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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 * 7 // * conditions of the Geant4 Software License 7 // * conditions of the Geant4 Software License, included in the file * 8 // * LICENSE and available at http://cern.ch/ 8 // * LICENSE and available at http://cern.ch/geant4/license . These * 9 // * include a list of copyright holders. 9 // * include a list of copyright holders. * 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 * 15 // * use. Please see the license in the file 15 // * use. Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 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 * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // G4Log 26 // G4Log 27 // 27 // 28 // Class description: 28 // Class description: 29 // 29 // 30 // The basic idea is to exploit Pade polynomia 30 // The basic idea is to exploit Pade polynomials. 31 // A lot of ideas were inspired by the cephes 31 // A lot of ideas were inspired by the cephes math library 32 // (by Stephen L. Moshier moshier@na-net.ornl. 32 // (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code. 33 // The Cephes library can be found here: http 33 // The Cephes library can be found here: http://www.netlib.org/cephes/ 34 // Code and algorithms for G4Exp have been ext 34 // Code and algorithms for G4Exp have been extracted and adapted for Geant4 35 // from the original implementation in the VDT 35 // from the original implementation in the VDT mathematical library 36 // (https://svnweb.cern.ch/trac/vdt), version 36 // (https://svnweb.cern.ch/trac/vdt), version 0.3.7. 37 37 38 // Original implementation created on: Jun 23, 38 // Original implementation created on: Jun 23, 2012 39 // Author: Danilo Piparo, Thomas Hauth, V 39 // Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente 40 // 40 // 41 // ------------------------------------------- 41 // -------------------------------------------------------------------- 42 /* 42 /* 43 * VDT is free software: you can redistribute 43 * VDT is free software: you can redistribute it and/or modify 44 * it under the terms of the GNU Lesser Public 44 * it under the terms of the GNU Lesser Public License as published by 45 * the Free Software Foundation, either versio 45 * the Free Software Foundation, either version 3 of the License, or 46 * (at your option) any later version. 46 * (at your option) any later version. 47 * 47 * 48 * This program is distributed in the hope tha 48 * This program is distributed in the hope that it will be useful, 49 * but WITHOUT ANY WARRANTY; without even the 49 * but WITHOUT ANY WARRANTY; without even the implied warranty of 50 * MERCHANTABILITY or FITNESS FOR A PARTICULAR 50 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 51 * GNU Lesser Public License for more details. 51 * GNU Lesser Public License for more details. 52 * 52 * 53 * You should have received a copy of the GNU 53 * You should have received a copy of the GNU Lesser Public License 54 * along with this program. If not, see <http 54 * along with this program. If not, see <http://www.gnu.org/licenses/>. 55 */ 55 */ 56 // ------------------------------------------- 56 // -------------------------------------------------------------------- 57 #ifndef G4Log_hh 57 #ifndef G4Log_hh 58 #define G4Log_hh 1 58 #define G4Log_hh 1 59 59 60 #ifdef WIN32 60 #ifdef WIN32 61 61 62 # define G4Log std::log 62 # define G4Log std::log 63 63 64 #else 64 #else 65 65 66 # include "G4Types.hh" 66 # include "G4Types.hh" 67 67 68 # include <cstdint> 68 # include <cstdint> 69 # include <limits> 69 # include <limits> 70 70 71 // local namespace for the constants/functions 71 // local namespace for the constants/functions which are necessary only here 72 // 72 // 73 namespace G4LogConsts 73 namespace G4LogConsts 74 { 74 { 75 const G4double LOG_UPPER_LIMIT = 1e307; 75 const G4double LOG_UPPER_LIMIT = 1e307; 76 const G4double LOG_LOWER_LIMIT = 0; 76 const G4double LOG_LOWER_LIMIT = 0; 77 77 78 const G4double SQRTH = 0.707106781186547524 78 const G4double SQRTH = 0.70710678118654752440; 79 const G4float MAXNUMF = 3.402823466385288598 79 const G4float MAXNUMF = 3.4028234663852885981170418348451692544e38f; 80 80 81 //------------------------------------------ 81 //---------------------------------------------------------------------------- 82 // Used to switch between different type of 82 // Used to switch between different type of interpretations of the data 83 // (64 bits) 83 // (64 bits) 84 // 84 // 85 union ieee754 85 union ieee754 86 { 86 { 87 ieee754()= default; 87 ieee754()= default; 88 ieee754(G4double thed) { d = thed; }; 88 ieee754(G4double thed) { d = thed; }; 89 ieee754(uint64_t thell) { ll = thell; }; 89 ieee754(uint64_t thell) { ll = thell; }; 90 ieee754(G4float thef) { f[0] = thef; }; 90 ieee754(G4float thef) { f[0] = thef; }; 91 ieee754(uint32_t thei) { i[0] = thei; }; 91 ieee754(uint32_t thei) { i[0] = thei; }; 92 G4double d; 92 G4double d; 93 G4float f[2]; 93 G4float f[2]; 94 uint32_t i[2]; 94 uint32_t i[2]; 95 uint64_t ll; 95 uint64_t ll; 96 uint16_t s[4]; 96 uint16_t s[4]; 97 }; 97 }; 98 98 99 inline G4double get_log_px(const G4double x) 99 inline G4double get_log_px(const G4double x) 100 { 100 { 101 const G4double PX1log = 1.0187566380458093 101 const G4double PX1log = 1.01875663804580931796E-4; 102 const G4double PX2log = 4.9749499497674700 102 const G4double PX2log = 4.97494994976747001425E-1; 103 const G4double PX3log = 4.7057911987888172 103 const G4double PX3log = 4.70579119878881725854E0; 104 const G4double PX4log = 1.4498922534161093 104 const G4double PX4log = 1.44989225341610930846E1; 105 const G4double PX5log = 1.7936867850781981 105 const G4double PX5log = 1.79368678507819816313E1; 106 const G4double PX6log = 7.7083873375588539 106 const G4double PX6log = 7.70838733755885391666E0; 107 107 108 G4double px = PX1log; 108 G4double px = PX1log; 109 px *= x; 109 px *= x; 110 px += PX2log; 110 px += PX2log; 111 px *= x; 111 px *= x; 112 px += PX3log; 112 px += PX3log; 113 px *= x; 113 px *= x; 114 px += PX4log; 114 px += PX4log; 115 px *= x; 115 px *= x; 116 px += PX5log; 116 px += PX5log; 117 px *= x; 117 px *= x; 118 px += PX6log; 118 px += PX6log; 119 return px; 119 return px; 120 } 120 } 121 121 122 inline G4double get_log_qx(const G4double x) 122 inline G4double get_log_qx(const G4double x) 123 { 123 { 124 const G4double QX1log = 1.1287358718916745 124 const G4double QX1log = 1.12873587189167450590E1; 125 const G4double QX2log = 4.5227914583753222 125 const G4double QX2log = 4.52279145837532221105E1; 126 const G4double QX3log = 8.2987526691277660 126 const G4double QX3log = 8.29875266912776603211E1; 127 const G4double QX4log = 7.1154475061856389 127 const G4double QX4log = 7.11544750618563894466E1; 128 const G4double QX5log = 2.3125162012676534 128 const G4double QX5log = 2.31251620126765340583E1; 129 129 130 G4double qx = x; 130 G4double qx = x; 131 qx += QX1log; 131 qx += QX1log; 132 qx *= x; 132 qx *= x; 133 qx += QX2log; 133 qx += QX2log; 134 qx *= x; 134 qx *= x; 135 qx += QX3log; 135 qx += QX3log; 136 qx *= x; 136 qx *= x; 137 qx += QX4log; 137 qx += QX4log; 138 qx *= x; 138 qx *= x; 139 qx += QX5log; 139 qx += QX5log; 140 return qx; 140 return qx; 141 } 141 } 142 142 143 //------------------------------------------ 143 //---------------------------------------------------------------------------- 144 // Converts a double to an unsigned long lon 144 // Converts a double to an unsigned long long 145 // 145 // 146 inline uint64_t dp2uint64(G4double x) 146 inline uint64_t dp2uint64(G4double x) 147 { 147 { 148 ieee754 tmp; 148 ieee754 tmp; 149 tmp.d = x; 149 tmp.d = x; 150 return tmp.ll; 150 return tmp.ll; 151 } 151 } 152 152 153 //------------------------------------------ 153 //---------------------------------------------------------------------------- 154 // Converts an unsigned long long to a doubl 154 // Converts an unsigned long long to a double 155 // 155 // 156 inline G4double uint642dp(uint64_t ll) 156 inline G4double uint642dp(uint64_t ll) 157 { 157 { 158 ieee754 tmp; 158 ieee754 tmp; 159 tmp.ll = ll; 159 tmp.ll = ll; 160 return tmp.d; 160 return tmp.d; 161 } 161 } 162 162 163 //------------------------------------------ 163 //---------------------------------------------------------------------------- 164 // Converts an int to a float 164 // Converts an int to a float 165 // 165 // 166 inline G4float uint322sp(G4int x) 166 inline G4float uint322sp(G4int x) 167 { 167 { 168 ieee754 tmp; 168 ieee754 tmp; 169 tmp.i[0] = x; 169 tmp.i[0] = x; 170 return tmp.f[0]; 170 return tmp.f[0]; 171 } 171 } 172 172 173 //------------------------------------------ 173 //---------------------------------------------------------------------------- 174 // Converts a float to an int 174 // Converts a float to an int 175 // 175 // 176 inline uint32_t sp2uint32(G4float x) 176 inline uint32_t sp2uint32(G4float x) 177 { 177 { 178 ieee754 tmp; 178 ieee754 tmp; 179 tmp.f[0] = x; 179 tmp.f[0] = x; 180 return tmp.i[0]; 180 return tmp.i[0]; 181 } 181 } 182 182 183 //------------------------------------------ 183 //---------------------------------------------------------------------------- 184 /// Like frexp but vectorising and the expon 184 /// Like frexp but vectorising and the exponent is a double. 185 inline G4double getMantExponent(const G4doub 185 inline G4double getMantExponent(const G4double x, G4double& fe) 186 { 186 { 187 uint64_t n = dp2uint64(x); 187 uint64_t n = dp2uint64(x); 188 188 189 // Shift to the right up to the beginning 189 // Shift to the right up to the beginning of the exponent. 190 // Then with a mask, cut off the sign bit 190 // Then with a mask, cut off the sign bit 191 uint64_t le = (n >> 52); 191 uint64_t le = (n >> 52); 192 192 193 // chop the head of the number: an int con 193 // chop the head of the number: an int contains more than 11 bits (32) 194 int32_t e = 194 int32_t e = 195 (int32_t)le; // This is important since 195 (int32_t)le; // This is important since sums on uint64_t do not vectorise 196 fe = e - 1023; 196 fe = e - 1023; 197 197 198 // This puts to 11 zeroes the exponent 198 // This puts to 11 zeroes the exponent 199 n &= 0x800FFFFFFFFFFFFFULL; 199 n &= 0x800FFFFFFFFFFFFFULL; 200 // build a mask which is 0.5, i.e. an expo 200 // build a mask which is 0.5, i.e. an exponent equal to 1022 201 // which means *2, see the above +1. 201 // which means *2, see the above +1. 202 const uint64_t p05 = 0x3FE0000000000000ULL 202 const uint64_t p05 = 0x3FE0000000000000ULL; // dp2uint64(0.5); 203 n |= p05; 203 n |= p05; 204 204 205 return uint642dp(n); 205 return uint642dp(n); 206 } 206 } 207 207 208 //------------------------------------------ 208 //---------------------------------------------------------------------------- 209 /// Like frexp but vectorising and the expon 209 /// Like frexp but vectorising and the exponent is a float. 210 inline G4float getMantExponentf(const G4floa 210 inline G4float getMantExponentf(const G4float x, G4float& fe) 211 { 211 { 212 uint32_t n = sp2uint32(x); 212 uint32_t n = sp2uint32(x); 213 int32_t e = (n >> 23) - 127; 213 int32_t e = (n >> 23) - 127; 214 fe = e; 214 fe = e; 215 215 216 // fractional part 216 // fractional part 217 const uint32_t p05f = 0x3f000000; // //sp 217 const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5); 218 n &= 0x807fffff; // ~0x7 218 n &= 0x807fffff; // ~0x7f800000; 219 n |= p05f; 219 n |= p05f; 220 220 221 return uint322sp(n); 221 return uint322sp(n); 222 } 222 } 223 } // namespace G4LogConsts 223 } // namespace G4LogConsts 224 224 225 // Log double precision ---------------------- 225 // Log double precision -------------------------------------------------------- 226 226 227 inline G4double G4Log(G4double x) 227 inline G4double G4Log(G4double x) 228 { 228 { 229 const G4double original_x = x; 229 const G4double original_x = x; 230 230 231 /* separate mantissa from exponent */ 231 /* separate mantissa from exponent */ 232 G4double fe; 232 G4double fe; 233 x = G4LogConsts::getMantExponent(x, fe); 233 x = G4LogConsts::getMantExponent(x, fe); 234 234 235 // blending 235 // blending 236 x > G4LogConsts::SQRTH ? fe += 1. : x += x; 236 x > G4LogConsts::SQRTH ? fe += 1. : x += x; 237 x -= 1.0; 237 x -= 1.0; 238 238 239 /* rational form */ 239 /* rational form */ 240 G4double px = G4LogConsts::get_log_px(x); 240 G4double px = G4LogConsts::get_log_px(x); 241 241 242 // for the final formula 242 // for the final formula 243 const G4double x2 = x * x; 243 const G4double x2 = x * x; 244 px *= x; 244 px *= x; 245 px *= x2; 245 px *= x2; 246 246 247 const G4double qx = G4LogConsts::get_log_qx( 247 const G4double qx = G4LogConsts::get_log_qx(x); 248 248 249 G4double res = px / qx; 249 G4double res = px / qx; 250 250 251 res -= fe * 2.121944400546905827679e-4; 251 res -= fe * 2.121944400546905827679e-4; 252 res -= 0.5 * x2; 252 res -= 0.5 * x2; 253 253 254 res = x + res; 254 res = x + res; 255 res += fe * 0.693359375; 255 res += fe * 0.693359375; 256 256 257 if(original_x > G4LogConsts::LOG_UPPER_LIMIT 257 if(original_x > G4LogConsts::LOG_UPPER_LIMIT) 258 res = std::numeric_limits<G4double>::infin 258 res = std::numeric_limits<G4double>::infinity(); 259 if(original_x < G4LogConsts::LOG_LOWER_LIMIT 259 if(original_x < G4LogConsts::LOG_LOWER_LIMIT) // THIS IS NAN! 260 res = -std::numeric_limits<G4double>::quie 260 res = -std::numeric_limits<G4double>::quiet_NaN(); 261 261 262 return res; 262 return res; 263 } 263 } 264 264 265 // Log single precision ---------------------- 265 // Log single precision -------------------------------------------------------- 266 266 267 namespace G4LogConsts 267 namespace G4LogConsts 268 { 268 { 269 const G4float LOGF_UPPER_LIMIT = MAXNUMF; 269 const G4float LOGF_UPPER_LIMIT = MAXNUMF; 270 const G4float LOGF_LOWER_LIMIT = 0; 270 const G4float LOGF_LOWER_LIMIT = 0; 271 271 272 const G4float PX1logf = 7.0376836292E-2f; 272 const G4float PX1logf = 7.0376836292E-2f; 273 const G4float PX2logf = -1.1514610310E-1f; 273 const G4float PX2logf = -1.1514610310E-1f; 274 const G4float PX3logf = 1.1676998740E-1f; 274 const G4float PX3logf = 1.1676998740E-1f; 275 const G4float PX4logf = -1.2420140846E-1f; 275 const G4float PX4logf = -1.2420140846E-1f; 276 const G4float PX5logf = 1.4249322787E-1f; 276 const G4float PX5logf = 1.4249322787E-1f; 277 const G4float PX6logf = -1.6668057665E-1f; 277 const G4float PX6logf = -1.6668057665E-1f; 278 const G4float PX7logf = 2.0000714765E-1f; 278 const G4float PX7logf = 2.0000714765E-1f; 279 const G4float PX8logf = -2.4999993993E-1f; 279 const G4float PX8logf = -2.4999993993E-1f; 280 const G4float PX9logf = 3.3333331174E-1f; 280 const G4float PX9logf = 3.3333331174E-1f; 281 281 282 inline G4float get_log_poly(const G4float x) 282 inline G4float get_log_poly(const G4float x) 283 { 283 { 284 G4float y = x * PX1logf; 284 G4float y = x * PX1logf; 285 y += PX2logf; 285 y += PX2logf; 286 y *= x; 286 y *= x; 287 y += PX3logf; 287 y += PX3logf; 288 y *= x; 288 y *= x; 289 y += PX4logf; 289 y += PX4logf; 290 y *= x; 290 y *= x; 291 y += PX5logf; 291 y += PX5logf; 292 y *= x; 292 y *= x; 293 y += PX6logf; 293 y += PX6logf; 294 y *= x; 294 y *= x; 295 y += PX7logf; 295 y += PX7logf; 296 y *= x; 296 y *= x; 297 y += PX8logf; 297 y += PX8logf; 298 y *= x; 298 y *= x; 299 y += PX9logf; 299 y += PX9logf; 300 return y; 300 return y; 301 } 301 } 302 302 303 const G4float SQRTHF = 0.707106781186547524f 303 const G4float SQRTHF = 0.707106781186547524f; 304 } // namespace G4LogConsts 304 } // namespace G4LogConsts 305 305 306 // Log single precision ---------------------- 306 // Log single precision -------------------------------------------------------- 307 307 308 inline G4float G4Logf(G4float x) 308 inline G4float G4Logf(G4float x) 309 { 309 { 310 const G4float original_x = x; 310 const G4float original_x = x; 311 311 312 G4float fe; 312 G4float fe; 313 x = G4LogConsts::getMantExponentf(x, fe); 313 x = G4LogConsts::getMantExponentf(x, fe); 314 314 315 x > G4LogConsts::SQRTHF ? fe += 1.f : x += x 315 x > G4LogConsts::SQRTHF ? fe += 1.f : x += x; 316 x -= 1.0f; 316 x -= 1.0f; 317 317 318 const G4float x2 = x * x; 318 const G4float x2 = x * x; 319 319 320 G4float res = G4LogConsts::get_log_poly(x); 320 G4float res = G4LogConsts::get_log_poly(x); 321 res *= x2 * x; 321 res *= x2 * x; 322 322 323 res += -2.12194440e-4f * fe; 323 res += -2.12194440e-4f * fe; 324 res += -0.5f * x2; 324 res += -0.5f * x2; 325 325 326 res = x + res; 326 res = x + res; 327 327 328 res += 0.693359375f * fe; 328 res += 0.693359375f * fe; 329 329 330 if(original_x > G4LogConsts::LOGF_UPPER_LIMI 330 if(original_x > G4LogConsts::LOGF_UPPER_LIMIT) 331 res = std::numeric_limits<G4float>::infini 331 res = std::numeric_limits<G4float>::infinity(); 332 if(original_x < G4LogConsts::LOGF_LOWER_LIMI 332 if(original_x < G4LogConsts::LOGF_LOWER_LIMIT) 333 res = -std::numeric_limits<G4float>::quiet 333 res = -std::numeric_limits<G4float>::quiet_NaN(); 334 334 335 return res; 335 return res; 336 } 336 } 337 337 338 //-------------------------------------------- 338 //------------------------------------------------------------------------------ 339 339 340 void logv(const uint32_t size, G4double const* 340 void logv(const uint32_t size, G4double const* __restrict__ iarray, 341 G4double* __restrict__ oarray); 341 G4double* __restrict__ oarray); 342 void G4Logv(const uint32_t size, G4double cons 342 void G4Logv(const uint32_t size, G4double const* __restrict__ iarray, 343 G4double* __restrict__ oarray); 343 G4double* __restrict__ oarray); 344 void logfv(const uint32_t size, G4float const* 344 void logfv(const uint32_t size, G4float const* __restrict__ iarray, 345 G4float* __restrict__ oarray); 345 G4float* __restrict__ oarray); 346 void G4Logfv(const uint32_t size, G4float cons 346 void G4Logfv(const uint32_t size, G4float const* __restrict__ iarray, 347 G4float* __restrict__ oarray); 347 G4float* __restrict__ oarray); 348 348 349 #endif /* WIN32 */ 349 #endif /* WIN32 */ 350 350 351 #endif /* LOG_H_ */ 351 #endif /* LOG_H_ */ 352 352