-
-
Notifications
You must be signed in to change notification settings - Fork 66
/
vna_math.c
830 lines (792 loc) · 35.7 KB
/
vna_math.c
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
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
/*
* Copyright (c) 2019-2021, Dmitry (DiSlord) [email protected]
* All rights reserved.
*
* This is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3, or (at your option)
* any later version.
*
* The software is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Radio; see the file COPYING. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street,
* Boston, MA 02110-1301, USA.
*/
#include "nanovna.h"
#include <stdint.h>
// Use table increase transform speed, but increase code size
// Use compact table, need 1/4 code size, and not decrease speed
// Used only if not defined __VNA_USE_MATH_TABLES__ (use self table for TTF or direct sin/cos calculations)
#define FFT_USE_SIN_COS_TABLE
// Use sin table and interpolation for sin/sos calculations
#ifdef __VNA_USE_MATH_TABLES__
// Use 512 table for calculation sin/cos value, also use this table for FFT
#define FAST_MATH_TABLE_SIZE 512
// Not use high part of table
#define GET_SIN_TABLE(idx) (((idx) < 256) ? sin_table_512[(idx)] : -sin_table_512[(idx)-256])
static const float sin_table_512[FAST_MATH_TABLE_SIZE/2 + 1] = {
/*
* float has about 7.2 digits of precision
for (int i = 0; i < FAST_MATH_TABLE_SIZE; i++) {
printf("% .8f,%c", sin(2 * M_PI * i / FAST_MATH_TABLE_SIZE), i % 8 == 7 ? '\n' : ' ');
}
*/
0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f, 0.07356456f, 0.08579731f,
0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f, 0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f,
0.19509032f, 0.20711138f, 0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f, 0.35989504f, 0.37131719f,
0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f, 0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f,
0.47139674f, 0.48218377f, 0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f, 0.61523159f, 0.62485949f,
0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f, 0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f,
0.70710678f, 0.71573083f, 0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f, 0.81758481f, 0.82458930f,
0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f, 0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f,
0.88192126f, 0.88763962f, 0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f, 0.94952818f, 0.95330604f,
0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f, 0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f,
0.98078528f, 0.98310549f, 0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f, 0.99969882f, 0.99992470f,
1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f, 0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f,
0.99518473f, 0.99390697f, 0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f, 0.96377607f, 0.96043052f,
0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f, 0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f,
0.92387953f, 0.91911385f, 0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f, 0.84485357f, 0.83822471f,
0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f, 0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f,
0.77301045f, 0.76516727f, 0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f, 0.65317284f, 0.64383154f,
0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f, 0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f,
0.55557023f, 0.54532499f, 0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f, 0.40524131f, 0.39399204f,
0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f, 0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f,
0.29028468f, 0.27851969f, 0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f, 0.12241068f, 0.11022221f,
0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f, 0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f,
0.00000000f,
/*
-0.01227154f,-0.02454123f,-0.03680722f,-0.04906767f,-0.06132074f,-0.07356456f,-0.08579731f,
-0.09801714f,-0.11022221f,-0.12241068f,-0.13458071f,-0.14673047f,-0.15885814f,-0.17096189f,-0.18303989f,
-0.19509032f,-0.20711138f,-0.21910124f,-0.23105811f,-0.24298018f,-0.25486566f,-0.26671276f,-0.27851969f,
-0.29028468f,-0.30200595f,-0.31368174f,-0.32531029f,-0.33688985f,-0.34841868f,-0.35989504f,-0.37131719f,
-0.38268343f,-0.39399204f,-0.40524131f,-0.41642956f,-0.42755509f,-0.43861624f,-0.44961133f,-0.46053871f,
-0.47139674f,-0.48218377f,-0.49289819f,-0.50353838f,-0.51410274f,-0.52458968f,-0.53499762f,-0.54532499f,
-0.55557023f,-0.56573181f,-0.57580819f,-0.58579786f,-0.59569930f,-0.60551104f,-0.61523159f,-0.62485949f,
-0.63439328f,-0.64383154f,-0.65317284f,-0.66241578f,-0.67155895f,-0.68060100f,-0.68954054f,-0.69837625f,
-0.70710678f,-0.71573083f,-0.72424708f,-0.73265427f,-0.74095113f,-0.74913639f,-0.75720885f,-0.76516727f,
-0.77301045f,-0.78073723f,-0.78834643f,-0.79583690f,-0.80320753f,-0.81045720f,-0.81758481f,-0.82458930f,
-0.83146961f,-0.83822471f,-0.84485357f,-0.85135519f,-0.85772861f,-0.86397286f,-0.87008699f,-0.87607009f,
-0.88192126f,-0.88763962f,-0.89322430f,-0.89867447f,-0.90398929f,-0.90916798f,-0.91420976f,-0.91911385f,
-0.92387953f,-0.92850608f,-0.93299280f,-0.93733901f,-0.94154407f,-0.94560733f,-0.94952818f,-0.95330604f,
-0.95694034f,-0.96043052f,-0.96377607f,-0.96697647f,-0.97003125f,-0.97293995f,-0.97570213f,-0.97831737f,
-0.98078528f,-0.98310549f,-0.98527764f,-0.98730142f,-0.98917651f,-0.99090264f,-0.99247953f,-0.99390697f,
-0.99518473f,-0.99631261f,-0.99729046f,-0.99811811f,-0.99879546f,-0.99932238f,-0.99969882f,-0.99992470f,
-1.00000000f,-0.99992470f,-0.99969882f,-0.99932238f,-0.99879546f,-0.99811811f,-0.99729046f,-0.99631261f,
-0.99518473f,-0.99390697f,-0.99247953f,-0.99090264f,-0.98917651f,-0.98730142f,-0.98527764f,-0.98310549f,
-0.98078528f,-0.97831737f,-0.97570213f,-0.97293995f,-0.97003125f,-0.96697647f,-0.96377607f,-0.96043052f,
-0.95694034f,-0.95330604f,-0.94952818f,-0.94560733f,-0.94154407f,-0.93733901f,-0.93299280f,-0.92850608f,
-0.92387953f,-0.91911385f,-0.91420976f,-0.90916798f,-0.90398929f,-0.89867447f,-0.89322430f,-0.88763962f,
-0.88192126f,-0.87607009f,-0.87008699f,-0.86397286f,-0.85772861f,-0.85135519f,-0.84485357f,-0.83822471f,
-0.83146961f,-0.82458930f,-0.81758481f,-0.81045720f,-0.80320753f,-0.79583690f,-0.78834643f,-0.78073723f,
-0.77301045f,-0.76516727f,-0.75720885f,-0.74913639f,-0.74095113f,-0.73265427f,-0.72424708f,-0.71573083f,
-0.70710678f,-0.69837625f,-0.68954054f,-0.68060100f,-0.67155895f,-0.66241578f,-0.65317284f,-0.64383154f,
-0.63439328f,-0.62485949f,-0.61523159f,-0.60551104f,-0.59569930f,-0.58579786f,-0.57580819f,-0.56573181f,
-0.55557023f,-0.54532499f,-0.53499762f,-0.52458968f,-0.51410274f,-0.50353838f,-0.49289819f,-0.48218377f,
-0.47139674f,-0.46053871f,-0.44961133f,-0.43861624f,-0.42755509f,-0.41642956f,-0.40524131f,-0.39399204f,
-0.38268343f,-0.37131719f,-0.35989504f,-0.34841868f,-0.33688985f,-0.32531029f,-0.31368174f,-0.30200595f,
-0.29028468f,-0.27851969f,-0.26671276f,-0.25486566f,-0.24298018f,-0.23105811f,-0.21910124f,-0.20711138f,
-0.19509032f,-0.18303989f,-0.17096189f,-0.15885814f,-0.14673047f,-0.13458071f,-0.12241068f,-0.11022221f,
-0.09801714f,-0.08579731f,-0.07356456f,-0.06132074f,-0.04906767f,-0.03680722f,-0.02454123f,-0.01227154f,
-0.00000000f*/
};
//
#if FFT_SIZE == 256
#define FFT_SIN(i) sin_table_512[ 2*(i)]
#define FFT_COS(i) ((i) > 64 ?-sin_table_512[2*(i)-128] : sin_table_512[128-2*(i)])
#elif FFT_SIZE == 512
#define FFT_SIN(i) sin_table_512[ (i)]
#define FFT_COS(i) ((i) > 128 ?-sin_table_512[ (i)-128] : sin_table_512[128- (i)])
#else
#error "Need use bigger sin/cos table for new FFT size"
#endif
#else
#ifdef FFT_USE_SIN_COS_TABLE
#if FFT_SIZE == 256
static const float sin_table_256[] = {
/*
* float has about 7.2 digits of precision
for (uint8_t i = 0; i < FFT_SIZE - (FFT_SIZE / 4); i++) {
printf("% .8f,%c", sin(2 * M_PI * i / FFT_SIZE), i % 8 == 7 ? '\n' : ' ');
}
*/
// for FFT_SIZE = 256
0.00000000, 0.02454123, 0.04906767, 0.07356456, 0.09801714, 0.12241068, 0.14673047, 0.17096189,
0.19509032, 0.21910124, 0.24298018, 0.26671276, 0.29028468, 0.31368174, 0.33688985, 0.35989504,
0.38268343, 0.40524131, 0.42755509, 0.44961133, 0.47139674, 0.49289819, 0.51410274, 0.53499762,
0.55557023, 0.57580819, 0.59569930, 0.61523159, 0.63439328, 0.65317284, 0.67155895, 0.68954054,
0.70710678, 0.72424708, 0.74095113, 0.75720885, 0.77301045, 0.78834643, 0.80320753, 0.81758481,
0.83146961, 0.84485357, 0.85772861, 0.87008699, 0.88192126, 0.89322430, 0.90398929, 0.91420976,
0.92387953, 0.93299280, 0.94154407, 0.94952818, 0.95694034, 0.96377607, 0.97003125, 0.97570213,
0.98078528, 0.98527764, 0.98917651, 0.99247953, 0.99518473, 0.99729046, 0.99879546, 0.99969882,
1.00000000,/* 0.99969882, 0.99879546, 0.99729046, 0.99518473, 0.99247953, 0.98917651, 0.98527764,
0.98078528, 0.97570213, 0.97003125, 0.96377607, 0.95694034, 0.94952818, 0.94154407, 0.93299280,
0.92387953, 0.91420976, 0.90398929, 0.89322430, 0.88192126, 0.87008699, 0.85772861, 0.84485357,
0.83146961, 0.81758481, 0.80320753, 0.78834643, 0.77301045, 0.75720885, 0.74095113, 0.72424708,
0.70710678, 0.68954054, 0.67155895, 0.65317284, 0.63439328, 0.61523159, 0.59569930, 0.57580819,
0.55557023, 0.53499762, 0.51410274, 0.49289819, 0.47139674, 0.44961133, 0.42755509, 0.40524131,
0.38268343, 0.35989504, 0.33688985, 0.31368174, 0.29028468, 0.26671276, 0.24298018, 0.21910124,
0.19509032, 0.17096189, 0.14673047, 0.12241068, 0.09801714, 0.07356456, 0.04906767, 0.02454123,
0.00000000, -0.02454123, -0.04906767, -0.07356456, -0.09801714, -0.12241068, -0.14673047, -0.17096189,
-0.19509032, -0.21910124, -0.24298018, -0.26671276, -0.29028468, -0.31368174, -0.33688985, -0.35989504,
-0.38268343, -0.40524131, -0.42755509, -0.44961133, -0.47139674, -0.49289819, -0.51410274, -0.53499762,
-0.55557023, -0.57580819, -0.59569930, -0.61523159, -0.63439328, -0.65317284, -0.67155895, -0.68954054,
-0.70710678, -0.72424708, -0.74095113, -0.75720885, -0.77301045, -0.78834643, -0.80320753, -0.81758481,
-0.83146961, -0.84485357, -0.85772861, -0.87008699, -0.88192126, -0.89322430, -0.90398929, -0.91420976,
-0.92387953, -0.93299280, -0.94154407, -0.94952818, -0.95694034, -0.96377607, -0.97003125, -0.97570213,
-0.98078528, -0.98527764, -0.98917651, -0.99247953, -0.99518473, -0.99729046, -0.99879546, -0.99969882,*/
};
// full size table:
// sin = sin_table_256[i ]
// cos = sin_table_256[i+64]
//#define FFT_SIN(i) sin_table_256[(i)]
//#define FFT_COS(i) sin_table_256[(i)+64]
// for size use only 0-64 indexes
// sin = i > 64 ? sin_table_256[128-i] : sin_table_256[ i];
// cos = i > 64 ?-sin_table_256[ i-64] : sin_table_256[64-i];
#define FFT_SIN(i) ((i) > 64 ? sin_table_256[128-(i)] : sin_table_256[ (i)])
#define FFT_COS(i) ((i) > 64 ?-sin_table_256[ (i)-64] : sin_table_256[64-(i)])
#elif FFT_SIZE == 512
static const float sin_table_512[] = {
/*
* float has about 7.2 digits of precision
for (int i = 0; i < FFT_SIZE - (FFT_SIZE / 4); i++) {
printf("% .8f,%c", sin(2 * M_PI * i / FFT_SIZE), i % 8 == 7 ? '\n' : ' ');
}
*/
// For FFT_SIZE = 512
0.00000000, 0.01227154, 0.02454123, 0.03680722, 0.04906767, 0.06132074, 0.07356456, 0.08579731,
0.09801714, 0.11022221, 0.12241068, 0.13458071, 0.14673047, 0.15885814, 0.17096189, 0.18303989,
0.19509032, 0.20711138, 0.21910124, 0.23105811, 0.24298018, 0.25486566, 0.26671276, 0.27851969,
0.29028468, 0.30200595, 0.31368174, 0.32531029, 0.33688985, 0.34841868, 0.35989504, 0.37131719,
0.38268343, 0.39399204, 0.40524131, 0.41642956, 0.42755509, 0.43861624, 0.44961133, 0.46053871,
0.47139674, 0.48218377, 0.49289819, 0.50353838, 0.51410274, 0.52458968, 0.53499762, 0.54532499,
0.55557023, 0.56573181, 0.57580819, 0.58579786, 0.59569930, 0.60551104, 0.61523159, 0.62485949,
0.63439328, 0.64383154, 0.65317284, 0.66241578, 0.67155895, 0.68060100, 0.68954054, 0.69837625,
0.70710678, 0.71573083, 0.72424708, 0.73265427, 0.74095113, 0.74913639, 0.75720885, 0.76516727,
0.77301045, 0.78073723, 0.78834643, 0.79583690, 0.80320753, 0.81045720, 0.81758481, 0.82458930,
0.83146961, 0.83822471, 0.84485357, 0.85135519, 0.85772861, 0.86397286, 0.87008699, 0.87607009,
0.88192126, 0.88763962, 0.89322430, 0.89867447, 0.90398929, 0.90916798, 0.91420976, 0.91911385,
0.92387953, 0.92850608, 0.93299280, 0.93733901, 0.94154407, 0.94560733, 0.94952818, 0.95330604,
0.95694034, 0.96043052, 0.96377607, 0.96697647, 0.97003125, 0.97293995, 0.97570213, 0.97831737,
0.98078528, 0.98310549, 0.98527764, 0.98730142, 0.98917651, 0.99090264, 0.99247953, 0.99390697,
0.99518473, 0.99631261, 0.99729046, 0.99811811, 0.99879546, 0.99932238, 0.99969882, 0.99992470,
1.00000000,/* 0.99992470, 0.99969882, 0.99932238, 0.99879546, 0.99811811, 0.99729046, 0.99631261,
0.99518473, 0.99390697, 0.99247953, 0.99090264, 0.98917651, 0.98730142, 0.98527764, 0.98310549,
0.98078528, 0.97831737, 0.97570213, 0.97293995, 0.97003125, 0.96697647, 0.96377607, 0.96043052,
0.95694034, 0.95330604, 0.94952818, 0.94560733, 0.94154407, 0.93733901, 0.93299280, 0.92850608,
0.92387953, 0.91911385, 0.91420976, 0.90916798, 0.90398929, 0.89867447, 0.89322430, 0.88763962,
0.88192126, 0.87607009, 0.87008699, 0.86397286, 0.85772861, 0.85135519, 0.84485357, 0.83822471,
0.83146961, 0.82458930, 0.81758481, 0.81045720, 0.80320753, 0.79583690, 0.78834643, 0.78073723,
0.77301045, 0.76516727, 0.75720885, 0.74913639, 0.74095113, 0.73265427, 0.72424708, 0.71573083,
0.70710678, 0.69837625, 0.68954054, 0.68060100, 0.67155895, 0.66241578, 0.65317284, 0.64383154,
0.63439328, 0.62485949, 0.61523159, 0.60551104, 0.59569930, 0.58579786, 0.57580819, 0.56573181,
0.55557023, 0.54532499, 0.53499762, 0.52458968, 0.51410274, 0.50353838, 0.49289819, 0.48218377,
0.47139674, 0.46053871, 0.44961133, 0.43861624, 0.42755509, 0.41642956, 0.40524131, 0.39399204,
0.38268343, 0.37131719, 0.35989504, 0.34841868, 0.33688985, 0.32531029, 0.31368174, 0.30200595,
0.29028468, 0.27851969, 0.26671276, 0.25486566, 0.24298018, 0.23105811, 0.21910124, 0.20711138,
0.19509032, 0.18303989, 0.17096189, 0.15885814, 0.14673047, 0.13458071, 0.12241068, 0.11022221,
0.09801714, 0.08579731, 0.07356456, 0.06132074, 0.04906767, 0.03680722, 0.02454123, 0.01227154,
0.00000000, -0.01227154, -0.02454123, -0.03680722, -0.04906767, -0.06132074, -0.07356456, -0.08579731,
-0.09801714, -0.11022221, -0.12241068, -0.13458071, -0.14673047, -0.15885814, -0.17096189, -0.18303989,
-0.19509032, -0.20711138, -0.21910124, -0.23105811, -0.24298018, -0.25486566, -0.26671276, -0.27851969,
-0.29028468, -0.30200595, -0.31368174, -0.32531029, -0.33688985, -0.34841868, -0.35989504, -0.37131719,
-0.38268343, -0.39399204, -0.40524131, -0.41642956, -0.42755509, -0.43861624, -0.44961133, -0.46053871,
-0.47139674, -0.48218377, -0.49289819, -0.50353838, -0.51410274, -0.52458968, -0.53499762, -0.54532499,
-0.55557023, -0.56573181, -0.57580819, -0.58579786, -0.59569930, -0.60551104, -0.61523159, -0.62485949,
-0.63439328, -0.64383154, -0.65317284, -0.66241578, -0.67155895, -0.68060100, -0.68954054, -0.69837625,
-0.70710678, -0.71573083, -0.72424708, -0.73265427, -0.74095113, -0.74913639, -0.75720885, -0.76516727,
-0.77301045, -0.78073723, -0.78834643, -0.79583690, -0.80320753, -0.81045720, -0.81758481, -0.82458930,
-0.83146961, -0.83822471, -0.84485357, -0.85135519, -0.85772861, -0.86397286, -0.87008699, -0.87607009,
-0.88192126, -0.88763962, -0.89322430, -0.89867447, -0.90398929, -0.90916798, -0.91420976, -0.91911385,
-0.92387953, -0.92850608, -0.93299280, -0.93733901, -0.94154407, -0.94560733, -0.94952818, -0.95330604,
-0.95694034, -0.96043052, -0.96377607, -0.96697647, -0.97003125, -0.97293995, -0.97570213, -0.97831737,
-0.98078528, -0.98310549, -0.98527764, -0.98730142, -0.98917651, -0.99090264, -0.99247953, -0.99390697,
-0.99518473, -0.99631261, -0.99729046, -0.99811811, -0.99879546, -0.99932238, -0.99969882, -0.99992470*/
};
// full size table:
// sin = sin_table_512[i ]
// cos = sin_table_512[i+128]
//#define FFT_SIN(i) sin_table_512[(i) ]
//#define FFT_COS(i) sin_table_512[(i)+128]
// for size use only 0-128 indexes
// sin = i > 128 ? sin_table_512[256-i] : sin_table_512[ i];
// cos = i > 128 ?-sin_table_512[i-128] : sin_table_512[128-i];
#define FFT_SIN(i) ((i) > 128 ? sin_table_512[256-(i)] : sin_table_512[ (i)])
#define FFT_COS(i) ((i) > 128 ?-sin_table_512[(i)-128] : sin_table_512[128-(i)])
#else
#error "Need build table for new FFT size"
#endif
#else
// Not use FFT_USE_SIN_COS_TABLE, use direct sin/cos calculations
#define FFT_SIN(k) sinf((2 * VNA_PI / FFT_SIZE) * (k))
#define FFT_COS(k) cosf((2 * VNA_PI / FFT_SIZE) * (k));
#endif // FFT_USE_SIN_COS_TABLE
#endif // __VNA_USE_MATH_TABLES__
#ifdef ARM_MATH_CM4
// Use CORTEX M4 rbit instruction (reverse bit order in 32bit value)
static uint32_t reverse_bits(uint32_t x, int n) {
uint32_t result;
__asm volatile ("rbit %0, %1" : "=r" (result) : "r" (x) );
return result>>(32-n); // made shift for correct result
}
#else
static uint16_t reverse_bits(uint16_t x, int n) {
uint16_t result = 0;
int i;
for (i = 0; i < n; i++, x >>= 1)
result = (result << 1) | (x & 1U);
return result;
}
#endif
/***
* dir = forward: 0, inverse: 1
* https://www.nayuki.io/res/free-small-fft-in-multiple-languages/fft.c
*/
void fft(float array[][2], const uint8_t dir) {
// FFT_SIZE = 2^FFT_N
#if FFT_SIZE == 256
#define FFT_N 8
#elif FFT_SIZE == 512
#define FFT_N 9
#else
#error "Need define FFT_N for this FFT size"
#endif
const uint16_t n = FFT_SIZE;
const uint8_t levels = FFT_N; // log2(n)
uint16_t i, j;
for (i = 0; i < n; i++) {
if ((j = reverse_bits(i, levels)) > i) {
SWAP(float, array[i][0], array[j][0]);
SWAP(float, array[i][1], array[j][1]);
}
}
const uint16_t size = 2;
uint16_t halfsize = size / 2;
uint16_t tablestep = n / size;
// Cooley-Tukey decimation-in-time radix-2 FFT
for (;tablestep; tablestep>>=1, halfsize<<=1) {
for (i = 0; i < n; i+= halfsize) {
for (j = 0; j < n / size; i++, j+= tablestep) {
const uint16_t l = i + halfsize;
const float s = dir ? FFT_SIN(j) : -FFT_SIN(j);
const float c = FFT_COS(j);
const float tpre = array[l][0] * c - array[l][1] * s;
const float tpim = array[l][0] * s + array[l][1] * c;
array[l][0] = array[i][0] - tpre; array[i][0]+= tpre;
array[l][1] = array[i][1] - tpim; array[i][1]+= tpim;
}
}
}
}
// Return sin/cos value angle in range 0.0 to 1.0 (0 is 0 degree, 1 is 360 degree)
void vna_sincosf(float angle, float * pSinVal, float * pCosVal)
{
#ifndef __VNA_USE_MATH_TABLES__
// Use default sin/cos functions
angle *= 2 * VNA_PI; // Convert to rad
*pSinVal = sinf(angle);
*pCosVal = cosf(angle);
#else
uint16_t indexS, indexC; // Index variable
float f1, f2, d1, d2; // Two nearest output values
float fract, temp;
// Round angle to range 0.0 to 1.0
temp = vna_fabsf(angle);
temp-= (uint32_t)temp;
// Scale input from range 0.0 to 1.0 to table size
temp*= FAST_MATH_TABLE_SIZE;
indexS = temp;
indexC = indexS + (FAST_MATH_TABLE_SIZE / 4); // cosine add 0.25 (pi/2) to read from sine table
// Calculation of fractional value
fract = temp - indexS;
// Align indexes to table
indexS&= (FAST_MATH_TABLE_SIZE-1);
indexC&= (FAST_MATH_TABLE_SIZE-1);
// Read two nearest values of input value from the cos & sin tables
#if 0
f1 = GET_SIN_TABLE(indexC );
f2 = GET_SIN_TABLE(indexC+1);
d1 = GET_SIN_TABLE(indexS );
d2 = GET_SIN_TABLE(indexS+1);
#else
if (indexC < 256){f1 = sin_table_512[indexC +0];f2 = sin_table_512[indexC +1];}
else {f1 =-sin_table_512[indexC-256+0];f2 =-sin_table_512[indexC-256+1];}
if (indexS < 256){d1 = sin_table_512[indexS +0];d2 = sin_table_512[indexS +1];}
else {d1 =-sin_table_512[indexS-256+0];d2 =-sin_table_512[indexS-256+1];}
#endif
#if 1
// 1e-7 error on 512 size table
const float Dn = 2 * VNA_PI / FAST_MATH_TABLE_SIZE; // delta between the two points in table (fixed);
float Df;
// Calculation of cos value
Df = f2 - f1; // delta between the values of the functions
temp = Dn * (d1 + d2) + 2 * Df;
temp = Df + (d1 * Dn + temp - fract * temp);
temp = fract * temp - d1 * Dn;
*pCosVal = f1 + fract * temp;
// Calculation of sin value
Df = d1 - d2; // delta between the values of the functions
temp = Dn * (f1 + f2) + 2 * Df;
temp = Df + (f1 * Dn + temp - fract * temp);
temp = fract * temp - f1 * Dn;
*pSinVal = d1 - fract * temp;
#else
// 1e-5 error on 512 size table
// Calculation of sin and cos value, use simple linear interpolation
*pCosVal = fract * (f2 - f1) + f1;
*pSinVal = fract * (d2 - d1) + d1;
#endif
if (angle < 0)
*pSinVal = -*pSinVal;
#endif
}
//**********************************************************************************
// VNA math
//**********************************************************************************
// Cleanup declarations if used default math.h functions
#undef vna_sqrtf
#undef vna_cbrtf
#undef vna_logf
#undef vna_atanf
#undef vna_atan2f
#undef vna_modff
//**********************************************************************************
// modff function - return fractional part and integer from float value x
//**********************************************************************************
float vna_modff(float x, float *iptr)
{
union {float f; uint32_t i;} u = {x};
int e = (int)((u.i>>23)&0xff) - 0x7f; // get exponent
if (e < 0) { // no integral part
if (iptr) *iptr = 0;
return u.f;
}
if (e >= 23) x = 0; // no fractional part
else {
x = u.f; u.i&= ~(0x007fffff>>e); // remove fractional part from u
x-= u.f; // calc fractional part
}
//if (iptr) *iptr = ((u.i&0x007fffff)|0x00800000)>>(23-e); // cut integer part from float as integer
if (iptr) *iptr = u.f; // cut integer part from float as float
return x;
}
//**********************************************************************************
// square root
//**********************************************************************************
#if (__FPU_PRESENT == 0) && (__FPU_USED == 0)
#if 1
// __ieee754_sqrtf, remove some check (NAN, inf, normalization), small code optimization to arm
float vna_sqrtf(float x)
{
int32_t ix,s,q,m,t;
uint32_t r;
union {float f; uint32_t i;} u = {x};
ix = u.i;
#if 0
// take care of Inf and NaN
if((ix&0x7f800000)==0x7f800000) return x*x+x; // sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN
// take care if x < 0
if (ix < 0) return (x-x)/0.0f;
#endif
if (ix == 0) return 0.0f;
m = (ix>>23);
#if 0 //
// normalize x
if(m==0) { // subnormal x
for(int i=0;(ix&0x00800000)==0;i++) ix<<=1;
m -= i-1;
}
#endif
m -= 127; // unbias exponent
ix = (ix&0x007fffff)|0x00800000;
// generate sqrt(x) bit by bit
ix<<= (m&1) ? 2 : 1; // odd m, double x to make it even, and after multiple by 2
m >>= 1; // m = [m/2]
q = s = 0; // q = sqrt(x)
r = 0x01000000; // r = moving bit from right to left
while(r!=0) {
t = s+r;
if(t<=ix) {
s = t+r;
ix -= t;
q += r;
}
ix += ix;
r>>=1;
}
// use floating add to find out rounding direction
if(ix!=0) {
if ((1.0f - 1e-30f) >= 1.0f) // trigger inexact flag.
q += ((1.0f + 1e-30f) > 1.0f) ? 2 : (q&1);
}
ix = (q>>1)+0x3f000000;
ix += (m <<23);
u.i = ix;
return u.f;
}
#else
// Simple implementation, but slow if no FPU used, and not usable if used hardware FPU sqrtf
float vna_sqrtf(float x)
{
union {float x; uint32_t i;} u = {x};
u.i = (1<<29) + (u.i >> 1) - (1<<22);
// Two Babylonian Steps (simplified from:)
// u.x = 0.5f * (u.x + x/u.x);
// u.x = 0.5f * (u.x + x/u.x);
u.x = u.x + x/u.x;
u.x = 0.25f*u.x + x/u.x;
return u.x;
}
#endif
#endif
//**********************************************************************************
// Cube root
//**********************************************************************************
float vna_cbrtf(float x)
{
#if 1
static const uint32_t
B1 = 709958130, // B1 = (127-127.0/3-0.03306235651)*2**23
B2 = 642849266; // B2 = (127-127.0/3-24/3-0.03306235651)*2**23
float r,T;
union {float f; uint32_t i;} u = {x};
uint32_t hx = u.i & 0x7fffffff;
// if (hx >= 0x7f800000) // cbrt(NaN,INF) is itself
// return x + x;
// rough cbrtf to 5 bits
if (hx < 0x00800000) { // zero or subnormal?
if (hx == 0)
return x; // cbrt(+-0) is itself
u.f = x*0x1p24f;
hx = u.i & 0x7fffffff;
hx = hx/3 + B2;
} else
hx = hx/3 + B1;
u.i &= 0x80000000;
u.i |= hx;
// First step Newton iteration (solving t*t-x/t == 0) to 16 bits.
T = u.f;
r = T*T*T;
T*= (x+x+r)/(x+r+r);
// Second step Newton iteration to 47 bits.
r = T*T*T;
T*= (x+x+r)/(x+r+r);
return T;
#else
if (x == 0) {
// would otherwise return something like 4.257959840008151e-109
return 0;
}
float b = 1.0f; // use any value except 0
float last_b_1 = 0;
float last_b_2 = 0;
while (last_b_1 != b && last_b_2 != b) {
last_b_1 = b;
// b = (b + x / (b * b)) / 2;
b = (2 * b + x / b / b) / 3; // for small numbers, as suggested by willywonka_dailyblah
last_b_2 = b;
// b = (b + x / (b * b)) / 2;
b = (2 * b + x / b / b) / 3; //for small numbers, as suggested by willywonka_dailyblah
}
return b;
#endif
}
//**********************************************************************************
// logf
//**********************************************************************************
float vna_logf(float x)
{
const float MULTIPLIER = logf(2.0f);
#if 0
// Give up to 0.006 error (2.5x faster original code)
union {float f; int32_t i;} u = {x};
const int log_2 = ((u.i >> 23) & 255) - 128;
if (u.i <=0) return -1/(x*x); // if <=0 return -inf
u.i = (u.i&0x007FFFFF) + 0x3F800000;
u.f = ((-1.0f/3) * u.f + 2) * u.f - (2.0f/3); // (1)
return (u.f + log_2) * MULTIPLIER;
#elif 1
// Give up to 0.00005 error (2x faster original code)
// fast log2f approximation, give 0.0002 error
union { float f; uint32_t i; } vx = { x };
union { uint32_t i; float f; } mx = { (vx.i & 0x007FFFFF) | 0x3f000000 };
// if <=0 return NAN
if (vx.i <=0) return -1/(x*x);
return vx.i * (MULTIPLIER / (1 << 23)) - (124.22544637f * MULTIPLIER) - (1.498030302f * MULTIPLIER) * mx.f - (1.72587999f * MULTIPLIER) / (0.3520887068f + mx.f);
#else
// use original code (20% faster default)
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
union {float f; uint32_t i;} u = {x};
float hfsq,f,s,z,R,w,t1,t2,dk;
uint32_t ix;
int k;
ix = u.i;
k = 0;
if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
if (ix<<1 == 0)
return -1/(x*x); /* log(+-0)=-inf */
if (ix>>31)
return (x-x)/0.0f; /* log(-#) = NaN */
/* subnormal number, scale up x */
k -= 25;
x *= two25;
u.f = x;
ix = u.i;
} else if (ix >= 0x7f800000) {
return x;
} else if (ix == 0x3f800000)
return 0;
/* reduce x into [sqrt(2)/2, sqrt(2)] */
ix += 0x3f800000 - 0x3f3504f3;
k += (int)(ix>>23) - 0x7f;
ix = (ix&0x007fffff) + 0x3f3504f3;
u.i = ix;
x = u.f;
f = x - 1.0f;
s = f/(2.0f + f);
z = s*s;
w = z*z;
t1= w*(Lg2+w*Lg4);
t2= z*(Lg1+w*Lg3);
R = t2 + t1;
hfsq = 0.5f * f * f;
dk = k;
return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi;
#endif
}
float vna_log10f_x_10(float x)
{
const float MULTIPLIER = (10.0f * logf(2.0f) / logf(10.0f));
#if 0
// Give up to 0.006 error (2.5x faster original code)
union {float f; int32_t i;} u = {x};
const int log_2 = ((u.i >> 23) & 255) - 128;
if (u.i <=0) return -1/(x*x); // if <=0 return -inf
u.i = (u.i&0x007FFFFF) + 0x3F800000;
u.f = ((-1.0f/3) * u.f + 2) * u.f - (2.0f/3); // (1)
return (u.f + log_2) * MULTIPLIER;
#else
// Give up to 0.0001 error (2x faster original code)
// fast log2f approximation, give 0.0004 error
union { float f; uint32_t i; } vx = { x };
union { uint32_t i; float f; } mx = { (vx.i & 0x007FFFFF) | 0x3f000000 };
// if <=0 return NAN
if (vx.i <=0) return -1/(x*x);
return vx.i * (MULTIPLIER / (1 << 23)) - (124.22544637f * MULTIPLIER) - (1.498030302f * MULTIPLIER) * mx.f - (1.72587999f * MULTIPLIER) / (0.3520887068f + mx.f);
#endif
}
//**********************************************************************************
// atanf
//**********************************************************************************
// __ieee754_atanf
float vna_atanf(float x)
{
static const float atanhi[] = {
4.6364760399e-01, // atan(0.5)hi 0x3eed6338
7.8539812565e-01, // atan(1.0)hi 0x3f490fda
9.8279368877e-01, // atan(1.5)hi 0x3f7b985e
1.5707962513e+00, // atan(inf)hi 0x3fc90fda
};
static const float atanlo[] = {
5.0121582440e-09, // atan(0.5)lo 0x31ac3769
3.7748947079e-08, // atan(1.0)lo 0x33222168
3.4473217170e-08, // atan(1.5)lo 0x33140fb4
7.5497894159e-08, // atan(inf)lo 0x33a22168
};
static const float aT[] = {
3.3333328366e-01,
-1.9999158382e-01,
1.4253635705e-01,
-1.0648017377e-01,
6.1687607318e-02,
};
float w,s1,s2,z;
uint32_t ix,sign;
int id;
union {float f; uint32_t i;} u = {x};
ix = u.i;
sign = ix>>31;
ix &= 0x7fffffff;
if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
if (ix > 0x7f800000)
return x;
z = atanhi[3] + 0x1p-120f;
return sign ? -z : z;
}
if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x39800000) { /* |x| < 2**-12 */
return x;
}
id = -1;
} else {
x = vna_fabsf(x);
if (ix < 0x3f980000) { /* |x| < 1.1875 */
if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */
id = 0;
x = (2.0f*x - 1.0f)/(2.0f + x);
} else { /* 11/16 <= |x| < 19/16 */
id = 1;
x = (x - 1.0f)/(x + 1.0f);
}
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2;
x = (x - 1.5f)/(1.0f + 1.5f*x);
} else { /* 2.4375 <= |x| < 2**26 */
id = 3;
x = -1.0f/x;
}
}
}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
s2 = w*(aT[1]+w*aT[3]);
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return sign ? -z : z;
}
//**********************************************************************************
// atan2f
//**********************************************************************************
#if 0
// __ieee754_atan2f
float vna_atan2f(float y, float x)
{
static const float pi = 3.1415927410e+00; // 0x40490fdb
static const float pi_lo =-8.7422776573e-08; // 0xb3bbbd2e
float z;
uint32_t m,ix,iy;
union {float f; uint32_t i;} ux = {x};
union {float f; uint32_t i;} uy = {y};
ix = ux.i;
iy = uy.i;
if (ix == 0x3f800000) /* x=1.0 */
return vna_atanf(y);
m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
ix &= 0x7fffffff;
iy &= 0x7fffffff;
/* when y = 0 */
if (iy == 0) {
switch (m) {
case 0:
case 1: return y; // atan(+-0,+anything)=+-0
case 2: return pi; // atan(+0,-anything) = pi
case 3: return -pi; // atan(-0,-anything) =-pi
}
}
/* when x = 0 */
if (ix == 0)
return m&1 ? -pi/2 : pi/2;
/* when x is INF */
if (ix == 0x7f800000) {
if (iy == 0x7f800000) {
switch (m) {
case 0: return pi/4; /* atan(+INF,+INF) */
case 1: return -pi/4; /* atan(-INF,+INF) */
case 2: return 3*pi/4; /*atan(+INF,-INF)*/
case 3: return -3*pi/4; /*atan(-INF,-INF)*/
}
} else {
switch (m) {
case 0: return 0.0f; /* atan(+...,+INF) */
case 1: return -0.0f; /* atan(-...,+INF) */
case 2: return pi; /* atan(+...,-INF) */
case 3: return -pi; /* atan(-...,-INF) */
}
}
}
/* |y/x| > 0x1p26 */
if (ix+(26<<23) < iy || iy == 0x7f800000)
return m&1 ? -pi/2 : pi/2;
/* z = atan(|y/x|) with correct underflow */
if ((m&2) && iy+(26<<23) < ix) /*|y/x| < 0x1p-26, x < 0 */
z = 0.0;
else
z = vna_atanf(vna_fabsf(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */
case 1: return -z; /* atan(-,+) */
case 2: return pi - (z-pi_lo); /* atan(+,-) */
default: /* case 3 */
return (z-pi_lo) - pi; /* atan(-,-) */
}
}
#else
// Polynomial approximation to atan2f
float vna_atan2f(float y, float x)
{
union {float f; int32_t i;} ux = {x};
union {float f; int32_t i;} uy = {y};
if (ux.i == 0 && uy.i == 0)
return 0.0f;
float ax, ay, r, s;
ax = vna_fabsf(x);
ay = vna_fabsf(y);
r = (ay < ax) ? ay / ax : ax / ay;
s = r * r;
// Polynomial approximation to atan(a) on [0,1]
#if 0
// give 0.31 degree error
r*= 0.970562748477141f - 0.189514164974601f * s;
//r*= vna_fmaf(-s, 0.189514164974601f, 0.970562748477141f);
#elif 0
// give 0.04 degree error
r*= 0.994949366116654f - s * (0.287060635532652f - 0.078037176446441f * s);
//r*= vna_fmaf(-s, vna_fmaf(-s, 0.078037176446441f, 0.287060635532652f), 0.994949366116654f);
//r*= 0.995354f − s * (0.288679f + 0.079331f * s);
#else
// give 0.005 degree error
r*= 0.999133448222780f - s * (0.320533292381664f - s * (0.144982490144465f - s * 0.038254464970299f));
//r*= vna_fmaf(-s, vna_fmaf(-s, vna_fmaf(-s, 0.038254464970299f, 0.144982490144465f), 0.320533292381664f), 0.999133448222780f);
#endif
// Map to full circle
if (ay > ax) r = VNA_PI/2.0f - r;
if (ux.i < 0) r = VNA_PI - r;
if (uy.i < 0) r = -r;
return r;
}
#endif
//**********************************************************************************
// Fast expf approximation
//**********************************************************************************
float vna_expf(float x)
{
union { float f; int32_t i; } v;
v.i = (int32_t)(12102203.0f*x) + 0x3F800000;
int32_t m = (v.i >> 7) & 0xFFFF; // copy mantissa
#if 1
// cubic spline approximation, empirical values for small maximum relative error (8.34e-5):
v.i += ((((((((1277*m) >> 14) + 14825)*m) >> 14) - 79749)*m) >> 11) - 626;
#else
// quartic spline approximation, empirical values for small maximum relative error (1.21e-5):
v.i += (((((((((((3537*m) >> 16) + 13668)*m) >> 18) + 15817)*m) >> 14) - 80470)*m) >> 11);
#endif
return v.f;
}