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VectorizedTMath.cxx
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1#include "VectorizedTMath.h"
2
3#if defined(R__HAS_VECCORE) && defined(R__HAS_VC)
4
5namespace TMath {
6////////////////////////////////////////////////////////////////////////////////
8{
9 return vecCore::math::Log2(x);
10}
11
12////////////////////////////////////////////////////////////////////////////////
13/// Calculate a Breit Wigner function with mean and gamma.
15{
16 return 0.5 * M_1_PI * (gamma / (0.25 * gamma * gamma + (x - mean) * (x - mean)));
17}
18
19////////////////////////////////////////////////////////////////////////////////
20/// Calculate a gaussian function with mean and sigma.
21/// If norm=kTRUE (default is kFALSE) the result is divided
22/// by sqrt(2*Pi)*sigma.
24{
25 if (sigma == 0)
26 return ::ROOT::Double_v(1.e30);
27
28 ::ROOT::Double_v inv_sigma = 1.0 / ::ROOT::Double_v(sigma);
29 ::ROOT::Double_v arg = (x - ::ROOT::Double_v(mean)) * inv_sigma;
30
31 // For those entries of |arg| > 39 result is zero in double precision
33 vecCore::Blend<::ROOT::Double_v>(vecCore::math::Abs(arg) < ::ROOT::Double_v(39.0),
34 vecCore::math::Exp(::ROOT::Double_v(-0.5) * arg * arg), ::ROOT::Double_v(0.0));
35 if (norm)
36 out *= 0.3989422804014327 * inv_sigma; // 1/sqrt(2*Pi)=0.3989422804014327
37 return out;
38}
39
40////////////////////////////////////////////////////////////////////////////////
41/// Computes the probability density function of Laplace distribution
42/// at point x, with location parameter alpha and shape parameter beta.
43/// By default, alpha=0, beta=1
44/// This distribution is known under different names, most common is
45/// double exponential distribution, but it also appears as
46/// the two-tailed exponential or the bilateral exponential distribution
48{
49 ::ROOT::Double_v beta_v_inv = ::ROOT::Double_v(1.0) / ::ROOT::Double_v(beta);
50 ::ROOT::Double_v out = vecCore::math::Exp(-vecCore::math::Abs((x - ::ROOT::Double_v(alpha)) * beta_v_inv));
51 out *= ::ROOT::Double_v(0.5) * beta_v_inv;
52 return out;
53}
54
55////////////////////////////////////////////////////////////////////////////////
56/// Computes the distribution function of Laplace distribution
57/// at point x, with location parameter alpha and shape parameter beta.
58/// By default, alpha=0, beta=1
59/// This distribution is known under different names, most common is
60/// double exponential distribution, but it also appears as
61/// the two-tailed exponential or the bilateral exponential distribution
63{
64 ::ROOT::Double_v alpha_v = ::ROOT::Double_v(alpha);
65 ::ROOT::Double_v beta_v_inv = ::ROOT::Double_v(1.0) / ::ROOT::Double_v(beta);
66 return vecCore::Blend<::ROOT::Double_v>(
67 x <= alpha_v, 0.5 * vecCore::math::Exp(-vecCore::math::Abs((x - alpha_v) * beta_v_inv)),
68 1 - 0.5 * vecCore::math::Exp(-vecCore::math::Abs((x - alpha_v) * beta_v_inv)));
69}
70
71////////////////////////////////////////////////////////////////////////////////
72/// Computation of the normal frequency function freq(x).
73/// Freq(x) = (1/sqrt(2pi)) Integral(exp(-t^2/2))dt between -infinity and x.
74///
75/// Translated from CERNLIB C300 by Rene Brun.
77{
78 Double_t c1 = 0.56418958354775629;
79 Double_t w2 = 1.41421356237309505;
80
81 Double_t p10 = 2.4266795523053175e+2, q10 = 2.1505887586986120e+2, p11 = 2.1979261618294152e+1,
82 q11 = 9.1164905404514901e+1, p12 = 6.9963834886191355e+0, q12 = 1.5082797630407787e+1,
83 p13 = -3.5609843701815385e-2;
84
85 Double_t p20 = 3.00459261020161601e+2, q20 = 3.00459260956983293e+2, p21 = 4.51918953711872942e+2,
86 q21 = 7.90950925327898027e+2, p22 = 3.39320816734343687e+2, q22 = 9.31354094850609621e+2,
87 p23 = 1.52989285046940404e+2, q23 = 6.38980264465631167e+2, p24 = 4.31622272220567353e+1,
88 q24 = 2.77585444743987643e+2, p25 = 7.21175825088309366e+0, q25 = 7.70001529352294730e+1,
89 p26 = 5.64195517478973971e-1, q26 = 1.27827273196294235e+1, p27 = -1.36864857382716707e-7;
90
91 Double_t p30 = -2.99610707703542174e-3, q30 = 1.06209230528467918e-2, p31 = -4.94730910623250734e-2,
92 q31 = 1.91308926107829841e-1, p32 = -2.26956593539686930e-1, q32 = 1.05167510706793207e+0,
93 p33 = -2.78661308609647788e-1, q33 = 1.98733201817135256e+0, p34 = -2.23192459734184686e-2, q34 = 1;
94
95 ::ROOT::Double_v v = vecCore::math::Abs(x) / w2;
96
97 ::ROOT::Double_v result;
98
102
106 ::ROOT::Double_v v5 = v4 * v;
107 ::ROOT::Double_v v6 = v5 * v;
108 ::ROOT::Double_v v7 = v6 * v;
109 ::ROOT::Double_v v8 = v7 * v;
110
112 result, mask1, v * (p10 + p11 * v2 + p12 * v4 + p13 * v6) / (q10 + q11 * v2 + q12 * v4 + v6));
115 ::ROOT::Double_v(1.0) -
116 (p20 + p21 * v + p22 * v2 + p23 * v3 + p24 * v4 + p25 * v5 + p26 * v6 + p27 * v7) /
117 (vecCore::math::Exp(v2) * (q20 + q21 * v + q22 * v2 + q23 * v3 + q24 * v4 + q25 * v5 + q26 * v6 + v7)));
119 ::ROOT::Double_v(1.0) -
120 (c1 + (p30 * v8 + p31 * v6 + p32 * v4 + p33 * v2 + p34) /
121 ((q30 * v8 + q31 * v6 + q32 * v4 + q33 * v2 + q34) * v2)) /
122 (v * vecCore::math::Exp(v2)));
123
124 return vecCore::Blend<::ROOT::Double_v>(x > 0, ::ROOT::Double_v(0.5) + ::ROOT::Double_v(0.5) * result,
125 ::ROOT::Double_v(0.5) * (::ROOT::Double_v(1) - result));
126}
127
128////////////////////////////////////////////////////////////////////////////////
129/// Vectorized implementation of Bessel function I_0(x) for a vector x.
130::ROOT::Double_v BesselI0_Split_More(::ROOT::Double_v &ax)
131{
132 ::ROOT::Double_v y = 3.75 / ax;
133 return (vecCore::math::Exp(ax) / vecCore::math::Sqrt(ax)) *
134 (0.39894228 +
135 y * (1.328592e-2 +
136 y * (2.25319e-3 +
137 y * (-1.57565e-3 +
138 y * (9.16281e-3 +
139 y * (-2.057706e-2 + y * (2.635537e-2 + y * (-1.647633e-2 + y * 3.92377e-3))))))));
140}
141
142::ROOT::Double_v BesselI0_Split_Less(::ROOT::Double_v &x)
143{
144 ::ROOT::Double_v y = x * x * 0.071111111;
145
146 return 1.0 +
147 y * (3.5156229 + y * (3.0899424 + y * (1.2067492 + y * (0.2659732 + y * (3.60768e-2 + y * 4.5813e-3)))));
148}
149
151{
152 ::ROOT::Double_v ax = vecCore::math::Abs(x);
153
154 return vecCore::Blend<::ROOT::Double_v>(ax <= 3.75, BesselI0_Split_Less(x), BesselI0_Split_More(ax));
155}
156
157////////////////////////////////////////////////////////////////////////////////
158/// Vectorized implementation of modified Bessel function I_1(x) for a vector x.
159::ROOT::Double_v BesselI1_Split_More(::ROOT::Double_v &ax, ::ROOT::Double_v &x)
160{
161 ::ROOT::Double_v y = 3.75 / ax;
162 ::ROOT::Double_v result =
163 (vecCore::math::Exp(ax) / vecCore::math::Sqrt(ax)) *
164 (0.39894228 + y * (-3.988024e-2 +
165 y * (-3.62018e-3 +
166 y * (1.63801e-3 + y * (-1.031555e-2 +
167 y * (2.282967e-2 + y * (-2.895312e-2 +
168 y * (1.787654e-2 + y * -4.20059e-3))))))));
169 return vecCore::Blend<::ROOT::Double_v>(x < 0, ::ROOT::Double_v(-1.0) * result, result);
170}
171
172::ROOT::Double_v BesselI1_Split_Less(::ROOT::Double_v &x)
173{
174 ::ROOT::Double_v y = x * x * 0.071111111;
175
176 return x * (0.5 + y * (0.87890594 +
177 y * (0.51498869 + y * (0.15084934 + y * (2.658733e-2 + y * (3.01532e-3 + y * 3.2411e-4))))));
178}
179
181{
182 ::ROOT::Double_v ax = vecCore::math::Abs(x);
183
184 return vecCore::Blend<::ROOT::Double_v>(ax <= 3.75, BesselI1_Split_Less(x), BesselI1_Split_More(ax, x));
185}
186
187////////////////////////////////////////////////////////////////////////////////
188/// Vectorized implementation of Bessel function J0(x) for a vector x.
189::ROOT::Double_v BesselJ0_Split1_More(::ROOT::Double_v &ax)
190{
191 ::ROOT::Double_v z = 8 / ax;
192 ::ROOT::Double_v y = z * z;
193 ::ROOT::Double_v xx = ax - 0.785398164;
194 ::ROOT::Double_v result1 =
195 1 + y * (-0.1098628627e-2 + y * (0.2734510407e-4 + y * (-0.2073370639e-5 + y * 0.2093887211e-6)));
196 ::ROOT::Double_v result2 =
197 -0.1562499995e-1 + y * (0.1430488765e-3 + y * (-0.6911147651e-5 + y * (0.7621095161e-6 - y * 0.934935152e-7)));
198 return vecCore::math::Sqrt(0.636619772 / ax) *
199 (vecCore::math::Cos(xx) * result1 - z * vecCore::math::Sin(xx) * result2);
200}
201
202::ROOT::Double_v BesselJ0_Split1_Less(::ROOT::Double_v &x)
203{
204 ::ROOT::Double_v y = x * x;
205 return (57568490574.0 +
206 y * (-13362590354.0 + y * (651619640.7 + y * (-11214424.18 + y * (77392.33017 + y * -184.9052456))))) /
207 (57568490411.0 + y * (1029532985.0 + y * (9494680.718 + y * (59272.64853 + y * (267.8532712 + y)))));
208}
209
211{
212 ::ROOT::Double_v ax = vecCore::math::Abs(x);
213 return vecCore::Blend<::ROOT::Double_v>(ax < 8, BesselJ0_Split1_Less(x), BesselJ0_Split1_More(ax));
214}
215
216////////////////////////////////////////////////////////////////////////////////
217/// Vectorized implementation of Bessel function J1(x) for a vector x.
218::ROOT::Double_v BesselJ1_Split1_More(::ROOT::Double_v &ax, ::ROOT::Double_v &x)
219{
220 ::ROOT::Double_v z = 8 / ax;
221 ::ROOT::Double_v y = z * z;
222 ::ROOT::Double_v xx = ax - 2.356194491;
223 ::ROOT::Double_v result1 =
224 1 + y * (0.183105e-2 + y * (-0.3516396496e-4 + y * (0.2457520174e-5 + y * -0.240337019e-6)));
225 ::ROOT::Double_v result2 =
226 0.04687499995 + y * (-0.2002690873e-3 + y * (0.8449199096e-5 + y * (-0.88228987e-6 - y * 0.105787412e-6)));
227 ::ROOT::Double_v result =
228 vecCore::math::Sqrt(0.636619772 / ax) * (vecCore::math::Cos(xx) * result1 - z * vecCore::math::Sin(xx) * result2);
229 vecCore::MaskedAssign<::ROOT::Double_v>(result, x < 0, -result);
230 return result;
231}
232
233::ROOT::Double_v BesselJ1_Split1_Less(::ROOT::Double_v &x)
234{
235 ::ROOT::Double_v y = x * x;
236 return x *
237 (72362614232.0 +
238 y * (-7895059235.0 + y * (242396853.1 + y * (-2972611.439 + y * (15704.48260 + y * -30.16036606))))) /
239 (144725228442.0 + y * (2300535178.0 + y * (18583304.74 + y * (99447.43394 + y * (376.9991397 + y)))));
240}
241
243{
244 ::ROOT::Double_v ax = vecCore::math::Abs(x);
245 return vecCore::Blend<::ROOT::Double_v>(ax < 8, BesselJ1_Split1_Less(x), BesselJ1_Split1_More(ax, x));
246}
247
248} // namespace TMath
249
250#endif
bool Bool_t
Definition RtypesCore.h:63
double Double_t
Definition RtypesCore.h:59
const Double_t sigma
return c1
Definition legend1.C:41
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17
double gamma(double x)
Double_t Double_v
Definition Types.h:51
TMath.
Definition TMathBase.h:35
Double_t Gaus(Double_t x, Double_t mean=0, Double_t sigma=1, Bool_t norm=kFALSE)
Calculate a gaussian function with mean and sigma.
Definition TMath.cxx:448
Double_t Log2(Double_t x)
Definition TMath.cxx:101
Double_t BesselI1(Double_t x)
modified Bessel function K_0(x)
Definition TMath.cxx:1469
Double_t LaplaceDistI(Double_t x, Double_t alpha=0, Double_t beta=1)
Computes the distribution function of Laplace distribution at point x, with location parameter alpha ...
Definition TMath.cxx:2341
Double_t BreitWigner(Double_t x, Double_t mean=0, Double_t gamma=1)
Calculate a Breit Wigner function with mean and gamma.
Definition TMath.cxx:437
Double_t LaplaceDist(Double_t x, Double_t alpha=0, Double_t beta=1)
Computes the probability density function of Laplace distribution at point x, with location parameter...
Definition TMath.cxx:2325
Double_t BesselJ0(Double_t x)
modified Bessel function K_1(x)
Definition TMath.cxx:1609
Double_t BesselJ1(Double_t x)
Bessel function J0(x) for any real x.
Definition TMath.cxx:1644
Double_t Freq(Double_t x)
Computation of the normal frequency function freq(x).
Definition TMath.cxx:265
Double_t BesselI0(Double_t x)
integer order modified Bessel function K_n(x)
Definition TMath.cxx:1401