-
Notifications
You must be signed in to change notification settings - Fork 3
/
listing7.html
executable file
·616 lines (464 loc) · 21.3 KB
/
listing7.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
<html>
<head>
<!-- BEGIN META TAG INFO -->
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<link rel="home" href="http://developer.apple.com/">
<link rel="find" href="http://developer.apple.com/search/">
<link rel="stylesheet" type="text/css" href="../../documentation/css/adcstyle.css" title="fonts">
<script language="JavaScript" src="../../documentation/js/adc.js" type="text/javascript"></script>
<!-- END META TAG INFO -->
<!-- BEGIN TITLE -->
<title>dist_fft - /dist_fft_twiddle.c</title>
<!-- END TITLE -->
<script language="JavaScript">
function JumpToNewPage() {
window.location=document.scpopupmenu.gotop.value;
return true;
}
</script>
</head>
<!-- BEGIN BODY OPEN -->
<body>
<!--END BODY OPEN -->
<!-- START CENTER OPEN -->
<center>
<!-- END CENTER OPEN -->
<!-- BEGIN LOGO AND SEARCH -->
<!--#include virtual="/includes/adcnavbar"-->
<!-- END LOGO AND SEARCH -->
<!-- START BREADCRUMB -->
<div id="breadcrumb">
<table width="680" border="0" cellpadding="0" cellspacing="0">
<tr>
<td scope="row"><img width="340" height="10" src="images/1dot.gif" alt=""></td>
<td><img width="340" height="10" src="images/1dot.gif" alt=""></td>
</tr>
<tr valign="middle">
<td align="left" colspan="2">
<a href="http://developer.apple.com/">ADC Home</a> > <a href="../../referencelibrary/index.html">Reference Library</a> > <a href="../../samplecode/index.html">Sample Code</a> > <a href="../../samplecode/Performance/index.html">Performance</a> > <a href="../../samplecode/Performance/idxVelocityEngine-date.html">Velocity Engine</a> > <A HREF="javascript:location.replace('index.html');">dist_fft</A> >
</td>
</tr>
<tr>
<td colspan="2" scope="row"><img width="680" height="35" src="images/1dot.gif" alt=""></td>
</tr>
</table>
</div>
<!-- END BREADCRUMB -->
<!-- START MAIN CONTENT -->
<!-- START TITLE GRAPHIC AND INTRO-->
<table width="680" border="0" cellpadding="0" cellspacing="0">
<tr align="left" valign="top">
<td><h1><div id="pagehead">dist_fft</div></h1></td>
</tr>
</table>
<!-- END TITLE GRAPHIC AND INTRO -->
<!-- START WIDE COLUMN -->
<table width="680" border="0" cellpadding="0" cellspacing="0">
<tr align="left" valign="top">
<td id="scdetails">
<h2>/dist_fft_twiddle.c</h2>
<form name="scpopupmenu" onSubmit="return false;" method=post>
<p><strong>View Source Code:</strong>
<select name="gotop" onChange="JumpToNewPage();" style="width:340px"><option selected value="ingnore">Select File</option>
<option value="listing1.html">/dist_fft.c</option>
<option value="listing2.html">/dist_fft.h</option>
<option value="listing3.html">/dist_fft_prefetch.c</option>
<option value="listing4.html">/dist_fft_prefetch.h</option>
<option value="listing5.html">/dist_fft_transpose.c</option>
<option value="listing6.html">/dist_fft_transpose.h</option>
<option value="listing7.html">/dist_fft_twiddle.c</option>
<option value="listing8.html">/dist_fft_twiddle.h</option>
<option value="listing9.html">/dist_fft_types.h</option>
<option value="listing10.html">/LnxMPI/LnxMPI_S.c</option>
<option value="listing11.html">/LnxMPI/mpi.h</option>
<option value="listing12.html">/sched.c</option>
<option value="listing13.html">/sched.h</option>
<option value="listing14.html">/test_main.c</option>
<option value="listing15.html">/test_main.h</option>
<option value="listing16.html">/TOMS_transpose.c</option>
<option value="listing17.html">/TOMS_transpose.h</option>
<option value="listing18.html">/transpose_mpi.c</option>
<option value="listing19.html">/transpose_mpi.h</option></select>
</p>
</form>
<p><strong><a href="dist_fft.zip">Download Sample</a></strong> (“dist_fft.zip”, 716.6K)<BR>
<strong><a href="dist_fft.dmg">Download Sample</a></strong> (“dist_fft.dmg”, 800.0K)</p>
<!--
<p><strong><a href="#">Download Sample</a></strong> (“filename.sit”, 500K)</p>
-->
</td>
</tr>
<tr>
<td scope="row"><img width="680" height="10" src="images/1dot.gif" alt=""><br>
<img height="1" width="680" src="images/1dot_919699.gif" alt=""><br>
<img width="680" height="20" src="images/1dot.gif" alt=""></td>
</tr>
<tr>
<td scope="row">
<!--googleon: index -->
<pre class="sourcecodebox">/*
Copyright 2004 Apple Computer, Inc. All rights reserved.
IMPORTANT: This Apple software is supplied to you by Apple Computer, Inc. (“Apple”) in consideration of your agreement to the following terms, and your use, installation, modification or redistribution of this Apple software constitutes acceptance of these terms. If you do not agree with these terms, please do not use, install, modify or redistribute this Apple software.
In consideration of your agreement to abide by the following terms, and subject to these terms, Apple grants you a personal, non-exclusive license, under Apple’s copyrights in this original Apple software (the “Apple Software”), to use, reproduce, modify and redistribute the Apple Software, with or without modifications, in source and/or binary forms; provided that if you redistribute the Apple Software in its entirety and without modifications, you must retain this notice and the following text and disclaimers in all such redistributions of the Apple Software. Neither the name, trademarks, service marks or logos of Apple Computer, Inc. may be used to endorse or promote products derived from the Apple Software without specific prior written permission from Apple. Except as expressly stated in this notice, no other rights or licenses, express or implied, are granted by Apple herein, including but not limited to any patent rights that may be infringed by your derivative works or by other works in which the Apple Software may be incorporated.
The Apple Software is provided by Apple on an "AS IS" basis. APPLE MAKES NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF NON-INFRINGEMENT, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE APPLE SOFTWARE OR ITS USE AND OPERATION ALONE OR IN COMBINATION WITH YOUR PRODUCTS.
IN NO EVENT SHALL APPLE BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) ARISING IN ANY WAY OUT OF THE USE, REPRODUCTION, MODIFICATION AND/OR DISTRIBUTION OF THE APPLE SOFTWARE, HOWEVER CAUSED AND WHETHER UNDER THEORY OF CONTRACT, TORT (INCLUDING NEGLIGENCE), STRICT LIABILITY OR OTHERWISE, EVEN IF APPLE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "dist_fft_twiddle.h"
#define DEBUG_ENDANGLE_PRINT 0
void twiddle_row_forward(dist_fft_storage data,
int local_row,
int local_row_start,
int dimension,
double two_pi_over_N)
{
int col;
int row = local_row + local_row_start;
int index = local_row * dimension;
int ij = 0;
double twiddle_re1;
double twiddle_im1;
double twiddle_re2;
double twiddle_im2;
double data_re1;
double data_im1;
double data_re2;
double data_im2;
int bigloopcount;
int bigloopindex;
// always skip the first column
index += 1;
ij += row;
// calculate the phase
double theta = two_pi_over_N * ij;
// incremental calculation of theta
double cos_theta_plus_delta1;
double sin_theta_plus_delta1;
double cos_theta_plus_delta2;
double sin_theta_plus_delta2;
double delta = two_pi_over_N * row;
double cos_theta1 = cos(theta);
double sin_theta1 = sin(theta);
double cos_theta2 = cos(theta+delta);
double sin_theta2 = sin(theta+delta);
double delta2 = 2*two_pi_over_N * row;
double delta2_over_two = delta2 / 2.0;
double sin_delta2 = sin(delta2);
double sin_delta2_over_two = sin(delta2_over_two);
double two_sin_squared_delta2_over_two = 2.0 * sin_delta2_over_two * sin_delta2_over_two;
double a_2 = two_sin_squared_delta2_over_two;
double b_2 = sin_delta2;
bigloopcount = (dimension-1)/2;
col = 1;
for (bigloopindex=0; bigloopindex<bigloopcount; bigloopindex++) {
// do the twiddle -- comments show mathematical calculation
// twiddle_re = cos(theta);
twiddle_re1 = cos_theta1;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im1 = DIST_FFT_FORWARD * sin_theta1;
// twiddle_re = cos(theta);
twiddle_re2 = cos_theta2;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im2 = DIST_FFT_FORWARD * sin_theta2;
data_re1 = c_re(data, index);
data_im1 = c_im(data, index);
data_re2 = c_re(data, index+1);
data_im2 = c_im(data, index+1);
c_re(data, index) = twiddle_re1 * data_re1 - twiddle_im1 * data_im1;
c_im(data, index) = twiddle_re1 * data_im1 + twiddle_im1 * data_re1;
c_re(data, index+1) = twiddle_re2 * data_re2 - twiddle_im2 * data_im2;
c_im(data, index+1) = twiddle_re2 * data_im2 + twiddle_im2 * data_re2;
// ij = col * row;
ij += row;
// theta = two_pi_over_N * ij;
cos_theta_plus_delta1 = cos_theta1 - a_2 * cos_theta1 - b_2 * sin_theta1;
sin_theta_plus_delta1 = sin_theta1 - a_2 * sin_theta1 + b_2 * cos_theta1;
cos_theta1 = cos_theta_plus_delta1;
sin_theta1 = sin_theta_plus_delta1;
// theta = two_pi_over_N * ij;
cos_theta_plus_delta2 = cos_theta2 - a_2 * cos_theta2 - b_2 * sin_theta2;
sin_theta_plus_delta2 = sin_theta2 - a_2 * sin_theta2 + b_2 * cos_theta2;
cos_theta2 = cos_theta_plus_delta2;
sin_theta2 = sin_theta_plus_delta2;
// index = col + local_row * dimension;
index += 2;
col += 2;
}
if (!(dimension & 1)) {
// do the twiddle -- comments show mathematical calculation
// twiddle_re = cos(theta);
twiddle_re1 = cos_theta1;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im1 = DIST_FFT_FORWARD * sin_theta1;
data_re1 = c_re(data, index);
data_im1 = c_im(data, index);
c_re(data, index) = twiddle_re1 * data_re1 - twiddle_im1 * data_im1;
c_im(data, index) = twiddle_re1 * data_im1 + twiddle_im1 * data_re1;
}
#if DEBUG_ENDANGLE_PRINT
// print final angle:
if (!(dimension & 1)) {
double endangle = theta+(dimension-1)*delta;
printf("NEW (even) angle:%.10f truecos:%.10f truesin:%.10f cos:%.10f sin:%.10f\n", endangle, cos(endangle), sin(endangle), twiddle_re1, twiddle_im1);
} else {
double endangle = theta+(dimension-1)*delta;
printf("NEW (odd) angle:%.10f truecos:%.10f truesin:%.10f cos:%.10f sin:%.10f\n", endangle, cos(endangle), sin(endangle), twiddle_re2, twiddle_im2);
}
#endif // DEBUG_ENDANGLE_PRINT
}
void twiddle_row_inverse(dist_fft_storage data,
int local_row,
int local_row_start,
int dimension,
double two_pi_over_N)
{
int col;
int row = local_row + local_row_start;
int index = local_row * dimension;
int ij = 0;
double twiddle_re1;
double twiddle_im1;
double twiddle_re2;
double twiddle_im2;
double data_re1;
double data_im1;
double data_re2;
double data_im2;
int bigloopcount;
int bigloopindex;
// always skip the first column
index += 1;
ij += row;
// calculate the phase
double theta = two_pi_over_N * ij;
// incremental calculation of theta
double cos_theta_plus_delta1;
double sin_theta_plus_delta1;
double cos_theta_plus_delta2;
double sin_theta_plus_delta2;
double delta = two_pi_over_N * row;
double cos_theta1 = cos(theta);
double sin_theta1 = sin(theta);
double cos_theta2 = cos(theta+delta);
double sin_theta2 = sin(theta+delta);
double delta2 = 2*two_pi_over_N * row;
double delta2_over_two = delta2 / 2.0;
double sin_delta2 = sin(delta2);
double sin_delta2_over_two = sin(delta2_over_two);
double two_sin_squared_delta2_over_two = 2.0 * sin_delta2_over_two * sin_delta2_over_two;
double a_2 = two_sin_squared_delta2_over_two;
double b_2 = sin_delta2;
bigloopcount = (dimension-1)/2;
col = 1;
for (bigloopindex=0; bigloopindex<bigloopcount; bigloopindex++) {
// do the twiddle -- comments show mathematical calculation
// twiddle_re = cos(theta);
twiddle_re1 = cos_theta1;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im1 = DIST_FFT_FORWARD * sin_theta1;
// twiddle_re = cos(theta);
twiddle_re2 = cos_theta2;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im2 = DIST_FFT_FORWARD * sin_theta2;
data_re1 = c_re(data, index);
data_im1 = c_im(data, index);
data_re2 = c_re(data, index+1);
data_im2 = c_im(data, index+1);
c_re(data, index) = twiddle_re1 * data_re1 + twiddle_im1 * data_im1;
c_im(data, index) = twiddle_re1 * data_im1 - twiddle_im1 * data_re1;
c_re(data, index+1) = twiddle_re2 * data_re2 + twiddle_im2 * data_im2;
c_im(data, index+1) = twiddle_re2 * data_im2 - twiddle_im2 * data_re2;
// ij = col * row;
ij += row;
// theta = two_pi_over_N * ij;
cos_theta_plus_delta1 = cos_theta1 - a_2 * cos_theta1 - b_2 * sin_theta1;
sin_theta_plus_delta1 = sin_theta1 - a_2 * sin_theta1 + b_2 * cos_theta1;
cos_theta1 = cos_theta_plus_delta1;
sin_theta1 = sin_theta_plus_delta1;
// theta = two_pi_over_N * ij;
cos_theta_plus_delta2 = cos_theta2 - a_2 * cos_theta2 - b_2 * sin_theta2;
sin_theta_plus_delta2 = sin_theta2 - a_2 * sin_theta2 + b_2 * cos_theta2;
cos_theta2 = cos_theta_plus_delta2;
sin_theta2 = sin_theta_plus_delta2;
// index = col + local_row * dimension;
index += 2;
col += 2;
}
if (!(dimension & 1)) {
// do the twiddle -- comments show mathematical calculation
// twiddle_re = cos(theta);
twiddle_re1 = cos_theta1;
// twiddle_im = DIST_FFT_FORWARD * sin(theta);
twiddle_im1 = DIST_FFT_FORWARD * sin_theta1;
data_re1 = c_re(data, index);
data_im1 = c_im(data, index);
c_re(data, index) = twiddle_re1 * data_re1 + twiddle_im1 * data_im1;
c_im(data, index) = twiddle_re1 * data_im1 - twiddle_im1 * data_re1;
}
#if DEBUG_ENDANGLE_PRINT
// print final angle:
if (!(dimension & 1)) {
double endangle = theta+(dimension-1)*delta;
printf("NEW (even) angle:%.10f truecos:%.10f truesin:%.10f cos:%.10f sin:%.10f\n", endangle, cos(endangle), sin(endangle), twiddle_re1, twiddle_im1);
} else {
double endangle = theta+(dimension-1)*delta;
printf("NEW (odd) angle:%.10f truecos:%.10f truesin:%.10f cos:%.10f sin:%.10f\n", endangle, cos(endangle), sin(endangle), twiddle_re2, twiddle_im2);
}
#endif // DEBUG_ENDANGLE_PRINT
}
/*
void twiddle_row_forward(dist_fft_storage data,
int local_row,
int local_row_start,
int dimension,
double two_pi_over_N)
{
int col;
int row = local_row + local_row_start;
// skip the first row
if (row == 0) return;
int index = local_row * dimension;
int ij = 0;
dist_fft_real twiddle_re;
dist_fft_real twiddle_im;
dist_fft_real data_re;
dist_fft_real data_im;
// always skip the first column
index += 1;
ij += row;
// calculate the phase
double theta = two_pi_over_N * ij;
// incremental calculation of theta
// double cos_theta = cos(theta);
// double sin_theta = sin(theta);
//
// double cos_theta_plus_delta;
// double sin_theta_plus_delta;
//
// double delta = two_pi_over_N * row;
// double delta_over_two = delta / 2.0;
//
// double sin_delta = sin(delta);
// double sin_delta_over_two = sin(delta_over_two);
//
// double two_sin_squared_delta_over_two = 2.0 * sin_delta_over_two * sin_delta_over_two;
//
// double a = two_sin_squared_delta_over_two;
// double b = sin_delta;
for (col=1; col<dimension; col++) {
// do the twiddle -- comments show mathematical calculation
twiddle_re = cos(theta);
// twiddle_re = cos_theta;
twiddle_im = DIST_FFT_FORWARD * sin(theta);
// twiddle_im = DIST_FFT_FORWARD * sin_theta;
data_re = c_re(data, index);
data_im = c_im(data, index);
c_re(data, index) = twiddle_re * data_re - twiddle_im * data_im;
c_im(data, index) = twiddle_re * data_im + twiddle_im * data_re;
// ij = col * row;
ij += row;
// theta = two_pi_over_N * ij;
// cos_theta_plus_delta = cos_theta - a * cos_theta - b * sin_theta;
// sin_theta_plus_delta = sin_theta - a * sin_theta + b * cos_theta;
// cos_theta = cos_theta_plus_delta;
// sin_theta = sin_theta_plus_delta;
// index = col + local_row * dimension;
index += 1;
}
}
void twiddle_row_inverse(dist_fft_storage data,
int local_row,
int local_row_start,
int dimension,
double two_pi_over_N)
{
int col;
int row = local_row + local_row_start;
// skip the first row
if (row == 0) return;
int index = local_row * dimension;
int ij = 0;
dist_fft_real twiddle_re;
dist_fft_real twiddle_im;
dist_fft_real data_re;
dist_fft_real data_im;
// always skip the first column
index += 1;
ij += row;
// calculate the phase
double theta = two_pi_over_N * ij;
// incremental calculation of theta
// double cos_theta = cos(theta);
// double sin_theta = sin(theta);
//
// double cos_theta_plus_delta;
// double sin_theta_plus_delta;
//
// double delta = two_pi_over_N * row;
// double delta_over_two = delta / 2.0;
//
// double sin_delta = sin(delta);
// double sin_delta_over_two = sin(delta_over_two);
//
// double two_sin_squared_delta_over_two = 2.0 * sin_delta_over_two * sin_delta_over_two;
//
// double a = two_sin_squared_delta_over_two;
// double b = sin_delta;
for (col=1; col<dimension; col++) {
// do the twiddle -- comments show mathematical calculation
twiddle_re = cos(theta);
// twiddle_re = cos_theta;
twiddle_im = DIST_FFT_FORWARD * sin(theta);
// twiddle_im = DIST_FFT_FORWARD * sin_theta;
data_re = c_re(data, index);
data_im = c_im(data, index);
c_re(data, index) = twiddle_re * data_re + twiddle_im * data_im;
c_im(data, index) = twiddle_re * data_im - twiddle_im * data_re;
// ij = col * row;
ij += row;
// theta = two_pi_over_N * ij;
// cos_theta_plus_delta = cos_theta - a * cos_theta - b * sin_theta;
// sin_theta_plus_delta = sin_theta - a * sin_theta + b * cos_theta;
// cos_theta = cos_theta_plus_delta;
// sin_theta = sin_theta_plus_delta;
// index = col + local_row * dimension;
index += 1;
}
}
*/</pre>
<!--googleoff: index -->
</td>
</tr>
</table>
<!-- END WIDE COLUMN -->
<!-- END MAIN CONTENT -->
<table width="680" border="0" cellpadding="0" cellspacing="0">
<tr>
<td><div style="width: 100%; height: 1px; background-color: #919699; margin-top: 5px; margin-bottom: 15px"></div></td>
</tr>
<tr>
<td align="center"><br/>
<table border="0" cellpadding="0" cellspacing="0" class="graybox">
<tr>
<th>Did this document help you?</th>
</tr>
<tr>
<td>
<div style="margin-bottom: 8px"><a href="http://developer.apple.com/feedback/?v=1&url=/samplecode/dist_fft/listing7.html%3Fid%3DDTS10003377-1.0&media=dvd" target=_new>Yes</a>: Tell us what works for you.</div>
<div style="margin-bottom: 8px"><a href="http://developer.apple.com/feedback/?v=2&url=/samplecode/dist_fft/listing7.html%3Fid%3DDTS10003377-1.0&media=dvd" target=_new>It’s good, but:</a> Report typos, inaccuracies, and so forth.</div>
<div><a href="http://developer.apple.com/feedback/?v=3&url=/samplecode/dist_fft/listing7.html%3Fid%3DDTS10003377-1.0&media=dvd" target=_new>It wasn’t helpful</a>: Tell us what would have helped.</div>
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- START BOTTOM APPLE NAVIGATION -->
<!--#include virtual="/includes/footer"-->
<!-- END BOTTOM APPLE NAVIGATION -->
<!-- START CENTER CLOSE -->
</center>
<!-- END CENTER CLOSE -->
</body>
</html>