GADGET-4
peano.cc
Go to the documentation of this file.
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#include "gadgetconfig.h"
13
14#include <math.h>
15#include <mpi.h>
16#include <stdio.h>
17#include <stdlib.h>
18#include <string.h>
19#include <algorithm>
20
21#include "../data/allvars.h"
22#include "../data/dtypes.h"
23#include "../data/mymalloc.h"
24#include "../logs/timer.h"
25#include "../main/simulation.h"
26#include "../sort/cxxsort.h"
27#include "../sort/peano.h"
28#include "../system/system.h"
29
30namespace
31{
32struct peano_hilbert_data
33{
34 peanokey key;
35 int index;
36};
37
38/*
39struct peano_comparator
40{
41bool operator() (const peano_hilbert_data & a, const peano_hilbert_data & b)
42{
43 return a.key < b.key;
44}
45};
46*/
47
48const unsigned char rottable3[48][8] = {
49 {36, 28, 25, 27, 10, 10, 25, 27}, {29, 11, 24, 24, 37, 11, 26, 26}, {8, 8, 25, 27, 30, 38, 25, 27},
50 {9, 39, 24, 24, 9, 31, 26, 26}, {40, 24, 44, 32, 40, 6, 44, 6}, {25, 7, 33, 7, 41, 41, 45, 45},
51 {4, 42, 4, 46, 26, 42, 34, 46}, {43, 43, 47, 47, 5, 27, 5, 35}, {33, 35, 36, 28, 33, 35, 2, 2},
52 {32, 32, 29, 3, 34, 34, 37, 3}, {33, 35, 0, 0, 33, 35, 30, 38}, {32, 32, 1, 39, 34, 34, 1, 31},
53 {24, 42, 32, 46, 14, 42, 14, 46}, {43, 43, 47, 47, 25, 15, 33, 15}, {40, 12, 44, 12, 40, 26, 44, 34},
54 {13, 27, 13, 35, 41, 41, 45, 45}, {28, 41, 28, 22, 38, 43, 38, 22}, {42, 40, 23, 23, 29, 39, 29, 39},
55 {41, 36, 20, 36, 43, 30, 20, 30}, {37, 31, 37, 31, 42, 40, 21, 21}, {28, 18, 28, 45, 38, 18, 38, 47},
56 {19, 19, 46, 44, 29, 39, 29, 39}, {16, 36, 45, 36, 16, 30, 47, 30}, {37, 31, 37, 31, 17, 17, 46, 44},
57 {12, 4, 1, 3, 34, 34, 1, 3}, {5, 35, 0, 0, 13, 35, 2, 2}, {32, 32, 1, 3, 6, 14, 1, 3},
58 {33, 15, 0, 0, 33, 7, 2, 2}, {16, 0, 20, 8, 16, 30, 20, 30}, {1, 31, 9, 31, 17, 17, 21, 21},
59 {28, 18, 28, 22, 2, 18, 10, 22}, {19, 19, 23, 23, 29, 3, 29, 11}, {9, 11, 12, 4, 9, 11, 26, 26},
60 {8, 8, 5, 27, 10, 10, 13, 27}, {9, 11, 24, 24, 9, 11, 6, 14}, {8, 8, 25, 15, 10, 10, 25, 7},
61 {0, 18, 8, 22, 38, 18, 38, 22}, {19, 19, 23, 23, 1, 39, 9, 39}, {16, 36, 20, 36, 16, 2, 20, 10},
62 {37, 3, 37, 11, 17, 17, 21, 21}, {4, 17, 4, 46, 14, 19, 14, 46}, {18, 16, 47, 47, 5, 15, 5, 15},
63 {17, 12, 44, 12, 19, 6, 44, 6}, {13, 7, 13, 7, 18, 16, 45, 45}, {4, 42, 4, 21, 14, 42, 14, 23},
64 {43, 43, 22, 20, 5, 15, 5, 15}, {40, 12, 21, 12, 40, 6, 23, 6}, {13, 7, 13, 7, 41, 41, 22, 20}};
65
66const unsigned char subpix3[48][8] = {
67 {0, 7, 1, 6, 3, 4, 2, 5}, {7, 4, 6, 5, 0, 3, 1, 2}, {4, 3, 5, 2, 7, 0, 6, 1}, {3, 0, 2, 1, 4, 7, 5, 6}, {1, 0, 6, 7, 2, 3, 5, 4},
68 {0, 3, 7, 4, 1, 2, 6, 5}, {3, 2, 4, 5, 0, 1, 7, 6}, {2, 1, 5, 6, 3, 0, 4, 7}, {6, 1, 7, 0, 5, 2, 4, 3}, {1, 2, 0, 3, 6, 5, 7, 4},
69 {2, 5, 3, 4, 1, 6, 0, 7}, {5, 6, 4, 7, 2, 1, 3, 0}, {7, 6, 0, 1, 4, 5, 3, 2}, {6, 5, 1, 2, 7, 4, 0, 3}, {5, 4, 2, 3, 6, 7, 1, 0},
70 {4, 7, 3, 0, 5, 6, 2, 1}, {6, 7, 5, 4, 1, 0, 2, 3}, {7, 0, 4, 3, 6, 1, 5, 2}, {0, 1, 3, 2, 7, 6, 4, 5}, {1, 6, 2, 5, 0, 7, 3, 4},
71 {2, 3, 1, 0, 5, 4, 6, 7}, {3, 4, 0, 7, 2, 5, 1, 6}, {4, 5, 7, 6, 3, 2, 0, 1}, {5, 2, 6, 1, 4, 3, 7, 0}, {7, 0, 6, 1, 4, 3, 5, 2},
72 {0, 3, 1, 2, 7, 4, 6, 5}, {3, 4, 2, 5, 0, 7, 1, 6}, {4, 7, 5, 6, 3, 0, 2, 1}, {6, 7, 1, 0, 5, 4, 2, 3}, {7, 4, 0, 3, 6, 5, 1, 2},
73 {4, 5, 3, 2, 7, 6, 0, 1}, {5, 6, 2, 1, 4, 7, 3, 0}, {1, 6, 0, 7, 2, 5, 3, 4}, {6, 5, 7, 4, 1, 2, 0, 3}, {5, 2, 4, 3, 6, 1, 7, 0},
74 {2, 1, 3, 0, 5, 6, 4, 7}, {0, 1, 7, 6, 3, 2, 4, 5}, {1, 2, 6, 5, 0, 3, 7, 4}, {2, 3, 5, 4, 1, 0, 6, 7}, {3, 0, 4, 7, 2, 1, 5, 6},
75 {1, 0, 2, 3, 6, 7, 5, 4}, {0, 7, 3, 4, 1, 6, 2, 5}, {7, 6, 4, 5, 0, 1, 3, 2}, {6, 1, 5, 2, 7, 0, 4, 3}, {5, 4, 6, 7, 2, 3, 1, 0},
76 {4, 3, 7, 0, 5, 2, 6, 1}, {3, 2, 0, 1, 4, 5, 7, 6}, {2, 5, 1, 6, 3, 4, 0, 7}};
77
78} // unnamed namespace
79
83peanokey peano_hilbert_key(MyIntPosType x, MyIntPosType y, MyIntPosType z, int bits)
84{
85 unsigned char rotation = 0;
86 peanokey key = {0, 0, 0};
87
88 for(MyIntPosType mask = ((MyIntPosType)1) << (bits - 1); mask > 0; mask >>= 1)
89 {
90 unsigned char pix = ((x & mask) ? 4 : 0) | ((y & mask) ? 2 : 0) | ((z & mask) ? 1 : 0);
91
92 key.hs <<= 3;
93 key.hs |= (key.is & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
94
95 key.is <<= 3;
96 key.is |= (key.ls & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
97
98 key.ls <<= 3;
99 key.ls |= subpix3[rotation][pix];
100
101 rotation = rottable3[rotation][pix];
102 }
103
104 return key;
105}
106
107unsigned char peano_incremental_key(unsigned char pix, unsigned char *rotation)
108{
109 unsigned char outpix = subpix3[*rotation][pix];
110 *rotation = rottable3[*rotation][pix];
111
112 return outpix;
113}
114
115const unsigned char irottable3[48][8] = {
116 {28, 27, 27, 10, 10, 25, 25, 36}, {29, 24, 24, 11, 11, 26, 26, 37}, {30, 25, 25, 8, 8, 27, 27, 38},
117 {31, 26, 26, 9, 9, 24, 24, 39}, {32, 44, 44, 6, 6, 40, 40, 24}, {33, 45, 45, 7, 7, 41, 41, 25},
118 {34, 46, 46, 4, 4, 42, 42, 26}, {35, 47, 47, 5, 5, 43, 43, 27}, {36, 33, 33, 2, 2, 35, 35, 28},
119 {37, 34, 34, 3, 3, 32, 32, 29}, {38, 35, 35, 0, 0, 33, 33, 30}, {39, 32, 32, 1, 1, 34, 34, 31},
120 {24, 42, 42, 14, 14, 46, 46, 32}, {25, 43, 43, 15, 15, 47, 47, 33}, {26, 40, 40, 12, 12, 44, 44, 34},
121 {27, 41, 41, 13, 13, 45, 45, 35}, {41, 28, 28, 22, 22, 38, 38, 43}, {42, 29, 29, 23, 23, 39, 39, 40},
122 {43, 30, 30, 20, 20, 36, 36, 41}, {40, 31, 31, 21, 21, 37, 37, 42}, {47, 38, 38, 18, 18, 28, 28, 45},
123 {44, 39, 39, 19, 19, 29, 29, 46}, {45, 36, 36, 16, 16, 30, 30, 47}, {46, 37, 37, 17, 17, 31, 31, 44},
124 {12, 1, 1, 34, 34, 3, 3, 4}, {13, 2, 2, 35, 35, 0, 0, 5}, {14, 3, 3, 32, 32, 1, 1, 6},
125 {15, 0, 0, 33, 33, 2, 2, 7}, {0, 16, 16, 30, 30, 20, 20, 8}, {1, 17, 17, 31, 31, 21, 21, 9},
126 {2, 18, 18, 28, 28, 22, 22, 10}, {3, 19, 19, 29, 29, 23, 23, 11}, {4, 11, 11, 26, 26, 9, 9, 12},
127 {5, 8, 8, 27, 27, 10, 10, 13}, {6, 9, 9, 24, 24, 11, 11, 14}, {7, 10, 10, 25, 25, 8, 8, 15},
128 {8, 22, 22, 38, 38, 18, 18, 0}, {9, 23, 23, 39, 39, 19, 19, 1}, {10, 20, 20, 36, 36, 16, 16, 2},
129 {11, 21, 21, 37, 37, 17, 17, 3}, {19, 14, 14, 46, 46, 4, 4, 17}, {16, 15, 15, 47, 47, 5, 5, 18},
130 {17, 12, 12, 44, 44, 6, 6, 19}, {18, 13, 13, 45, 45, 7, 7, 16}, {21, 4, 4, 42, 42, 14, 14, 23},
131 {22, 5, 5, 43, 43, 15, 15, 20}, {23, 6, 6, 40, 40, 12, 12, 21}, {20, 7, 7, 41, 41, 13, 13, 22}};
132
133const unsigned char ipixtable3[48][8] = {
134 {1, 3, 7, 5, 4, 6, 2, 0}, {0, 2, 3, 1, 5, 7, 6, 4}, {4, 6, 2, 0, 1, 3, 7, 5}, {5, 7, 6, 4, 0, 2, 3, 1}, {3, 2, 6, 7, 5, 4, 0, 1},
135 {2, 6, 7, 3, 1, 5, 4, 0}, {6, 7, 3, 2, 0, 1, 5, 4}, {7, 3, 2, 6, 4, 0, 1, 5}, {2, 0, 4, 6, 7, 5, 1, 3}, {6, 4, 5, 7, 3, 1, 0, 2},
136 {7, 5, 1, 3, 2, 0, 4, 6}, {3, 1, 0, 2, 6, 4, 5, 7}, {0, 1, 5, 4, 6, 7, 3, 2}, {4, 0, 1, 5, 7, 3, 2, 6}, {5, 4, 0, 1, 3, 2, 6, 7},
137 {1, 5, 4, 0, 2, 6, 7, 3}, {1, 0, 2, 3, 7, 6, 4, 5}, {0, 4, 6, 2, 3, 7, 5, 1}, {4, 5, 7, 6, 2, 3, 1, 0}, {5, 1, 3, 7, 6, 2, 0, 4},
138 {7, 6, 4, 5, 1, 0, 2, 3}, {3, 7, 5, 1, 0, 4, 6, 2}, {2, 3, 1, 0, 4, 5, 7, 6}, {6, 2, 0, 4, 5, 1, 3, 7}, {0, 2, 6, 4, 5, 7, 3, 1},
139 {4, 6, 7, 5, 1, 3, 2, 0}, {5, 7, 3, 1, 0, 2, 6, 4}, {1, 3, 2, 0, 4, 6, 7, 5}, {1, 0, 4, 5, 7, 6, 2, 3}, {0, 4, 5, 1, 3, 7, 6, 2},
140 {4, 5, 1, 0, 2, 3, 7, 6}, {5, 1, 0, 4, 6, 2, 3, 7}, {3, 1, 5, 7, 6, 4, 0, 2}, {2, 0, 1, 3, 7, 5, 4, 6}, {6, 4, 0, 2, 3, 1, 5, 7},
141 {7, 5, 4, 6, 2, 0, 1, 3}, {2, 3, 7, 6, 4, 5, 1, 0}, {6, 2, 3, 7, 5, 1, 0, 4}, {7, 6, 2, 3, 1, 0, 4, 5}, {3, 7, 6, 2, 0, 4, 5, 1},
142 {5, 4, 6, 7, 3, 2, 0, 1}, {1, 5, 7, 3, 2, 6, 4, 0}, {0, 1, 3, 2, 6, 7, 5, 4}, {4, 0, 2, 6, 7, 3, 1, 5}, {3, 2, 0, 1, 5, 4, 6, 7},
143 {2, 6, 4, 0, 1, 5, 7, 3}, {6, 7, 5, 4, 0, 1, 3, 2}, {7, 3, 1, 5, 4, 0, 2, 6},
144};
145
146void peano_hilbert_key_inverse(peanokey key, int bits, MyIntPosType *x, MyIntPosType *y, MyIntPosType *z)
147{
148 for(int i = bits; i < BITS_FOR_POSITIONS; i++)
149 {
150 key.hs <<= 3;
151 key.hs |= (key.is & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
152
153 key.is <<= 3;
154 key.is |= (key.ls & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
155
156 key.ls <<= 3;
157 }
158
159 int rot = 24;
160
161 *x = *y = *z = 0;
162
163 for(int i = 0; i < bits; i++)
164 {
165 unsigned int keypart = (key.hs & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
166
167 int quad = ipixtable3[rot][keypart];
168
169 *x = (*x << 1) + (quad >> 2);
170 *y = (*y << 1) + ((quad & 2) >> 1);
171 *z = (*z << 1) + (quad & 1);
172 rot = irottable3[rot][keypart];
173
174 key.hs <<= 3;
175 key.hs |= (key.is & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
176
177 key.is <<= 3;
178 key.is |= (key.ls & (~((~((MyIntPosType)0)) >> 3))) >> (BITS_FOR_POSITIONS - 3);
179
180 key.ls <<= 3;
181 }
182}
peanokey::hs
MyIntPosType hs
Definition: dtypes.h:210
peanokey::is
MyIntPosType is
Definition: dtypes.h:210
peanokey::ls
MyIntPosType ls
Definition: dtypes.h:210
MyIntPosType
uint32_t MyIntPosType
Definition: dtypes.h:35
BITS_FOR_POSITIONS
#define BITS_FOR_POSITIONS
Definition: dtypes.h:37
peano_hilbert_key_inverse
void peano_hilbert_key_inverse(peanokey key, int bits, MyIntPosType *x, MyIntPosType *y, MyIntPosType *z)
Definition: peano.cc:146
peano_incremental_key
unsigned char peano_incremental_key(unsigned char pix, unsigned char *rotation)
Definition: peano.cc:107
peano_hilbert_key
peanokey peano_hilbert_key(MyIntPosType x, MyIntPosType y, MyIntPosType z, int bits)
Definition: peano.cc:83
irottable3
const unsigned char irottable3[48][8]
Definition: peano.cc:115
ipixtable3
const unsigned char ipixtable3[48][8]
Definition: peano.cc:133