Geant4  10.00.p01
G4Log.hh
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27 // $Id:$
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29 //
30 // --------------------------------------------------------------------
31 //
32 // Class Description:
33 //
34 //
35 // The basic idea is to exploit Pade polynomials.
36 // A lot of ideas were inspired by the cephes math library
37 // (by Stephen L. Moshier moshier@na-net.ornl.gov) as well as actual code.
38 // The Cephes library can be found here: http://www.netlib.org/cephes/
39 
40 // Created on: Jun 23, 2012
41 // Author: Danilo Piparo, Thomas Hauth, Vincenzo Innocente
42 //
43 // --------------------------------------------------------------------
44 /*
45  * VDT is free software: you can redistribute it and/or modify
46  * it under the terms of the GNU Lesser Public License as published by
47  * the Free Software Foundation, either version 3 of the License, or
48  * (at your option) any later version.
49  *
50  * This program is distributed in the hope that it will be useful,
51  * but WITHOUT ANY WARRANTY; without even the implied warranty of
52  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
53  * GNU Lesser Public License for more details.
54  *
55  * You should have received a copy of the GNU Lesser Public License
56  * along with this program. If not, see <http://www.gnu.org/licenses/>.
57  */
58 // --------------------------------------------------------------------
59 #ifndef G4Log_h
60 #define G4Log_h 1
61 
62 #ifdef WIN32
63 
64  #define G4Log std::log
65 
66 #else
67 
68 #include <limits>
69 #include <stdint.h>
70 #include "G4Types.hh"
71 
72 // local namespace for the constants/functions which are necessary only here
73 //
74 namespace G4LogConsts
75 {
76  const G4double LOG_UPPER_LIMIT = 1e307;
78 
79  const G4double SQRTH = 0.70710678118654752440;
80  const G4float MAXNUMF = 3.4028234663852885981170418348451692544e38f;
81 
82  //----------------------------------------------------------------------------
83  // Used to switch between different type of interpretations of the data
84  // (64 bits)
85  //
86  union ieee754
87  {
88  ieee754 () {};
89  ieee754 (G4double thed) {d=thed;};
90  ieee754 (uint64_t thell) {ll=thell;};
91  ieee754 (G4float thef) {f[0]=thef;};
92  ieee754 (uint32_t thei) {i[0]=thei;};
93  G4double d;
94  G4float f[2];
95  uint32_t i[2];
96  uint64_t ll;
97  uint16_t s[4];
98  };
99 
100  inline G4double get_log_px(const G4double x)
101  {
102  const G4double PX1log = 1.01875663804580931796E-4;
103  const G4double PX2log = 4.97494994976747001425E-1;
104  const G4double PX3log = 4.70579119878881725854E0;
105  const G4double PX4log = 1.44989225341610930846E1;
106  const G4double PX5log = 1.79368678507819816313E1;
107  const G4double PX6log = 7.70838733755885391666E0;
108 
109  G4double px = PX1log;
110  px *= x;
111  px += PX2log;
112  px *= x;
113  px += PX3log;
114  px *= x;
115  px += PX4log;
116  px *= x;
117  px += PX5log;
118  px *= x;
119  px += PX6log;
120  return px;
121  }
122 
123  inline G4double get_log_qx(const G4double x)
124  {
125  const G4double QX1log = 1.12873587189167450590E1;
126  const G4double QX2log = 4.52279145837532221105E1;
127  const G4double QX3log = 8.29875266912776603211E1;
128  const G4double QX4log = 7.11544750618563894466E1;
129  const G4double QX5log = 2.31251620126765340583E1;
130 
131  G4double qx = x;
132  qx += QX1log;
133  qx *=x;
134  qx += QX2log;
135  qx *=x;
136  qx += QX3log;
137  qx *=x;
138  qx += QX4log;
139  qx *=x;
140  qx += QX5log;
141  return qx;
142  }
143 
144  //----------------------------------------------------------------------------
145  // Converts a double to an unsigned long long
146  //
147  inline uint64_t dp2uint64(G4double x)
148  {
149  ieee754 tmp;
150  tmp.d=x;
151  return tmp.ll;
152  }
153 
154  //----------------------------------------------------------------------------
155  // Converts an unsigned long long to a double
156  //
157  inline G4double uint642dp(uint64_t ll)
158  {
159  ieee754 tmp;
160  tmp.ll=ll;
161  return tmp.d;
162  }
163 
164  //----------------------------------------------------------------------------
165  // Converts an int to a float
166  //
168  {
169  ieee754 tmp;
170  tmp.i[0]=x;
171  return tmp.f[0];
172  }
173 
174  //----------------------------------------------------------------------------
175  // Converts a float to an int
176  //
177  inline uint32_t sp2uint32(G4float x)
178  {
179  ieee754 tmp;
180  tmp.f[0]=x;
181  return tmp.i[0];
182  }
183 
184  //----------------------------------------------------------------------------
187  {
188  uint64_t n = dp2uint64(x);
189 
190  // Shift to the right up to the beginning of the exponent.
191  // Then with a mask, cut off the sign bit
192  uint64_t le = (n >> 52);
193 
194  // chop the head of the number: an int contains more than 11 bits (32)
195  int32_t e = le; // This is important since sums on uint64_t do not vectorise
196  fe = e-1023 ;
197 
198  // This puts to 11 zeroes the exponent
199  n &=0x800FFFFFFFFFFFFFULL;
200  // build a mask which is 0.5, i.e. an exponent equal to 1022
201  // which means *2, see the above +1.
202  const uint64_t p05 = 0x3FE0000000000000ULL; //dp2uint64(0.5);
203  n |= p05;
204 
205  return uint642dp(n);
206  }
207 
208  //----------------------------------------------------------------------------
211  {
212  uint32_t n = sp2uint32(x);
213  int32_t e = (n >> 23)-127;
214  fe = e;
215 
216  // fractional part
217  const uint32_t p05f = 0x3f000000; // //sp2uint32(0.5);
218  n &= 0x807fffff;// ~0x7f800000;
219  n |= p05f;
220 
221  return uint322sp(n);
222  }
223 }
224 
225 // Log double precision --------------------------------------------------------
226 
228 {
229  const G4double original_x = x;
230 
231  /* separate mantissa from exponent */
232  G4double fe;
234 
235  // blending
236  x > G4LogConsts::SQRTH? fe+=1. : x+=x ;
237  x -= 1.0;
238 
239  /* rational form */
241 
242  //for the final formula
243  const G4double x2 = x*x;
244  px *= x;
245  px *= x2;
246 
247  const G4double qx = G4LogConsts::get_log_qx(x);
248 
249  G4double res = px / qx ;
250 
251  res -= fe * 2.121944400546905827679e-4;
252  res -= 0.5 * x2 ;
253 
254  res = x + res;
255  res += fe * 0.693359375;
256 
257  if (original_x > G4LogConsts::LOG_UPPER_LIMIT)
258  res = std::numeric_limits<G4double>::infinity();
259  if (original_x < G4LogConsts::LOG_LOWER_LIMIT) // THIS IS NAN!
260  res = - std::numeric_limits<G4double>::quiet_NaN();
261 
262  return res;
263 }
264 
265 // Log single precision --------------------------------------------------------
266 
267 namespace G4LogConsts
268 {
271 
272  const G4float PX1logf = 7.0376836292E-2f;
273  const G4float PX2logf = -1.1514610310E-1f;
274  const G4float PX3logf = 1.1676998740E-1f;
275  const G4float PX4logf = -1.2420140846E-1f;
276  const G4float PX5logf = 1.4249322787E-1f;
277  const G4float PX6logf = -1.6668057665E-1f;
278  const G4float PX7logf = 2.0000714765E-1f;
279  const G4float PX8logf = -2.4999993993E-1f;
280  const G4float PX9logf = 3.3333331174E-1f;
281 
282  inline G4float get_log_poly(const G4float x)
283  {
284  G4float y = x*PX1logf;
285  y += PX2logf;
286  y *= x;
287  y += PX3logf;
288  y *= x;
289  y += PX4logf;
290  y *= x;
291  y += PX5logf;
292  y *= x;
293  y += PX6logf;
294  y *= x;
295  y += PX7logf;
296  y *= x;
297  y += PX8logf;
298  y *= x;
299  y += PX9logf;
300  return y;
301  }
302 
303  const G4float SQRTHF = 0.707106781186547524f;
304 }
305 
306 // Log single precision --------------------------------------------------------
307 
308 inline G4float G4Logf( G4float x )
309 {
310  const G4float original_x = x;
311 
312  G4float fe;
313  x = G4LogConsts::getMantExponentf( x, fe);
314 
315  x > G4LogConsts::SQRTHF? fe+=1.f : x+=x ;
316  x -= 1.0f;
317 
318  const G4float x2 = x*x;
319 
321  res *= x2*x;
322 
323  res += -2.12194440e-4f * fe;
324  res += -0.5f * x2;
325 
326  res= x + res;
327 
328  res += 0.693359375f * fe;
329 
330  if (original_x > G4LogConsts::LOGF_UPPER_LIMIT)
331  res = std::numeric_limits<G4float>::infinity();
332  if (original_x < G4LogConsts::LOGF_LOWER_LIMIT)
333  res = -std::numeric_limits<G4float>::quiet_NaN();
334 
335  return res;
336 }
337 
338 //------------------------------------------------------------------------------
339 
340 void logv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
341 void G4Logv(const uint32_t size, G4double const * __restrict__ iarray, G4double* __restrict__ oarray);
342 void logfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
343 void G4Logfv(const uint32_t size, G4float const * __restrict__ iarray, G4float* __restrict__ oarray);
344 
345 #endif /* WIN32 */
346 
347 #endif /* LOG_H_ */
G4float getMantExponentf(const G4float x, G4float &fe)
Like frexp but vectorising and the exponent is a float.
Definition: G4Log.hh:210
ieee754(G4double thed)
Definition: G4Log.hh:89
const G4float PX1logf
Definition: G4Log.hh:272
uint16_t s[4]
Definition: G4Log.hh:97
const G4float PX2logf
Definition: G4Log.hh:273
const G4float LOGF_UPPER_LIMIT
Definition: G4Log.hh:269
ieee754(uint64_t thell)
Definition: G4Log.hh:90
void G4Logfv(const uint32_t size, G4float const *__restrict__ iarray, G4float *__restrict__ oarray)
float G4float
Definition: G4Types.hh:77
void logfv(const uint32_t size, G4float const *__restrict__ iarray, G4float *__restrict__ oarray)
uint32_t i[2]
Definition: G4Log.hh:95
const G4float PX4logf
Definition: G4Log.hh:275
int G4int
Definition: G4Types.hh:78
G4double get_log_qx(const G4double x)
Definition: G4Log.hh:123
const G4float PX6logf
Definition: G4Log.hh:277
void logv(const uint32_t size, G4double const *__restrict__ iarray, G4double *__restrict__ oarray)
const G4float LOGF_LOWER_LIMIT
Definition: G4Log.hh:270
const G4float PX9logf
Definition: G4Log.hh:280
void G4Logv(const uint32_t size, G4double const *__restrict__ iarray, G4double *__restrict__ oarray)
const G4float MAXNUMF
Definition: G4Log.hh:80
const G4float PX7logf
Definition: G4Log.hh:278
uint32_t sp2uint32(G4float x)
Definition: G4Log.hh:177
const G4double SQRTH
Definition: G4Log.hh:79
const G4int n
G4double uint642dp(uint64_t ll)
Definition: G4Log.hh:157
G4float uint322sp(G4int x)
Definition: G4Log.hh:167
G4double G4Log(G4double x)
Definition: G4Log.hh:227
const G4float SQRTHF
Definition: G4Log.hh:303
const G4float PX5logf
Definition: G4Log.hh:276
G4double getMantExponent(const G4double x, G4double &fe)
Like frexp but vectorising and the exponent is a double.
Definition: G4Log.hh:186
uint64_t dp2uint64(G4double x)
Definition: G4Log.hh:147
ieee754(G4float thef)
Definition: G4Log.hh:91
G4double get_log_px(const G4double x)
Definition: G4Log.hh:100
const G4double LOG_LOWER_LIMIT
Definition: G4Log.hh:77
ieee754(uint32_t thei)
Definition: G4Log.hh:92
G4float G4Logf(G4float x)
Definition: G4Log.hh:308
const G4double LOG_UPPER_LIMIT
Definition: G4Log.hh:76
G4float get_log_poly(const G4float x)
Definition: G4Log.hh:282
const G4float PX8logf
Definition: G4Log.hh:279
G4float f[2]
Definition: G4Log.hh:94
double G4double
Definition: G4Types.hh:76
const G4float PX3logf
Definition: G4Log.hh:274
G4fissionEvent * fe