GADGET-4
kernel.h
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1 /*******************************************************************************
2  * \copyright This file is part of the GADGET4 N-body/SPH code developed
3  * \copyright by Volker Springel. Copyright (C) 2014-2020 by Volker Springel
4  * \copyright (vspringel@mpa-garching.mpg.de) and all contributing authors.
5  *******************************************************************************/
6 
12 #ifndef KERNEL_H
13 #define KERNEL_H
14 
15 struct kernel_density
16 {
17  double dpos[NUMDIMS];
18  double r;
19  double dv[NUMDIMS];
20  double wk, dwk;
21  double hinv, hinv3, hinv4;
22  double mj_wk, mj_dwk_r;
23 };
24 
25 struct kernel_hydra
26 {
27  double dx, dy, dz;
28  double r, vsig, sound_i, sound_j;
29  double dvx, dvy, dvz, vdotr2;
30  double wk_i, wk_j, dwk_i, dwk_j;
31  double h_i, h_j, dwk_ij, rho_ij_inv;
32 };
33 
34 #if !defined(CUBIC_SPLINE_KERNEL) && !defined(WENDLAND_C2_KERNEL) && !defined(WENDLAND_C4_KERNEL) && !defined(WENDLAND_C6_KERNEL)
35 #define CUBIC_SPLINE_KERNEL /* fall back to cubic spline kernel */
36 #endif
37 
38 /* fall back to three dimensions */
39 #if !defined(TWODIMS) && !defined(ONEDIMS)
40 #define THREEDIMS
41 #endif
42 
43 /* Norms */
44 #ifdef CUBIC_SPLINE_KERNEL
45 
46 #ifdef THREEDIMS
47 #define NORM (8.0 / M_PI)
48 #endif
49 
50 #ifdef TWODIMS
51 #define NORM (40.0 / (7.0 * M_PI))
52 #endif
53 
54 #ifdef ONEDIMS
55 #define NORM (4.0 / 3.0)
56 #endif
57 
58 #endif /* CUBIC_SPLINE_KERNEL */
59 
60 #ifdef WENDLAND_C2_KERNEL
61 
62 #ifdef THREEDIMS
63 #define NORM (21.0 / (2.0 * M_PI))
64 #endif
65 
66 #ifdef TWODIMS
67 #define NORM (7.0 / M_PI)
68 #endif
69 
70 #ifdef ONEDIMS
71 #define NORM (5.0 / 4.0)
72 #endif
73 
74 #endif /* WENDLAND_C2_KERNEL */
75 
76 #ifdef WENDLAND_C4_KERNEL
77 
78 #ifdef THREEDIMS
79 #define NORM (495.0 / (32.0 * M_PI))
80 #endif
81 
82 #ifdef TWODIMS
83 #define NORM (9.0 / M_PI)
84 #endif
85 
86 #ifdef ONEDIMS
87 #define NORM (3.0 / 2.0)
88 #endif
89 
90 #endif /* WENDLAND_C4_KERNEL */
91 
92 #ifdef WENDLAND_C6_KERNEL
93 
94 #ifdef THREEDIMS
95 #define NORM (1365.0 / (64.0 * M_PI))
96 #endif
97 
98 #ifdef TWODIMS
99 #define NORM (78.0 / (7.0 * M_PI))
100 #endif
101 
102 #ifdef ONEDIMS
103 #define NORM (55.0 / 32.0)
104 #endif
105 
106 #endif /* WENDLAND_C6_KERNEL */
107 
108 #define COMPUTE_WK -1
109 #define COMPUTE_WK_AND_DWK 0
110 #define COMPUTE_DWK 1
111 
112 static inline void kernel_hinv(double h, double *hinv, double *hinv3, double *hinv4)
113 {
114  *hinv = 1.0 / h;
115 
116 #ifdef THREEDIMS
117  *hinv3 = *hinv * *hinv * *hinv;
118 #endif
119 
120 #ifdef TWODIMS
121  *hinv3 = *hinv * *hinv;
122 #endif
123 
124 #ifdef ONEDIMS
125  *hinv3 = *hinv;
126 #endif
127 
128  *hinv4 = *hinv3 * *hinv;
129 }
130 
131 /* Attention: Here we assume that kernel is only called
132  with range 0..1 for u as done in hydra or density !!
133  Call with mode COMPUTE_WK_AND_DWK to calculate dwk and wk
134  Call with mode COMPUTE_WK to calculate only wk
135  Call with mode COMPUTE_DWK to calculate only dwk */
136 static inline void kernel_main(double u, double hinv3, double hinv4, double *wk, double *dwk, int mode)
137 {
138 #ifdef CUBIC_SPLINE_KERNEL
139 #if defined(WENDLAND_C2_KERNEL) || defined(WENDLAND_C4_KERNEL) || defined(WENDLAND_C6_KERNEL)
140 #error "Only one SPH kernel can be used"
141 #endif
142  if(u < 0.5)
143  {
144  if(mode >= COMPUTE_WK_AND_DWK)
145  *dwk = u * (18.0 * u - 12.0);
146  if(mode <= COMPUTE_WK_AND_DWK)
147  *wk = (1.0 + 6.0 * (u - 1.0) * u * u);
148  }
149  else
150  {
151  double t1 = (1.0 - u);
152  double t2 = t1 * t1;
153  if(mode >= COMPUTE_WK_AND_DWK)
154  *dwk = -6.0 * t2;
155  if(mode <= COMPUTE_WK_AND_DWK)
156  *wk = 2.0 * t2 * t1;
157  }
158 #endif
159 
160 #ifdef WENDLAND_C2_KERNEL /* Dehnen & Aly 2012 */
161 #ifdef ONEDIMS
162  double t1 = (1.0 - u);
163  double t2 = (t1 * t1);
164 
165  if(mode >= COMPUTE_WK_AND_DWK)
166  *dwk = -12.0 * u * t2;
167  if(mode <= COMPUTE_WK_AND_DWK)
168  *wk = t2 * t1 * (1.0 + u * 3.0);
169 
170 #else /* 2d or 3d */
171  double t1 = (1.0 - u);
172  double t2 = (t1 * t1);
173  double t4 = t2 * t2;
174  if(mode >= COMPUTE_WK_AND_DWK)
175  *dwk = -20.0 * u * t2 * t1;
176  if(mode <= COMPUTE_WK_AND_DWK)
177  *wk = t4 * (1.0 + u * 4.0);
178 
179 #endif
180 #endif /* WENDLAND_C2_KERNEL */
181 
182 #ifdef WENDLAND_C4_KERNEL /* Dehnen & Aly 2012 */
183 #ifdef ONEDIMS
184  double t1 = (1.0 - u);
185  double t2 = t1 * t1;
186  double t4 = t2 * t2;
187  double t5 = t4 * t1;
188 
189  if(mode >= COMPUTE_WK_AND_DWK)
190  *dwk = -14.0 * t4 * (4.0 * u + 1) * u;
191  if(mode <= COMPUTE_WK_AND_DWK)
192  *wk = t5 * (1.0 + u * (5.0 + 8.0 * u));
193 
194 #else /* 2d or 3d */
195  double t1 = (1.0 - u);
196  double t2 = (t1 * t1);
197  double t4 = t2 * t2;
198  double t6 = t2 * t2 * t2;
199  if(mode >= COMPUTE_WK_AND_DWK)
200  *dwk = -56.0 / 3.0 * u * t4 * t1 * (5.0 * u + 1);
201  if(mode <= COMPUTE_WK_AND_DWK)
202  *wk = t6 * (1.0 + u * (6.0 + 35.0 / 3.0 * u));
203 
204 #endif
205 #endif /* WENDLAND_C4_KERNEL */
206 
207 #ifdef WENDLAND_C6_KERNEL /* Dehnen & Aly 2012 */
208 #ifdef ONEDIMS
209  double t1 = (1.0 - u);
210  double t2 = (t1 * t1);
211  double t4 = t2 * t2;
212  double t6 = t4 * t2;
213  double t7 = t4 * t2 * t1;
214  if(mode >= COMPUTE_WK_AND_DWK)
215  *dwk = -6.0 * u * t6 * (3.0 + u * (18.0 + 35.0 * u));
216  if(mode <= COMPUTE_WK_AND_DWK)
217  *wk = t7 * (1.0 + u * (7.0 + u * (19.0 + 21.0 * u)));
218 
219 #else /* 2d or 3d */
220  double t1 = (1.0 - u);
221  double t2 = (t1 * t1);
222  double t4 = t2 * t2;
223  double t7 = t4 * t2 * t1;
224  double t8 = t4 * t4;
225  if(mode >= COMPUTE_WK_AND_DWK)
226  *dwk = -22.0 * u * (1.0 + u * (7.0 + 16.0 * u)) * t7;
227  if(mode <= COMPUTE_WK_AND_DWK)
228  *wk = t8 * (1.0 + u * (8.0 + u * (25.0 + 32.0 * u)));
229 
230 #endif
231 #endif /* WENDLAND_C6_KERNEL */
232  if(mode >= COMPUTE_WK_AND_DWK)
233  *dwk *= NORM * hinv4;
234  if(mode <= COMPUTE_WK_AND_DWK)
235  *wk *= NORM * hinv3;
236 }
237 
238 #if defined(WENDLAND_BIAS_CORRECTION) && (!(defined(WENDLAND_C2_KERNEL) || defined(WENDLAND_C4_KERNEL) || defined(WENDLAND_C6_KERNEL)))
239 #error "WENDLAND_BIAS_CORRECTION only works with a Wendland kernel"
240 #endif
241 
242 #if defined(WENDLAND_BIAS_CORRECTION) && (defined(WENDLAND_C2_KERNEL) || defined(WENDLAND_C4_KERNEL) || defined(WENDLAND_C6_KERNEL))
243 
244 #if defined(ONEDIMS) || defined(TWODIMS)
245 #error "WENDLAND_BIAS_CORRECTION is only implemented for 3D"
246 #endif
247 
248 static inline void get_bias_correction_parameters(double *alpha, double *eps100)
249 {
250 #ifdef WENDLAND_C2_KERNEL
251  *eps100 = 0.0294;
252  *alpha = 0.977;
253 #endif
254 #ifdef WENDLAND_C4_KERNEL
255  *eps100 = 0.01342;
256  *alpha = 1.579;
257 #endif
258 #ifdef WENDLAND_C6_KERNEL
259  *eps100 = 0.0116;
260  *alpha = 2.236;
261 #endif
262 }
263 static inline double get_density_bias(double hsml, double mass, int DesNumNgb)
264 {
265  kernel_density kernel;
266  kernel_hinv(hsml, &kernel.hinv, &kernel.hinv3, &kernel.hinv4);
267  kernel_main(0, kernel.hinv3, kernel.hinv4, &kernel.wk, &kernel.dwk, COMPUTE_WK);
268  double alpha = 0;
269  double eps100 = 0;
270  get_bias_correction_parameters(&alpha, &eps100);
271  double wc_correction = eps100 * pow(DesNumNgb * 0.01, -alpha) * mass * kernel.wk;
272  return wc_correction;
273 }
274 #endif
275 
276 #ifdef EXPLICIT_VECTORIZATION
277 static inline void kernel_main_vector(Vec4d u, Vec4d hinv3, Vec4d hinv4, Vec4d *wk, Vec4d *dwk)
278 {
279 #ifdef CUBIC_SPLINE_KERNEL
280  Vec4d ucompl = u - 1.0;
281  Vec4db decision = (u < 0.5);
282  Vec4d wksub = 6.0 * u;
283 
284  Vec4d ucompsq = ucompl * ucompl;
285  Vec4d uucomp = u * ucompl;
286  Vec4d wk1 = 1.0 + uucomp * wksub;
287  Vec4d dwk1 = wksub + uucomp * 18.0;
288  Vec4d wk2 = ucompsq * -2.0 * ucompl;
289  Vec4d dwk2 = ucompsq * -6.0;
290  *wk = select(decision, wk1, wk2);
291  *dwk = select(decision, dwk1, dwk2);
292 #endif
293 
294 #ifdef WENDLAND_C2_KERNEL /* Dehnen & Aly 2012 */
295 #ifdef ONEDIMS
296  Vec4d t1 = 1.0 - u;
297 
298  Vec4d t2 = t1 * t1;
299 
300  *dwk = -12.0 * u * t2;
301  *wk = t2 * t1 * (1.0 + u * 3.0);
302 
303 #else /* 2d or 3d */
304  Vec4d t1 = (1.0 - u);
305  Vec4d t2 = (t1 * t1);
306 
307  *dwk = -20.0 * u * t2 * t1;
308  *wk = t2 * t2 * (1.0 + u * 4.0);
309 #endif
310 #endif /* WENDLAND_C2_KERNEL */
311 
312 #ifdef WENDLAND_C4_KERNEL /* Dehnen & Aly 2012 */
313 #ifdef ONEDIMS
314  Vec4d t1 = (1.0 - u);
315  Vec4d t2 = t1 * t1;
316  Vec4d t4 = t2 * t2;
317 
318  *dwk = -14.0 * t4 * (4.0 * u + 1) * u;
319  *wk = t1 * t4 * (1.0 + u * (5.0 + 8.0 * u));
320 
321 #else /* 2d or 3d */
322  Vec4d t1 = (1.0 - u);
323  Vec4d t2 = (t1 * t1);
324  Vec4d t4 = t2 * t2;
325  Vec4d t6 = t2 * t2 * t2;
326  *dwk = -56.0 / 3.0 * u * t4 * t1 * (5.0 * u + 1);
327 
328  *wk = t6 * (1.0 + u * (6.0 + 35.0 / 3.0 * u));
329 
330 #endif
331 #endif /* WENDLAND_C4_KERNEL */
332 
333 #ifdef WENDLAND_C6_KERNEL /* Dehnen & Aly 2012 */
334 #ifdef ONEDIMS
335  Vec4d t1 = (1.0 - u);
336  Vec4d t2 = (t1 * t1);
337  Vec4d t4 = t2 * t2;
338  Vec4d t6 = t4 * t2;
339  Vec4d t7 = t4 * t2 * t1;
340  *dwk = -6.0 * u * t6 * (3.0 + u * (18.0 + 35.0 * u));
341  *wk = t7 * (1.0 + u * (7.0 + u * (19.0 + 21.0 * u)));
342 
343 #else /* 2d or 3d */
344  Vec4d t1 = (1.0 - u);
345  Vec4d t2 = (t1 * t1);
346  Vec4d t4 = t2 * t2;
347  Vec4d t7 = t4 * t2 * t1;
348  Vec4d t8 = t4 * t4;
349  *dwk = -22.0 * u * (1.0 + u * (7.0 + 16.0 * u)) * t7;
350  *wk = t8 * (1.0 + u * (8.0 + u * (25.0 + 32.0 * u)));
351 
352 #endif
353 #endif /* WENDLAND_C6_KERNEL */
354  *dwk *= hinv4;
355  *wk *= hinv3;
356 }
357 #endif /* EXPLICIT_VECTORIZATION */
358 #endif
NUMDIMS
#define NUMDIMS
Definition: constants.h:369
COMPUTE_WK_AND_DWK
#define COMPUTE_WK_AND_DWK
Definition: kernel.h:109
COMPUTE_WK
#define COMPUTE_WK
Definition: kernel.h:108
NORM
#define NORM
Definition: kernel.h:47
half_float::detail::pow
expr pow(half base, half exp)
Definition: half.hpp:2803
kernel_density
Definition: kernel.h:16
kernel_density::mj_wk
double mj_wk
Definition: kernel.h:22
kernel_density::dpos
double dpos[NUMDIMS]
Definition: kernel.h:17
kernel_density::wk
double wk
Definition: kernel.h:20
kernel_density::hinv
double hinv
Definition: kernel.h:21
kernel_density::dv
double dv[NUMDIMS]
Definition: kernel.h:19
kernel_density::r
double r
Definition: kernel.h:18
kernel_density::mj_dwk_r
double mj_dwk_r
Definition: kernel.h:22
kernel_density::hinv4
double hinv4
Definition: kernel.h:21
kernel_density::hinv3
double hinv3
Definition: kernel.h:21
kernel_density::dwk
double dwk
Definition: kernel.h:20
kernel_hydra
Definition: kernel.h:26
kernel_hydra::h_i
double h_i
Definition: kernel.h:31
kernel_hydra::dx
double dx
Definition: kernel.h:27
kernel_hydra::dvx
double dvx
Definition: kernel.h:29
kernel_hydra::dwk_ij
double dwk_ij
Definition: kernel.h:31
kernel_hydra::dwk_j
double dwk_j
Definition: kernel.h:30
kernel_hydra::vdotr2
double vdotr2
Definition: kernel.h:29
kernel_hydra::vsig
double vsig
Definition: kernel.h:28
kernel_hydra::dz
double dz
Definition: kernel.h:27
kernel_hydra::sound_j
double sound_j
Definition: kernel.h:28
kernel_hydra::dvy
double dvy
Definition: kernel.h:29
kernel_hydra::h_j
double h_j
Definition: kernel.h:31
kernel_hydra::r
double r
Definition: kernel.h:28
kernel_hydra::dy
double dy
Definition: kernel.h:27
kernel_hydra::wk_i
double wk_i
Definition: kernel.h:30
kernel_hydra::wk_j
double wk_j
Definition: kernel.h:30
kernel_hydra::sound_i
double sound_i
Definition: kernel.h:28
kernel_hydra::dvz
double dvz
Definition: kernel.h:29
kernel_hydra::rho_ij_inv
double rho_ij_inv
Definition: kernel.h:31
kernel_hydra::dwk_i
double dwk_i
Definition: kernel.h:30