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1 // 1 //
2 // ******************************************* 2 // ********************************************************************
3 // * License and Disclaimer 3 // * License and Disclaimer *
4 // * 4 // * *
5 // * The Geant4 software is copyright of th 5 // * The Geant4 software is copyright of the Copyright Holders of *
6 // * the Geant4 Collaboration. It is provided 6 // * the Geant4 Collaboration. It is provided under the terms and *
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8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These *
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10 // * 10 // * *
11 // * Neither the authors of this software syst 11 // * Neither the authors of this software system, nor their employing *
12 // * institutes,nor the agencies providing fin 12 // * institutes,nor the agencies providing financial support for this *
13 // * work make any representation or warran 13 // * work make any representation or warranty, express or implied, *
14 // * regarding this software system or assum 14 // * regarding this software system or assume any liability for its *
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17 // * 17 // * *
18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and *
19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. *
20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or *
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24 // ******************************************* 24 // ********************************************************************
25 // 25 //
26 // G4Log <<
27 // 26 //
28 // Class description: << 27 //
>> 28 //
>> 29 // --------------------------------------------------------------------
>> 30 //
>> 31 // Class Description:
>> 32 //
29 // 33 //
30 // The basic idea is to exploit Pade polynomia 34 // The basic idea is to exploit Pade polynomials.
31 // A lot of ideas were inspired by the cephes 35 // A lot of ideas were inspired by the cephes math library
32 // (by Stephen L. Moshier moshier@na-net.ornl. << 36 // (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
33 // The Cephes library can be found here: http 37 // The Cephes library can be found here: http://www.netlib.org/cephes/
34 // Code and algorithms for G4Exp have been ext 38 // Code and algorithms for G4Exp have been extracted and adapted for Geant4
35 // from the original implementation in the VDT 39 // from the original implementation in the VDT mathematical library
36 // (https://svnweb.cern.ch/trac/vdt), version 40 // (https://svnweb.cern.ch/trac/vdt), version 0.3.7.
37 41
38 // Original implementation created on: Jun 23, 42 // Original implementation created on: Jun 23, 2012
39 // Author: Danilo Piparo, Thomas Hauth, V 43 // Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
40 // 44 //
41 // ------------------------------------------- 45 // --------------------------------------------------------------------
42 /* << 46 /*
43 * VDT is free software: you can redistribute 47 * VDT is free software: you can redistribute it and/or modify
44 * it under the terms of the GNU Lesser Public 48 * it under the terms of the GNU Lesser Public License as published by
45 * the Free Software Foundation, either versio 49 * the Free Software Foundation, either version 3 of the License, or
46 * (at your option) any later version. 50 * (at your option) any later version.
47 * << 51 *
48 * This program is distributed in the hope tha 52 * This program is distributed in the hope that it will be useful,
49 * but WITHOUT ANY WARRANTY; without even the 53 * but WITHOUT ANY WARRANTY; without even the implied warranty of
50 * MERCHANTABILITY or FITNESS FOR A PARTICULAR 54 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
51 * GNU Lesser Public License for more details. 55 * GNU Lesser Public License for more details.
52 * << 56 *
53 * You should have received a copy of the GNU 57 * You should have received a copy of the GNU Lesser Public License
54 * along with this program. If not, see <http 58 * along with this program. If not, see <http://www.gnu.org/licenses/>.
55 */ 59 */
56 // ------------------------------------------- 60 // --------------------------------------------------------------------
57 #ifndef G4Log_hh << 61 #ifndef G4Log_h
58 #define G4Log_hh 1 << 62 #define G4Log_h 1
59 63
60 #ifdef WIN32 64 #ifdef WIN32
61 65
62 # define G4Log std::log << 66 #define G4Log std::log
63 67
64 #else 68 #else
65 69
66 # include "G4Types.hh" << 70 #include <limits>
67 << 71 #include <stdint.h>
68 # include <cstdint> << 72 #include "G4Types.hh"
69 # include <limits> <<
70 73
71 // local namespace for the constants/functions 74 // local namespace for the constants/functions which are necessary only here
72 // 75 //
73 namespace G4LogConsts 76 namespace G4LogConsts
74 { 77 {
75 const G4double LOG_UPPER_LIMIT = 1e307; 78 const G4double LOG_UPPER_LIMIT = 1e307;
76 const G4double LOG_LOWER_LIMIT = 0; 79 const G4double LOG_LOWER_LIMIT = 0;
77 80
78 const G4double SQRTH = 0.707106781186547524 << 81 const G4double SQRTH = 0.70710678118654752440;
79 const G4float MAXNUMF = 3.402823466385288598 82 const G4float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
80 83
81 //------------------------------------------ 84 //----------------------------------------------------------------------------
82 // Used to switch between different type of 85 // Used to switch between different type of interpretations of the data
83 // (64 bits) 86 // (64 bits)
84 // 87 //
85 union ieee754 88 union ieee754
86 { 89 {
87 ieee754()= default; << 90 ieee754 () {};
88 ieee754(G4double thed) { d = thed; }; << 91 ieee754 (G4double thed) {d=thed;};
89 ieee754(uint64_t thell) { ll = thell; }; << 92 ieee754 (uint64_t thell) {ll=thell;};
90 ieee754(G4float thef) { f[0] = thef; }; << 93 ieee754 (G4float thef) {f[0]=thef;};
91 ieee754(uint32_t thei) { i[0] = thei; }; << 94 ieee754 (uint32_t thei) {i[0]=thei;};
92 G4double d; 95 G4double d;
93 G4float f[2]; 96 G4float f[2];
94 uint32_t i[2]; 97 uint32_t i[2];
95 uint64_t ll; 98 uint64_t ll;
96 uint16_t s[4]; 99 uint16_t s[4];
97 }; 100 };
98 101
99 inline G4double get_log_px(const G4double x) 102 inline G4double get_log_px(const G4double x)
100 { 103 {
101 const G4double PX1log = 1.0187566380458093 << 104 const G4double PX1log = 1.01875663804580931796E-4;
102 const G4double PX2log = 4.9749499497674700 << 105 const G4double PX2log = 4.97494994976747001425E-1;
103 const G4double PX3log = 4.7057911987888172 << 106 const G4double PX3log = 4.70579119878881725854E0;
104 const G4double PX4log = 1.4498922534161093 << 107 const G4double PX4log = 1.44989225341610930846E1;
105 const G4double PX5log = 1.7936867850781981 << 108 const G4double PX5log = 1.79368678507819816313E1;
106 const G4double PX6log = 7.7083873375588539 << 109 const G4double PX6log = 7.70838733755885391666E0;
107 << 110
108 G4double px = PX1log; << 111 G4double px = PX1log;
109 px *= x; << 112 px *= x;
110 px += PX2log; << 113 px += PX2log;
111 px *= x; << 114 px *= x;
112 px += PX3log; << 115 px += PX3log;
113 px *= x; << 116 px *= x;
114 px += PX4log; << 117 px += PX4log;
115 px *= x; << 118 px *= x;
116 px += PX5log; << 119 px += PX5log;
117 px *= x; << 120 px *= x;
118 px += PX6log; << 121 px += PX6log;
119 return px; << 122 return px;
120 } 123 }
121 124
122 inline G4double get_log_qx(const G4double x) 125 inline G4double get_log_qx(const G4double x)
123 { 126 {
124 const G4double QX1log = 1.1287358718916745 << 127 const G4double QX1log = 1.12873587189167450590E1;
125 const G4double QX2log = 4.5227914583753222 << 128 const G4double QX2log = 4.52279145837532221105E1;
126 const G4double QX3log = 8.2987526691277660 << 129 const G4double QX3log = 8.29875266912776603211E1;
127 const G4double QX4log = 7.1154475061856389 << 130 const G4double QX4log = 7.11544750618563894466E1;
128 const G4double QX5log = 2.3125162012676534 << 131 const G4double QX5log = 2.31251620126765340583E1;
129 << 132
130 G4double qx = x; << 133 G4double qx = x;
131 qx += QX1log; << 134 qx += QX1log;
132 qx *= x; << 135 qx *=x;
133 qx += QX2log; << 136 qx += QX2log;
134 qx *= x; << 137 qx *=x;
135 qx += QX3log; << 138 qx += QX3log;
136 qx *= x; << 139 qx *=x;
137 qx += QX4log; << 140 qx += QX4log;
138 qx *= x; << 141 qx *=x;
139 qx += QX5log; << 142 qx += QX5log;
140 return qx; << 143 return qx;
141 } 144 }
142 145
143 //------------------------------------------ 146 //----------------------------------------------------------------------------
144 // Converts a double to an unsigned long lon 147 // Converts a double to an unsigned long long
145 // 148 //
146 inline uint64_t dp2uint64(G4double x) 149 inline uint64_t dp2uint64(G4double x)
147 { 150 {
148 ieee754 tmp; 151 ieee754 tmp;
149 tmp.d = x; << 152 tmp.d=x;
150 return tmp.ll; 153 return tmp.ll;
151 } 154 }
152 155
153 //------------------------------------------ 156 //----------------------------------------------------------------------------
154 // Converts an unsigned long long to a doubl 157 // Converts an unsigned long long to a double
155 // 158 //
156 inline G4double uint642dp(uint64_t ll) 159 inline G4double uint642dp(uint64_t ll)
157 { 160 {
158 ieee754 tmp; 161 ieee754 tmp;
159 tmp.ll = ll; << 162 tmp.ll=ll;
160 return tmp.d; 163 return tmp.d;
161 } 164 }
162 165
163 //------------------------------------------ 166 //----------------------------------------------------------------------------
164 // Converts an int to a float 167 // Converts an int to a float
165 // 168 //
166 inline G4float uint322sp(G4int x) 169 inline G4float uint322sp(G4int x)
167 { 170 {
168 ieee754 tmp; 171 ieee754 tmp;
169 tmp.i[0] = x; << 172 tmp.i[0]=x;
170 return tmp.f[0]; 173 return tmp.f[0];
171 } 174 }
172 175
173 //------------------------------------------ 176 //----------------------------------------------------------------------------
174 // Converts a float to an int 177 // Converts a float to an int
175 // 178 //
176 inline uint32_t sp2uint32(G4float x) 179 inline uint32_t sp2uint32(G4float x)
177 { 180 {
178 ieee754 tmp; 181 ieee754 tmp;
179 tmp.f[0] = x; << 182 tmp.f[0]=x;
180 return tmp.i[0]; 183 return tmp.i[0];
181 } 184 }
182 185
183 //------------------------------------------ 186 //----------------------------------------------------------------------------
184 /// Like frexp but vectorising and the expon 187 /// Like frexp but vectorising and the exponent is a double.
185 inline G4double getMantExponent(const G4doub << 188 inline G4double getMantExponent(const G4double x, G4double & fe)
186 { 189 {
187 uint64_t n = dp2uint64(x); 190 uint64_t n = dp2uint64(x);
188 191
189 // Shift to the right up to the beginning 192 // Shift to the right up to the beginning of the exponent.
190 // Then with a mask, cut off the sign bit 193 // Then with a mask, cut off the sign bit
191 uint64_t le = (n >> 52); 194 uint64_t le = (n >> 52);
192 195
193 // chop the head of the number: an int con 196 // chop the head of the number: an int contains more than 11 bits (32)
194 int32_t e = << 197 int32_t e = le; // This is important since sums on uint64_t do not vectorise
195 (int32_t)le; // This is important since << 198 fe = e-1023 ;
196 fe = e - 1023; <<
197 199
198 // This puts to 11 zeroes the exponent 200 // This puts to 11 zeroes the exponent
199 n &= 0x800FFFFFFFFFFFFFULL; << 201 n &=0x800FFFFFFFFFFFFFULL;
200 // build a mask which is 0.5, i.e. an expo 202 // build a mask which is 0.5, i.e. an exponent equal to 1022
201 // which means *2, see the above +1. 203 // which means *2, see the above +1.
202 const uint64_t p05 = 0x3FE0000000000000ULL << 204 const uint64_t p05 = 0x3FE0000000000000ULL; //dp2uint64(0.5);
203 n |= p05; 205 n |= p05;
204 206
205 return uint642dp(n); 207 return uint642dp(n);
206 } 208 }
207 209
208 //------------------------------------------ 210 //----------------------------------------------------------------------------
209 /// Like frexp but vectorising and the expon 211 /// Like frexp but vectorising and the exponent is a float.
210 inline G4float getMantExponentf(const G4floa << 212 inline G4float getMantExponentf(const G4float x, G4float & fe)
211 { 213 {
212 uint32_t n = sp2uint32(x); 214 uint32_t n = sp2uint32(x);
213 int32_t e = (n >> 23) - 127; << 215 int32_t e = (n >> 23)-127;
214 fe = e; << 216 fe = e;
215 217
216 // fractional part 218 // fractional part
217 const uint32_t p05f = 0x3f000000; // //sp << 219 const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5);
218 n &= 0x807fffff; // ~0x7 << 220 n &= 0x807fffff;// ~0x7f800000;
219 n |= p05f; 221 n |= p05f;
220 222
221 return uint322sp(n); 223 return uint322sp(n);
222 } 224 }
223 } // namespace G4LogConsts << 225 }
224 226
225 // Log double precision ---------------------- 227 // Log double precision --------------------------------------------------------
226 228
227 inline G4double G4Log(G4double x) 229 inline G4double G4Log(G4double x)
228 { 230 {
229 const G4double original_x = x; << 231 const G4double original_x = x;
230 232
231 /* separate mantissa from exponent */ << 233 /* separate mantissa from exponent */
232 G4double fe; << 234 G4double fe;
233 x = G4LogConsts::getMantExponent(x, fe); << 235 x = G4LogConsts::getMantExponent(x,fe);
234 236
235 // blending << 237 // blending
236 x > G4LogConsts::SQRTH ? fe += 1. : x += x; << 238 x > G4LogConsts::SQRTH? fe+=1. : x+=x ;
237 x -= 1.0; << 239 x -= 1.0;
238 240
239 /* rational form */ << 241 /* rational form */
240 G4double px = G4LogConsts::get_log_px(x); << 242 G4double px = G4LogConsts::get_log_px(x);
241 243
242 // for the final formula << 244 //for the final formula
243 const G4double x2 = x * x; << 245 const G4double x2 = x*x;
244 px *= x; << 246 px *= x;
245 px *= x2; << 247 px *= x2;
246 248
247 const G4double qx = G4LogConsts::get_log_qx( << 249 const G4double qx = G4LogConsts::get_log_qx(x);
248 250
249 G4double res = px / qx; << 251 G4double res = px / qx ;
250 252
251 res -= fe * 2.121944400546905827679e-4; << 253 res -= fe * 2.121944400546905827679e-4;
252 res -= 0.5 * x2; << 254 res -= 0.5 * x2 ;
253 255
254 res = x + res; << 256 res = x + res;
255 res += fe * 0.693359375; << 257 res += fe * 0.693359375;
256 258
257 if(original_x > G4LogConsts::LOG_UPPER_LIMIT << 259 if (original_x > G4LogConsts::LOG_UPPER_LIMIT)
258 res = std::numeric_limits<G4double>::infin << 260 res = std::numeric_limits<G4double>::infinity();
259 if(original_x < G4LogConsts::LOG_LOWER_LIMIT << 261 if (original_x < G4LogConsts::LOG_LOWER_LIMIT) // THIS IS NAN!
260 res = -std::numeric_limits<G4double>::quie << 262 res = - std::numeric_limits<G4double>::quiet_NaN();
261 263
262 return res; << 264 return res;
263 } 265 }
264 266
265 // Log single precision ---------------------- 267 // Log single precision --------------------------------------------------------
266 268
267 namespace G4LogConsts 269 namespace G4LogConsts
268 { 270 {
269 const G4float LOGF_UPPER_LIMIT = MAXNUMF; 271 const G4float LOGF_UPPER_LIMIT = MAXNUMF;
270 const G4float LOGF_LOWER_LIMIT = 0; 272 const G4float LOGF_LOWER_LIMIT = 0;
271 273
272 const G4float PX1logf = 7.0376836292E-2f; 274 const G4float PX1logf = 7.0376836292E-2f;
273 const G4float PX2logf = -1.1514610310E-1f; 275 const G4float PX2logf = -1.1514610310E-1f;
274 const G4float PX3logf = 1.1676998740E-1f; 276 const G4float PX3logf = 1.1676998740E-1f;
275 const G4float PX4logf = -1.2420140846E-1f; 277 const G4float PX4logf = -1.2420140846E-1f;
276 const G4float PX5logf = 1.4249322787E-1f; 278 const G4float PX5logf = 1.4249322787E-1f;
277 const G4float PX6logf = -1.6668057665E-1f; 279 const G4float PX6logf = -1.6668057665E-1f;
278 const G4float PX7logf = 2.0000714765E-1f; 280 const G4float PX7logf = 2.0000714765E-1f;
279 const G4float PX8logf = -2.4999993993E-1f; 281 const G4float PX8logf = -2.4999993993E-1f;
280 const G4float PX9logf = 3.3333331174E-1f; 282 const G4float PX9logf = 3.3333331174E-1f;
281 283
282 inline G4float get_log_poly(const G4float x) 284 inline G4float get_log_poly(const G4float x)
283 { 285 {
284 G4float y = x * PX1logf; << 286 G4float y = x*PX1logf;
285 y += PX2logf; << 287 y += PX2logf;
286 y *= x; << 288 y *= x;
287 y += PX3logf; << 289 y += PX3logf;
288 y *= x; << 290 y *= x;
289 y += PX4logf; << 291 y += PX4logf;
290 y *= x; << 292 y *= x;
291 y += PX5logf; << 293 y += PX5logf;
292 y *= x; << 294 y *= x;
293 y += PX6logf; << 295 y += PX6logf;
294 y *= x; << 296 y *= x;
295 y += PX7logf; << 297 y += PX7logf;
296 y *= x; << 298 y *= x;
297 y += PX8logf; << 299 y += PX8logf;
298 y *= x; << 300 y *= x;
299 y += PX9logf; << 301 y += PX9logf;
300 return y; << 302 return y;
301 } 303 }
302 304
303 const G4float SQRTHF = 0.707106781186547524f 305 const G4float SQRTHF = 0.707106781186547524f;
304 } // namespace G4LogConsts << 306 }
305 307
306 // Log single precision ---------------------- 308 // Log single precision --------------------------------------------------------
307 309
308 inline G4float G4Logf(G4float x) << 310 inline G4float G4Logf( G4float x )
309 { 311 {
310 const G4float original_x = x; << 312 const G4float original_x = x;
311 313
312 G4float fe; << 314 G4float fe;
313 x = G4LogConsts::getMantExponentf(x, fe); << 315 x = G4LogConsts::getMantExponentf( x, fe);
314 316
315 x > G4LogConsts::SQRTHF ? fe += 1.f : x += x << 317 x > G4LogConsts::SQRTHF? fe+=1.f : x+=x ;
316 x -= 1.0f; << 318 x -= 1.0f;
317 319
318 const G4float x2 = x * x; << 320 const G4float x2 = x*x;
319 321
320 G4float res = G4LogConsts::get_log_poly(x); << 322 G4float res = G4LogConsts::get_log_poly(x);
321 res *= x2 * x; << 323 res *= x2*x;
322 324
323 res += -2.12194440e-4f * fe; << 325 res += -2.12194440e-4f * fe;
324 res += -0.5f * x2; << 326 res += -0.5f * x2;
325 327
326 res = x + res; << 328 res= x + res;
327 329
328 res += 0.693359375f * fe; << 330 res += 0.693359375f * fe;
329 331
330 if(original_x > G4LogConsts::LOGF_UPPER_LIMI << 332 if (original_x > G4LogConsts::LOGF_UPPER_LIMIT)
331 res = std::numeric_limits<G4float>::infini << 333 res = std::numeric_limits<G4float>::infinity();
332 if(original_x < G4LogConsts::LOGF_LOWER_LIMI << 334 if (original_x < G4LogConsts::LOGF_LOWER_LIMIT)
333 res = -std::numeric_limits<G4float>::quiet << 335 res = -std::numeric_limits<G4float>::quiet_NaN();
334 336
335 return res; << 337 return res;
336 } 338 }
337 339
338 //-------------------------------------------- 340 //------------------------------------------------------------------------------
339 341
340 void logv(const uint32_t size, G4double const* << 342 void logv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
341 G4double* __restrict__ oarray); << 343 void G4Logv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
342 void G4Logv(const uint32_t size, G4double cons << 344 void logfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
343 G4double* __restrict__ oarray); << 345 void G4Logfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
344 void logfv(const uint32_t size, G4float const* <<
345 G4float* __restrict__ oarray); <<
346 void G4Logfv(const uint32_t size, G4float cons <<
347 G4float* __restrict__ oarray); <<
348 346
349 #endif /* WIN32 */ 347 #endif /* WIN32 */
350 348
351 #endif /* LOG_H_ */ 349 #endif /* LOG_H_ */
352 350