ROOT  6.06/09
Reference Guide
const.cpp
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1 /* This file is part of the Vc library.
2 
3  Copyright (C) 2009-2012 Matthias Kretz <kretz@kde.org>
4 
5  Vc is free software: you can redistribute it and/or modify
6  it under the terms of the GNU Lesser General Public License as
7  published by the Free Software Foundation, either version 3 of
8  the License, or (at your option) any later version.
9 
10  Vc is distributed in the hope that it will be useful, but
11  WITHOUT ANY WARRANTY; without even the implied warranty of
12  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13  GNU Lesser General Public License for more details.
14 
15  You should have received a copy of the GNU Lesser General Public
16  License along with Vc. If not, see <http://www.gnu.org/licenses/>.
17 
18 */
19 
20 #ifndef V_ALIGN
21 # ifdef __GNUC__
22 # define V_ALIGN(n) __attribute__((aligned(n)))
23 # else
24 # define V_ALIGN(n) __declspec(align(n))
25 # endif
26 #endif
27 
28 #include "Vc/avx/const_data.h"
29 #include "Vc/sse/const_data.h"
30 #include <Vc/version.h>
31 
32 #include <cstdio>
33 #include <cstdlib>
34 #include <cstring>
35 
36 #include "Vc/common/macros.h"
37 
38 namespace ROOT {
39 namespace Vc
40 {
41 namespace AVX
42 {
43  // cacheline 1
44  V_ALIGN(64) extern const unsigned int _IndexesFromZero32[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
45  V_ALIGN(16) extern const unsigned short _IndexesFromZero16[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
46  V_ALIGN(16) extern const unsigned char _IndexesFromZero8 [16]= { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
47 
48  template<> const double c_trig<double>::data[] = {
49  // cacheline 4
50  Vc_buildDouble(1, 0x921fb54442d18ull, -1), // π/4
51  Vc_buildDouble(1, 0x921fb40000000ull, -1), // π/4 - 30bits precision
52  Vc_buildDouble(1, 0x4442d00000000ull, -25), // π/4 remainder1 - 32bits precision
53  Vc_buildDouble(1, 0x8469898cc5170ull, -49), // π/4 remainder2
54  0.0625,
55  16.,
56  0., // padding
57  0., // padding
58  // cacheline 5
59  Vc_buildDouble( 1, 0x555555555554bull, -5), // ~ 1/4!
60  Vc_buildDouble(-1, 0x6c16c16c14f91ull, -10), // ~-1/6!
61  Vc_buildDouble( 1, 0xa01a019c844f5ull, -16), // ~ 1/8!
62  Vc_buildDouble(-1, 0x27e4f7eac4bc6ull, -22), // ~-1/10!
63  Vc_buildDouble( 1, 0x1ee9d7b4e3f05ull, -29), // ~ 1/12!
64  Vc_buildDouble(-1, 0x8fa49a0861a9bull, -37), // ~-1/14!
65  Vc_buildDouble(-1, 0x5555555555548ull, -3), // ~-1/3!
66  Vc_buildDouble( 1, 0x111111110f7d0ull, -7), // ~ 1/5!
67  // cacheline 8
68  Vc_buildDouble(-1, 0xa01a019bfdf03ull, -13), // ~-1/7!
69  Vc_buildDouble( 1, 0x71de3567d48a1ull, -19), // ~ 1/9!
70  Vc_buildDouble(-1, 0xae5e5a9291f5dull, -26), // ~-1/11!
71  Vc_buildDouble( 1, 0x5d8fd1fd19ccdull, -33), // ~ 1/13!
72  0., // padding (for alignment with float)
73  Vc_buildDouble(1, 0x8BE60DB939105ull, 0), // 4/π
74  Vc_buildDouble(1, 0x921fb54442d18ull, 0), // π/2
75  Vc_buildDouble(1, 0x921fb54442d18ull, 1), // π
76  // cacheline 10
77  Vc_buildDouble(-1, 0xc007fa1f72594ull, -1), // atan P coefficients
78  Vc_buildDouble(-1, 0x028545b6b807aull, 4), // atan P coefficients
79  Vc_buildDouble(-1, 0x2c08c36880273ull, 6), // atan P coefficients
80  Vc_buildDouble(-1, 0xeb8bf2d05ba25ull, 6), // atan P coefficients
81  Vc_buildDouble(-1, 0x03669fd28ec8eull, 6), // atan P coefficients
82  Vc_buildDouble( 1, 0x8dbc45b14603cull, 4), // atan Q coefficients
83  Vc_buildDouble( 1, 0x4a0dd43b8fa25ull, 7), // atan Q coefficients
84  Vc_buildDouble( 1, 0xb0e18d2e2be3bull, 8), // atan Q coefficients
85  // cacheline 12
86  Vc_buildDouble( 1, 0xe563f13b049eaull, 8), // atan Q coefficients
87  Vc_buildDouble( 1, 0x8519efbbd62ecull, 7), // atan Q coefficients
88  Vc_buildDouble( 1, 0x3504f333f9de6ull, 1), // tan( 3/8 π )
89  0.66, // lower threshold for special casing in atan
90  Vc_buildDouble(1, 0x1A62633145C07ull, -54), // remainder of pi/2
91  1.e-8, // small asin input threshold
92  0.625, // large asin input threshold
93  0., // padding
94  // cacheline 14
95  Vc_buildDouble( 1, 0x84fc3988e9f08ull, -9), // asinCoeff0
96  Vc_buildDouble(-1, 0x2079259f9290full, -1), // asinCoeff0
97  Vc_buildDouble( 1, 0xbdff5baf33e6aull, 2), // asinCoeff0
98  Vc_buildDouble(-1, 0x991aaac01ab68ull, 4), // asinCoeff0
99  Vc_buildDouble( 1, 0xc896240f3081dull, 4), // asinCoeff0
100  Vc_buildDouble(-1, 0x5f2a2b6bf5d8cull, 4), // asinCoeff1
101  Vc_buildDouble( 1, 0x26219af6a7f42ull, 7), // asinCoeff1
102  Vc_buildDouble(-1, 0x7fe08959063eeull, 8), // asinCoeff1
103  // cacheline 16
104  Vc_buildDouble( 1, 0x56709b0b644beull, 8), // asinCoeff1
105  Vc_buildDouble( 1, 0x16b9b0bd48ad3ull, -8), // asinCoeff2
106  Vc_buildDouble(-1, 0x34341333e5c16ull, -1), // asinCoeff2
107  Vc_buildDouble( 1, 0x5c74b178a2dd9ull, 2), // asinCoeff2
108  Vc_buildDouble(-1, 0x04331de27907bull, 4), // asinCoeff2
109  Vc_buildDouble( 1, 0x39007da779259ull, 4), // asinCoeff2
110  Vc_buildDouble(-1, 0x0656c06ceafd5ull, 3), // asinCoeff2
111  Vc_buildDouble(-1, 0xd7b590b5e0eabull, 3), // asinCoeff3
112  // cacheline 18
113  Vc_buildDouble( 1, 0x19fc025fe9054ull, 6), // asinCoeff3
114  Vc_buildDouble(-1, 0x265bb6d3576d7ull, 7), // asinCoeff3
115  Vc_buildDouble( 1, 0x1705684ffbf9dull, 7), // asinCoeff3
116  Vc_buildDouble(-1, 0x898220a3607acull, 5), // asinCoeff3
117  };
118 #define _4(x) x
119  template<> const float c_trig<float>::data[] = {
120  // cacheline
121  _4(Vc_buildFloat( 1, 0x490FDB, -1)), // π/4
122  _4(Vc_buildFloat( 1, 0x491000, -1)), // π/4 - 12 bits precision
123  _4(Vc_buildFloat(-1, 0x157000, -19)), // π/4 remainder1 - 12 bits precision
124  _4(Vc_buildFloat(-1, 0x6F4B9F, -32)), // π/4 remainder2
125  _4(0.0625f),
126  _4(16.f),
127  _4(0.f), // padding
128  _4(0.f), // padding
129  _4(4.166664568298827e-2f), // ~ 1/4!
130  _4(-1.388731625493765e-3f), // ~-1/6!
131  _4(2.443315711809948e-5f), // ~ 1/8!
132  _4(0.f), // padding (for alignment with double)
133  _4(0.f), // padding (for alignment with double)
134  _4(0.f), // padding (for alignment with double)
135  _4(-1.6666654611e-1f), // ~-1/3!
136  _4(8.3321608736e-3f), // ~ 1/5!
137  // cacheline
138  _4(-1.9515295891e-4f), // ~-1/7!
139  _4(0.f), // padding (for alignment with double)
140  _4(0.f), // padding (for alignment with double)
141  _4(0.f), // padding (for alignment with double)
142  _4(8192.f), // loss threshold
143  _4(Vc_buildFloat(1, 0x22F983, 0)), // 1.27323949337005615234375 = 4/π
144  _4(Vc_buildFloat(1, 0x490FDB, 0)), // π/2
145  _4(Vc_buildFloat(1, 0x490FDB, 1)), // π
146  _4(8.05374449538e-2f), // atan P coefficients
147  _4(1.38776856032e-1f), // atan P coefficients
148  _4(1.99777106478e-1f), // atan P coefficients
149  _4(3.33329491539e-1f), // atan P coefficients
150  _4(0.f), // padding (for alignment with double)
151  _4(0.f), // padding (for alignment with double)
152  _4(0.f), // padding (for alignment with double)
153  _4(0.f), // padding (for alignment with double)
154  // cacheline
155  _4(0.f), // padding (for alignment with double)
156  _4(0.f), // padding (for alignment with double)
157  _4(2.414213562373095f), // tan( 3/8 π )
158  _4(0.414213562373095f), // tan( 1/8 π ) lower threshold for special casing in atan
159  _4(Vc_buildFloat(-1, 0x3BBD2E, -25)), // remainder of pi/2
160  _4(1.e-4f), // small asin input threshold
161  _4(0.f), // padding (for alignment with double)
162  _4(0.f), // padding (for alignment with double)
163  _4(4.2163199048e-2f), // asinCoeff0
164  _4(2.4181311049e-2f), // asinCoeff0
165  _4(4.5470025998e-2f), // asinCoeff0
166  _4(7.4953002686e-2f), // asinCoeff0
167  _4(1.6666752422e-1f), // asinCoeff0
168  _4(0.f), // padding (for alignment with double)
169  _4(0.f), // padding (for alignment with double)
170  _4(0.f), // padding (for alignment with double)
171  // cacheline
172  _4(0.f), // padding (for alignment with double)
173  _4(0.f), // padding (for alignment with double)
174  _4(0.f), // padding (for alignment with double)
175  _4(0.f), // padding (for alignment with double)
176  _4(0.f), // padding (for alignment with double)
177  _4(0.f), // padding (for alignment with double)
178  _4(0.f), // padding (for alignment with double)
179  _4(0.f), // padding (for alignment with double)
180  _4(0.f), // padding (for alignment with double)
181  _4(0.f), // padding (for alignment with double)
182  _4(0.f), // padding (for alignment with double)
183  _4(0.f), // padding (for alignment with double)
184  };
185 #undef _4
186 
187  const unsigned int c_general::absMaskFloat[2] = { 0xffffffffu, 0x7fffffffu };
188  const unsigned int c_general::signMaskFloat[2] = { 0x0u, 0x80000000u };
189  const unsigned int c_general::highMaskFloat = 0xfffff000u;
190  const float c_general::oneFloat = 1.f;
191  const unsigned short c_general::minShort[2] = { 0x8000u, 0x8000u };
192  const unsigned short c_general::one16[2] = { 1, 1 };
193  const float c_general::_2power31 = 1u << 31;
194 
195  // cacheline 4
196  const unsigned long long c_general::highMaskDouble = 0xfffffffff8000000ull;
197  const double c_general::oneDouble = 1.;
198  const unsigned long long c_general::frexpMask = 0xbfefffffffffffffull;
199 
200  const unsigned long long c_log<double>::data[21] = {
201  0x000003ff000003ffull // bias TODO: remove
202  , 0x7ff0000000000000ull // exponentMask (+inf)
203 
204  , 0x3f1ab4c293c31bb0ull // P[0]
205  , 0x3fdfd6f53f5652f2ull // P[1]
206  , 0x4012d2baed926911ull // P[2]
207  , 0x402cff72c63eeb2eull // P[3]
208  , 0x4031efd6924bc84dull // P[4]
209  , 0x401ed5637d7edcf8ull // P[5]
210 
211  , 0x40269320ae97ef8eull // Q[0]
212  , 0x40469d2c4e19c033ull // Q[1]
213  , 0x4054bf33a326bdbdull // Q[2]
214  , 0x4051c9e2eb5eae21ull // Q[3]
215  , 0x4037200a9e1f25b2ull // Q[4]
216 
217  , 0xfff0000000000000ull // -inf
218  , 0x0010000000000000ull // min()
219  , 0x3fe6a09e667f3bcdull // 1/sqrt(2)
220  , 0x3fe6300000000000ull // round(ln(2) * 512) / 512
221  , 0xbf2bd0105c610ca8ull // ln(2) - round(ln(2) * 512) / 512
222  , 0x3fe0000000000000ull // 0.5
223  , 0x3fdbcb7b1526e50eull // log10(e)
224  , 0x3ff71547652b82feull // log2(e)
225  };
226 
227  template<> const unsigned int c_log<float>::data[21] = {
228  0x0000007fu // bias TODO: remove
229  , 0x7f800000u // exponentMask (+inf)
230 
231  , 0x3d9021bbu // 7.0376836292e-2f // P[0]
232  , 0xbdebd1b8u // -1.1514610310e-1f // P[1]
233  , 0x3def251au // 1.1676998740e-1f // P[2]
234  , 0xbdfe5d4fu // -1.2420140846e-1f // P[3]
235  , 0x3e11e9bfu // 1.4249322787e-1f // P[4]
236  , 0xbe2aae50u // -1.6668057665e-1f // P[5]
237  , 0x3e4cceacu // 2.0000714765e-1f // P[6]
238  , 0xbe7ffffcu // -2.4999993993e-1f // P[7]
239  , 0x3eaaaaaau // 3.3333331174e-1f // P[8]
240  , 0 // padding because of c_log<double>
241  , 0 // padding because of c_log<double>
242 
243  , 0xff800000u // -inf
244  , 0x00800000u // min()
245  , 0x3f3504f3u // 1/sqrt(2)
246  , 0x3f318000u // round(ln(2) * 512) / 512
247  , 0xb95e8083u // ln(2) - round(ln(2) * 512) / 512
248  , 0x3f000000u // 0.5
249  , 0x3ede5bd9u // log10(e)
250  , 0x3fb8aa3bu // log2(e)
251  };
252 } // namespace AVX
253 
254 namespace SSE
255 {
256  // cacheline 1
257  V_ALIGN(64) const int c_general::absMaskFloat[4] = { 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff };
258  V_ALIGN(16) const unsigned int c_general::signMaskFloat[4] = { 0x80000000, 0x80000000, 0x80000000, 0x80000000 };
259  V_ALIGN(16) const unsigned int c_general::highMaskFloat[4] = { 0xfffff000u, 0xfffff000u, 0xfffff000u, 0xfffff000u };
260  V_ALIGN(16) const short c_general::minShort[8] = { -0x8000, -0x8000, -0x8000, -0x8000, -0x8000, -0x8000, -0x8000, -0x8000 };
261  V_ALIGN(16) extern const unsigned short _IndexesFromZero8[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
262 
263  // cacheline 2
264  V_ALIGN(16) extern const unsigned int _IndexesFromZero4[4] = { 0, 1, 2, 3 };
265  V_ALIGN(16) const unsigned short c_general::one16[8] = { 1, 1, 1, 1, 1, 1, 1, 1 };
266  V_ALIGN(16) const unsigned int c_general::one32[4] = { 1, 1, 1, 1 };
267  V_ALIGN(16) const float c_general::oneFloat[4] = { 1.f, 1.f, 1.f, 1.f };
268 
269  // cacheline 3
270  V_ALIGN(16) const unsigned long long c_general::highMaskDouble[2] = { 0xfffffffff8000000ull, 0xfffffffff8000000ull };
271  V_ALIGN(16) const double c_general::oneDouble[2] = { 1., 1. };
272  V_ALIGN(16) const long long c_general::absMaskDouble[2] = { 0x7fffffffffffffffll, 0x7fffffffffffffffll };
273  V_ALIGN(16) const unsigned long long c_general::signMaskDouble[2] = { 0x8000000000000000ull, 0x8000000000000000ull };
274  V_ALIGN(16) const unsigned long long c_general::frexpMask[2] = { 0xbfefffffffffffffull, 0xbfefffffffffffffull };
275 
276 #define _2(x) x, x
277  template<> const double c_trig<double>::data[] = {
278  // cacheline 4
279  _2(Vc_buildDouble(1, 0x921fb54442d18ull, -1)), // π/4
280  _2(Vc_buildDouble(1, 0x921fb40000000ull, -1)), // π/4 - 30bits precision
281  _2(Vc_buildDouble(1, 0x4442d00000000ull, -25)), // π/4 remainder1 - 32bits precision
282  _2(Vc_buildDouble(1, 0x8469898cc5170ull, -49)), // π/4 remainder2
283  // cacheline 5
284  _2(0.0625),
285  _2(16.),
286  _2(0.), // padding
287  _2(0.), // padding
288  // cacheline 6
289  _2(Vc_buildDouble( 1, 0x555555555554bull, -5)), // ~ 1/4!
290  _2(Vc_buildDouble(-1, 0x6c16c16c14f91ull, -10)), // ~-1/6!
291  _2(Vc_buildDouble( 1, 0xa01a019c844f5ull, -16)), // ~ 1/8!
292  _2(Vc_buildDouble(-1, 0x27e4f7eac4bc6ull, -22)), // ~-1/10!
293  // cacheline 7
294  _2(Vc_buildDouble( 1, 0x1ee9d7b4e3f05ull, -29)), // ~ 1/12!
295  _2(Vc_buildDouble(-1, 0x8fa49a0861a9bull, -37)), // ~-1/14!
296  _2(Vc_buildDouble(-1, 0x5555555555548ull, -3)), // ~-1/3!
297  _2(Vc_buildDouble( 1, 0x111111110f7d0ull, -7)), // ~ 1/5!
298  // cacheline 8
299  _2(Vc_buildDouble(-1, 0xa01a019bfdf03ull, -13)), // ~-1/7!
300  _2(Vc_buildDouble( 1, 0x71de3567d48a1ull, -19)), // ~ 1/9!
301  _2(Vc_buildDouble(-1, 0xae5e5a9291f5dull, -26)), // ~-1/11!
302  _2(Vc_buildDouble( 1, 0x5d8fd1fd19ccdull, -33)), // ~ 1/13!
303  // cacheline 9
304  _2(0.), // padding (for alignment with float)
305  _2(Vc_buildDouble(1, 0x8BE60DB939105ull, 0)), // 4/π
306  _2(Vc_buildDouble(1, 0x921fb54442d18ull, 0)), // π/2
307  _2(Vc_buildDouble(1, 0x921fb54442d18ull, 1)), // π
308  // cacheline 10
309  _2(Vc_buildDouble(-1, 0xc007fa1f72594ull, -1)), // atan P coefficients
310  _2(Vc_buildDouble(-1, 0x028545b6b807aull, 4)), // atan P coefficients
311  _2(Vc_buildDouble(-1, 0x2c08c36880273ull, 6)), // atan P coefficients
312  _2(Vc_buildDouble(-1, 0xeb8bf2d05ba25ull, 6)), // atan P coefficients
313  // cacheline 11
314  _2(Vc_buildDouble(-1, 0x03669fd28ec8eull, 6)), // atan P coefficients
315  _2(Vc_buildDouble( 1, 0x8dbc45b14603cull, 4)), // atan Q coefficients
316  _2(Vc_buildDouble( 1, 0x4a0dd43b8fa25ull, 7)), // atan Q coefficients
317  _2(Vc_buildDouble( 1, 0xb0e18d2e2be3bull, 8)), // atan Q coefficients
318  // cacheline 12
319  _2(Vc_buildDouble( 1, 0xe563f13b049eaull, 8)), // atan Q coefficients
320  _2(Vc_buildDouble( 1, 0x8519efbbd62ecull, 7)), // atan Q coefficients
321  _2(Vc_buildDouble( 1, 0x3504f333f9de6ull, 1)), // tan( 3/8 π )
322  _2(0.66), // lower threshold for special casing in atan
323  // cacheline 13
324  _2(Vc_buildDouble(1, 0x1A62633145C07ull, -54)), // remainder of pi/2
325  _2(1.e-8), // small asin input threshold
326  _2(0.625), // large asin input threshold
327  _2(0.), // padding
328  // cacheline 14
329  _2(Vc_buildDouble( 1, 0x84fc3988e9f08ull, -9)), // asinCoeff0
330  _2(Vc_buildDouble(-1, 0x2079259f9290full, -1)), // asinCoeff0
331  _2(Vc_buildDouble( 1, 0xbdff5baf33e6aull, 2)), // asinCoeff0
332  _2(Vc_buildDouble(-1, 0x991aaac01ab68ull, 4)), // asinCoeff0
333  // cacheline 15
334  _2(Vc_buildDouble( 1, 0xc896240f3081dull, 4)), // asinCoeff0
335  _2(Vc_buildDouble(-1, 0x5f2a2b6bf5d8cull, 4)), // asinCoeff1
336  _2(Vc_buildDouble( 1, 0x26219af6a7f42ull, 7)), // asinCoeff1
337  _2(Vc_buildDouble(-1, 0x7fe08959063eeull, 8)), // asinCoeff1
338  // cacheline 16
339  _2(Vc_buildDouble( 1, 0x56709b0b644beull, 8)), // asinCoeff1
340  _2(Vc_buildDouble( 1, 0x16b9b0bd48ad3ull, -8)), // asinCoeff2
341  _2(Vc_buildDouble(-1, 0x34341333e5c16ull, -1)), // asinCoeff2
342  _2(Vc_buildDouble( 1, 0x5c74b178a2dd9ull, 2)), // asinCoeff2
343  // cacheline 17
344  _2(Vc_buildDouble(-1, 0x04331de27907bull, 4)), // asinCoeff2
345  _2(Vc_buildDouble( 1, 0x39007da779259ull, 4)), // asinCoeff2
346  _2(Vc_buildDouble(-1, 0x0656c06ceafd5ull, 3)), // asinCoeff2
347  _2(Vc_buildDouble(-1, 0xd7b590b5e0eabull, 3)), // asinCoeff3
348  // cacheline 18
349  _2(Vc_buildDouble( 1, 0x19fc025fe9054ull, 6)), // asinCoeff3
350  _2(Vc_buildDouble(-1, 0x265bb6d3576d7ull, 7)), // asinCoeff3
351  _2(Vc_buildDouble( 1, 0x1705684ffbf9dull, 7)), // asinCoeff3
352  _2(Vc_buildDouble(-1, 0x898220a3607acull, 5)), // asinCoeff3
353  };
354 #undef _2
355 #define _4(x) x, x, x, x
356  template<> const float c_trig<float>::data[] = {
357  // cacheline
358  _4(Vc_buildFloat( 1, 0x490FDB, -1)), // π/4
359  _4(Vc_buildFloat( 1, 0x491000, -1)), // π/4 - 12 bits precision
360  _4(Vc_buildFloat(-1, 0x157000, -19)), // π/4 remainder1 - 12 bits precision
361  _4(Vc_buildFloat(-1, 0x6F4B9F, -32)), // π/4 remainder2
362  // cacheline
363  _4(0.0625f),
364  _4(16.f),
365  _4(0.f), // padding
366  _4(0.f), // padding
367  // cacheline
368  _4(4.166664568298827e-2f), // ~ 1/4!
369  _4(-1.388731625493765e-3f), // ~-1/6!
370  _4(2.443315711809948e-5f), // ~ 1/8!
371  _4(0.f), // padding (for alignment with double)
372  // cacheline
373  _4(0.f), // padding (for alignment with double)
374  _4(0.f), // padding (for alignment with double)
375  _4(-1.6666654611e-1f), // ~-1/3!
376  _4(8.3321608736e-3f), // ~ 1/5!
377  // cacheline
378  _4(-1.9515295891e-4f), // ~-1/7!
379  _4(0.f), // padding (for alignment with double)
380  _4(0.f), // padding (for alignment with double)
381  _4(0.f), // padding (for alignment with double)
382  // cacheline
383  _4(8192.f), // loss threshold
384  _4(Vc_buildFloat(1, 0x22F983, 0)), // 1.27323949337005615234375 = 4/π
385  _4(Vc_buildFloat(1, 0x490FDB, 0)), // π/2
386  _4(Vc_buildFloat(1, 0x490FDB, 1)), // π
387  // cacheline
388  _4(8.05374449538e-2f), // atan P coefficients
389  _4(1.38776856032e-1f), // atan P coefficients
390  _4(1.99777106478e-1f), // atan P coefficients
391  _4(3.33329491539e-1f), // atan P coefficients
392  // cacheline
393  _4(0.f), // padding (for alignment with double)
394  _4(0.f), // padding (for alignment with double)
395  _4(0.f), // padding (for alignment with double)
396  _4(0.f), // padding (for alignment with double)
397  // cacheline
398  _4(0.f), // padding (for alignment with double)
399  _4(0.f), // padding (for alignment with double)
400  _4(2.414213562373095f), // tan( 3/8 π )
401  _4(0.414213562373095f), // tan( 1/8 π ) lower threshold for special casing in atan
402  // cacheline
403  _4(Vc_buildFloat(-1, 0x3BBD2E, -25)), // remainder of pi/2
404  _4(1.e-4f), // small asin input threshold
405  _4(0.f), // padding (for alignment with double)
406  _4(0.f), // padding (for alignment with double)
407  // cacheline
408  _4(4.2163199048e-2f), // asinCoeff0
409  _4(2.4181311049e-2f), // asinCoeff0
410  _4(4.5470025998e-2f), // asinCoeff0
411  _4(7.4953002686e-2f), // asinCoeff0
412  // cacheline
413  _4(1.6666752422e-1f), // asinCoeff0
414  _4(0.f), // padding (for alignment with double)
415  _4(0.f), // padding (for alignment with double)
416  _4(0.f), // padding (for alignment with double)
417  // cacheline
418  _4(0.f), // padding (for alignment with double)
419  _4(0.f), // padding (for alignment with double)
420  _4(0.f), // padding (for alignment with double)
421  _4(0.f), // padding (for alignment with double)
422  // cacheline
423  _4(0.f), // padding (for alignment with double)
424  _4(0.f), // padding (for alignment with double)
425  _4(0.f), // padding (for alignment with double)
426  _4(0.f), // padding (for alignment with double)
427  // cacheline
428  _4(0.f), // padding (for alignment with double)
429  _4(0.f), // padding (for alignment with double)
430  _4(0.f), // padding (for alignment with double)
431  _4(0.f), // padding (for alignment with double)
432  };
433 #undef _4
434 
435  // cacheline 8
436  V_ALIGN(16) extern const unsigned char _IndexesFromZero16[16] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
437 
438  V_ALIGN(64) const unsigned long long c_log<double>::data[21 * 2] = {
439  /* 0*/ 0x000003ff000003ffull, 0x000003ff000003ffull // bias TODO: remove
440  /* 1*/ , 0x7ff0000000000000ull, 0x7ff0000000000000ull // exponentMask (+inf)
441 
442  /* 2*/ , 0x3f1ab4c293c31bb0ull, 0x3f1ab4c293c31bb0ull // P[0]
443  /* 3*/ , 0x3fdfd6f53f5652f2ull, 0x3fdfd6f53f5652f2ull // P[1]
444  /* 4*/ , 0x4012d2baed926911ull, 0x4012d2baed926911ull // P[2]
445  /* 5*/ , 0x402cff72c63eeb2eull, 0x402cff72c63eeb2eull // P[3]
446  /* 6*/ , 0x4031efd6924bc84dull, 0x4031efd6924bc84dull // P[4]
447  /* 7*/ , 0x401ed5637d7edcf8ull, 0x401ed5637d7edcf8ull // P[5]
448 
449  /* 8*/ , 0x40269320ae97ef8eull, 0x40269320ae97ef8eull // Q[0]
450  /* 9*/ , 0x40469d2c4e19c033ull, 0x40469d2c4e19c033ull // Q[1]
451  /*10*/ , 0x4054bf33a326bdbdull, 0x4054bf33a326bdbdull // Q[2]
452  /*11*/ , 0x4051c9e2eb5eae21ull, 0x4051c9e2eb5eae21ull // Q[3]
453  /*12*/ , 0x4037200a9e1f25b2ull, 0x4037200a9e1f25b2ull // Q[4]
454 
455  /*13*/ , 0xfff0000000000000ull, 0xfff0000000000000ull // -inf
456  /*14*/ , 0x0010000000000000ull, 0x0010000000000000ull // min()
457  /*15*/ , 0x3fe6a09e667f3bcdull, 0x3fe6a09e667f3bcdull // 1/sqrt(2)
458  /*16*/ , 0x3fe6300000000000ull, 0x3fe6300000000000ull // round(ln(2) * 512) / 512
459  /*17*/ , 0xbf2bd0105c610ca8ull, 0xbf2bd0105c610ca8ull // ln(2) - round(ln(2) * 512) / 512
460  /*18*/ , 0x3fe0000000000000ull, 0x3fe0000000000000ull // 0.5
461  /*19*/ , 0x3fdbcb7b1526e50eull, 0x3fdbcb7b1526e50eull // log10(e)
462  /*20*/ , 0x3ff71547652b82feull, 0x3ff71547652b82feull // log2(e)
463  };
464 
465  template<> V_ALIGN(64) const unsigned int c_log<float>::data[21 * 4] = {
466  0x0000007fu, 0x0000007fu, 0x0000007fu, 0x0000007fu, // bias TODO: remove
467  0x7f800000u, 0x7f800000u, 0x7f800000u, 0x7f800000u, // exponentMask (+inf)
468 
469  0x3d9021bbu, 0x3d9021bbu, 0x3d9021bbu, 0x3d9021bbu, // 7.0376836292e-2f // P[0]
470  0xbdebd1b8u, 0xbdebd1b8u, 0xbdebd1b8u, 0xbdebd1b8u, // -1.1514610310e-1f // P[1]
471  0x3def251au, 0x3def251au, 0x3def251au, 0x3def251au, // 1.1676998740e-1f // P[2]
472  0xbdfe5d4fu, 0xbdfe5d4fu, 0xbdfe5d4fu, 0xbdfe5d4fu, // -1.2420140846e-1f // P[3]
473  0x3e11e9bfu, 0x3e11e9bfu, 0x3e11e9bfu, 0x3e11e9bfu, // 1.4249322787e-1f // P[4]
474  0xbe2aae50u, 0xbe2aae50u, 0xbe2aae50u, 0xbe2aae50u, // -1.6668057665e-1f // P[5]
475  0x3e4cceacu, 0x3e4cceacu, 0x3e4cceacu, 0x3e4cceacu, // 2.0000714765e-1f // P[6]
476  0xbe7ffffcu, 0xbe7ffffcu, 0xbe7ffffcu, 0xbe7ffffcu, // -2.4999993993e-1f // P[7]
477  0x3eaaaaaau, 0x3eaaaaaau, 0x3eaaaaaau, 0x3eaaaaaau, // 3.3333331174e-1f // P[8]
478  0, 0, 0, 0, // padding because of c_log<double>
479  0, 0, 0, 0, // padding because of c_log<double>
480 
481  0xff800000u, 0xff800000u, 0xff800000u, 0xff800000u, // -inf
482  0x00800000u, 0x00800000u, 0x00800000u, 0x00800000u, // min()
483  0x3f3504f3u, 0x3f3504f3u, 0x3f3504f3u, 0x3f3504f3u, // 1/sqrt(2)
484  // ln(2) = 0x3fe62e42fefa39ef
485  // ln(2) = Vc_buildDouble( 1, 0x00062e42fefa39ef, -1)
486  // = Vc_buildFloat( 1, 0x00317217(f7d), -1) + Vc_buildFloat( 1, 0x0077d1cd, -25)
487  // = Vc_buildFloat( 1, 0x00318000(000), -1) + Vc_buildFloat(-1, 0x005e8083, -13)
488  0x3f318000u, 0x3f318000u, 0x3f318000u, 0x3f318000u, // round(ln(2) * 512) / 512
489  0xb95e8083u, 0xb95e8083u, 0xb95e8083u, 0xb95e8083u, // ln(2) - round(ln(2) * 512) / 512
490  0x3f000000u, 0x3f000000u, 0x3f000000u, 0x3f000000u, // 0.5
491  0x3ede5bd9u, 0x3ede5bd9u, 0x3ede5bd9u, 0x3ede5bd9u, // log10(e)
492  0x3fb8aa3bu, 0x3fb8aa3bu, 0x3fb8aa3bu, 0x3fb8aa3bu, // log2(e)
493  // log10(2) = 0x3fd34413509f79ff
494  // = Vc_buildDouble( 1, 0x00034413509f79ff, -2)
495  // = Vc_buildFloat( 1, 0x001a209a(84fbcff8), -2) + Vc_buildFloat( 1, 0x0004fbcff(8), -26)
496  //Vc_buildFloat( 1, 0x001a209a, -2), // log10(2)
497  //Vc_buildFloat( 1, 0x001a209a, -2), // log10(2)
498  //Vc_buildFloat( 1, 0x001a209a, -2), // log10(2)
499  //Vc_buildFloat( 1, 0x001a209a, -2), // log10(2)
500  };
501 } // namespace SSE
502 
503 V_ALIGN(64) unsigned int RandomState[16] = {
504  0x5a383a4fu, 0xc68bd45eu, 0x691d6d86u, 0xb367e14fu,
505  0xd689dbaau, 0xfde442aau, 0x3d265423u, 0x1a77885cu,
506  0x36ed2684u, 0xfb1f049du, 0x19e52f31u, 0x821e4dd7u,
507  0x23996d25u, 0x5962725au, 0x6aced4ceu, 0xd4c610f3u
508 };
509 
510 // dummy symbol to emit warnings with GCC 4.3
511 namespace Warnings {
512  void _operator_bracket_warning() {}
513 } // namespace Warnings
514 
515 const char LIBRARY_VERSION[] = VC_VERSION_STRING;
516 const unsigned int LIBRARY_VERSION_NUMBER = VC_VERSION_NUMBER;
517 const unsigned int LIBRARY_ABI_VERSION = VC_LIBRARY_ABI_VERSION;
518 
519 void checkLibraryAbi(unsigned int compileTimeAbi, unsigned int versionNumber, const char *compileTimeVersion) {
520  if (LIBRARY_ABI_VERSION != compileTimeAbi || LIBRARY_VERSION_NUMBER < versionNumber) {
521  printf("The versions of libVc.a (%s) and Vc/version.h (%s) are incompatible. Aborting.\n", LIBRARY_VERSION, compileTimeVersion);
522  abort();
523  }
524 }
525 
526 } // namespace Vc
527 } // namespace ROOT
528 
529 #undef V_ALIGN
ROOT
Namespace for new ROOT classes and functions.
Definition: ROOT.py:1
const_data.h
ROOT::Vc::AVX::V_ALIGN
V_ALIGN(64) extern const unsigned int _IndexesFromZero32[8]
Definition: const.cpp:257
ROOT::Vc::LIBRARY_ABI_VERSION
const unsigned int LIBRARY_ABI_VERSION
Definition: const.cpp:517
ROOT::Vc::checkLibraryAbi
void checkLibraryAbi(unsigned int compileTimeAbi, unsigned int versionNumber, const char *versionString)
Definition: const.cpp:519
ROOT::Vc::LIBRARY_VERSION_NUMBER
const unsigned int LIBRARY_VERSION_NUMBER
Definition: const.cpp:516
ROOT::Vc::LIBRARY_VERSION
const char LIBRARY_VERSION[]
Definition: const.cpp:515
ROOT::Vc::AVX::c_trig
Definition: const_data.h:48
VC_LIBRARY_ABI_VERSION
#define VC_LIBRARY_ABI_VERSION
Definition: version.h:26
ROOT::Vc::Warnings::_operator_bracket_warning
void _operator_bracket_warning()
Definition: const.cpp:512
VC_VERSION_STRING
#define VC_VERSION_STRING
Definition: version.h:23
ROOT::Vc::versionNumber
static unsigned int versionNumber()
Definition: version.h:35
_2
#define _2(x)
Definition: const.cpp:276
ROOT::Vc::AVX::c_log
Definition: const_data.h:53
AVX
#define AVX
Definition: global.h:90
ROOT::Vc::V_ALIGN
V_ALIGN(64) unsigned int RandomState[16]
RooFit::Warnings
RooCmdArg Warnings(Bool_t flag=kTRUE)
Definition: RooGlobalFunc.cxx:187
Vc_buildDouble
#define Vc_buildDouble(sign, mantissa, exponent)
Definition: macros.h:283
const_data.h
ROOT::Vc::SSE::c_trig
Definition: const_data.h:52
ROOT::Vc::SSE::c_general
Definition: const_data.h:35
Vc_buildFloat
#define Vc_buildFloat(sign, mantissa, exponent)
Definition: macros.h:294
f
double f(double x)
Definition: testIntegration.cxx:12
printf
ClassImp(TMCParticle) void TMCParticle printf(": p=(%7.3f,%7.3f,%9.3f) ;", fPx, fPy, fPz)
SSE
#define SSE
Definition: global.h:84
_4
#define _4(x)
Definition: const.cpp:355
ROOT::Vc
Definition: casts.h:28
VC_VERSION_NUMBER
#define VC_VERSION_NUMBER
Definition: version.h:24
ROOT::Vc::SSE::V_ALIGN
V_ALIGN(64) const int c_general
Definition: const.cpp:257