Geant4_10
G4Exp.hh
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27 // $Id:$
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29 //
30 // --------------------------------------------------------------------
31 //
32 // Class Description:
33 //
34 // The basic idea is to exploit Pade polynomials.
35 // A lot of ideas were inspired by the cephes math library
36 // (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
37 // The Cephes library can be found here: http://www.netlib.org/cephes/
38 
39 // Created on: Jun 23, 2012
40 // Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
41 //
42 // --------------------------------------------------------------------
43 /*
44  * VDT is free software: you can redistribute it and/or modify
45  * it under the terms of the GNU Lesser Public License as published by
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47  * (at your option) any later version.
48  *
49  * This program is distributed in the hope that it will be useful,
50  * but WITHOUT ANY WARRANTY; without even the implied warranty of
51  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
52  * GNU Lesser Public License for more details.
53  *
54  * You should have received a copy of the GNU Lesser Public License
55  * along with this program. If not, see <http://www.gnu.org/licenses/>.
56  */
57 // --------------------------------------------------------------------
58 #ifndef G4Exp_h
59 #define G4Exp_h 1
60 
61 #ifdef WIN32
62 
63  #define G4Exp std::exp
64 
65 #else
66 
67 #include <limits>
68 #include <stdint.h>
69 #include "G4Types.hh"
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 () {};
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  //
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  //----------------------------------------------------------------------------
154  inline G4double fpfloor(const G4double x)
155  {
156  // no problem since exp is defined between -708 and 708. Int is enough for it!
157  int32_t ret = int32_t (x);
158  ret-=(sp2uint32(x)>>31);
159  return ret;
160  }
161 
162  //----------------------------------------------------------------------------
168  inline G4float fpfloor(const G4float x)
169  {
170  int32_t ret = int32_t (x);
171  ret-=(sp2uint32(x)>>31);
172  return ret;
173  }
174 }
175 
176 // Exp double precision --------------------------------------------------------
177 
178 
180 inline G4double G4Exp(G4double initial_x)
181 {
182  G4double x = initial_x;
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).
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 
227 inline G4float G4Expf(G4float initial_x)
228 {
229  G4float x = initial_x;
230 
231  G4float z = G4ExpConsts::fpfloor( G4ExpConsts::LOG2EF * x +0.5f ); /* floor() truncates toward -infinity. */
232 
233  x -= z * G4ExpConsts::C1F;
234  x -= z * G4ExpConsts::C2F;
235  const int32_t n = int32_t ( z );
236 
237  const G4float x2 = x * x;
238 
239  z = x*G4ExpConsts::PX1expf;
241  z *= x;
243  z *= x;
245  z *= x;
247  z *= x;
249  z *= x;
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) z=std::numeric_limits<G4float>::infinity();
258  if (initial_x < G4ExpConsts::MINLOGF) z=0.f;
259 
260  return z;
261 }
262 
263 //------------------------------------------------------------------------------
264 
265 void expv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
266 void G4Expv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
267 void expfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
268 void G4Expfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
269 
270 #endif /* WIN32 */
271 
272 #endif
const G4double QX1exp
Definition: G4Exp.hh:78
ieee754(G4float thef)
Definition: G4Exp.hh:109
G4double fpfloor(const G4double x)
Definition: G4Exp.hh:154
uint32_t sp2uint32(G4float x)
Definition: G4Exp.hh:141
Float_t tmp
Definition: plot.C:37
void expfv(const uint32_t size, G4float const *__restrict__ iarray, G4float *__restrict__ oarray)
Double_t x2[nxs]
Definition: Style.C:19
const G4double EXP_LIMIT
Definition: G4Exp.hh:73
const XML_Char * s
Definition: expat.h:262
void G4Expfv(const uint32_t size, G4float const *__restrict__ iarray, G4float *__restrict__ oarray)
float G4float
Definition: G4Types.hh:77
const G4float PX1expf
Definition: G4Exp.hh:91
Double_t xx
Definition: macro.C:10
const G4double LOG2E
Definition: G4Exp.hh:83
const G4double QX2exp
Definition: G4Exp.hh:79
const G4double PX3exp
Definition: G4Exp.hh:77
tuple x
Definition: test.py:50
const G4float C1F
Definition: G4Exp.hh:88
const G4float PX4expf
Definition: G4Exp.hh:94
const G4double PX1exp
Definition: G4Exp.hh:75
G4float f[2]
Definition: G4Exp.hh:112
int G4int
Definition: G4Types.hh:78
const G4float PX2expf
Definition: G4Exp.hh:92
TFile f
Definition: plotHisto.C:6
const G4double QX4exp
Definition: G4Exp.hh:81
Char_t n[5]
const G4float MAXLOGF
Definition: G4Exp.hh:85
G4float G4Expf(G4float initial_x)
Exponential Function single precision.
Definition: G4Exp.hh:227
const G4float PX3expf
Definition: G4Exp.hh:93
G4float uint322sp(G4int x)
Definition: G4Exp.hh:131
const G4float C2F
Definition: G4Exp.hh:89
G4double G4Exp(G4double initial_x)
Exponential Function double precision.
Definition: G4Exp.hh:180
const G4float LOG2EF
Definition: G4Exp.hh:98
const G4float PX6expf
Definition: G4Exp.hh:96
ieee754(uint64_t thell)
Definition: G4Exp.hh:108
const G4double QX3exp
Definition: G4Exp.hh:80
tuple z
Definition: test.py:28
ieee754(uint32_t thei)
Definition: G4Exp.hh:110
void G4Expv(const uint32_t size, G4double const *__restrict__ iarray, G4double *__restrict__ oarray)
const G4float MINLOGF
Definition: G4Exp.hh:86
ieee754(G4double thed)
Definition: G4Exp.hh:107
G4double uint642dp(uint64_t ll)
Definition: G4Exp.hh:121
double G4double
Definition: G4Types.hh:76
uint32_t i[2]
Definition: G4Exp.hh:113
void expv(const uint32_t size, G4double const *__restrict__ iarray, G4double *__restrict__ oarray)
const G4double PX2exp
Definition: G4Exp.hh:76
const G4float PX5expf
Definition: G4Exp.hh:95