You are now following this question
- You will see updates in your followed content feed.
- You may receive emails, depending on your communication preferences.
CIC decimation output is strange (Output word length and negative fractional length)
6 views (last 30 days)
Show older comments
I'm implementing fixed point CIC decimation filter with following requirements --
- Decimation factor: 20
- Number of CIC stages: 4
- Input and output bit width of the CIC: Signed 12-bit
Based on the above requirement, I created a CIC filter
cicDecimOut = dsp.CICDecimator(DecimationFactor=20,...
NumSections=4,...
FixedPointDataType="Specify word lengths",...
SectionWordLengths=12,...
OutputWordLength=12);
As an input, 12-bit signed data generated as follow.
x = randi([-2048 2047], 100000, 1);
in = fi(x,1,12);
Now the singned 12-bit input data plug-in to the CIC decimation filter.
out = cicDecimOut(in)
out =
0
-327155712
-479723520
146014208
-237502464
132120576
365428736
162529280
197394432
55574528
136052736
-407896064
30932992
-214958080
-67633152
-473956352
-123994112
-124256256
344719360
267649024
519831552
-233570304
-363069440
-427032576
-56360960
122159104
517996544
238288896
-14942208
230686720
30932992
56098816
305659904
-315621376
-211288064
333971456
-534511616
41156608
510394368
174587904
429654016
-288882688
-154402816
-22544384
160694272
509870080
-427556864
373817344
-137101312
-108527616
-83623936
-241172480
-299368448
115081216
-339214336
416284672
-231997440
335282176
-324272128
425721856
505937920
-284688384
-369623040
380895232
347865088
-451674112
-428867584
238813184
-148897792
-110100480
240386048
-415498240
292552704
70516736
43253760
-3670016
367525888
-361758720
-152305664
449576960
-157286400
-92798976
-308543488
-187170816
-341835776
18087936
476839936
-138674176
40370176
536346624
-65011712
380370944
73662464
-401342464
200278016
-216006656
-506200064
-11010048
139722752
-78643200
-112984064
424148992
114556928
428081152
-249298944
399769600
160956416
162529280
-470548480
-74448896
-12845056
-375390208
460324864
475791360
486801408
-398458880
-339476480
-329515008
308543488
391643136
-152829952
222298112
-536084480
-146800640
479723520
-278659072
201588736
391643136
-323223552
-168296448
374079488
-7077888
-504365056
393740288
-281280512
-424935424
20971520
-497811456
32768000
-157024256
-262930432
390594560
-235929600
-174063616
-312475648
-186384384
210239488
506200064
526909440
286523392
526909440
271056896
419692544
143130624
361758720
530841600
235405312
371720192
-296222720
535560192
-279707648
-219414528
474742784
-514326528
193724416
-472907776
-101449728
-338690048
-485490688
445906944
-510394368
-362283008
216793088
204472320
-132120576
115605504
516947968
-513540096
105119744
-30932992
-325320704
137887744
-221773824
-189267968
139198464
-374341632
-47185920
217579520
122421248
138149888
-398983168
-409206784
96468992
452984832
418643968
409468928
-67108864
-114556928
-31981568
518782976
271581184
92798976
283115520
385613824
-236978176
229638144
74186752
-327680000
-69468160
340787200
535560192
-430440448
219676672
-111149056
-208928768
213123072
470024192
169607168
139460608
450101248
497287168
271056896
320602112
-217055232
500432896
-47972352
-113246208
531103744
-472121344
-509607936
513802240
-480772096
531365888
287834112
467664896
-169082880
148897792
-398196736
369623040
-299630592
255066112
-193986560
-254279680
-268435456
460587008
459800576
-280756224
157024256
-70254592
386400256
150994944
-27525120
-180092928
536608768
259784704
-143392768
510394368
254541824
-500170752
407896064
-403963904
-349175808
-173539328
421527552
177209344
-396623872
-367001600
217055232
-120324096
-94633984
-7864320
-441450496
483393536
-521404416
479199232
-136577024
44302336
492306432
304087040
81002496
-346816512
106168320
-260046848
-477364224
525336576
161480704
98304000
-60293120
-99876864
167772160
501481472
-234881024
-5242880
-281542656
351010816
-273154048
532152320
269221888
-459014144
530055168
-472121344
-34603008
-150732800
139722752
270008320
400293888
85196800
35389440
326631424
-440401920
500170752
51642368
192937984
-225181696
492306432
-510656512
-219938816
-480509952
-353370112
148635648
-8650752
-81264640
237764608
-480772096
47448064
-366477312
478412800
-22020096
-349700096
290193408
483131392
236191744
274989056
12845056
523239424
-3932160
-316407808
-92012544
-124518400
-68943872
391643136
-189530112
341049344
264241152
-178520064
-299368448
-370409472
279183360
-326107136
10485760
-520617984
490995712
520093696
310902784
-12582912
-262144000
88604672
166461440
33030144
169345024
-74973184
143917056
-374603776
-431226880
43253760
-304611328
-214433792
-312999936
-467664896
469499904
-60817408
-381943808
445120512
16777216
440401920
-121372672
-85458944
-245366784
-107741184
-438304768
-199753728
-161742848
-247201792
-371982336
-313524224
-301465600
-335544320
-58458112
445120512
347602944
-219152384
68419584
-285474816
-515375104
-284426240
332922880
-49020928
87031808
-427556864
-375128064
-50069504
22544384
227278848
-233570304
-405536768
-459014144
-48234496
-391118848
-15466496
262668288
228065280
244318208
397672448
-243007488
252182528
190840832
139460608
-241958912
-2359296
-199229440
523763712
-378011648
-464781312
-407109632
-217579520
66060288
-369885184
-309067776
-215220224
357826560
-368312320
-213123072
-242483200
439877632
-409993216
-470286336
506200064
-185597952
-485228544
437780480
440139776
263716864
-370933760
178782208
371982336
2359296
462159872
369098752
176685056
38010880
212336640
-302514176
-7077888
25427968
236716032
-364642304
484704256
380108800
-61341696
76808192
-265814016
-358612992
505937920
-469499904
-359923712
423362560
-393740288
432275456
-272367616
-388497408
-528220160
-529268736
-480509952
-149159936
125829120
-11010048
284426240
-424148992
19398656
487587840
427556864
165412864
290455552
29884416
454557696
358088704
-386400256
320077824
-331874304
299368448
50855936
264241152
64749568
-528220160
-436731904
-396361728
192151552
439615488
406847488
267124736
246939648
109051904
188481536
40894464
94371840
-130547712
516423680
225443840
-475529216
90439680
7340032
-235405312
-8388608
503054336
-340787200
-339214336
-88342528
-343670784
320864256
-298319872
123994112
148897792
-437256192
35913728
27000832
219414528
-94633984
101974016
396361728
56098816
14680064
-194510848
398983168
-240648192
231211008
-419954688
-496238592
-76283904
420216832
-82837504
284164096
516947968
-202637312
51118080
-443547648
-131858432
454033408
-341573632
224395264
-174063616
490471424
-377487360
-305922048
-33816576
-111149056
-111935488
240386048
153092096
4456448
516947968
-255328256
396623872
57671680
306970624
370147328
-254017536
-109838336
-117178368
-281280512
-244318208
-6553600
-194510848
155713536
40632320
131072000
-304873472
524550144
85983232
109576192
-138412032
-406585344
32768000
104071168
-521928704
186646528
476577792
294649856
-381419520
-344457216
-41418752
200802304
-464781312
216006656
235405312
-117440512
255590400
-21757952
445382656
-487849984
-36962304
248512512
-498597888
-486801408
375652352
-447217664
-159907840
-475267072
-198180864
235143168
-535035904
260571136
256901120
435683328
519045120
-4194304
516423680
-166199296
-480509952
-104595456
-284950528
404488192
-147849216
319291392
139984896
495190016
-138412032
-301465600
-136577024
-22806528
-361758720
525074432
445120512
215482368
-225181696
164888576
-81788928
244842496
-317456384
368312320
11796480
-363593728
448004096
268435456
-520355840
-256114688
-306446336
-189005824
-191102976
-5505024
-225443840
-491782144
84934656
-481034240
-309067776
-522452992
-524288
-55050240
-290979840
-295436288
-483393536
88604672
353370112
-332136448
46399488
-56360960
-508559360
9699328
-374603776
464257024
-16777216
-228851712
-471334912
240910336
43515904
64487424
-452984832
-257425408
357826560
-233570304
240910336
-336330752
95682560
190578688
243793920
308019200
309854208
24379392
-218365952
-526123008
53215232
-336330752
399769600
498073600
234881024
-340262912
432537600
427032576
488112128
83623936
-106692608
-399245312
-265027584
47185920
-18087936
328204288
177995776
513015808
526909440
372244480
-360448000
336068608
-54525952
216268800
469762048
-177733632
-279445504
51642368
470286336
-441450496
68419584
488636416
-342097920
-246415360
-407109632
209453056
-246939648
279183360
-433324032
525336576
489422848
-377487360
-458489856
-104857600
189267968
162529280
-109051904
-168820736
-420478976
-76808192
101974016
-160169984
484966400
-347340800
-28049408
141557760
172490752
124256256
-501743616
484966400
-172490752
161218560
-285736960
-53215232
-312999936
401342464
-106430464
72876032
344719360
-452984832
-376438784
-221511680
389545984
-320864256
498073600
532152320
505413632
362020864
386662400
-478674944
-533200896
470810624
-416546816
-124780544
-127401984
-203685888
-338690048
184025088
225443840
-182976512
513802240
-427556864
529268736
-259260416
195559424
-34603008
-304349184
351010816
76546048
65273856
-46661632
-518258688
-386400256
189267968
460062720
-8126464
187170816
320602112
-428343296
515375104
-207355904
468451328
-363331584
-52166656
-86245376
-112721920
427556864
-344719360
114556928
-159383552
-358612992
-423624704
-237502464
-432013312
37486592
13893632
-200015872
379060224
213909504
-133693440
127139840
246939648
224919552
-425721856
40108032
390332416
-237764608
229900288
-324009984
228327424
-388759552
236191744
-76283904
314310656
202637312
289669120
-122683392
-168558592
-17039360
-6553600
353894400
473432064
298844160
471859200
396886016
-1572864
-510394368
202375168
100401152
296484864
-520617984
-166723584
-390070272
476315648
287834112
133955584
207093760
-56623104
-312999936
264241152
353632256
-421789696
23330816
300941312
-156762112
-247726080
-158597120
-32768000
83099648
253755392
-509083648
-141295616
438566912
-38010880
137887744
-445644800
-76546048
7340032
374341632
276561920
-303038464
-279445504
-269746176
293601280
444858368
-137363456
-122945536
-1310720
149159936
-503578624
96731136
181927936
76283904
-277610496
356253696
-484442112
101449728
-429391872
371458048
383778816
-135266304
-368836608
-295698432
90963968
490471424
309854208
-59244544
166723584
41418752
-92274688
487063552
-314048512
273154048
-222560256
175636480
382730240
-428081152
519045120
211288064
340262912
-428343296
-327680000
535822336
386138112
-479723520
159383552
110362624
73924608
-508821504
-381157376
456916992
475004928
141819904
-517210112
311951360
-52690944
-18874368
-93323264
136839168
436994048
-220725248
447741952
211550208
-1835008
201326592
79167488
-527171584
-273940480
135004160
-117702656
-263716864
355467264
150470656
-428605440
503840768
310378496
384040960
243531776
-337641472
-476315648
275513344
-37224448
153092096
-536870912
386924544
-110624768
-60555264
230424576
94371840
338427904
250609664
-499646464
365690880
-265814016
276824064
148373504
466878464
499122176
27000832
101449728
-64749568
-519307264
231211008
-312475648
-478674944
265814016
392167424
-106430464
165150720
224395264
-483917824
484442112
-303562752
-498073600
-106168320
239337472
-251658240
102236160
-244580352
-139984896
342884352
187957248
16515072
-374865920
-322437120
-275513344
440401920
-523763712
185597952
391905280
187170816
-143392768
-461635584
-170393600
286261248
-461111296
467664896
515637248
460849152
382468096
449839104
400031744
229113856
520880128
258736128
395575296
483655680
-326893568
175374336
451936256
-49807360
173277184
128712704
377225216
173539328
133169152
-356777984
133955584
386400256
113246208
222035968
-533987328
260571136
385351680
455344128
409206784
-266338304
495976448
-206831616
-132644864
-142606336
213123072
239861760
418906112
-480247808
-502530048
207355904
288358400
-49020928
395051008
-309329920
468975616
119799808
400293888
307757056
-451936256
111149056
-307494912
108527616
265814016
36962304
-127401984
246153216
-488898560
33816576
-378535936
110886912
-101711872
-127401984
54263808
-220200960
-50069504
-487325696
-363855872
136052736
28573696
369623040
289406976
-52690944
96993280
-164626432
371982336
-283377664
432013312
-8912896
88342528
-307494912
-449576960
242221056
384565248
-328204288
210239488
231997440
-133169152
-234618880
-176685056
-190578688
-291504128
83623936
514588672
-87556096
341049344
-186646528
524288000
228065280
128974848
-110886912
37224448
-504627200
103809024
482869248
-435421184
417857536
-391118848
-8912896
180092928
-198967296
-386924544
-222035968
188481536
508559360
139722752
-49807360
177733632
3932160
-403963904
220725248
-58195968
-536608768
-2883584
219414528
-126353408
-392429568
-488112128
-105119744
-514326528
-123469824
465567744
394264576
-139460608
277086208
-258473984
493879296
176160768
498597888
-86507520
120586240
-421265408
82313216
215744512
-477888512
99352576
-15466496
390856704
511705088
2097152
-243269632
-11534336
44302336
-110362624
-279969792
-343408640
-427032576
-174063616
93847552
-122421248
-165675008
-331612160
-337379328
-196608000
195559424
-112984064
150732800
-151257088
185860096
-246677504
256901120
-135266304
-260833280
-468189184
-394002432
78381056
189005824
336592896
143392768
-52428800
467402752
530055168
139198464
-500432896
171704320
147062784
489422848
-142868480
-67633152
-66060288
200802304
-88866816
-35389440
262144
113508352
344457216
373030912
-183500800
-117702656
331350016
53215232
159645696
59244544
252444672
335544320
-338165760
-104333312
97255424
-13631488
-248512512
371720192
-193724416
431489024
-386138112
-279707648
-155189248
-83099648
-17825792
-281018368
266600448
-273678336
279183360
-276561920
478412800
-12582912
218628096
61341696
-350224384
60817408
40632320
433848320
-26738688
389283840
285999104
342360064
-503840768
-26214400
-292028416
463470592
-531365888
40108032
184549376
-140771328
101449728
136577024
-487325696
-290979840
-262144000
-162791424
476577792
-389808128
-216530944
-257163264
104857600
282853376
139984896
-379584512
531628032
-317194240
-283115520
-525598720
-294912000
-373555200
220725248
110886912
-153354240
-213385216
-260571136
466878464
-306970624
-390332416
-331087872
-268959744
176160768
-209715200
-178257920
233570304
-517472256
-180879360
341049344
-155975680
512753664
-245891072
329777152
457441280
-338165760
195559424
-366739456
-494927872
-16515072
45613056
-254279680
361234432
1572864
132120576
-227016704
-239337472
212860928
-124780544
458752000
340787200
-427032576
-150208512
-351535104
-50593792
89391104
-94371840
-29097984
-106430464
43515904
-80478208
-440664064
-26214400
327680000
532414464
187432960
33554432
367788032
-194510848
265551872
-183238656
75759616
-153092096
-370147328
212336640
502267904
466878464
355729408
-95682560
240386048
-342097920
524812288
147062784
106692608
26476544
-30932992
-142344192
458489856
353107968
-369098752
-451674112
251658240
-473432064
320077824
452722688
-333971456
-423624704
526385152
518520832
400556032
-158859264
-342884352
22282240
306970624
282329088
-245366784
-143392768
381157376
-430178304
455344128
432013312
-27525120
-243007488
385875968
-289406976
-525074432
-174063616
-414187520
407371776
201064448
-300154880
-284688384
42729472
-172228608
305659904
-185597952
419954688
-317980672
-481558528
517734400
-127139840
-51380224
-501481472
-132907008
-19660800
-301203456
471597056
336068608
219938816
71303168
282853376
257949696
283377664
-385351680
384565248
139722752
-417333248
165150720
-164364288
65011712
15728640
195821568
-497549312
452198400
461635584
-114556928
43778048
-376963072
-503840768
392953856
282853376
-481034240
-527171584
-475791360
282066944
-138936320
153878528
-54788096
435945472
-503316480
57933824
-428867584
204996608
326893568
90701824
461897728
468713472
278921216
321912832
51118080
-520880128
-507510784
-391380992
-43253760
-125304832
40632320
-328204288
473956352
-492568576
384040960
-229900288
-160169984
173801472
185335808
18350080
-386662400
303038464
-310902784
168296448
384827392
-321388544
325058560
5242880
421789696
-457441280
96731136
50331648
-348651520
-462946304
30408704
70516736
326369280
-268173312
228589568
-7340032
242483200
519831552
-314310656
-231997440
-502005760
-107216896
-4456448
-462422016
6815744
-442761216
-406061056
-228589568
-374865920
244318208
-146014208
-96468992
486539264
-249823232
269221888
-335544320
533987328
-526909440
441450496
-342097920
-255852544
-53215232
453771264
284688384
-18612224
179568640
388759552
301727744
508821504
-360185856
-281018368
445906944
-375652352
319553536
445644800
286523392
176685056
156237824
370933760
-410779648
112197632
441188352
30670848
-235667456
-364380160
317980672
-80216064
-339214336
142082048
317194240
-65011712
-133693440
59768832
519831552
67633152
-493617152
-107479040
493092864
486014976
145489920
272891904
70778880
-498335744
390594560
131858432
-95158272
415236096
56360960
63176704
-107479040
-24903680
493355008
381419520
32505856
344457216
375914496
-215744512
464519168
-437518336
-378535936
282591232
-4980736
112197632
110624768
110362624
-495452160
414449664
277348352
-35127296
250871808
519045120
-129499136
-198180864
-392167424
-84672512
-50069504
42467328
-413401088
-218628096
101187584
362807296
508559360
430964736
171966464
-217055232
-370409472
490209280
8126464
221773824
-412352512
-281542656
126091264
378273792
-54525952
455344128
-403701760
-255852544
-352059392
-495976448
-46923776
-261881856
512491520
-98828288
243007488
-230162432
304873472
520093696
346030080
-397410304
530317312
415236096
151519232
-486014976
339476480
418643968
102760448
446431232
399245312
-12845056
-399769600
-150208512
378535936
-119537664
-23592960
357826560
92012544
170655744
70778880
-343408640
-236191744
83361792
2621440
-476839936
-401080320
481558528
18350080
-487325696
172228608
256638976
137625600
108003328
177733632
-518520832
-440401920
133431296
-322174976
-87293952
-146276352
331874304
307757056
478150656
-297795584
194772992
173539328
-258211840
-148897792
-465043456
-220725248
-310378496
136577024
-17039360
494141440
-334495744
497287168
462946304
-425197568
-42991616
213909504
301727744
327155712
496238592
116129792
-127401984
-438304768
-17563648
-308805632
-225968128
441974784
70254592
216268800
-280494080
103546880
198180864
-287834112
386138112
-105644032
373030912
-83886080
-215744512
-136577024
-75759616
268959744
393740288
487063552
-251396096
-220200960
247201792
80216064
-3670016
150208512
-461111296
402391040
266076160
-437256192
-204210176
-493355008
271319040
231211008
510656512
534511616
-240910336
379322368
-516685824
-47972352
73662464
-449839104
-330825728
-28835840
-108003328
114556928
-424411136
471597056
-44040192
-526647296
28049408
-325058560
-51904512
-438042624
-9699328
220987392
-148373504
15204352
493879296
33554432
271843328
89653248
274726912
120586240
-141033472
-137625600
174850048
-524288000
-194248704
148635648
416546816
304087040
-381157376
150732800
369885184
-298844160
426246144
-237240320
219152384
183762944
534773760
-126353408
137363456
273678336
-265814016
-233046016
-226230272
520617984
61341696
-379322368
-164888576
-215220224
279969792
392691712
-147587072
-139198464
477102080
326107136
131858432
489684992
153092096
-202899456
419168256
260308992
367001600
200278016
-206831616
-294912000
-439091200
-377487360
-214695936
-115605504
293601280
420478976
139460608
428343296
-8912896
122421248
-398721024
-116129792
414187520
-404488192
114819072
27000832
212074496
523763712
362807296
-109838336
-331612160
-77856768
-15728640
139460608
-205783040
258473984
-482607104
124780544
509083648
-35913728
475791360
-46137344
403963904
261619712
509345792
-88866816
-171442176
-195821568
-302514176
-120324096
511967232
-523763712
-234356736
-498860032
362020864
-374079488
-481034240
-231735296
-454295552
-403963904
-88866816
-59506688
-142082048
450101248
-421789696
467927040
247463936
175374336
458752000
-392953856
-499122176
-305922048
80216064
-205258752
160694272
-473956352
-383516672
-475529216
467664896
-308543488
-102498304
263454720
489422848
-424148992
-342622208
234618880
-418381824
420741120
-331874304
354418688
120324096
-527433728
165675008
-498073600
274726912
-487587840
338427904
33292288
162791424
444858368
-510656512
446955520
148373504
355467264
-250085376
-390594560
45613056
453771264
-181403648
-475004928
-2883584
-154402816
86245376
-168820736
359923712
-41156608
516423680
-99876864
-370671616
24903680
-445644800
-390856704
494927872
452198400
57671680
151781376
-152567808
444071936
482082816
-92798976
535298048
-193200128
-39845888
186646528
457965568
-250347520
-314048512
-230424576
-316669952
51118080
-322961408
158859264
-344981504
-401604608
525860864
488898560
-418381824
-440401920
-320602112
230686720
234618880
-378273792
-242745344
225443840
-208142336
-160432128
491257856
132382720
-243531776
-465043456
-420741120
-212074496
-329515008
-469237760
1572864
-297009152
512491520
286785536
178257920
-260571136
23330816
100139008
-533987328
52428800
266862592
-505675776
-521142272
-76546048
-388235264
517996544
287834112
82837504
509345792
-277610496
-106430464
-343670784
-237240320
67108864
449576960
354156544
86245376
491520000
-297009152
154140672
-489684992
-259784704
23068672
391905280
217841664
-16252928
-388497408
9961472
-511705088
-343146496
384303104
533987328
1048576
452460544
-352583680
-439091200
341311488
469499904
113770496
-281280512
142344192
62914560
67371008
-80216064
463732736
-403439616
-278134784
-475791360
-51904512
183500800
-316932096
-395575296
-500695040
8126464
116916224
-342097920
133169152
-18087936
-521928704
180092928
-187957248
492568576
182976512
193986560
-413401088
-247463936
492830720
-136839168
465043456
521404416
69468160
-123731968
276824064
172228608
-228851712
336592896
84672512
146014208
-477102080
-473694208
-222560256
-464519168
214695936
429654016
285212672
-182452224
-257163264
-32768000
143130624
-469499904
213123072
457441280
189267968
117702656
-146276352
54263808
17825792
126353408
43515904
-112984064
476053504
275513344
434110464
46137344
-296222720
-126091264
303562752
385613824
28049408
27525120
-76808192
302252032
-375128064
-28049408
-352583680
74186752
-320077824
-492306432
23068672
223084544
-345767936
-294649856
148897792
-33292288
-142868480
-172752896
-486277120
-24379392
-246939648
322961408
-435683328
-519307264
-176947200
251920384
328990720
30146560
156237824
-507772928
305659904
492568576
-527695872
-486539264
510656512
275513344
253493248
-209190912
320339968
-93847552
26214400
263716864
114556928
293601280
-56098816
501743616
-434634752
-280231936
14942208
-116916224
327155712
-307494912
390070272
347340800
-192413696
422838272
-434372608
39583744
408158208
-111411200
18612224
-146014208
-382468096
-90701824
328728576
270270464
-19136512
505413632
-291241984
-271581184
-299892736
-410779648
294387712
-410779648
391118848
364642304
-72351744
-173801472
413138944
-53739520
-488112128
-314834944
47972352
-38797312
296747008
-99614720
-17039360
-191889408
-512491520
277610496
-506986496
-4980736
391118848
-228327424
460062720
452722688
-480772096
43778048
-306970624
250871808
227803136
442761216
416808960
238026752
150994944
-66322432
166985728
-504627200
-207355904
10223616
359661568
19398656
-497025024
126353408
295174144
189530112
-526385152
174850048
262668288
336330752
356253696
432013312
-61079552
453771264
-228851712
-226230272
488636416
127139840
176947200
505151488
62914560
-64487424
-11796480
309854208
108789760
449052672
-277610496
-402915328
514850816
233832448
-172752896
390594560
280231936
-495976448
144179200
366739456
157548544
-276299776
-62390272
308019200
-449052672
-114294784
-224395264
76021760
443285504
-134742016
510394368
-58982400
-427819008
62390272
-472645632
222560256
311689216
433586176
519569408
162267136
80216064
530055168
-258211840
-174325760
531890176
271319040
-110100480
233046016
-211550208
60030976
-204734464
209715200
179830784
-39583744
-146276352
-228327424
331350016
-195035136
303562752
-139198464
158859264
360185856
498073600
-46661632
-372768768
-104595456
-53739520
421003264
-283639808
-44302336
91226112
-159645696
518520832
318242816
533200896
355729408
269484032
309854208
428867584
147062784
-234356736
13631488
-138412032
276037632
177471488
154927104
-468451328
-45613056
-385351680
529006592
178257920
-284950528
-98304000
-105644032
384303104
-142082048
340262912
-195559424
495714304
-327680000
-453771264
189792256
-339476480
-311427072
445644800
-283901952
-176422912
-297533440
89653248
390856704
-1572864
-438566912
-219414528
127926272
156237824
123731968
160169984
114032640
-243269632
-238813184
138674176
-65011712
259522560
-438042624
84934656
-70778880
102236160
-448528384
490209280
-465829888
177733632
-430964736
-153354240
-8388608
118226944
-288620544
370671616
358350848
-290193408
67371008
-521928704
-348913664
395837440
390594560
120848384
530579456
-496762880
-478412800
-182714368
-405798912
18350080
12845056
-42729472
392167424
137887744
94896128
281018368
-45613056
-58982400
440926208
358875136
353632256
-355467264
31981568
69468160
35127296
-175636480
-492568576
-29360128
-534773760
164626432
-518258688
-63963136
-433848320
347078656
308281344
160956416
492044288
-8650752
-48234496
-309854208
164364288
264503296
374079488
-471334912
452984832
-16515072
335544320
480509952
112984064
236978176
17039360
-224657408
-166461440
-164364288
434372608
-508559360
-146276352
-51118080
-33816576
-216268800
160694272
127664128
97779712
-397934592
-230948864
-84672512
-378273792
386662400
-184025088
127401984
-4456448
-463470592
-496500736
41943040
436994048
-95158272
-459538432
111935488
-247463936
-53477376
-137101312
-164888576
354156544
-110624768
-509870080
528220160
-22282240
-269746176
137101312
487849984
-204472320
-56360960
112459776
-527695872
-512229376
-397934592
343932928
138149888
301989888
-321912832
504889344
472907776
182714368
-103809024
-6291456
376176640
-396361728
-303562752
162791424
328204288
143654912
-65798144
208142336
-183762944
176160768
-291241984
-491257856
397148160
-133955584
-98304000
-447741952
491782144
146800640
-39321600
-289144832
-157286400
-484966400
-287571968
-252706816
-244056064
-413663232
233570304
-263454720
108265472
-302252032
-367263744
-298844160
271843328
-270794752
-87031808
83623936
232783872
-62652416
359137280
67371008
43515904
-485752832
38797312
32768000
192413696
301203456
-508035072
-193724416
-194510848
502005760
494403584
-83623936
-184025088
29097984
-124518400
141819904
395575296
91488256
117964800
287309824
-362807296
341311488
515375104
-84410368
122683392
157286400
-385089536
254017536
477364224
-182976512
-312737792
-169345024
-433586176
213385216
363069440
-405274624
-455081984
-446169088
280231936
456130560
5767168
-172752896
445120512
-96731136
-51380224
-364904448
-87818240
-338165760
308805632
-387973120
83361792
-196870144
384565248
-68419584
466092032
-409206784
29622272
164626432
-142082048
70254592
325582848
-107216896
302252032
132907008
178257920
299106304
-145489920
-9437184
-82313216
322699264
-212598784
424935424
37486592
-10223616
47710208
318767104
-218890240
-445382656
134742016
-278396928
360710144
-171704320
450625536
-488898560
-437256192
16777216
-387448832
-187695104
-475529216
-310640640
-375390208
113770496
184025088
-126091264
469499904
128188416
390856704
-163053568
69730304
-458227712
35389440
-360448000
-470548480
530579456
86507520
-521928704
-207880192
-174325760
-123469824
430702592
458489856
327155712
362020864
-221511680
-304087040
-285212672
352321536
413925376
-298319872
-472121344
209977344
133169152
-328728576
85983232
-382205952
-525336576
271843328
-1048576
-55050240
340787200
525860864
206569472
-142868480
-10223616
262930432
481820672
-203685888
-379322368
317718528
298319872
-301465600
335020032
270008320
-423362560
40894464
311951360
477102080
-485228544
42729472
81526784
204734464
-283115520
306446336
-460849152
457703424
-373030912
-371720192
-216793088
136577024
-340262912
-6553600
-358612992
160432128
216268800
-472907776
89653248
-214695936
398458880
-499908608
500695040
58458112
282329088
-464519168
-340262912
23330816
259784704
-343408640
196345856
-283115520
414973952
-104333312
429916160
1572864
-382468096
-170917888
499646464
94371840
-488898560
199229440
-289144832
-221773824
262406144
187957248
-80478208
-112197632
-207618048
405274624
170917888
396623872
513015808
64225280
443023360
-335020032
131596288
224919552
471334912
-356515840
-185597952
-9699328
164102144
296484864
312999936
49283072
532152320
-82837504
526909440
-385875968
412614656
-409731072
197918720
-533725184
139460608
-171442176
363593728
277872640
157286400
371982336
-412352512
488112128
495714304
-502530048
268697600
-249561088
251133952
189792256
-166985728
-257949696
-267649024
128974848
499908608
250347520
-132120576
-277086208
-270794752
-336068608
-346030080
-2359296
347340800
326107136
-374603776
302776320
-414711808
-163577856
-139198464
-51904512
34078720
-48758784
50331648
74186752
374603776
322437120
153616384
365690880
-87031808
402391040
174587904
-478412800
-185335808
-233308160
7864320
-512229376
365428736
479461376
-51118080
110100480
235143168
122945536
57409536
148111360
-308543488
-25427968
-378011648
386138112
391380992
137363456
346554368
161218560
104333312
-112721920
-483655680
506200064
-329252864
-56098816
-290193408
-402653184
488636416
-19136512
-10485760
121634816
-250347520
-270270464
476315648
-307757056
170917888
-351797248
-94371840
3407872
-125042688
446955520
184811520
184287232
94109696
361234432
-320602112
219938816
34078720
-477102080
370671616
190316544
-302776320
433061888
382992384
-518520832
-12582912
-268959744
-168034304
-140771328
137363456
428867584
-162267136
359137280
209977344
-129499136
101974016
-39845888
-463208448
306708480
-278921216
-464257024
380633088
-126353408
-14417920
131334144
-502792192
-444071936
-347602944
26214400
-442236928
337641472
-103022592
443547648
511967232
327942144
-41156608
34603008
531890176
94371840
-531103744
-41943040
507510784
-313786368
-252182528
-287834112
-418119680
-512491520
149159936
399507456
-235143168
-264503296
-310902784
-329777152
457179136
-115343360
40894464
262144
-110362624
-354942976
267386880
4718592
-40894464
231473152
377749504
-29622272
-524288
-40632320
286785536
434896896
-250871808
458489856
234094592
-76283904
-25427968
-433586176
375128064
262668288
185073664
-246677504
299892736
191627264
-105119744
418906112
-414711808
371982336
322699264
-525336576
-344981504
20185088
157810688
210763776
-489160704
401080320
-231997440
-510656512
457703424
-244318208
-85983232
474742784
-34340864
335020032
-165412864
226230272
287309824
273154048
-316669952
197918720
450363392
-199753728
254017536
-311427072
-332398592
-424148992
500957184
-220725248
-305135616
-351272960
483131392
268959744
-115343360
-76546048
-146276352
531628032
165412864
105381888
497287168
185335808
532414464
333447168
-154927104
-408944640
-122945536
-57409536
477888512
-430702592
190054400
-293863424
35913728
-126091264
-198967296
-399769600
512753664
376438784
-11796480
-192413696
235667456
464781312
331350016
-381157376
-503840768
-289669120
30932992
181665792
254803968
-529268736
206569472
66060288
23592960
-93323264
489422848
-331612160
464519168
487325696
-71827456
-501481472
-170393600
49545216
-425984000
-314048512
30670848
-89653248
-108003328
189792256
-419168256
-76021760
223346688
348651520
-396623872
-127926272
153616384
389021696
-59244544
339738624
282853376
436731904
520617984
-211812352
514064384
155975680
256638976
-486801408
506986496
-422051840
-88342528
-185073664
102760448
345505792
381943808
-77070336
-275251200
416022528
-460324864
-516423680
-428081152
423886848
244318208
-210763776
294912000
-246677504
335020032
303824896
463732736
519045120
-351272960
32505856
-499908608
-12845056
-42205184
-180355072
-82837504
-147062784
-472907776
293339136
103546880
-151257088
-519045120
-174587904
-389545984
305135616
391905280
-52953088
275513344
-506200064
-325844992
-466878464
-397934592
-465829888
-308805632
-386138112
-155713536
-69730304
-283377664
-477364224
186646528
-150208512
99614720
-50855936
-429391872
223346688
-60555264
352845824
147324928
56885248
-523501568
137363456
219152384
-44302336
494403584
284688384
-100139008
48234496
416284672
492830720
340262912
117178368
-313524224
374603776
-465305600
138674176
384565248
96993280
468975616
424411136
-61079552
312737792
-487063552
88866816
-247988224
87293952
433586176
77332480
-160956416
-401342464
402653184
-292290560
31719424
22282240
-123469824
73662464
-56098816
172752896
-18612224
414711808
528482304
-293076992
105906176
-317718528
-190316544
176685056
514326528
169345024
-42991616
-525336576
459538432
242483200
-477888512
64749568
-169082880
173801472
177471488
-33030144
-429916160
-303824896
265814016
-451674112
-140509184
522190848
441450496
-299368448
-47185920
413663232
-63176704
397934592
-304611328
-138674176
-336855040
-395837440
-150208512
-11534336
-508559360
-149946368
-276299776
-433586176
6291456
-49807360
-454295552
-282329088
318242816
-252706816
-530579456
-34340864
258736128
325320704
-119537664
-443809792
-52166656
-17301504
-514588672
60817408
-516161536
238288896
266338304
327417856
-52953088
-176160768
177209344
95944704
143917056
-360448000
-474480640
356253696
375652352
195821568
-383778816
-425984000
-133169152
222560256
290455552
315883520
-85721088
-249298944
-475791360
-463994880
-294387712
180879360
449314816
50593792
142868480
416022528
-205520896
86769664
303038464
261357568
249561088
-520880128
430964736
-279445504
313786368
397672448
495714304
-386138112
457441280
253755392
72876032
-111149056
23330816
-448266240
454557696
180879360
359923712
-525598720
-409993216
139722752
786432
-367788032
-369360896
154140672
-320602112
-308805632
-265814016
-299368448
461373440
-1835008
-31719424
-24641536
504889344
-513540096
440664064
-127401984
392691712
90963968
364380160
-257425408
-81002496
124518400
125304832
-425197568
137101312
336330752
300941312
-63176704
525074432
94371840
-504365056
426508288
-66322432
-420216832
-276561920
43778048
-526909440
483655680
-198180864
384040960
48496640
433061888
-213123072
99876864
450625536
-52690944
-69468160
-232259584
-10485760
-276299776
-60030976
-8126464
-364118016
-316669952
-518782976
-99352576
450101248
428343296
333709312
-234618880
-489160704
-178520064
203948032
-415760384
-418643968
-45613056
127139840
-97255424
-471597056
124256256
-346554368
178257920
163840000
-120324096
108527616
303038464
240123904
294387712
-472645632
420478976
-413925376
78381056
503054336
-205258752
-330039296
324009984
-352059392
-487063552
223084544
-166985728
393216000
165675008
165412864
-456392704
239075328
-304611328
-269746176
330301440
-268959744
132382720
-465305600
-256901120
-129761280
-11796480
155189248
-132644864
500432896
268173312
-229638144
-183500800
315621376
401604608
-174587904
96993280
-72613888
-142606336
374865920
-163315712
-31981568
-201588736
-22806528
-358875136
313524224
-7602176
-398721024
-425459712
365428736
409206784
153354240
-174325760
-123994112
189792256
198180864
1572864
182714368
170655744
144179200
478150656
-219152384
527958016
-262406144
112197632
-333447168
-255066112
231735296
-279707648
312737792
115867648
-317980672
440139776
-18350080
317980672
-384303104
489684992
-432799744
506724352
484704256
269746176
437256192
-470286336
-476053504
-46399488
-307232768
-349962240
514326528
-368574464
457441280
-93847552
186908672
250609664
355991552
-45350912
-380895232
-220725248
7340032
139460608
300679168
-467664896
278396928
136577024
-46661632
86245376
-221249536
289669120
197394432
-281804800
-246415360
-251396096
-216268800
81264640
350224384
-34340864
-119799808
402915328
178520064
-521666560
7077888
237240320
26738688
522977280
-51642368
-87031808
194248704
-220200960
-167510016
-354156544
296484864
-460849152
57933824
-341311488
78118912
-373817344
54525952
348389376
239075328
-198443008
373030912
73662464
456916992
-470548480
-372506624
275251200
-267649024
-218890240
-506986496
352321536
-404488192
185860096
-185597952
-189792256
-184025088
-411303936
-202113024
172490752
438304768
81264640
187432960
423362560
-166985728
455081984
477102080
453246976
436207616
38273024
226492416
482869248
415498240
240648192
429916160
121110528
-25165824
45088768
43253760
-19136512
-405798912
-498335744
-148635648
470810624
-71041024
-514850816
-172490752
-535560192
-304611328
10223616
104071168
437780480
529530880
92012544
220200960
394264576
-240648192
533463040
-482869248
-393740288
-455081984
37224448
58195968
-375652352
-392691712
12582912
72089600
227803136
-156237824
268697600
217317376
-361496576
51904512
-88866816
-244318208
67108864
-508559360
473694208
-129761280
418906112
518258688
-120848384
-60030976
74973184
480509952
-63963136
322961408
-284164096
-221511680
-518520832
-395051008
-408944640
96993280
-183238656
252444672
443809792
-7602176
-180355072
73400320
-38797312
-349175808
169869312
371458048
29622272
-357826560
-139198464
154664960
-280494080
-287047680
314310656
255852544
387710976
-337641472
-324796416
460062720
-460849152
126877696
95158272
-23855104
68943872
-366215168
209453056
387973120
-66322432
-13107200
370147328
241696768
-525336576
48496640
-28311552
230162432
-116129792
-329252864
-344195072
503054336
-440139776
365953024
355991552
-501743616
108265472
358088704
-509870080
374603776
-271581184
394002432
-277348352
-32768000
-81788928
-92274688
345243648
442499072
-485752832
208666624
-386138112
-128450560
-336592896
-388497408
208404480
323485696
-347602944
470286336
54788096
-536084480
184549376
149946368
476839936
362545152
535560192
446431232
-190316544
331087872
110100480
400556032
-282329088
-442499072
-44564480
-46661632
-218628096
-258998272
127401984
168034304
234094592
399507456
-443023360
318504960
170393600
114556928
76808192
108527616
386662400
-52166656
7077888
-119799808
206569472
-170393600
-73924608
306970624
464781312
-427819008
438042624
90701824
363593728
236453888
319291392
-516685824
145489920
-4194304
-170917888
-44302336
-172490752
-259260416
363331584
-29884416
-307757056
245628928
-165150720
502005760
-430440448
-38535168
520355840
-163315712
-518782976
147849216
-117702656
-8650752
-24379392
-430702592
260571136
-213647360
-62914560
-481034240
135266304
-439877632
-106692608
-380633088
-465829888
196608000
-124518400
267124736
-164626432
-29884416
-198967296
-41943040
-526909440
-138412032
315883520
-358088704
202899456
27525120
-153616384
66060288
128188416
-322437120
217841664
6291456
-424148992
126877696
326369280
216006656
-321126400
-521928704
63176704
-454295552
183500800
-384565248
-126353408
-460324864
-149946368
-105119744
4980736
266862592
-399245312
103284736
-55836672
-503578624
-341835776
19660800
60817408
-472383488
-65798144
-420478976
-51904512
203423744
-71565312
335806464
55574528
169607168
-219676672
321126400
-137887744
-150208512
41943040
-32768000
155451392
-158597120
-413663232
31981568
202375168
-103546880
-77332480
-451411968
-478150656
491520000
488112128
-204734464
-314048512
-241958912
314572800
-390594560
267649024
460324864
-388235264
-471597056
76808192
-264503296
368574464
-212598784
424411136
4980736
-156762112
225181696
241696768
-404750336
252968960
143917056
-80478208
-476053504
263716864
386400256
106692608
-409993216
-194772992
-360185856
398721024
335544320
786432
-522715136
-130547712
68419584
-224657408
-169082880
481296384
89391104
-272105472
227803136
-171966464
-37486592
-206307328
163840000
509345792
286785536
163577856
-22806528
-329777152
135004160
-125304832
490471424
240910336
276037632
-477364224
-375914496
440401920
378011648
29360128
-130023424
123731968
-372506624
379584512
-521666560
441712640
70778880
-108265472
-86507520
-417071104
-468451328
346292224
-402391040
-90177536
27262976
30146560
-164888576
129761280
458227712
-458489856
-233832448
256376832
506986496
-206569472
-406585344
-54788096
385613824
-184287232
375914496
-515375104
-330563584
354156544
429916160
-450625536
527958016
141033472
-274989056
-270794752
-71041024
-277872640
-157286400
298319872
31457280
-255590400
140509184
446955520
114032640
514326528
-452460544
-216006656
419692544
38797312
-247463936
-488374272
-7340032
-310116352
-176160768
-237764608
-274464768
104857600
501219328
499646464
482344960
473956352
166199296
-48496640
502792192
203423744
-527171584
-330563584
454033408
325320704
186384384
128188416
-341311488
-400031744
-249561088
161742848
-471072768
192937984
-237502464
-490733568
465043456
141557760
-266076160
-304087040
51642368
-190316544
-20185088
487063552
-361234432
-107741184
-503054336
191102976
290193408
-119013376
-224657408
523763712
58982400
260046848
90439680
44564480
517996544
-310378496
-365428736
386662400
501743616
465305600
465829888
-110886912
226230272
397934592
448266240
113770496
-110362624
-359399424
-322437120
-142606336
-128188416
-411041792
378798080
433848320
-277610496
89391104
-360710144
195559424
331874304
-255328256
-158334976
75235328
148897792
437780480
148635648
-374865920
40370176
72351744
-161480704
-277610496
465567744
201064448
-121372672
-401866752
501743616
-183762944
-122159104
336592896
487849984
435421184
159907840
-142344192
-518782976
-137363456
-111673344
-4718592
-69992448
5242880
-193462272
459800576
396099584
276299776
329515008
135790592
211550208
-318242816
-501481472
-236191744
412614656
309592064
347078656
200278016
498597888
499908608
15990784
214171648
147849216
506986496
-306708480
-236978176
-294387712
101711872
-118751232
193986560
423886848
-91226112
141557760
-57409536
-344719360
293863424
-260046848
332136448
217317376
62390272
-159645696
-57933824
-56098816
192413696
-266600448
-488374272
320602112
383254528
-223870976
135266304
110362624
444596224
230162432
342622208
-79167488
136052736
-480772096
309854208
-7602176
257949696
329515008
-406847488
-246415360
203161600
-414187520
396099584
-389545984
229638144
233046016
505413632
-180355072
258211840
495452160
178782208
344719360
37486592
-397148160
523501568
-434896896
-406585344
-464781312
-82313216
-128188416
61865984
381943808
178257920
-202113024
132382720
-520617984
-292028416
355729408
-147324928
265027584
-111673344
-257163264
17825792
172490752
247726080
-33554432
446693376
227803136
-481558528
141557760
-104595456
-394002432
267911168
131334144
-219938816
432275456
465305600
116391936
-235929600
76546048
116391936
-104857600
267911168
388759552
-86245376
434110464
-76808192
206307328
341573632
57933824
93061120
-144441344
67371008
294649856
357564416
-331874304
341311488
361496576
65011712
432537600
463470592
-450625536
-389283840
-426508288
-101974016
-476577792
-429129728
389545984
505151488
114556928
-434110464
-275775488
-207880192
116391936
-72351744
-317980672
164626432
218103808
259522560
266338304
-186908672
170655744
-174587904
-115605504
91750400
-364380160
287047680
89915392
153354240
344457216
33030144
490733568
-315359232
-485228544
57147392
448004096
-341573632
-248774656
-274464768
109051904
-154664960
-155713536
-207880192
-432799744
-316669952
207880192
-85983232
-229376000
-166985728
225968128
505675776
-157548544
-229113856
-459538432
67108864
230424576
364380160
-143130624
340787200
-123469824
496500736
424673280
-214433792
-159907840
468451328
-427032576
-461373440
-513540096
-262406144
-455868416
461373440
-9699328
252968960
209453056
-422838272
-75497472
-386138112
-327680000
97517568
-488636416
317980672
-502530048
74448896
-356777984
-36438016
31195136
-280231936
-500432896
127926272
-96731136
-26738688
446431232
124780544
-186908672
498860032
-226230272
363593728
-397934592
464519168
397672448
-53215232
-171180032
-515375104
-49807360
-286261248
396623872
-389545984
48496640
-209977344
45088768
482869248
455868416
99614720
-472121344
204734464
-507772928
-125304832
476839936
-7340032
108265472
526909440
-191627264
216268800
-304087040
-343146496
-319815680
135004160
-142868480
41156608
323223552
-171442176
413401088
-519045120
132382720
-4194304
-23068672
489160704
30670848
304349184
416546816
-377225216
-454819840
138412032
352059392
-271056896
-464519168
195559424
55050240
515375104
120586240
-372768768
-172752896
-379846656
-467927040
300154880
56360960
133169152
-41418752
3407872
-69206016
-78643200
405274624
-1048576
-73662464
-121634816
418906112
331612160
-233832448
224395264
483393536
318504960
29360128
508297216
-365166592
-334495744
248774656
381419520
445906944
439353344
108789760
532938752
98304000
-430702592
-494665728
94633984
216006656
-32768000
-172752896
216793088
410779648
473956352
124518400
-308543488
-24903680
508297216
-310378496
494927872
-458752000
146800640
-411828224
-440926208
119013376
-163577856
-216268800
-306446336
492044288
109838336
-170393600
-304873472
-120324096
425459712
130023424
-352583680
-279969792
338165760
-531628032
411828224
312737792
-16515072
-372244480
512753664
-85983232
314048512
-164102144
-534249472
53739520
329777152
-388497408
318504960
469762048
214958080
-385613824
-473956352
-205520896
-343408640
275251200
-326631424
141819904
-46661632
-417333248
-306184192
-267911168
94109696
186908672
231473152
-67108864
-95158272
11534336
186908672
-79429632
-189267968
-500695040
-136052736
61603840
-362283008
329777152
429391872
182714368
294387712
-270532608
334495744
-232783872
-127664128
-498335744
-405798912
-408420352
-279707648
94109696
-65798144
35913728
149946368
-138936320
268435456
407371776
-432275456
77332480
-20185088
-179568640
442761216
-505413632
527171584
445644800
32768000
-205258752
456130560
270008320
341573632
272367616
-58195968
395313152
-242483200
-92012544
-144965632
103022592
-323223552
-315883520
478412800
292552704
197656576
312999936
-135266304
-26476544
-529793024
23068672
16777216
72613888
195559424
194248704
-46661632
-338427904
481296384
-367001600
-290979840
-282853376
101187584
-449576960
-18874368
449314816
-76808192
-468713472
159907840
-330563584
-482344960
-317194240
-325320704
97517568
-44826624
-249298944
-292028416
-449314816
379060224
-407109632
403701760
-350224384
-73662464
-160694272
-87556096
321126400
128188416
-413138944
-286785536
198967296
-168820736
293863424
-523239424
369098752
-271056896
-189792256
37224448
-481034240
266076160
-349700096
-49020928
-284164096
-274202624
-269221888
-420741120
-505675776
-434896896
502530048
-293601280
-162529280
-342884352
-228851712
-391905280
-76808192
128712704
-94633984
320602112
-96993280
-335806464
115343360
343408640
-478937088
-122683392
-118489088
-304873472
-435945472
405012480
-213385216
101974016
-433586176
130285568
357564416
-126877696
239075328
229900288
-80478208
-208404480
395575296
246677504
304349184
-338952192
446693376
-78643200
-150208512
465567744
-163840000
355467264
338165760
66060288
-94633984
-115605504
-484179968
-44564480
263716864
523239424
-85196800
-378535936
-287309824
500170752
-38535168
289669120
-385875968
-454295552
-140247040
276299776
504102912
-292028416
-284164096
494141440
-444858368
289144832
-158597120
467140608
-511967232
437518336
472383488
338427904
-429129728
193724416
-131596288
-120324096
305659904
-106692608
296222720
-322174976
-464781312
-484704256
-159645696
503054336
111411200
292028416
249298944
-22282240
109838336
-464257024
-277610496
-194510848
348651520
-529530880
230686720
-475529216
-155713536
227016704
241434624
487325696
480247808
68419584
420216832
-531103744
292814848
-113770496
324272128
445120512
-125566976
-190840832
-456392704
-245366784
-182714368
-338165760
177471488
-479461376
-212860928
60555264
199491584
36700160
379060224
333447168
-319553536
184025088
503840768
444596224
394788864
-147587072
-38273024
527433728
-456130560
-300154880
58720256
-301203456
97255424
430702592
293863424
222035968
68419584
-247201792
492568576
-295698432
150208512
183500800
-355467264
-386138112
504102912
-115605504
403177472
-461635584
-2359296
480772096
-432013312
-62390272
110362624
95420416
-115343360
402391040
-345243648
-299106304
517734400
107479040
44302336
-472645632
8650752
78381056
-78905344
-135004160
295174144
426246144
-250871808
-110624768
142344192
393740288
-343932928
-395575296
-316145664
407109632
32505856
-94371840
-488374272
34865152
-4980736
-440664064
481296384
-472645632
167247872
85983232
-34340864
-247726080
-252182528
304349184
230162432
-430178304
489947136
-455606272
-512753664
247726080
-406847488
-437256192
221249536
262144000
364380160
444334080
However, checking the out shows the following at the end,
Two questions I have --
- I was expecting signed 12-bit output as I set the OutputWordLength=12. However, out is much larger than 12-bit range. Why this happened. Not sure I was missing something. How could I fix this?
- FractionLength is a negative value (-18). Can this be 0 as I wanted to see signed 12-bit? How could I compare this out with the values from the real RTL implementation?
Accepted Answer
Andy Bartlett
on 11 Dec 2023
Edited: Andy Bartlett
on 12 Dec 2023
In that section, take a look at Gain Correction and Output Data Type subsections.
Those sections explain that the block will amplify the input signal by an effective gain value Gain.
In your example, the Gain is as follows.
R_decimation_factor = 20;
M_differential_delay = 1;
N_number_of_sections = 4;
Gain = (R_decimation_factor * M_differential_delay)^N_number_of_sections
A fixed-point representation of that gain would use 18 bits.
GainFi = fi( Gain, 0, ceil(log2(Gain)), 0)
So given your 12 bit integer valued input, a full precision output would be 30 bits.
inExample = upperbound(numerictype(1,12,0));
yFullPrecisionExample = inExample * GainFi
You've requested that the output be only 12 bits. So the block must throw away 18 bits from the 30 bits that the full precision output would have. The block is design to throw those bits away from the least significant end which reduces precision, but avoids overflows.
nty = numerictype(1,12,-18 );
yExample = removefimath( fi( yFullPrecisionExample, nty, 'RoundingMethod','Floor') )
For this specific example, dropping the least significant 18 bits
% Type Real World Notation: Integer Mantissa
% Value and Pow2 Exponent
% numerictype(1,30,0) 327520000 = 010011100001011000111100000000 * 2^0
% numerictype(1,12,-18) 327417856 = 010011100001 * 2^18
Dropping the least significant 18 bits produces a relatively modest error for this specific example.
absoluteError = abs( double( yExample ) - double( yFullPrecisionExample ) )
relativeErr = absoluteError / double( yFullPrecisionExample )
errorInParts = ceil(1/relativeErr)
The output is accurate to 1 part in 3207, which is in the vicinity of what would be expected for a signed 12 bits fixed point type if well scaled.
Compare using Stored Integer Value and/or Real-World Value
Fixed-point signals always have two values.
For binary-point types as being discussed here, the Fixed-Point Scaling Equation is
V = Q * 2^-FractionLength
where
V is the Real-World Value (RWV) in units prefered by the human engineers
Q is the Stored-Integer (SI) value
When modeling, it is usally far easier to work with Real-World Values (RWV). Fixed-Point Designer works with the real-world values by default. Designer automatically manages all the book keeping related to scaling and storage data types.
The actual embedded implementation produced by Coders will efficiently operate on the stored integers (SI) to produce the high level math desired by the engineers.
When using generic tools on the embedded device such as target debuggers, signals will typically be shown using the stored integer values.
When values for a signal being tested or examined are provided in both real-world value form and stored-integer value form, naturally, it is necessary convert in either direction, SI to RWV or RWV to SI.
Convert RWV to SI
Given a fixed-point fi object produce it's stored integer value.
si_approach_1 = yExample.storedInteger
si_approach_2 = yExample.storedIntegerToDouble
si_approach_3 = stripscaling(yExample)
Notice that si_approach_3 is a fi object with trivial scaling (FractionLength == 0). With trivial scaling, RWV == SI.
Convert SI to RWV
Given a stored integer value and knowledge of the scaling to be applied, it is straightforward to produce a scaled fixed-point fi object or a double holding the real-world value.
RWV in double
si_from_target = int16(1518)
rwv1_in_double = double(si_from_target) * yExample.Slope % Note: Slope = 2^-FractionLength
Apply scaling knowledge to a raw SI to create a fixed-point fi object.
Reinterpcast is the key tool to use to apply the scaling information, but preserve the stored integer value.
si_in_raw_fi = fi( si_from_target, 1, 12, 0 )
nty = numerictype( yExample )
rwv2_in_fi = reinterpretcast( si_in_raw_fi, nty)
check_si_still_same = rwv2_in_fi.storedIntegerToDouble
3 Comments
Jay
on 11 Dec 2023
Thanks Andy for the reply. It's insightful and informative which I overlooked in the MATLAB document!
Jay
on 11 Dec 2023
Edited: Jay
on 11 Dec 2023
One minor question is the Gain in your code. In MATLAB document, the Gain term is given by (R x M)^N, e.g., the product of R and M, while it was written by (R + M)^N in your example, e.g., the sum of R and M. I assume this is a typo while it doesn't change the number of bits to represent a fixed-point number?
R_decimation_factor = 20;
M_differential_delay = 1;
N_number_of_sections = 4;
Gain = (R_decimation_factor + M_differential_delay)^N_number_of_sections
Gain = 194481
Andy Bartlett
on 12 Dec 2023
Hi Jay,
Good catch. You are correct. The formula should be multiply and not add. I updated the answer. Numbers are a bit different, but the overall message of needing to drop 18 LS bits from the ideal 30 bits to get down to 12 is the same.
More Answers (0)
See Also
Categories
Find more on Fixed-Point Filters in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!An Error Occurred
Unable to complete the action because of changes made to the page. Reload the page to see its updated state.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom(English)
Asia Pacific
- Australia (English)
- India (English)
- New Zealand (English)
- 中国
- 日本Japanese (日本語)
- 한국Korean (한국어)