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Trigo.cxx
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1 /*
2  Copyright (C) 2002-2021 CERN for the benefit of the ATLAS collaboration
3 */
4 /*********************************
5  * Trigo.cxx
6  * author : Ignacio Aracena <ignacio.aracena@cern.ch>
7  * Created June 2015
8  *
9  * @brief Lookup table for trigonometric functions.
10  * Resolution is in PI/32. Values is in Qm.n format
11  * with the MSB reserved for sign, and m=1, n = 7
12  *
13  **********************************/
14 
15 #include "L1TopoSimulationUtils/Trigo.h"
16 #include "L1TopoSimulationUtils/Conversions.h"
17 #include <cmath>
18 
19 //helper to convert entire vectors
20 std::vector<int> convertVector(const std::vector<std::string>& stringVector) {
21  std::vector<int> values;
22  for (const std::string& binStr: stringVector) {
23  values.push_back( TSU::toSigned(binStr) );
24  }
25  return values;
26 }
27 
28 const std::vector<std::string> TSU::Trigo::Cosleg=
29  {
30  //legacy
31  "010000000", // 1.0
32  "001111111", // 0.9951847266721969
33  "001111110", // 0.9807852804032304
34  "001111010", // 0.9569403357322088
35  "001110110", // 0.9238795325112867
36  "001110001", // 0.881921264348355 // 5
37  "001101010", // 0.8314696123025452
38  "001100011", // 0.773010453362737
39  "001011011", // 0.7071067811865476
40  "001010001", // 0.6343932841636455
41  "001000111", // 0.5555702330196023 // 10
42  "000111100", // 0.4713967368259978
43  "000110001", // 0.38268343236508984
44  "000100101", // 0.29028467725446233
45  "000011001", // 0.19509032201612833
46  "000001101", // 0.09801714032956077 // 15
47  "000000000", // 6.123233995736766e-17
48  "111110011", // -0.09801714032956065
49  "111100111", // -0.1950903220161282
50  "111011011", // -0.29028467725446216
51  "111001111", // -0.3826834323650897 // 20
52  "111000100", // -0.4713967368259977
53  "110111001", // -0.555570233019602
54  "110101111", // -0.6343932841636454
55  "110100101", // -0.7071067811865475
56  "110011101", // -0.773010453362737 // 25
57  "110010110", // -0.8314696123025453
58  "110001111", // -0.8819212643483549
59  "110001010", // -0.9238795325112867
60  "110000110", // -0.9569403357322088
61  "110000010", // -0.9807852804032304 // 30
62  "110000001", // -0.9951847266721968
63  "110000000", // -1.0
64  "110000001", // -0.9951847266721969
65  "110000010", // -0.9807852804032304
66  "110000110", // -0.9569403357322089 // 35
67  "110001010", // -0.9238795325112868
68  "110001111", // -0.881921264348355
69  "110010110", // -0.8314696123025455
70  "110011101", // -0.7730104533627371
71  "110100101", // -0.7071067811865477 // 40
72  "110101111", // -0.6343932841636459
73  "110111001", // -0.5555702330196022
74  "111000100", // -0.47139673682599786
75  "111001111", // -0.38268343236509034
76  "111011011", // -0.29028467725446244 // 45
77  "111100111", // -0.19509032201612866
78  "111110011", // -0.09801714032956045
79  "000000000", // -1.8369701987210297e-16
80  "000001101", // 0.09801714032956009
81  "000011001", // 0.1950903220161283
82  "000100101", // 0.29028467725446205
83  "000110001", // 0.38268343236509
84  "000111100", // 0.4713967368259976
85  "001000111", // 0.5555702330196018
86  "001010001", // 0.6343932841636456
87  "001011011", // 0.7071067811865474
88  "001100011", // 0.7730104533627367
89  "001101010", // 0.8314696123025452
90  "001110001", // 0.8819212643483548
91  "001110110", // 0.9238795325112865
92  "001111010", // 0.9569403357322088
93  "001111110", // 0.9807852804032303
94  "001111111" // 0.9951847266721969
95  };
96 
97 const std::vector<int> TSU::Trigo::CoslegInt = convertVector(TSU::Trigo::Cosleg);
98 
99 //phase1
100 const std::vector<std::string> TSU::Trigo::Cos=
101  {
102  "010000000000", // value = 1.0(1.0) argument value = 0.0
103  "001111111111", // value = 0.9987954562051724(0.9990234375) argument value = 0.04908738521234052
104  "001111111011", // value = 0.9951847266721969(0.9951171875) argument value = 0.09817477042468103
105  "001111110101", // value = 0.989176509964781(0.9892578125) argument value = 0.14726215563702155
106  "001111101100", // value = 0.9807852804032304(0.98046875) argument value = 0.19634954084936207
107  "001111100001", // value = 0.970031253194544(0.9697265625) argument value = 0.2454369260617026
108  "001111010100", // value = 0.9569403357322088(0.95703125) argument value = 0.2945243112740431
109  "001111000100", // value = 0.9415440651830208(0.94140625) argument value = 0.3436116964863836
110  "001110110010", // value = 0.9238795325112867(0.923828125) argument value = 0.39269908169872414
111  "001110011110", // value = 0.9039892931234433(0.904296875) argument value = 0.44178646691106466
112  "001110000111", // value = 0.881921264348355(0.8818359375) argument value = 0.4908738521234052
113  "001101101110", // value = 0.8577286100002721(0.857421875) argument value = 0.5399612373357456
114  "001101010011", // value = 0.8314696123025452(0.8310546875) argument value = 0.5890486225480862
115  "001100110110", // value = 0.8032075314806449(0.802734375) argument value = 0.6381360077604268
116  "001100011000", // value = 0.773010453362737(0.7734375) argument value = 0.6872233929727672
117  "001011110111", // value = 0.7409511253549591(0.7412109375) argument value = 0.7363107781851077
118  "001011010100", // value = 0.7071067811865476(0.70703125) argument value = 0.7853981633974483
119  "001010110000", // value = 0.6715589548470183(0.671875) argument value = 0.8344855486097889
120  "001010001010", // value = 0.6343932841636455(0.634765625) argument value = 0.8835729338221293
121  "001001100010", // value = 0.5956993044924335(0.595703125) argument value = 0.9326603190344698
122  "001000111001", // value = 0.5555702330196023(0.5556640625) argument value = 0.9817477042468103
123  "001000001110", // value = 0.5141027441932217(0.513671875) argument value = 1.030835089459151
124  "000111100011", // value = 0.4713967368259978(0.4716796875) argument value = 1.0799224746714913
125  "000110110110", // value = 0.4275550934302822(0.427734375) argument value = 1.1290098598838318
126  "000110001000", // value = 0.38268343236508984(0.3828125) argument value = 1.1780972450961724
127  "000101011001", // value = 0.33688985339222005(0.3369140625) argument value = 1.227184630308513
128  "000100101001", // value = 0.29028467725446233(0.2900390625) argument value = 1.2762720155208536
129  "000011111001", // value = 0.24298017990326398(0.2431640625) argument value = 1.325359400733194
130  "000011001000", // value = 0.19509032201612833(0.1953125) argument value = 1.3744467859455345
131  "000010010110", // value = 0.14673047445536175(0.146484375) argument value = 1.423534171157875
132  "000001100100", // value = 0.09801714032956077(0.09765625) argument value = 1.4726215563702154
133  "000000110010", // value = 0.049067674327418126(0.048828125) argument value = 1.521708941582556
134  "000000000000", // value = 6.123233995736766e-17(0.0) argument value = 1.5707963267948966
135  "111111001110", // value = -0.04906767432741801(-0.048828125) argument value = 1.6198837120072371
136  "111110011100", // value = -0.09801714032956065(-0.09765625) argument value = 1.6689710972195777
137  "111101101010", // value = -0.14673047445536164(-0.146484375) argument value = 1.718058482431918
138  "111100111000", // value = -0.1950903220161282(-0.1953125) argument value = 1.7671458676442586
139  "111100000111", // value = -0.24298017990326387(-0.2431640625) argument value = 1.8162332528565992
140  "111011010111", // value = -0.29028467725446216(-0.2900390625) argument value = 1.8653206380689396
141  "111010100111", // value = -0.33688985339221994(-0.3369140625) argument value = 1.9144080232812801
142  "111001111000", // value = -0.3826834323650897(-0.3828125) argument value = 1.9634954084936207
143  "111001001010", // value = -0.42755509343028186(-0.427734375) argument value = 2.012582793705961
144  "111000011101", // value = -0.4713967368259977(-0.4716796875) argument value = 2.061670178918302
145  "110111110010", // value = -0.5141027441932217(-0.513671875) argument value = 2.110757564130642
146  "110111000111", // value = -0.555570233019602(-0.5556640625) argument value = 2.1598449493429825
147  "110110011110", // value = -0.5956993044924334(-0.595703125) argument value = 2.2089323345553233
148  "110101110110", // value = -0.6343932841636454(-0.634765625) argument value = 2.2580197197676637
149  "110101010000", // value = -0.6715589548470184(-0.671875) argument value = 2.3071071049800045
150  "110100101100", // value = -0.7071067811865475(-0.70703125) argument value = 2.356194490192345
151  "110100001001", // value = -0.7409511253549589(-0.7412109375) argument value = 2.405281875404685
152  "110011101000", // value = -0.773010453362737(-0.7734375) argument value = 2.454369260617026
153  "110011001010", // value = -0.8032075314806448(-0.802734375) argument value = 2.5034566458293663
154  "110010101101", // value = -0.8314696123025453(-0.8310546875) argument value = 2.552544031041707
155  "110010010010", // value = -0.857728610000272(-0.857421875) argument value = 2.6016314162540475
156  "110001111001", // value = -0.8819212643483549(-0.8818359375) argument value = 2.650718801466388
157  "110001100010", // value = -0.9039892931234433(-0.904296875) argument value = 2.6998061866787286
158  "110001001110", // value = -0.9238795325112867(-0.923828125) argument value = 2.748893571891069
159  "110000111100", // value = -0.9415440651830207(-0.94140625) argument value = 2.7979809571034093
160  "110000101100", // value = -0.9569403357322088(-0.95703125) argument value = 2.84706834231575
161  "110000011111", // value = -0.970031253194544(-0.9697265625) argument value = 2.8961557275280905
162  "110000010100", // value = -0.9807852804032304(-0.98046875) argument value = 2.945243112740431
163  "110000001011", // value = -0.989176509964781(-0.9892578125) argument value = 2.9943304979527716
164  "110000000101", // value = -0.9951847266721968(-0.9951171875) argument value = 3.043417883165112
165  "110000000001", // value = -0.9987954562051724(-0.9990234375) argument value = 3.0925052683774528
166  "110000000000", // value = -1.0(-1.0) argument value = 3.141592653589793
167  "110000000001", // value = -0.9987954562051724(-0.9990234375) argument value = 3.1906800388021335
168  "110000000101", // value = -0.9951847266721969(-0.9951171875) argument value = 3.2397674240144743
169  "110000001011", // value = -0.989176509964781(-0.9892578125) argument value = 3.2888548092268146
170  "110000010100", // value = -0.9807852804032304(-0.98046875) argument value = 3.3379421944391554
171  "110000011111", // value = -0.970031253194544(-0.9697265625) argument value = 3.3870295796514958
172  "110000101100", // value = -0.9569403357322089(-0.95703125) argument value = 3.436116964863836
173  "110000111100", // value = -0.9415440651830208(-0.94140625) argument value = 3.485204350076177
174  "110001001110", // value = -0.9238795325112868(-0.923828125) argument value = 3.5342917352885173
175  "110001100010", // value = -0.9039892931234434(-0.904296875) argument value = 3.5833791205008576
176  "110001111001", // value = -0.881921264348355(-0.8818359375) argument value = 3.6324665057131984
177  "110010010010", // value = -0.8577286100002721(-0.857421875) argument value = 3.6815538909255388
178  "110010101101", // value = -0.8314696123025455(-0.8310546875) argument value = 3.730641276137879
179  "110011001010", // value = -0.8032075314806449(-0.802734375) argument value = 3.77972866135022
180  "110011101000", // value = -0.7730104533627371(-0.7734375) argument value = 3.8288160465625602
181  "110100001001", // value = -0.7409511253549591(-0.7412109375) argument value = 3.877903431774901
182  "110100101100", // value = -0.7071067811865477(-0.70703125) argument value = 3.9269908169872414
183  "110101010000", // value = -0.6715589548470187(-0.671875) argument value = 3.9760782021995817
184  "110101110110", // value = -0.6343932841636459(-0.634765625) argument value = 4.025165587411922
185  "110110011110", // value = -0.5956993044924331(-0.595703125) argument value = 4.074252972624263
186  "110111000111", // value = -0.5555702330196022(-0.5556640625) argument value = 4.123340357836604
187  "110111110010", // value = -0.5141027441932218(-0.513671875) argument value = 4.172427743048944
188  "111000011101", // value = -0.47139673682599786(-0.4716796875) argument value = 4.221515128261284
189  "111001001010", // value = -0.4275550934302825(-0.427734375) argument value = 4.270602513473625
190  "111001111000", // value = -0.38268343236509034(-0.3828125) argument value = 4.319689898685965
191  "111010100111", // value = -0.33688985339221994(-0.3369140625) argument value = 4.368777283898306
192  "111011010111", // value = -0.29028467725446244(-0.2900390625) argument value = 4.417864669110647
193  "111100000111", // value = -0.24298017990326412(-0.2431640625) argument value = 4.466952054322987
194  "111100111000", // value = -0.19509032201612866(-0.1953125) argument value = 4.516039439535327
195  "111101101010", // value = -0.1467304744553623(-0.146484375) argument value = 4.565126824747668
196  "111110011100", // value = -0.09801714032956045(-0.09765625) argument value = 4.614214209960009
197  "111111001110", // value = -0.04906767432741803(-0.048828125) argument value = 4.663301595172349
198  "000000000000", // value = -1.8369701987210297e-16(0.0) argument value = 4.71238898038469
199  "000000110010", // value = 0.04906767432741766(0.048828125) argument value = 4.76147636559703
200  "000001100100", // value = 0.09801714032956009(0.09765625) argument value = 4.81056375080937
201  "000010010110", // value = 0.14673047445536194(0.146484375) argument value = 4.859651136021712
202  "000011001000", // value = 0.1950903220161283(0.1953125) argument value = 4.908738521234052
203  "000011111001", // value = 0.24298017990326376(0.2431640625) argument value = 4.957825906446392
204  "000100101001", // value = 0.29028467725446205(0.2900390625) argument value = 5.006913291658733
205  "000101011001", // value = 0.3368898533922196(0.3369140625) argument value = 5.056000676871073
206  "000110001000", // value = 0.38268343236509(0.3828125) argument value = 5.105088062083414
207  "000110110110", // value = 0.42755509343028214(0.427734375) argument value = 5.154175447295755
208  "000111100011", // value = 0.4713967368259976(0.4716796875) argument value = 5.203262832508095
209  "001000001110", // value = 0.5141027441932216(0.513671875) argument value = 5.252350217720435
210  "001000111001", // value = 0.5555702330196018(0.5556640625) argument value = 5.301437602932776
211  "001001100010", // value = 0.5956993044924329(0.595703125) argument value = 5.350524988145116
212  "001010001010", // value = 0.6343932841636456(0.634765625) argument value = 5.399612373357457
213  "001010110000", // value = 0.6715589548470183(0.671875) argument value = 5.448699758569798
214  "001011010100", // value = 0.7071067811865474(0.70703125) argument value = 5.497787143782138
215  "001011110111", // value = 0.7409511253549589(0.7412109375) argument value = 5.546874528994478
216  "001100011000", // value = 0.7730104533627367(0.7734375) argument value = 5.595961914206819
217  "001100110110", // value = 0.803207531480645(0.802734375) argument value = 5.64504929941916
218  "001101010011", // value = 0.8314696123025452(0.8310546875) argument value = 5.6941366846315
219  "001101101110", // value = 0.857728610000272(0.857421875) argument value = 5.743224069843841
220  "001110000111", // value = 0.8819212643483548(0.8818359375) argument value = 5.792311455056181
221  "001110011110", // value = 0.9039892931234431(0.904296875) argument value = 5.841398840268521
222  "001110110010", // value = 0.9238795325112865(0.923828125) argument value = 5.890486225480862
223  "001111000100", // value = 0.9415440651830208(0.94140625) argument value = 5.939573610693203
224  "001111010100", // value = 0.9569403357322088(0.95703125) argument value = 5.988660995905543
225  "001111100001", // value = 0.970031253194544(0.9697265625) argument value = 6.037748381117884
226  "001111101100", // value = 0.9807852804032303(0.98046875) argument value = 6.086835766330224
227  "001111110101", // value = 0.9891765099647809(0.9892578125) argument value = 6.135923151542564
228  "001111111011", // value = 0.9951847266721969(0.9951171875) argument value = 6.1850105367549055
229  "001111111111" // value = 0.9987954562051724(0.9990234375) argument value = 6.234097921967246
230  };
231 
232 const std::vector<int> TSU::Trigo::CosInt = convertVector(TSU::Trigo::Cos);
233 
234 const std::vector<std::string> TSU::Trigo::Sinleg =
235  {
236  "000000000", // 0.0 // 0
237  "000001101", // 0.0980171403295606
238  "000011001", // 0.19509032201612825
239  "000100101", // 0.29028467725446233
240  "000110001", // 0.3826834323650898
241  "000111100", // 0.47139673682599764 // 5
242  "001000111", // 0.5555702330196022
243  "001010001", // 0.6343932841636455
244  "001011011", // 0.7071067811865475
245  "001100011", // 0.773010453362737
246  "001101010", // 0.8314696123025452 // 10
247  "001110001", // 0.8819212643483549
248  "001110110", // 0.9238795325112867
249  "001111010", // 0.9569403357322089
250  "001111110", // 0.9807852804032304
251  "001111111", // 0.9951847266721968 // 15
252  "010000000", // 1.0
253  "001111111", // 0.9951847266721969
254  "001111110", // 0.9807852804032304
255  "001111010", // 0.9569403357322089
256  "001110110", // 0.9238795325112867 // 20
257  "001110001", // 0.881921264348355
258  "001101010", // 0.8314696123025455
259  "001100011", // 0.7730104533627371
260  "001011011", // 0.7071067811865476
261  "001010001", // 0.6343932841636455 // 25
262  "001000111", // 0.5555702330196022
263  "000111100", // 0.47139673682599786
264  "000110001", // 0.3826834323650899
265  "000100101", // 0.2902846772544624
266  "000011001", // 0.1950903220161286 // 30
267  "000001101", // 0.09801714032956083
268  "000000000", // 1.2246467991473532e-16
269  "111110011", // -0.09801714032956059
270  "111100111", // -0.19509032201612836
271  "111011011", // -0.2902846772544621 // 35
272  "111001111", // -0.38268343236508967
273  "111000100", // -0.47139673682599764
274  "110111001", // -0.555570233019602
275  "110101111", // -0.6343932841636453
276  "110100101", // -0.7071067811865475 // 40
277  "110011101", // -0.7730104533627367
278  "110010110", // -0.8314696123025452
279  "110001111", // -0.8819212643483549
280  "110001010", // -0.9238795325112865
281  "110000110", // -0.9569403357322088 // 45
282  "110000010", // -0.9807852804032303
283  "110000001", // -0.9951847266721969
284  "110000000", // -1.0
285  "110000001", // -0.9951847266721969
286  "110000010", // -0.9807852804032304 // 50
287  "110000110", // -0.9569403357322089
288  "110001010", // -0.9238795325112866
289  "110001111", // -0.881921264348355
290  "110010110", // -0.8314696123025455
291  "110011101", // -0.7730104533627369 // 55
292  "110100101", // -0.7071067811865477
293  "110101111", // -0.6343932841636459
294  "110111001", // -0.5555702330196022
295  "111000100", // -0.4713967368259979
296  "111001111", // -0.3826834323650904 // 60
297  "111011011", // -0.2902846772544625
298  "111100111", // -0.19509032201612872
299  "111110011" // -0.0980171403295605 // 63
300  };
301 
302 const std::vector<int> TSU::Trigo::SinlegInt = convertVector(TSU::Trigo::Sinleg);
303 
304 //phase1
305 const std::vector<std::string> TSU::Trigo::Sin=
306  {
307  "000000000000", // 0.0
308  "000000110010", // 0.049067674327418015
309  "000001100100", // 0.0980171403295606
310  "000010010110", // 0.14673047445536175
311  "000011001000", // 0.19509032201612825
312  "000011111001", // 0.24298017990326387
313  "000100101001", // 0.29028467725446233
314  "000101011001", // 0.33688985339222005
315  "000110001000", // 0.3826834323650898
316  "000110110110", // 0.4275550934302821
317  "000111100011", // 0.47139673682599764
318  "001000001110", // 0.5141027441932217
319  "001000111001", // 0.5555702330196022
320  "001001100010", // 0.5956993044924334
321  "001010001010", // 0.6343932841636455
322  "001010110000", // 0.6715589548470183
323  "001011010100", // 0.7071067811865475
324  "001011110111", // 0.7409511253549591
325  "001100011000", // 0.773010453362737
326  "001100110110", // 0.8032075314806448
327  "001101010011", // 0.8314696123025452
328  "001101101110", // 0.8577286100002721
329  "001110000111", // 0.8819212643483549
330  "001110011110", // 0.9039892931234433
331  "001110110010", // 0.9238795325112867
332  "001111000100", // 0.9415440651830208
333  "001111010100", // 0.9569403357322089
334  "001111100001", // 0.970031253194544
335  "001111101100", // 0.9807852804032304
336  "001111110101", // 0.989176509964781
337  "001111111011", // 0.9951847266721968
338  "001111111111", // 0.9987954562051724
339  "010000000000", // 1.0
340  "001111111111", // 0.9987954562051724
341  "001111111011", // 0.9951847266721969
342  "001111110101", // 0.989176509964781
343  "001111101100", // 0.9807852804032304
344  "001111100001", // 0.970031253194544
345  "001111010100", // 0.9569403357322089
346  "001111000100", // 0.9415440651830208
347  "001110110010", // 0.9238795325112867
348  "001110011110", // 0.9039892931234434
349  "001110000111", // 0.881921264348355
350  "001101101110", // 0.8577286100002721
351  "001101010011", // 0.8314696123025455
352  "001100110110", // 0.8032075314806449
353  "001100011000", // 0.7730104533627371
354  "001011110111", // 0.740951125354959
355  "001011010100", // 0.7071067811865476
356  "001010110000", // 0.6715589548470186
357  "001010001010", // 0.6343932841636455
358  "001001100010", // 0.5956993044924335
359  "001000111001", // 0.5555702330196022
360  "001000001110", // 0.5141027441932218
361  "000111100011", // 0.47139673682599786
362  "000110110110", // 0.42755509343028203
363  "000110001000", // 0.3826834323650899
364  "000101011001", // 0.33688985339222033
365  "000100101001", // 0.2902846772544624
366  "000011111001", // 0.24298017990326407
367  "000011001000", // 0.1950903220161286
368  "000010010110", // 0.1467304744553618
369  "000001100100", // 0.09801714032956083
370  "000000110010", // 0.049067674327417966
371  "000000000000", // 1.2246467991473532e-16
372  "111111001110", // -0.049067674327417724
373  "111110011100", // -0.09801714032956059
374  "111101101010", // -0.14673047445536158
375  "111100111000", // -0.19509032201612836
376  "111100000111", // -0.24298017990326382
377  "111011010111", // -0.2902846772544621
378  "111010100111", // -0.3368898533922201
379  "111001111000", // -0.38268343236508967
380  "111001001010", // -0.4275550934302818
381  "111000011101", // -0.47139673682599764
382  "110111110010", // -0.5141027441932216
383  "110111000111", // -0.555570233019602
384  "110110011110", // -0.5956993044924332
385  "110101110110", // -0.6343932841636453
386  "110101010000", // -0.6715589548470184
387  "110100101100", // -0.7071067811865475
388  "110100001001", // -0.7409511253549589
389  "110011101000", // -0.7730104533627367
390  "110011001010", // -0.803207531480645
391  "110010101101", // -0.8314696123025452
392  "110010010010", // -0.857728610000272
393  "110001111001", // -0.8819212643483549
394  "110001100010", // -0.9039892931234431
395  "110001001110", // -0.9238795325112865
396  "110000111100", // -0.9415440651830208
397  "110000101100", // -0.9569403357322088
398  "110000011111", // -0.970031253194544
399  "110000010100", // -0.9807852804032303
400  "110000001011", // -0.9891765099647809
401  "110000000101", // -0.9951847266721969
402  "110000000001", // -0.9987954562051724
403  "110000000000", // -1.0
404  "110000000001", // -0.9987954562051724
405  "110000000101", // -0.9951847266721969
406  "110000001011", // -0.9891765099647809
407  "110000010100", // -0.9807852804032304
408  "110000011111", // -0.970031253194544
409  "110000101100", // -0.9569403357322089
410  "110000111100", // -0.9415440651830209
411  "110001001110", // -0.9238795325112866
412  "110001100010", // -0.9039892931234433
413  "110001111001", // -0.881921264348355
414  "110010010010", // -0.8577286100002722
415  "110010101101", // -0.8314696123025455
416  "110011001010", // -0.8032075314806453
417  "110011101000", // -0.7730104533627369
418  "110100001001", // -0.7409511253549591
419  "110100101100", // -0.7071067811865477
420  "110101010000", // -0.6715589548470187
421  "110101110110", // -0.6343932841636459
422  "110110011110", // -0.5956993044924332
423  "110111000111", // -0.5555702330196022
424  "110111110010", // -0.5141027441932219
425  "111000011101", // -0.4713967368259979
426  "111001001010", // -0.42755509343028253
427  "111001111000", // -0.3826834323650904
428  "111010100111", // -0.33688985339222
429  "111011010111", // -0.2902846772544625
430  "111100000111", // -0.24298017990326418
431  "111100111000", // -0.19509032201612872
432  "111101101010", // -0.1467304744553624
433  "111110011100", // -0.0980171403295605
434  "111111001110" // -0.04906767432741809
435  };
436 
437 const std::vector<int> TSU::Trigo::SinInt = convertVector(TSU::Trigo::Sin);
438 
439 
440 int TSU::Trigo::atan2leg(TSU::L1TopoDataTypes<16,0> x, TSU::L1TopoDataTypes<16,0> y){
441  short int octant=0;
442  if((x.value()&(1<<16))&&(y.value()&(1<<16))){ // Ex and Ey negative
443  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 4; //100
444  else octant = 5; // 101
445  } else if(x.value()&(1<<16)){
446  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 3; //011
447  else octant = 2; // 010
448  } else if(y.value()&(1<<16)){
449  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 7; //111
450  else octant = 6; // 110
451  } else { // Ex and Ey both positive
452  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 0; //000
453  else octant = 1; // 001
454  }
455 
456  auto signed_x_f = x;
457  auto signed_y_f = y;
458  if(octant==0||octant==3||octant==4||octant==7){
459  //signed_x_f = (abs(int(x)));
460  signed_x_f = x.abs();
461  signed_y_f = y.abs();
462  } else {
463  //signed_x_f = (abs(int(y)));
464  signed_x_f = y.abs();
465  signed_y_f = x.abs();
466  }
467 
468  const std::vector<std::string> atan2_thresholds = {
469  "000010011101100", // 1.260 (0.9)
470  "000011000010101", // 1.557 (1.0)
471  "000011110101100", // 1.964 (1.1)
472  "000101000001100", // 2.572 (1.2)
473  "000111000010010", // 3.602 (1.3)
474  "001011010100101", // 5.797 (1.4)
475  "011011100010101"}; // 14.101 (1.5)
476  unsigned int flag = 0;
477  for(size_t j=0;j<atan2_thresholds.size(); ++j){
478  auto thresh = TSU::L1TopoDataTypes<15,10>(atan2_thresholds.at(j));
479  auto yy = signed_y_f*thresh;
480  if(signed_x_f.to_float() > yy.to_float()) flag = (flag | (1<<j));
481  }
482  unsigned int octant_fine = 0;
483  if(flag==0) octant_fine = 7;
484  else if(flag==1) octant_fine = 6;
485  else if(flag==3) octant_fine = 5;
486  else if(flag==7) octant_fine = 4;
487  else if(flag==15) octant_fine = 3;
488  else if(flag==31) octant_fine = 2;
489  else if(flag==63) octant_fine = 1;
490  else if(flag==127) octant_fine = 0;
491 
492  unsigned int octant_fine2 = 0;
493  if(flag==0) octant_fine2 = 0;
494  else if(flag==1) octant_fine2 = 1;
495  else if(flag==3) octant_fine2 = 2;
496  else if(flag==7) octant_fine2 = 3;
497  else if(flag==15) octant_fine2 = 4;
498  else if(flag==31) octant_fine2 = 5;
499  else if(flag==63) octant_fine2 = 6;
500  else if(flag==127) octant_fine2 = 7;
501 
502  int intphi = octant << 3;
503  if(octant==0||octant==2||octant==4||octant==6){
504  intphi |= octant_fine;
505  } else {
506  intphi |= octant_fine2;
507  }
508 
509  return intphi;
510 }
511 
512 int TSU::Trigo::atan2(TSU::L1TopoDataTypes<16,0> x, TSU::L1TopoDataTypes<16,0> y){
513  short int octant=0;
514  if((x.value()&(1<<16))&&(y.value()&(1<<16))){ // Ex and Ey negative
515  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 4; //100
516  else octant = 5; // 101
517  } else if(x.value()&(1<<16)){
518  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 3; //011
519  else octant = 2; // 010
520  } else if(y.value()&(1<<16)){
521  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 7; //111
522  else octant = 6; // 110
523  } else { // Ex and Ey both positive
524  if(std::abs(y.to_float()) < std::abs(x.to_float())) octant = 0; //000
525  else octant = 1; // 001
526  }
527 
528  auto signed_x_f = x;
529  auto signed_y_f = y;
530  if(octant==0||octant==3||octant==4||octant==7){
531  //signed_x_f = (abs(int(x)));
532  signed_x_f = x.abs();
533  signed_y_f = y.abs();
534  } else {
535  //signed_x_f = (abs(int(y)));
536  signed_x_f = y.abs();
537  signed_y_f = x.abs();
538  }
539 
540  // For phi in the first sector (0.8 < phi < 1.6) store the possible values of the tan
541  const std::vector<std::string> atan2_thresholds =
542  {
543  "00000010010001101", // tan(0.85)=1.1383327132284393 rounded to 1.1376953125
544  "00000010100001010", // tan(0.9)=1.2601582175503392 rounded to 1.259765625
545  "00000010110010111", // tan(0.95)=1.398382589287699 rounded to 1.3974609375
546  "00000011000111010", // tan(1.0)=1.5574077246549023 rounded to 1.556640625
547  "00000011011111001", // tan(1.05)=1.7433153099831704 rounded to 1.7431640625
548  "00000011111011011", // tan(1.1)=1.9647596572486523 rounded to 1.9638671875
549  "00000100011110000", // tan(1.15)=2.2344969487553255 rounded to 2.234375
550  "00000101001001001", // tan(1.2)=2.5721516221263188 rounded to 2.5712890625
551  "00000110000001001", // tan(1.25)=3.0095696738628313 rounded to 3.0087890625
552  "00000111001101000", // tan(1.3)=3.6021024479679786 rounded to 3.6015625
553  "00001000111010010", // tan(1.35)=4.455221759562705 rounded to 4.455078125
554  "00001011100110001", // tan(1.4)=5.797883715482887 rounded to 5.7978515625
555  "00010000011110011", // tan(1.4500000000000002)=8.238092752965619 rounded to 8.2373046875
556  "00011100001100111", // tan(1.5)=14.101419947171719 rounded to 14.1005859375
557  "01100000001010000" // tan(1.55)=48.07848247921907 rounded to 48.078125
558  };
559 
560  unsigned int thresholdsPassed = atan2_thresholds.size();
561  for(size_t j=0;j<atan2_thresholds.size(); ++j){
562  auto thresh = TSU::L1TopoDataTypes<17,10>(atan2_thresholds.at(j));
563  auto yy = signed_y_f*thresh;
564  if(! (signed_x_f.to_float() > yy.to_float()) ) {
565  //if the current threshold is not passed, then the previous one must have been the last one passed
566  //(no) off-by-one consideration: j starts at 0, so if the first threshold is already failed, that's just the number we're looking for
567  thresholdsPassed = j;
568  break;
569  }
570  }
571 
572  //for first half of a quadrant fine steps are counted in downward
573  // (range: 15 downto 0)
574  unsigned int octant_fine = 16 - (thresholdsPassed + 1);
575 
576  //for second half of a quadrant count fine steps upwards
577  // (range: 0 to 15)
578  unsigned int octant_fine2 = thresholdsPassed;
579 
580  int intphi = octant << 4;
581  if(octant==0||octant==2||octant==4||octant==6){
582  intphi |= octant_fine;
583  } else {
584  intphi |= octant_fine2;
585  }
586 
587  return intphi;
588 }
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Definition: Trigo.h:41
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Definition: Trigo.cxx:512
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Definition: Trigo.h:36
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static const std::vector< int > SinInt
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static const std::vector< std::string > Cos
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Definition: Trigo.cxx:440
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static const std::vector< int > CoslegInt
Definition: Trigo.h:40
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