + 1];
+ yr = a[k];
+ yi = a[k + 1];
+ a[j] = yr;
+ a[j + 1] = yi;
+ a[k] = xr;
+ a[k + 1] = xi;
+ j1 = j + m;
+ k1 = k + m;
+ 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 += nh;
+ k1 += 2;
+ 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 -= m;
+ k1 -= m;
+ 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;
+ k1 += nh;
+ 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 += m;
+ k1 += m;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= m;
+ k1 -= m;
+ 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;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 2;
+ k1 += nh;
+ 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 += m;
+ k1 += m;
+ 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;
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ }
+ }
+}
+
+
+void bitrv2conj(int n, double *a)
+{
+ int j0, k0, j1, k1, l, m, i, j, k, nh;
+ double xr, xi, yr, yi;
+
+ m = 4;
+ for (l = n >> 2; l > 8; l >>= 2) {
+ m <<= 1;
+ }
+ nh = n >> 1;
+ if (l == 8) {
+ j0 = 0;
+ for (k0 = 0; k0 < m; k0 += 4) {
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 4) {
+ xr = a[j];
+ xi = -a[j + 1];
+ yr = a[k];
+ yi = -a[k + 1];
+ a[j] = yr;
+ a[j + 1] = yi;
+ a[k] = xr;
+ a[k + 1] = xi;
+ j1 = j + m;
+ k1 = k + 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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 += m;
+ k1 += 2 * m;
+ 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 += nh;
+ k1 += 2;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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 -= m;
+ k1 += m;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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;
+ k1 += nh;
+ 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 += m;
+ k1 += 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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 += m;
+ k1 += 2 * m;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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 -= m;
+ k1 += m;
+ 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 -= m;
+ k1 -= 2 * m;
+ 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;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 2;
+ k1 += nh;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ j1 += m;
+ k1 += 2 * m;
+ 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 += m;
+ k1 -= m;
+ 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;
+ k1 -= nh;
+ 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 += nh + 2;
+ k1 += nh + 2;
+ 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 -= nh - m;
+ k1 += 2 * m - 2;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ }
+ } else {
+ j0 = 0;
+ for (k0 = 0; k0 < m; k0 += 4) {
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 4) {
+ xr = a[j];
+ xi = -a[j + 1];
+ yr = a[k];
+ yi = -a[k + 1];
+ a[j] = yr;
+ a[j + 1] = yi;
+ a[k] = xr;
+ a[k + 1] = xi;
+ j1 = j + m;
+ k1 = k + m;
+ 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 += nh;
+ k1 += 2;
+ 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 -= m;
+ k1 -= m;
+ 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;
+ k1 += nh;
+ 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 += m;
+ k1 += m;
+ 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 -= nh;
+ k1 -= 2;
+ 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 -= m;
+ k1 -= m;
+ 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;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 2;
+ k1 += nh;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ j1 += m;
+ k1 += m;
+ a[j1 - 1] = -a[j1 - 1];
+ 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;
+ a[k1 + 3] = -a[k1 + 3];
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ }
+ }
+}
+
+
+void bitrv216(double *a)
+{
+ double 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(double *a)
+{
+ double 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(double *a)
+{
+ double 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(double *a)
+{
+ double 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 bitrv1(int n, double *a)
+{
+ int j0, k0, j1, k1, l, m, i, j, k, nh;
+ double x;
+
+ nh = n >> 1;
+ x = a[1];
+ a[1] = a[nh];
+ a[nh] = x;
+ m = 2;
+ for (l = n >> 2; l > 2; l >>= 2) {
+ m <<= 1;
+ }
+ if (l == 2) {
+ j1 = m + 1;
+ k1 = m + nh;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j0 = 0;
+ for (k0 = 2; k0 < m; k0 += 2) {
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 2) {
+ x = a[j];
+ a[j] = a[k];
+ a[k] = x;
+ j1 = j + m;
+ k1 = k + m;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 += nh;
+ k1++;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 -= m;
+ k1 -= m;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1++;
+ k1 += nh;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 += m;
+ k1 += m;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 -= nh;
+ k1--;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 -= m;
+ k1 -= m;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 1;
+ k1 += nh;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 += m;
+ k1 += m;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ }
+ } else {
+ j0 = 0;
+ for (k0 = 2; k0 < m; k0 += 2) {
+ for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
+ k = k0;
+ for (j = j0; j < j0 + k0; j += 2) {
+ x = a[j];
+ a[j] = a[k];
+ a[k] = x;
+ j1 = j + nh;
+ k1 = k + 1;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1++;
+ k1 += nh;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ j1 -= nh;
+ k1--;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ for (i = nh >> 1; i > (k ^= i); i >>= 1);
+ }
+ k1 = j0 + k0;
+ j1 = k1 + 1;
+ k1 += nh;
+ x = a[j1];
+ a[j1] = a[k1];
+ a[k1] = x;
+ }
+ }
+}
+
+
+void cftb1st(int n, double *a)
+{
+ int i, i0, j, j0, j1, j2, j3, m, mh;
+ double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i, ss1, ss3;
+ double 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;
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ ew = M_PI_2 / m;
+ w1r = cos(2 * ew);
+ w1i = sin(2 * ew);
+ wk1r = w1r;
+ wk1i = w1i;
+ ss1 = 2 * w1i;
+ wk3i = 2 * ss1 * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ ss3 = 2 * wk3i;
+ i = 0;
+ for (;;) {
+ i0 = i + 4 * CDFT_LOOP_DIV;
+ if (i0 > mh - 4) {
+ i0 = mh - 4;
+ }
+ for (j = i + 2; j < i0; j += 4) {
+ wd1r -= ss1 * wk1i;
+ wd1i += ss1 * wk1r;
+ wd3r -= ss3 * wk3i;
+ wd3i += ss3 * wk3r;
+ 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;
+ x0r = a[j + 2] + a[j2 + 2];
+ x0i = -a[j + 3] - a[j2 + 3];
+ x1r = a[j + 2] - a[j2 + 2];
+ x1i = -a[j + 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[j + 2] = x0r + x2r;
+ a[j + 3] = x0i - x2i;
+ a[j1 + 2] = x0r - x2r;
+ a[j1 + 3] = x0i + x2i;
+ x0r = x1r + x3i;
+ x0i = x1i + x3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ 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];
+ 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;
+ 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] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ wk1r -= ss1 * wd1i;
+ wk1i += ss1 * wd1r;
+ wk3r -= ss3 * wd3i;
+ wk3i += ss3 * wd3r;
+ }
+ if (i0 == mh - 4) {
+ break;
+ }
+ wd1r = cos(ew * i0);
+ wd1i = sin(ew * i0);
+ wd3i = 4 * wd1i * wd1r;
+ wd3r = wd1r - wd3i * wd1i;
+ wd3i = wd1i - wd3i * wd1r;
+ wk1r = w1r * wd1r - w1i * wd1i;
+ wk1i = w1r * wd1i + w1i * wd1r;
+ wk3i = 4 * wk1i * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ i = i0;
+ }
+ wd1r = WR5000;
+ 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] = wd1r * (x0r - x0i);
+ a[j2 + 1] = wd1r * (x0i + x0r);
+ x0r = x1r - x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wd1r * (x0r + x0i);
+ a[j3 + 1] = -wd1r * (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;
+}
+
+
+#ifdef USE_CDFT_THREADS
+struct cdft_arg_st {
+ int n0;
+ int n;
+ double *a;
+};
+typedef struct cdft_arg_st cdft_arg_t;
+
+
+void cftrec4_th(int n, double *a)
+{
+ void *cftrec1_th(void *p);
+ void *cftrec2_th(void *p);
+ int i, idiv4, m, nthread;
+ cdft_thread_t th[4];
+ cdft_arg_t ag[4];
+
+ nthread = 2;
+ idiv4 = 0;
+ m = n >> 1;
+ if (n > CDFT_4THREADS_BEGIN_N) {
+ nthread = 4;
+ idiv4 = 1;
+ m >>= 1;
+ }
+ for (i = 0; i < nthread; i++) {
+ ag[i].n0 = n;
+ ag[i].n = m;
+ ag[i].a = &a[i * m];
+ if (i != idiv4) {
+ cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
+ } else {
+ cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
+ }
+ }
+ for (i = 0; i < nthread; i++) {
+ cdft_thread_wait(th[i]);
+ }
+}
+
+
+void *cftrec1_th(void *p)
+{
+ int cfttree(int n, int j, int k, double *a);
+ void cftleaf(int n, int isplt, double *a);
+ void cftmdl1(int n, double *a);
+ int isplt, j, k, m, n, n0;
+ double *a;
+
+ n0 = ((cdft_arg_t *) p)->n0;
+ n = ((cdft_arg_t *) p)->n;
+ a = ((cdft_arg_t *) p)->a;
+ m = n0;
+ while (m > 512) {
+ m >>= 2;
+ cftmdl1(m, &a[n - m]);
+ }
+ cftleaf(m, 1, &a[n - m]);
+ k = 0;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a);
+ cftleaf(m, isplt, &a[j - m]);
+ }
+ return (void *) 0;
+}
+
+
+void *cftrec2_th(void *p)
+{
+ int cfttree(int n, int j, int k, double *a);
+ void cftleaf(int n, int isplt, double *a);
+ void cftmdl2(int n, double *a);
+ int isplt, j, k, m, n, n0;
+ double *a;
+
+ n0 = ((cdft_arg_t *) p)->n0;
+ n = ((cdft_arg_t *) p)->n;
+ a = ((cdft_arg_t *) p)->a;
+ k = 1;
+ m = n0;
+ while (m > 512) {
+ m >>= 2;
+ k <<= 2;
+ cftmdl2(m, &a[n - m]);
+ }
+ cftleaf(m, 0, &a[n - m]);
+ k >>= 1;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a);
+ cftleaf(m, isplt, &a[j - m]);
+ }
+ return (void *) 0;
+}
+#endif /* USE_CDFT_THREADS */
+
+
+void cftrec4(int n, double *a)
+{
+ int cfttree(int n, int j, int k, double *a);
+ void cftleaf(int n, int isplt, double *a);
+ void cftmdl1(int n, double *a);
+ int isplt, j, k, m;
+
+ m = n;
+ while (m > 512) {
+ m >>= 2;
+ cftmdl1(m, &a[n - m]);
+ }
+ cftleaf(m, 1, &a[n - m]);
+ k = 0;
+ for (j = n - m; j > 0; j -= m) {
+ k++;
+ isplt = cfttree(m, j, k, a);
+ cftleaf(m, isplt, &a[j - m]);
+ }
+}
+
+
+int cfttree(int n, int j, int k, double *a)
+{
+ void cftmdl1(int n, double *a);
+ void cftmdl2(int n, double *a);
+ int i, isplt, m;
+
+ if ((k & 3) != 0) {
+ isplt = k & 1;
+ if (isplt != 0) {
+ cftmdl1(n, &a[j - n]);
+ } else {
+ cftmdl2(n, &a[j - n]);
+ }
+ } else {
+ m = n;
+ for (i = k; (i & 3) == 0; i >>= 2) {
+ m <<= 2;
+ }
+ isplt = i & 1;
+ if (isplt != 0) {
+ while (m > 128) {
+ cftmdl1(m, &a[j - m]);
+ m >>= 2;
+ }
+ } else {
+ while (m > 128) {
+ cftmdl2(m, &a[j - m]);
+ m >>= 2;
+ }
+ }
+ }
+ return isplt;
+}
+
+
+void cftleaf(int n, int isplt, double *a)
+{
+ void cftmdl1(int n, double *a);
+ void cftmdl2(int n, double *a);
+ void cftf161(double *a);
+ void cftf162(double *a);
+ void cftf081(double *a);
+ void cftf082(double *a);
+
+ if (n == 512) {
+ cftmdl1(128, a);
+ cftf161(a);
+ cftf162(&a[32]);
+ cftf161(&a[64]);
+ cftf161(&a[96]);
+ cftmdl2(128, &a[128]);
+ cftf161(&a[128]);
+ cftf162(&a[160]);
+ cftf161(&a[192]);
+ cftf162(&a[224]);
+ cftmdl1(128, &a[256]);
+ cftf161(&a[256]);
+ cftf162(&a[288]);
+ cftf161(&a[320]);
+ cftf161(&a[352]);
+ if (isplt != 0) {
+ cftmdl1(128, &a[384]);
+ cftf161(&a[480]);
+ } else {
+ cftmdl2(128, &a[384]);
+ cftf162(&a[480]);
+ }
+ cftf161(&a[384]);
+ cftf162(&a[416]);
+ cftf161(&a[448]);
+ } else {
+ cftmdl1(64, a);
+ cftf081(a);
+ cftf082(&a[16]);
+ cftf081(&a[32]);
+ cftf081(&a[48]);
+ cftmdl2(64, &a[64]);
+ cftf081(&a[64]);
+ cftf082(&a[80]);
+ cftf081(&a[96]);
+ cftf082(&a[112]);
+ cftmdl1(64, &a[128]);
+ cftf081(&a[128]);
+ cftf082(&a[144]);
+ cftf081(&a[160]);
+ cftf081(&a[176]);
+ if (isplt != 0) {
+ cftmdl1(64, &a[192]);
+ cftf081(&a[240]);
+ } else {
+ cftmdl2(64, &a[192]);
+ cftf082(&a[240]);
+ }
+ cftf081(&a[192]);
+ cftf082(&a[208]);
+ cftf081(&a[224]);
+ }
+}
+
+
+void cftmdl1(int n, double *a)
+{
+ int i, i0, j, j0, j1, j2, j3, m, mh;
+ double ew, w1r, w1i, wk1r, wk1i, wk3r, wk3i,
+ wd1r, wd1i, wd3r, wd3i, ss1, ss3;
+ double 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;
+ wd1r = 1;
+ wd1i = 0;
+ wd3r = 1;
+ wd3i = 0;
+ ew = M_PI_2 / m;
+ w1r = cos(2 * ew);
+ w1i = sin(2 * ew);
+ wk1r = w1r;
+ wk1i = w1i;
+ ss1 = 2 * w1i;
+ wk3i = 2 * ss1 * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ ss3 = 2 * wk3i;
+ i = 0;
+ for (;;) {
+ i0 = i + 4 * CDFT_LOOP_DIV;
+ if (i0 > mh - 4) {
+ i0 = mh - 4;
+ }
+ for (j = i + 2; j < i0; j += 4) {
+ wd1r -= ss1 * wk1i;
+ wd1i += ss1 * wk1r;
+ wd3r -= ss3 * wk3i;
+ wd3i += ss3 * wk3r;
+ 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;
+ x0r = a[j + 2] + a[j2 + 2];
+ x0i = a[j + 3] + a[j2 + 3];
+ x1r = a[j + 2] - a[j2 + 2];
+ x1i = a[j + 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[j + 2] = x0r + x2r;
+ a[j + 3] = x0i + x2i;
+ a[j1 + 2] = x0r - x2r;
+ a[j1 + 3] = x0i - x2i;
+ x0r = x1r - x3i;
+ x0i = x1i + x3r;
+ a[j2 + 2] = wd1r * x0r - wd1i * x0i;
+ a[j2 + 3] = wd1r * x0i + wd1i * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ 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];
+ 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;
+ 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] = wd1i * x0r - wd1r * x0i;
+ a[j2 - 1] = wd1i * x0i + wd1r * x0r;
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3 - 2] = wd3i * x0r + wd3r * x0i;
+ a[j3 - 1] = wd3i * x0i - wd3r * x0r;
+ wk1r -= ss1 * wd1i;
+ wk1i += ss1 * wd1r;
+ wk3r -= ss3 * wd3i;
+ wk3i += ss3 * wd3r;
+ }
+ if (i0 == mh - 4) {
+ break;
+ }
+ wd1r = cos(ew * i0);
+ wd1i = sin(ew * i0);
+ wd3i = 4 * wd1i * wd1r;
+ wd3r = wd1r - wd3i * wd1i;
+ wd3i = wd1i - wd3i * wd1r;
+ wk1r = w1r * wd1r - w1i * wd1i;
+ wk1i = w1r * wd1i + w1i * wd1r;
+ wk3i = 4 * wk1i * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ i = i0;
+ }
+ wd1r = WR5000;
+ 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] = wd1r * (x0r - x0i);
+ a[j2 + 1] = wd1r * (x0i + x0r);
+ x0r = x1r + x3i;
+ x0i = x1i - x3r;
+ a[j3] = -wd1r * (x0r + x0i);
+ a[j3 + 1] = -wd1r * (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 cftmdl2(int n, double *a)
+{
+ int i, i0, j, j0, j1, j2, j3, m, mh;
+ double ew, w1r, w1i, wn4r, wk1r, wk1i, wk3r, wk3i,
+ wl1r, wl1i, wl3r, wl3i, wd1r, wd1i, wd3r, wd3i,
+ we1r, we1i, we3r, we3i, ss1, ss3;
+ double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
+
+ mh = n >> 3;
+ m = 2 * mh;
+ wn4r = WR5000;
+ 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;
+ wl1r = 1;
+ wl1i = 0;
+ wl3r = 1;
+ wl3i = 0;
+ we1r = wn4r;
+ we1i = wn4r;
+ we3r = -wn4r;
+ we3i = -wn4r;
+ ew = M_PI_2 / (2 * m);
+ w1r = cos(2 * ew);
+ w1i = sin(2 * ew);
+ wk1r = w1r;
+ wk1i = w1i;
+ wd1r = wn4r * (w1r - w1i);
+ wd1i = wn4r * (w1i + w1r);
+ ss1 = 2 * w1i;
+ wk3i = 2 * ss1 * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ ss3 = 2 * wk3i;
+ wd3r = -wn4r * (wk3r - wk3i);
+ wd3i = -wn4r * (wk3i + wk3r);
+ i = 0;
+ for (;;) {
+ i0 = i + 4 * CDFT_LOOP_DIV;
+ if (i0 > mh - 4) {
+ i0 = mh - 4;
+ }
+ for (j = i + 2; j < i0; j += 4) {
+ wl1r -= ss1 * wk1i;
+ wl1i += ss1 * wk1r;
+ wl3r -= ss3 * wk3i;
+ wl3i += ss3 * wk3r;
+ we1r -= ss1 * wd1i;
+ we1i += ss1 * wd1r;
+ we3r -= ss3 * wd3i;
+ we3i += ss3 * wd3r;
+ 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;
+ x0r = a[j + 2] - a[j2 + 3];
+ x0i = a[j + 3] + a[j2 + 2];
+ x1r = a[j + 2] + a[j2 + 3];
+ x1i = a[j + 3] - a[j2 + 2];
+ x2r = a[j1 + 2] - a[j3 + 3];
+ x2i = a[j1 + 3] + a[j3 + 2];
+ x3r = a[j1 + 2] + a[j3 + 3];
+ x3i = a[j1 + 3] - a[j3 + 2];
+ y0r = wl1r * x0r - wl1i * x0i;
+ y0i = wl1r * x0i + wl1i * x0r;
+ y2r = we1r * x2r - we1i * x2i;
+ y2i = we1r * x2i + we1i * x2r;
+ a[j + 2] = y0r + y2r;
+ a[j + 3] = y0i + y2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i - y2i;
+ y0r = wl3r * x1r + wl3i * x1i;
+ y0i = wl3r * x1i - wl3i * x1r;
+ y2r = we3r * x3r + we3i * x3i;
+ y2i = we3r * x3i - we3i * x3r;
+ a[j2 + 2] = y0r + y2r;
+ a[j2 + 3] = y0i + y2i;
+ a[j3 + 2] = y0r - y2r;
+ a[j3 + 3] = 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;
+ x0r = a[j0 - 2] - a[j2 - 1];
+ x0i = a[j0 - 1] + a[j2 - 2];
+ x1r = a[j0 - 2] + a[j2 - 1];
+ x1i = a[j0 - 1] - a[j2 - 2];
+ x2r = a[j1 - 2] - a[j3 - 1];
+ x2i = a[j1 - 1] + a[j3 - 2];
+ x3r = a[j1 - 2] + a[j3 - 1];
+ x3i = a[j1 - 1] - a[j3 - 2];
+ y0r = we1i * x0r - we1r * x0i;
+ y0i = we1i * x0i + we1r * x0r;
+ y2r = wl1i * x2r - wl1r * x2i;
+ y2i = wl1i * x2i + wl1r * x2r;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i + y2i;
+ a[j1 - 2] = y0r - y2r;
+ a[j1 - 1] = y0i - y2i;
+ y0r = we3i * x1r + we3r * x1i;
+ y0i = we3i * x1i - we3r * x1r;
+ y2r = wl3i * x3r + wl3r * x3i;
+ y2i = wl3i * x3i - wl3r * x3r;
+ a[j2 - 2] = y0r + y2r;
+ a[j2 - 1] = y0i + y2i;
+ a[j3 - 2] = y0r - y2r;
+ a[j3 - 1] = y0i - y2i;
+ wk1r -= ss1 * wl1i;
+ wk1i += ss1 * wl1r;
+ wk3r -= ss3 * wl3i;
+ wk3i += ss3 * wl3r;
+ wd1r -= ss1 * we1i;
+ wd1i += ss1 * we1r;
+ wd3r -= ss3 * we3i;
+ wd3i += ss3 * we3r;
+ }
+ if (i0 == mh - 4) {
+ break;
+ }
+ wl1r = cos(ew * i0);
+ wl1i = sin(ew * i0);
+ wl3i = 4 * wl1i * wl1r;
+ wl3r = wl1r - wl3i * wl1i;
+ wl3i = wl1i - wl3i * wl1r;
+ we1r = wn4r * (wl1r - wl1i);
+ we1i = wn4r * (wl1i + wl1r);
+ we3r = -wn4r * (wl3r - wl3i);
+ we3i = -wn4r * (wl3i + wl3r);
+ wk1r = w1r * wl1r - w1i * wl1i;
+ wk1i = w1r * wl1i + w1i * wl1r;
+ wk3i = 4 * wk1i * wk1r;
+ wk3r = wk1r - wk3i * wk1i;
+ wk3i = wk1i - wk3i * wk1r;
+ wd1r = wn4r * (wk1r - wk1i);
+ wd1i = wn4r * (wk1i + wk1r);
+ wd3r = -wn4r * (wk3r - wk3i);
+ wd3i = -wn4r * (wk3i + wk3r);
+ i = i0;
+ }
+ wl1r = WR2500;
+ wl1i = WI2500;
+ j0 = mh;
+ j1 = j0 + m;
+ j2 = j1 + m;
+ j3 = j2 + m;
+ x0r = a[j0 - 2] - a[j2 - 1];
+ x0i = a[j0 - 1] + a[j2 - 2];
+ x1r = a[j0 - 2] + a[j2 - 1];
+ x1i = a[j0 - 1] - a[j2 - 2];
+ x2r = a[j1 - 2] - a[j3 - 1];
+ x2i = a[j1 - 1] + a[j3 - 2];
+ x3r = a[j1 - 2] + a[j3 - 1];
+ x3i = a[j1 - 1] - a[j3 - 2];
+ y0r = wk1r * x0r - wk1i * x0i;
+ y0i = wk1r * x0i + wk1i * x0r;
+ y2r = wd1r * x2r - wd1i * x2i;
+ y2i = wd1r * x2i + wd1i * x2r;
+ a[j0 - 2] = y0r + y2r;
+ a[j0 - 1] = y0i + y2i;
+ a[j1 - 2] = 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 - 2] = y0r + y2r;
+ a[j2 - 1] = y0i + y2i;
+ a[j3 - 2] = y0r - y2r;
+ a[j3 - 1] = y0i - y2i;
+ 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 = wl1r * x0r - wl1i * x0i;
+ y0i = wl1r * x0i + wl1i * x0r;
+ y2r = wl1i * x2r - wl1r * x2i;
+ y2i = wl1i * x2i + wl1r * x2r;
+ a[j0] = y0r + y2r;
+ a[j0 + 1] = y0i + y2i;
+ a[j1] = y0r - y2r;
+ a[j1 + 1] = y0i - y2i;
+ y0r = wl1i * x1r - wl1r * x1i;
+ y0i = wl1i * x1i + wl1r * x1r;
+ y2r = wl1r * x3r - wl1i * x3i;
+ y2i = wl1r * x3i + wl1i * x3r;
+ a[j2] = y0r - y2r;
+ a[j2 + 1] = y0i - y2i;
+ a[j3] = y0r + y2r;
+ a[j3 + 1] = y0i + y2i;
+ x0r = a[j0 + 2] - a[j2 + 3];
+ x0i = a[j0 + 3] + a[j2 + 2];
+ x1r = a[j0 + 2] + a[j2 + 3];
+ x1i = a[j0 + 3] - a[j2 + 2];
+ x2r = a[j1 + 2] - a[j3 + 3];
+ x2i = a[j1 + 3] + a[j3 + 2];
+ x3r = a[j1 + 2] + a[j3 + 3];
+ x3i = a[j1 + 3] - a[j3 + 2];
+ y0r = wd1i * x0r - wd1r * x0i;
+ y0i = wd1i * x0i + wd1r * x0r;
+ y2r = wk1i * x2r - wk1r * x2i;
+ y2i = wk1i * x2i + wk1r * x2r;
+ a[j0 + 2] = y0r + y2r;
+ a[j0 + 3] = y0i + y2i;
+ a[j1 + 2] = y0r - y2r;
+ a[j1 + 3] = y0i - y2i;
+ y0r = wd3i * x1r + wd3r * x1i;
+ y0i = wd3i * x1i - wd3r * x1r;
+ y2r = wk3i * x3r + wk3r * x3i;
+ y2i = wk3i * x3i - wk3r * x3r;
+ a[j2 + 2] = y0r + y2r;
+ a[j2 + 3] = y0i + y2i;
+ a[j3 + 2] = y0r - y2r;
+ a[j3 + 3] = y0i - y2i;
+}
+
+
+void cftfx41(int n, double *a)
+{
+ void cftf161(double *a);
+ void cftf162(double *a);
+ void cftf081(double *a);
+ void cftf082(double *a);
+
+ if (n == 128) {
+ cftf161(a);
+ cftf162(&a[32]);
+ cftf161(&a[64]);
+ cftf161(&a[96]);
+ } else {
+ cftf081(a);
+ cftf082(&a[16]);
+ cftf081(&a[32]);
+ cftf081(&a[48]);
+ }
+}
+
+
+void cftf161(double *a)
+{
+ double 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 = WR5000;
+ wk1r = WR2500;
+ wk1i = WI2500;
+ 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(double *a)
+{
+ double 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 = WR5000;
+ wk1r = WR1250;
+ wk1i = WI1250;
+ wk2r = WR2500;
+ wk2i = WI2500;
+ wk3r = WR3750;
+ wk3i = WI3750;
+ 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(double *a)
+{
+ double 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 = WR5000;
+ 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(double *a)
+{
+ double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
+ y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
+ y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
+
+ wn4r = WR5000;
+ wk1r = WR2500;
+ wk1i = WI2500;
+ 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(double *a)
+{
+ double 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[2] = x1r - x3i;
+ a[3] = x1i + x3r;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[6] = x1r + x3i;
+ a[7] = x1i - x3r;
+}
+
+
+void cftb040(double *a)
+{
+ double 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[2] = x1r + x3i;
+ a[3] = x1i - x3r;
+ a[4] = x0r - x2r;
+ a[5] = x0i - x2i;
+ a[6] = x1r - x3i;
+ a[7] = x1i + x3r;
+}
+
+
+void cftx020(double *a)
+{
+ double 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, double *a)
+{
+ int i, i0, j, k;
+ double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
+
+ ec = 2 * M_PI_2 / n;
+ wkr = 0;
+ wki = 0;
+ wdi = cos(ec);
+ wdr = sin(ec);
+ wdi *= wdr;
+ wdr *= wdr;
+ w1r = 1 - 2 * wdr;
+ w1i = 2 * wdi;
+ ss = 2 * w1i;
+ i = n >> 1;
+ for (;;) {
+ i0 = i - 4 * RDFT_LOOP_DIV;
+ if (i0 < 4) {
+ i0 = 4;
+ }
+ for (j = i - 4; j >= i0; j -= 4) {
+ k = n - j;
+ xr = a[j + 2] - a[k - 2];
+ xi = a[j + 3] + a[k - 1];
+ yr = wdr * xr - wdi * xi;
+ yi = wdr * xi + wdi * xr;
+ a[j + 2] -= yr;
+ a[j + 3] -= yi;
+ a[k - 2] += yr;
+ a[k - 1] -= yi;
+ wkr += ss * wdi;
+ wki += ss * (0.5 - wdr);
+ 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;
+ wdr += ss * wki;
+ wdi += ss * (0.5 - wkr);
+ }
+ if (i0 == 4) {
+ break;
+ }
+ wkr = 0.5 * sin(ec * i0);
+ wki = 0.5 * cos(ec * i0);
+ wdr = 0.5 - (wkr * w1r - wki * w1i);
+ wdi = wkr * w1i + wki * w1r;
+ wkr = 0.5 - wkr;
+ i = i0;
+ }
+ xr = a[2] - a[n - 2];
+ xi = a[3] + a[n - 1];
+ yr = wdr * xr - wdi * xi;
+ yi = wdr * xi + wdi * xr;
+ a[2] -= yr;
+ a[3] -= yi;
+ a[n - 2] += yr;
+ a[n - 1] -= yi;
+}
+
+
+void rftbsub(int n, double *a)
+{
+ int i, i0, j, k;
+ double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
+
+ ec = 2 * M_PI_2 / n;
+ wkr = 0;
+ wki = 0;
+ wdi = cos(ec);
+ wdr = sin(ec);
+ wdi *= wdr;
+ wdr *= wdr;
+ w1r = 1 - 2 * wdr;
+ w1i = 2 * wdi;
+ ss = 2 * w1i;
+ i = n >> 1;
+ for (;;) {
+ i0 = i - 4 * RDFT_LOOP_DIV;
+ if (i0 < 4) {
+ i0 = 4;
+ }
+ for (j = i - 4; j >= i0; j -= 4) {
+ k = n - j;
+ xr = a[j + 2] - a[k - 2];
+ xi = a[j + 3] + a[k - 1];
+ yr = wdr * xr + wdi * xi;
+ yi = wdr * xi - wdi * xr;
+ a[j + 2] -= yr;
+ a[j + 3] -= yi;
+ a[k - 2] += yr;
+ a[k - 1] -= yi;
+ wkr += ss * wdi;
+ wki += ss * (0.5 - wdr);
+ 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;
+ wdr += ss * wki;
+ wdi += ss * (0.5 - wkr);
+ }
+ if (i0 == 4) {
+ break;
+ }
+ wkr = 0.5 * sin(ec * i0);
+ wki = 0.5 * cos(ec * i0);
+ wdr = 0.5 - (wkr * w1r - wki * w1i);
+ wdi = wkr * w1i + wki * w1r;
+ wkr = 0.5 - wkr;
+ i = i0;
+ }
+ xr = a[2] - a[n - 2];
+ xi = a[3] + a[n - 1];
+ yr = wdr * xr + wdi * xi;
+ yi = wdr * xi - wdi * xr;
+ a[2] -= yr;
+ a[3] -= yi;
+ a[n - 2] += yr;
+ a[n - 1] -= yi;
+}
+
+
+void dctsub(int n, double *a)
+{
+ int i, i0, j, k, m;
+ double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
+
+ ec = M_PI_2 / n;
+ wkr = 0.5;
+ wki = 0.5;
+ w1r = cos(ec);
+ w1i = sin(ec);
+ wdr = 0.5 * (w1r - w1i);
+ wdi = 0.5 * (w1r + w1i);
+ ss = 2 * w1i;
+ m = n >> 1;
+ i = 0;
+ for (;;) {
+ i0 = i + 2 * DCST_LOOP_DIV;
+ if (i0 > m - 2) {
+ i0 = m - 2;
+ }
+ for (j = i + 2; j <= i0; j += 2) {
+ k = n - j;
+ xr = wdi * a[j - 1] - wdr * a[k + 1];
+ xi = wdr * a[j - 1] + wdi * a[k + 1];
+ wkr -= ss * wdi;
+ wki += ss * wdr;
+ yr = wki * a[j] - wkr * a[k];
+ yi = wkr * a[j] + wki * a[k];
+ wdr -= ss * wki;
+ wdi += ss * wkr;
+ a[k + 1] = xr;
+ a[k] = yr;
+ a[j - 1] = xi;
+ a[j] = yi;
+ }
+ if (i0 == m - 2) {
+ break;
+ }
+ wdr = cos(ec * i0);
+ wdi = sin(ec * i0);
+ wkr = 0.5 * (wdr - wdi);
+ wki = 0.5 * (wdr + wdi);
+ wdr = wkr * w1r - wki * w1i;
+ wdi = wkr * w1i + wki * w1r;
+ i = i0;
+ }
+ xr = wdi * a[m - 1] - wdr * a[m + 1];
+ a[m - 1] = wdr * a[m - 1] + wdi * a[m + 1];
+ a[m + 1] = xr;
+ a[m] *= WR5000;
+}
+
+
+void dstsub(int n, double *a)
+{
+ int i, i0, j, k, m;
+ double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi;
+
+ ec = M_PI_2 / n;
+ wkr = 0.5;
+ wki = 0.5;
+ w1r = cos(ec);
+ w1i = sin(ec);
+ wdr = 0.5 * (w1r - w1i);
+ wdi = 0.5 * (w1r + w1i);
+ ss = 2 * w1i;
+ m = n >> 1;
+ i = 0;
+ for (;;) {
+ i0 = i + 2 * DCST_LOOP_DIV;
+ if (i0 > m - 2) {
+ i0 = m - 2;
+ }
+ for (j = i + 2; j <= i0; j += 2) {
+ k = n - j;
+ xr = wdi * a[k + 1] - wdr * a[j - 1];
+ xi = wdr * a[k + 1] + wdi * a[j - 1];
+ wkr -= ss * wdi;
+ wki += ss * wdr;
+ yr = wki * a[k] - wkr * a[j];
+ yi = wkr * a[k] + wki * a[j];
+ wdr -= ss * wki;
+ wdi += ss * wkr;
+ a[j - 1] = xr;
+ a[j] = yr;
+ a[k + 1] = xi;
+ a[k] = yi;
+ }
+ if (i0 == m - 2) {
+ break;
+ }
+ wdr = cos(ec * i0);
+ wdi = sin(ec * i0);
+ wkr = 0.5 * (wdr - wdi);
+ wki = 0.5 * (wdr + wdi);
+ wdr = wkr * w1r - wki * w1i;
+ wdi = wkr * w1i + wki * w1r;
+ i = i0;
+ }
+ xr = wdi * a[m + 1] - wdr * a[m - 1];
+ a[m + 1] = wdr * a[m + 1] + wdi * a[m - 1];
+ a[m - 1] = xr;
+ a[m] *= WR5000;
+}
+
+
+void dctsub4(int n, double *a)
+{
+ int m;
+ double wki, wdr, wdi, xr;
+
+ wki = WR5000;
+ m = n >> 1;
+ if (m == 2) {
+ wdr = wki * WI2500;
+ wdi = wki * WR2500;
+ xr = wdi * a[1] - wdr * a[3];
+ a[1] = wdr * a[1] + wdi * a[3];
+ a[3] = xr;
+ }
+ a[m] *= wki;
+}
+
+
+void dstsub4(int n, double *a)
+{
+ int m;
+ double wki, wdr, wdi, xr;
+
+ wki = WR5000;
+ m = n >> 1;
+ if (m == 2) {
+ wdr = wki * WI2500;
+ wdi = wki * WR2500;
+ xr = wdi * a[3] - wdr * a[1];
+ a[3] = wdr * a[3] + wdi * a[1];
+ a[1] = xr;
+ }
+ a[m] *= wki;
+}
+
generated by cgit v1.2.1 (git 2.18.0) at 2024-12-24 17:52:05 +0000