-
Notifications
You must be signed in to change notification settings - Fork 0
/
rrcfir.h
212 lines (191 loc) · 22.4 KB
/
rrcfir.h
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
#include <math.h>
void build_rrc_filter(double *filter, float rolloff, int ntaps, int samples_per_symbol) {
double a, b, c, d;
double B = rolloff+0.0001;// Rolloff factor .0001 stops infinite filter coefficient with 0.25 rolloff
double t = -(ntaps - 1) / 2;// First tap
double Ts = samples_per_symbol;// Samples per symbol
// Create the filter
for (int i = 0; i < (ntaps); i++) {
a = 2.0 * B / (M_PI*sqrt(Ts));
b = cos((1.0 + B)*M_PI*t / Ts);
// Check for infinity in calculation (computers don't have infinite precision)
if (t == 0)
c = (1.0 - B)*M_PI / (4 * B);
else
c = sin((1.0 - B)*M_PI*t / Ts) / (4.0*B*t / Ts);
d = (1.0 - (4.0*B*t / Ts)*(4.0*B*t / Ts));
//filter[i] = (b+c)/(a*d);//beardy
filter[i] = (float)(a*(b + c) / d);//nasa
t = t + 1.0;
}
}
void build_lpf_filter(double *filter, float bw, int ntaps ) {
double a;
double B = bw;// filter bandwidth
double t = -( ntaps - 1) / 2;// First tap
// Create the filter
for (int i = 0; i < ntaps; i++) {
if (t == 0)
a = 2.0 * B;
else
a = 2.0 * B * sin(M_PI * t * B)/ (M_PI * t * B);
filter[i] = (double)a;
t = t + 1.0;
}
}
float set_filter_gain(double *filter, float gain, int ntaps) {
double sum = 0;
double max=0;
for (int i = 0; i < ntaps; i++) {
sum += filter[i];
}
gain = gain / sum;
for (int i = 0; i < ntaps; i++) {
filter[i] = filter[i] * gain;
if(fabs(filter[i])>fabs(max))
max=filter[i];
}
return max;
}
//==========================================================================================
// + + + This Software is released under the "Simplified BSD License" + + +
// Copyright 2014 F4GKR Sylvain AZARIAN . All rights reserved.
//
//Redistribution and use in source and binary forms, with or without modification, are
//permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other materials
// provided with the distribution.
//
//THIS SOFTWARE IS PROVIDED BY Sylvain AZARIAN F4GKR ``AS IS'' AND ANY EXPRESS OR IMPLIED
//WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
//FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Sylvain AZARIAN OR
//CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
//CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
//SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
//ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
//NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
//ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//The views and conclusions contained in the software and documentation are those of the
//authors and should not be interpreted as representing official policies, either expressed
//or implied, of Sylvain AZARIAN F4GKR.
//==========================================================================================
struct FIR {
float *coeffs;
int filterLength;
float *delay_line;
};
typedef struct _cpx {
float re;
float im;
} TYPECPX;
struct cFIR {
float *coeffs;
int filterLength;
TYPECPX *delay_line;
float rms;
};
// Create a FIR struct, used to store a copy of coeffs and delay line
// in : coeffs_len = coeff tab length
// double *coeff_tab = pointer to the coefficients
// out: a struct FIR
struct FIR* init_fir( int coeffs_len, double *coeff_tab )
{
struct FIR *result;
int i;
// alloc and init buffers
result = (struct FIR *)malloc( sizeof( struct FIR ));
result->filterLength = coeffs_len;
result->coeffs = (float*)malloc( coeffs_len * sizeof( float));
result->delay_line = (float*)malloc( coeffs_len * sizeof( float));
// copy coeffs to struct
for( i=0 ; i < coeffs_len ; i++ ) {
result->delay_line[i] = 0.0;
result->coeffs[i] = coeff_tab[i];
}
return( result );
}
// init a complex in -> complex out fir with real coeffs
struct cFIR* init_cfir( int coeffs_len, double *coeff_tab )
{
struct cFIR *result;
int i;
// alloc and init buffers
result = (struct cFIR *)malloc( sizeof( struct cFIR ));
result->filterLength = coeffs_len ;
result->coeffs = (float*)malloc( coeffs_len * sizeof( float));
result->delay_line = (TYPECPX*)malloc( coeffs_len * sizeof( TYPECPX));
// copy coeffs to struct
for( i=0 ; i < coeffs_len ; i++ ) {
result->delay_line[i].re = 0.0;
result->delay_line[i].im = 0.0;
result->coeffs[i] = coeff_tab[i];
}
return( result );
}
float fir_filt( struct FIR* f, double in )
{
int i;
float acc;
float *pt_coeffs;
float *pt_sample;
int L;
// shift input left for one sample
L = f->filterLength;
for( i=0 ; i < L - 1 ; i++ ) {
f->delay_line[i] = f->delay_line[i+1];
}
// add new sample to the end of delay line
f->delay_line[ L - 1 ] = in;
acc = 0 ;
pt_sample = f->delay_line;
pt_coeffs = f->coeffs;
// do the compute loop
for( i=0 ; i < L ; i++ ) {
acc += (*pt_sample) * (*pt_coeffs );
pt_sample++;
pt_coeffs++;
}
return( acc );
}
// same but we filter a complex number at input, out is a complex
TYPECPX cfir_filt( struct cFIR* f, TYPECPX in )
{
int i;
TYPECPX acc;
float *pt_coeffs, rms;
TYPECPX *pt_sample;
int L;
// shift input left for one sample
L = f->filterLength;
for( i=0 ; i < L - 1 ; i++ ){
f->delay_line[i] = f->delay_line[i+1];
}
// add new sample to the end of delay line
f->delay_line[ L - 1 ] = in;
acc.re = acc.im = 0;
pt_sample = f->delay_line;
pt_coeffs = f->coeffs;
// do the compute loop
rms = 0;
for( i=0 ; i < L ; i++ ) {
acc.re += (pt_sample->re) * (*pt_coeffs );
acc.im += (pt_sample->im) * (*pt_coeffs );
rms += (pt_sample->re)*(pt_sample->re) + (pt_sample->im)*(pt_sample->im);
pt_sample++;
pt_coeffs++;
}
f->rms = sqrt( rms / L );
return( acc );
}
double xcoeffs2[]= {1.2805533515347634e-05, -0.00021340473904274404, 0.00021151425607968122, 6.0186816881468985e-06, -0.00021959937294013798, 0.00023801837232895195, -2.8975933673791587e-05, -0.00023913703626021743, 0.00028095548623241484, -4.067101326654665e-05, -0.00024071410007309169, 0.0003172782890032977, -9.122618212131783e-05, -0.000264814036199823, 0.0003712314646691084, -0.00011090978659922257, -0.00025811875821091235, 0.0004228523466736078, -0.0001852382265496999, -0.0002887784503400326, 0.0004922013613395393, -0.0002187022619182244, -0.00026694912230595946, 0.0005691690021194518, -0.00033155796700157225, -0.0003074800770264119, 0.0006612851866520941, -0.0003905819612555206, -0.00025655553326942027, 0.0007836406002752483, -0.0005709670367650688, -0.00031280063558369875, 0.0009120248723775148, -0.0006820967537350953, -0.00020114821381866932, 0.0011245263740420341, -0.000994345755316317, -0.00028434404521249235, 0.0013169205049052835, -0.001226545195095241, -2.854519334505312e-05, 0.001737056765705347, -0.0018402881687507033, -0.0001632451603654772, 0.0020608280319720507, -0.0024152372498065233, 0.0005141948931850493, 0.003085298230871558, -0.0039174193516373634, 0.00026095236535184085, 0.0037535291630774736, -0.005857567302882671, 0.002750313375145197, 0.007503064814954996, -0.011627281084656715, 0.0020431256853044033, 0.009572923183441162, -0.025455128401517868, 0.02561645768582821, 0.057122569531202316, -0.1351718306541443, -0.08469510078430176, 0.6078083515167236, 1.0956964492797852, 0.6078083515167236, -0.08469510078430176, -0.1351718306541443, 0.057122569531202316, 0.02561645768582821, -0.025455128401517868, 0.009572923183441162, 0.0020431256853044033, -0.011627281084656715, 0.007503064814954996, 0.002750313375145197, -0.005857567302882671, 0.0037535291630774736, 0.00026095236535184085, -0.0039174193516373634, 0.003085298230871558, 0.0005141948931850493, -0.0024152372498065233, 0.0020608280319720507, -0.0001632451603654772, -0.0018402881687507033, 0.001737056765705347, -2.854519334505312e-05, -0.001226545195095241, 0.0013169205049052835, -0.00028434404521249235, -0.000994345755316317, 0.0011245263740420341, -0.00020114821381866932, -0.0006820967537350953, 0.0009120248723775148, -0.00031280063558369875, -0.0005709670367650688, 0.0007836406002752483, -0.00025655553326942027, -0.0003905819612555206, 0.0006612851866520941, -0.0003074800770264119, -0.00033155796700157225, 0.0005691690021194518, -0.00026694912230595946, -0.0002187022619182244, 0.0004922013613395393, -0.0002887784503400326, -0.0001852382265496999, 0.0004228523466736078, -0.00025811875821091235, -0.00011090978659922257, 0.0003712314646691084, -0.000264814036199823, -9.122618212131783e-05, 0.0003172782890032977, -0.00024071410007309169, -4.067101326654665e-05, 0.00028095548623241484, -0.00023913703626021743, -2.8975933673791587e-05, 0.00023801837232895195, -0.00021959937294013798, 6.0186816881468985e-06, 0.00021151425607968122, -0.00021340473904274404, 1.2805533515347634e-05,0};
double xcoeffs4[] = {0.0005948974867351353, 0.0009115553693845868, 0.00027828614111058414, -0.0006817456451244652, -0.0009589190012775362, -0.00020104466238990426, 0.0008651951211504638, 0.0011239474406465888, 0.00022292527137324214, -0.000993833877146244, -0.0012836591340601444, -0.000284197652945295, 0.0010396202560514212, 0.0013162426184862852, 0.00018902479496318847, -0.0012259137583896518, -0.0014091989723965526, -2.8530497729661874e-05, 0.0015942379832267761, 0.0017361625796183944, 7.239625119837001e-05, -0.0018393407808616757, -0.002028661547228694, -0.00016316112305503339, 0.0019434461137279868, 0.00205976702272892, -0.00011300298501737416, -0.002413993701338768, -0.0022817798890173435, 0.0005139301647432148, 0.003319702809676528, 0.0030837098602205515, -0.000407199579058215, -0.003915402572602034, -0.0037664929404854774, 0.00026081802207045257, 0.004231776110827923, 0.00375159690156579, -0.0012814607471227646, -0.0058545516803860664, -0.004489745479077101, 0.0027488975320011377, 0.00918541569262743, 0.007499201688915491, -0.002376680728048086, -0.011621295474469662, -0.010265957564115524, 0.0020420739892870188, 0.013314166106283665, 0.009567995555698872, -0.009544706903398037, -0.02544202283024788, -0.014768400229513645, 0.025603270158171654, 0.06531448662281036, 0.05709316208958626, -0.022062532603740692, -0.13510224223136902, -0.18854673206806183, -0.08465149998664856, 0.20677652955055237, 0.6074954271316528, 0.956687867641449, 1.0951323509216309, 0.956687867641449, 0.6074954271316528, 0.20677652955055237, -0.08465149998664856, -0.18854673206806183, -0.13510224223136902, -0.022062532603740692, 0.05709316208958626, 0.06531448662281036, 0.025603270158171654, -0.014768400229513645, -0.02544202283024788, -0.009544706903398037, 0.009567995555698872, 0.013314166106283665, 0.0020420739892870188, -0.010265957564115524, -0.011621295474469662, -0.002376680728048086, 0.007499201688915491, 0.00918541569262743, 0.0027488975320011377, -0.004489745479077101, -0.0058545516803860664, -0.0012814607471227646, 0.00375159690156579, 0.004231776110827923, 0.00026081802207045257, -0.0037664929404854774, -0.003915402572602034, -0.000407199579058215, 0.0030837098602205515, 0.003319702809676528, 0.0005139301647432148, -0.0022817798890173435, -0.002413993701338768, -0.00011300298501737416, 0.00205976702272892, 0.0019434461137279868, -0.00016316112305503339, -0.002028661547228694, -0.0018393407808616757, 7.239625119837001e-05, 0.0017361625796183944, 0.0015942379832267761, -2.8530497729661874e-05, -0.0014091989723965526, -0.0012259137583896518, 0.00018902479496318847, 0.0013162426184862852, 0.0010396202560514212, -0.000284197652945295, -0.0012836591340601444, -0.000993833877146244, 0.00022292527137324214, 0.0011239474406465888, 0.0008651951211504638, -0.00020104466238990426, -0.0009589190012775362, -0.0006817456451244652, 0.00027828614111058414, 0.0009115553693845868, 0.0005948974867351353,0};
double xcoeffs8[] = {0.001606374979019165, -0.0004080820071976632, -0.0024359466042369604, -0.003923887386918068, -0.004434230737388134, -0.003774655284360051, -0.002067992463707924, 0.0002613832475617528, 0.002586567774415016, 0.004240946378558874, 0.004703972954303026, 0.003759726881980896, 0.001581895281560719, -0.0012842378346249461, -0.004045937675982714, -0.005867238622158766, -0.0061029125936329365, -0.004499475006014109, -0.001304417965002358, 0.002754854504019022, 0.006628258619457483, 0.009205320850014687, 0.009619668126106262, 0.007515453267842531, 0.0031983761582523584, -0.0023818311747163534, -0.007829617708921432, -0.011646479368209839, -0.012639228254556656, -0.010288204997777939, -0.004969553556293249, 0.0020464991685003042, 0.008847571909427643, 0.013343018479645252, 0.013839897699654102, 0.009588729590177536, 0.0011467351578176022, -0.009565390646457672, -0.019573146477341652, -0.025497158989310265, -0.02442297711968422, -0.014800404198467731, 0.0028537041507661343, 0.025658752769231796, 0.04862036556005478, 0.06545602530241013, 0.0698937401175499, 0.057216886430978775, 0.025741973891854286, -0.0221103448420763, -0.07944413274526596, -0.13539502024650574, -0.17652802169322968, -0.18895532190799713, -0.16083920001983643, -0.08483494818210602, 0.039998188614845276, 0.20722462236881256, 0.4032552242279053, 0.6088119149208069, 0.8014516234397888, 0.9587610960006714, 1.0616978406906128, 1.0975055694580078, 1.0616978406906128, 0.9587610960006714, 0.8014516234397888, 0.6088119149208069, 0.4032552242279053, 0.20722462236881256, 0.039998188614845276, -0.08483494818210602, -0.16083920001983643, -0.18895532190799713, -0.17652802169322968, -0.13539502024650574, -0.07944413274526596, -0.0221103448420763, 0.025741973891854286, 0.057216886430978775, 0.0698937401175499, 0.06545602530241013, 0.04862036556005478, 0.025658752769231796, 0.0028537041507661343, -0.014800404198467731, -0.02442297711968422, -0.025497158989310265, -0.019573146477341652, -0.009565390646457672, 0.0011467351578176022, 0.009588729590177536, 0.013839897699654102, 0.013343018479645252, 0.008847571909427643, 0.0020464991685003042, -0.004969553556293249, -0.010288204997777939, -0.012639228254556656, -0.011646479368209839, -0.007829617708921432, -0.0023818311747163534, 0.0031983761582523584, 0.007515453267842531, 0.009619668126106262, 0.009205320850014687, 0.006628258619457483, 0.002754854504019022, -0.001304417965002358, -0.004499475006014109, -0.0061029125936329365, -0.005867238622158766, -0.004045937675982714, -0.0012842378346249461, 0.001581895281560719, 0.003759726881980896, 0.004703972954303026, 0.004240946378558874, 0.002586567774415016, 0.0002613832475617528, -0.002067992463707924, -0.003774655284360051, -0.004434230737388134, -0.003923887386918068, -0.0024359466042369604, -0.0004080820071976632, 0.001606374979019165,0};
double xcoeff16[] = {0.005563570186495781, 0.008779175579547882, 0.011416609399020672, 0.01323987077921629, 0.014056227169930935, 0.01373290829360485, 0.012210879474878311, 0.00951460376381874, 0.005756843835115433, 0.0011378703638911247, -0.004061272833496332, -0.009491445496678352, -0.014753616414964199, -0.019421838223934174, -0.023069873452186584, -0.025300052016973495, -0.02577267214655876, -0.02423417568206787, -0.020542247220873833, -0.01468598935753107, -0.006799628026783466, 0.0028316436801105738, 0.013774625025689602, 0.02546039968729019, 0.03720593824982643, 0.04824450612068176, 0.05776376649737358, 0.06495001912117004, 0.06903651356697083, 0.06935342401266098, 0.06537695229053497, 0.0567745715379715, 0.043443985283374786, 0.0255429744720459, 0.003508127061650157, -0.021939421072602272, -0.04980232194066048, -0.07882998883724213, -0.10755591094493866, -0.13434834778308868, -0.15747277438640594, -0.1751633733510971, -0.1857011318206787, -0.18749460577964783, -0.17915986478328705, -0.15959583222866058, -0.12805117666721344, -0.08417913317680359, -0.028077486902475357, 0.03968898579478264, 0.11808524280786514, 0.20562267303466797, 0.30039578676223755, 0.40013784170150757, 0.5022934079170227, 0.6041054725646973, 0.702713131904602, 0.7952560186386108, 0.8789815306663513, 0.9513493776321411, 1.0101299285888672, 1.053490400314331, 1.0800676345825195, 1.0890213251113892, 1.0800676345825195, 1.053490400314331, 1.0101299285888672, 0.9513493776321411, 0.8789815306663513, 0.7952560186386108, 0.702713131904602, 0.6041054725646973, 0.5022934079170227, 0.40013784170150757, 0.30039578676223755, 0.20562267303466797, 0.11808524280786514, 0.03968898579478264, -0.028077486902475357, -0.08417913317680359, -0.12805117666721344, -0.15959583222866058, -0.17915986478328705, -0.18749460577964783, -0.1857011318206787, -0.1751633733510971, -0.15747277438640594, -0.13434834778308868, -0.10755591094493866, -0.07882998883724213, -0.04980232194066048, -0.021939421072602272, 0.003508127061650157, 0.0255429744720459, 0.043443985283374786, 0.0567745715379715, 0.06537695229053497, 0.06935342401266098, 0.06903651356697083, 0.06495001912117004, 0.05776376649737358, 0.04824450612068176, 0.03720593824982643, 0.02546039968729019, 0.013774625025689602, 0.0028316436801105738, -0.006799628026783466, -0.01468598935753107, -0.020542247220873833, -0.02423417568206787, -0.02577267214655876, -0.025300052016973495, -0.023069873452186584, -0.019421838223934174, -0.014753616414964199, -0.009491445496678352, -0.004061272833496332, 0.0011378703638911247, 0.005756843835115433, 0.00951460376381874, 0.012210879474878311, 0.01373290829360485, 0.014056227169930935, 0.01323987077921629, 0.011416609399020672, 0.008779175579547882, 0.005563570186495781,0};
double xcoeff32[] = {0.05339697003364563, 0.045757848769426346, 0.03691064566373825, 0.026903415098786354, 0.01580296829342842, 0.0036949727218598127, -0.0093162152916193, -0.02310793101787567, -0.03753984346985817, -0.052454832941293716, -0.06768010556697845, -0.08302854001522064, -0.0983002558350563, -0.11328442394733429, -0.12776118516921997, -0.14150385558605194, -0.15428121387958527, -0.1658598929643631, -0.17600701749324799, -0.18449270725250244, -0.1910928636789322, -0.19559171795845032, -0.1977846622467041, -0.1974807232618332, -0.19450518488883972, -0.1887020617723465, -0.17993631958961487, -0.16809603571891785, -0.15309441089630127, -0.13487128913402557, -0.1133948415517807, -0.08866257965564728, -0.060702357441186905, -0.02957291714847088, 0.004635835066437721, 0.04180284962058067, 0.08177635818719864, 0.12437455356121063, 0.16938666999340057, 0.2165742963552475, 0.2656731903553009, 0.316395103931427, 0.3684302270412445, 0.4214495122432709, 0.47510766983032227, 0.5290459394454956, 0.5828955769538879, 0.6362806558609009, 0.6888219118118286, 0.7401401996612549, 0.7898597121238708, 0.837611973285675, 0.8830389380455017, 0.9257967472076416, 0.9655588269233704, 1.0020190477371216, 1.0348949432373047, 1.0639301538467407, 1.088897466659546, 1.1096001863479614, 1.1258748769760132, 1.1375929117202759, 1.1446611881256104, 1.1470234394073486, 1.1446611881256104, 1.1375929117202759, 1.1258748769760132, 1.1096001863479614, 1.088897466659546, 1.0639301538467407, 1.0348949432373047, 1.0020190477371216, 0.9655588269233704, 0.9257967472076416, 0.8830389380455017, 0.837611973285675, 0.7898597121238708, 0.7401401996612549, 0.6888219118118286, 0.6362806558609009, 0.5828955769538879, 0.5290459394454956, 0.47510766983032227, 0.4214495122432709, 0.3684302270412445, 0.316395103931427, 0.2656731903553009, 0.2165742963552475, 0.16938666999340057, 0.12437455356121063, 0.08177635818719864, 0.04180284962058067, 0.004635835066437721, -0.02957291714847088, -0.060702357441186905, -0.08866257965564728, -0.1133948415517807, -0.13487128913402557, -0.15309441089630127, -0.16809603571891785, -0.17993631958961487, -0.1887020617723465, -0.19450518488883972, -0.1974807232618332, -0.1977846622467041, -0.19559171795845032, -0.1910928636789322, -0.18449270725250244, -0.17600701749324799, -0.1658598929643631, -0.15428121387958527, -0.14150385558605194, -0.12776118516921997, -0.11328442394733429, -0.0983002558350563, -0.08302854001522064, -0.06768010556697845, -0.052454832941293716, -0.03753984346985817, -0.02310793101787567, -0.0093162152916193, 0.0036949727218598127, 0.01580296829342842, 0.026903415098786354, 0.03691064566373825, 0.045757848769426346, 0.05339697003364563,0};
double xcoeff64[] = {-0.062455836683511734, -0.05049366131424904, -0.03787201642990112, -0.024599451571702957, -0.01068611815571785, 0.003856197465211153, 0.019014103338122368, 0.0347726009786129, 0.05111512169241905, 0.06802351027727127, 0.08547809720039368, 0.10345769673585892, 0.12193963676691055, 0.14089983701705933, 0.16031278669834137, 0.18015164136886597, 0.20038825273513794, 0.2209932655096054, 0.24193604290485382, 0.26318493485450745, 0.2847071588039398, 0.30646899342536926, 0.32843565940856934, 0.3505716919898987, 0.3728407323360443, 0.3952057957649231, 0.41762927174568176, 0.4400729537010193, 0.4624983072280884, 0.48486635088920593, 0.5071377754211426, 0.529273271560669, 0.5512333512306213, 0.5729783773422241, 0.5944690704345703, 0.6156661510467529, 0.6365306377410889, 0.6570240259170532, 0.6771081686019897, 0.6967454552650452, 0.7158990502357483, 0.7345326542854309, 0.7526110410690308, 0.7700996398925781, 0.786965012550354, 0.8031746745109558, 0.8186973929405212, 0.8335031270980835, 0.8475632071495056, 0.8608501553535461, 0.873337984085083, 0.8850023150444031, 0.8958203792572021, 0.9057707190513611, 0.9148337841033936, 0.9229916930198669, 0.9302282929420471, 0.9365293979644775, 0.9418824911117554, 0.9462767243385315, 0.949703574180603, 0.9521562457084656, 0.9536297917366028, 0.9541212916374207, 0.9536297917366028, 0.9521562457084656, 0.949703574180603, 0.9462767243385315, 0.9418824911117554, 0.9365293979644775, 0.9302282929420471, 0.9229916930198669, 0.9148337841033936, 0.9057707190513611, 0.8958203792572021, 0.8850023150444031, 0.873337984085083, 0.8608501553535461, 0.8475632071495056, 0.8335031270980835, 0.8186973929405212, 0.8031746745109558, 0.786965012550354, 0.7700996398925781, 0.7526110410690308, 0.7345326542854309, 0.7158990502357483, 0.6967454552650452, 0.6771081686019897, 0.6570240259170532, 0.6365306377410889, 0.6156661510467529, 0.5944690704345703, 0.5729783773422241, 0.5512333512306213, 0.529273271560669, 0.5071377754211426, 0.48486635088920593, 0.4624983072280884, 0.4400729537010193, 0.41762927174568176, 0.3952057957649231, 0.3728407323360443, 0.3505716919898987, 0.32843565940856934, 0.30646899342536926, 0.2847071588039398, 0.26318493485450745, 0.24193604290485382, 0.2209932655096054, 0.20038825273513794, 0.18015164136886597, 0.16031278669834137, 0.14089983701705933, 0.12193963676691055, 0.10345769673585892, 0.08547809720039368, 0.06802351027727127, 0.05111512169241905, 0.0347726009786129, 0.019014103338122368, 0.003856197465211153, -0.01068611815571785, -0.024599451571702957, -0.03787201642990112, -0.05049366131424904, -0.062455836683511734,0};