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1 //
2 // ********************************************************************
3 // * License and Disclaimer *
4 // * *
5 // * The Geant4 software is copyright of the Copyright Holders of *
6 // * the Geant4 Collaboration. It is provided under the terms and *
7 // * conditions of the Geant4 Software License, included in the file *
8 // * LICENSE and available at http://cern.ch/geant4/license . These *
9 // * include a list of copyright holders. *
10 // * *
11 // * Neither the authors of this software system, nor their employing *
12 // * institutes,nor the agencies providing financial support for this *
13 // * work make any representation or warranty, express or implied, *
14 // * regarding this software system or assume any liability for its *
15 // * use. Please see the license in the file LICENSE and URL above *
16 // * for the full disclaimer and the limitation of liability. *
17 // * *
18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboration. *
20 // * By using, copying, modifying or distributing the software (or *
21 // * any work based on the software) you agree to acknowledge its *
22 // * use in resulting scientific publications, and indicate your *
23 // * acceptance of all terms of the Geant4 Software license. *
24 // ********************************************************************
25 //
26 // G4Exp
27 //
28 // Class description:
29 //
30 // The basic idea is to exploit Pade polynomials.
31 // A lot of ideas were inspired by the cephes math library
32 // (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
33 // The Cephes library can be found here: http://www.netlib.org/cephes/
34 // Code and algorithms for G4Exp have been extracted and adapted for Geant4
35 // from the original implementation in the VDT mathematical library
36 // (https://svnweb.cern.ch/trac/vdt), version 0.3.7.
37
38 // Original implementation created on: Jun 23, 2012
39 // Authors: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
40 //
41 // --------------------------------------------------------------------
42 /*
43 * VDT is free software: you can redistribute it and/or modify
44 * it under the terms of the GNU Lesser Public License as published by
45 * the Free Software Foundation, either version 3 of the License, or
46 * (at your option) any later version.
47 *
48 * This program is distributed in the hope that it will be useful,
49 * but WITHOUT ANY WARRANTY; without even the implied warranty of
50 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
51 * GNU Lesser Public License for more details.
52 *
53 * You should have received a copy of the GNU Lesser Public License
54 * along with this program. If not, see <http://www.gnu.org/licenses/>.
55 */
56 // --------------------------------------------------------------------
57 #ifndef G4Exp_hh
58 #define G4Exp_hh 1
59
60 #ifdef WIN32
61
62 # define G4Exp std::exp
63
64 #else
65
66 # include "G4Types.hh"
67
68 # include <cstdint>
69 # include <limits>
70
71 namespace G4ExpConsts
72 {
73 const G4double EXP_LIMIT = 708;
74
75 const G4double PX1exp = 1.26177193074810590878E-4;
76 const G4double PX2exp = 3.02994407707441961300E-2;
77 const G4double PX3exp = 9.99999999999999999910E-1;
78 const G4double QX1exp = 3.00198505138664455042E-6;
79 const G4double QX2exp = 2.52448340349684104192E-3;
80 const G4double QX3exp = 2.27265548208155028766E-1;
81 const G4double QX4exp = 2.00000000000000000009E0;
82
83 const G4double LOG2E = 1.4426950408889634073599; // 1/log(2)
84
85 const G4float MAXLOGF = 88.72283905206835f;
86 const G4float MINLOGF = -88.f;
87
88 const G4float C1F = 0.693359375f;
89 const G4float C2F = -2.12194440e-4f;
90
91 const G4float PX1expf = 1.9875691500E-4f;
92 const G4float PX2expf = 1.3981999507E-3f;
93 const G4float PX3expf = 8.3334519073E-3f;
94 const G4float PX4expf = 4.1665795894E-2f;
95 const G4float PX5expf = 1.6666665459E-1f;
96 const G4float PX6expf = 5.0000001201E-1f;
97
98 const G4float LOG2EF = 1.44269504088896341f;
99
100 //----------------------------------------------------------------------------
101 // Used to switch between different type of interpretations of the data
102 // (64 bits)
103 //
104 union ieee754
105 {
106 ieee754()= default;
107 ieee754(G4double thed) { d = thed; };
108 ieee754(uint64_t thell) { ll = thell; };
109 ieee754(G4float thef) { f[0] = thef; };
110 ieee754(uint32_t thei) { i[0] = thei; };
111 G4double d;
112 G4float f[2];
113 uint32_t i[2];
114 uint64_t ll;
115 uint16_t s[4];
116 };
117
118 //----------------------------------------------------------------------------
119 // Converts an unsigned long long to a double
120 //
121 inline G4double uint642dp(uint64_t ll)
122 {
123 ieee754 tmp;
124 tmp.ll = ll;
125 return tmp.d;
126 }
127
128 //----------------------------------------------------------------------------
129 // Converts an int to a float
130 //
131 inline G4float uint322sp(G4int x)
132 {
133 ieee754 tmp;
134 tmp.i[0] = x;
135 return tmp.f[0];
136 }
137
138 //----------------------------------------------------------------------------
139 // Converts a float to an int
140 //
141 inline uint32_t sp2uint32(G4float x)
142 {
143 ieee754 tmp;
144 tmp.f[0] = x;
145 return tmp.i[0];
146 }
147
148 //----------------------------------------------------------------------------
149 /**
150 * A vectorisable floor implementation, not only triggered by fast-math.
151 * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
152 * compliant for argument -0.0
153 **/
154 inline G4double fpfloor(const G4double x)
155 {
156 // no problem since exp is defined between -708 and 708. Int is enough for
157 // it!
158 int32_t ret = int32_t(x);
159 ret -= (sp2uint32(x) >> 31);
160 return ret;
161 }
162
163 //----------------------------------------------------------------------------
164 /**
165 * A vectorisable floor implementation, not only triggered by fast-math.
166 * These functions do not distinguish between -0.0 and 0.0, so are not IEC6509
167 * compliant for argument -0.0
168 **/
169 inline G4float fpfloor(const G4float x)
170 {
171 int32_t ret = int32_t(x);
172 ret -= (sp2uint32(x) >> 31);
173 return ret;
174 }
175 } // namespace G4ExpConsts
176
177 // Exp double precision --------------------------------------------------------
178
179 /// Exponential Function double precision
180 inline G4double G4Exp(G4double initial_x)
181 {
182 G4double x = initial_x;
183 G4double px = G4ExpConsts::fpfloor(G4ExpConsts::LOG2E * x + 0.5);
184
185 const int32_t n = int32_t(px);
186
187 x -= px * 6.93145751953125E-1;
188 x -= px * 1.42860682030941723212E-6;
189
190 const G4double xx = x * x;
191
192 // px = x * P(x**2).
193 px = G4ExpConsts::PX1exp;
194 px *= xx;
195 px += G4ExpConsts::PX2exp;
196 px *= xx;
197 px += G4ExpConsts::PX3exp;
198 px *= x;
199
200 // Evaluate Q(x**2).
201 G4double qx = G4ExpConsts::QX1exp;
202 qx *= xx;
203 qx += G4ExpConsts::QX2exp;
204 qx *= xx;
205 qx += G4ExpConsts::QX3exp;
206 qx *= xx;
207 qx += G4ExpConsts::QX4exp;
208
209 // e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
210 x = px / (qx - px);
211 x = 1.0 + 2.0 * x;
212
213 // Build 2^n in double.
214 x *= G4ExpConsts::uint642dp((((uint64_t) n) + 1023) << 52);
215
216 if(initial_x > G4ExpConsts::EXP_LIMIT)
217 x = std::numeric_limits<G4double>::infinity();
218 if(initial_x < -G4ExpConsts::EXP_LIMIT)
219 x = 0.;
220
221 return x;
222 }
223
224 // Exp single precision --------------------------------------------------------
225
226 /// Exponential Function single precision
227 inline G4float G4Expf(G4float initial_x)
228 {
229 G4float x = initial_x;
230
231 G4float z =
232 G4ExpConsts::fpfloor(G4ExpConsts::LOG2EF * x +
233 0.5f); /* std::floor() truncates toward -infinity. */
234
235 x -= z * G4ExpConsts::C1F;
236 x -= z * G4ExpConsts::C2F;
237 const int32_t n = int32_t(z);
238
239 const G4float x2 = x * x;
240
241 z = x * G4ExpConsts::PX1expf;
242 z += G4ExpConsts::PX2expf;
243 z *= x;
244 z += G4ExpConsts::PX3expf;
245 z *= x;
246 z += G4ExpConsts::PX4expf;
247 z *= x;
248 z += G4ExpConsts::PX5expf;
249 z *= x;
250 z += G4ExpConsts::PX6expf;
251 z *= x2;
252 z += x + 1.0f;
253
254 /* multiply by power of 2 */
255 z *= G4ExpConsts::uint322sp((n + 0x7f) << 23);
256
257 if(initial_x > G4ExpConsts::MAXLOGF)
258 z = std::numeric_limits<G4float>::infinity();
259 if(initial_x < G4ExpConsts::MINLOGF)
260 z = 0.f;
261
262 return z;
263 }
264
265 //------------------------------------------------------------------------------
266
267 void expv(const uint32_t size, G4double const* __restrict__ iarray,
268 G4double* __restrict__ oarray);
269 void G4Expv(const uint32_t size, G4double const* __restrict__ iarray,
270 G4double* __restrict__ oarray);
271 void expfv(const uint32_t size, G4float const* __restrict__ iarray,
272 G4float* __restrict__ oarray);
273 void G4Expfv(const uint32_t size, G4float const* __restrict__ iarray,
274 G4float* __restrict__ oarray);
275
276 #endif /* WIN32 */
277
278 #endif
279