forked from mirror/toddcox-faster
refactor into cmake project, tweak api
This commit is contained in:
4
.gitignore
vendored
Normal file
4
.gitignore
vendored
Normal file
@@ -0,0 +1,4 @@
|
||||
.idea
|
||||
|
||||
*.[oa]
|
||||
cmake-build*
|
||||
11
CMakeLists.txt
Normal file
11
CMakeLists.txt
Normal file
@@ -0,0 +1,11 @@
|
||||
cmake_minimum_required(VERSION 3.10)
|
||||
project(toddcox-faster)
|
||||
|
||||
add_library(tc STATIC
|
||||
src/groups.cpp
|
||||
src/solve.cpp
|
||||
src/core.cpp)
|
||||
|
||||
target_include_directories(tc PUBLIC include)
|
||||
|
||||
add_subdirectory(example)
|
||||
5
example/CMakeLists.txt
Normal file
5
example/CMakeLists.txt
Normal file
@@ -0,0 +1,5 @@
|
||||
add_executable(bench bench.cpp)
|
||||
target_link_libraries(bench PRIVATE tc)
|
||||
|
||||
add_executable(path path.cpp)
|
||||
target_link_libraries(path PRIVATE tc)
|
||||
35
example/bench.cpp
Normal file
35
example/bench.cpp
Normal file
@@ -0,0 +1,35 @@
|
||||
#include "tc/core.hpp"
|
||||
#include "tc/groups.hpp"
|
||||
|
||||
#include <ctime>
|
||||
#include <vector>
|
||||
#include <iostream>
|
||||
|
||||
int main() {
|
||||
std::vector<tc::Group> groups = {
|
||||
tc::group::H(2),
|
||||
tc::group::H(3),
|
||||
tc::group::H(4),
|
||||
tc::group::T(100),
|
||||
tc::group::T(500),
|
||||
tc::group::T(1000),
|
||||
tc::group::E(6),
|
||||
tc::group::E(7),
|
||||
tc::group::B(6),
|
||||
tc::group::B(7),
|
||||
tc::group::B(8),
|
||||
};
|
||||
|
||||
for (const auto &group : groups) {
|
||||
auto s = std::clock(); // to measure CPU time
|
||||
auto cosets = group.solve();
|
||||
auto e = std::clock();
|
||||
|
||||
double diff = (double) (e - s) / CLOCKS_PER_SEC;
|
||||
int order = cosets.size();
|
||||
|
||||
std::cout << group.name << "," << order << "," << diff << std::endl;
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
17
example/path.cpp
Normal file
17
example/path.cpp
Normal file
@@ -0,0 +1,17 @@
|
||||
#include "tc/solver.h"
|
||||
#include "tc/groups.h"
|
||||
|
||||
#include <ctime>
|
||||
#include <iostream>
|
||||
|
||||
int main() {
|
||||
auto cube = tc::group::B(3);
|
||||
auto vars = tc::solve(cube, {});
|
||||
|
||||
for (int target = 1; target < vars.len; target++) {
|
||||
auto &action = vars.path[target];
|
||||
std::cout << action.coset << " " << action.gen << " " << target << std::endl;
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
52
groups.cpp
52
groups.cpp
@@ -1,52 +0,0 @@
|
||||
#include "solver.cpp"
|
||||
|
||||
Group A(const int n) {
|
||||
if (n == 0)
|
||||
return Group(0);
|
||||
|
||||
return Group::schlafli(std::vector<int>(n-1,3));
|
||||
}
|
||||
|
||||
Group B(const int n) {
|
||||
std::vector<int> mults(n-1,3);
|
||||
mults[0] = 4;
|
||||
return Group::schlafli(mults);
|
||||
}
|
||||
|
||||
Group D(const int n) {
|
||||
std::vector<int> mults(n-1,3);
|
||||
mults[n-2] = 2;
|
||||
Group g = Group::schlafli(mults);
|
||||
g.setmult({1,n-1,3});
|
||||
return g;
|
||||
}
|
||||
|
||||
Group E(const int n) {
|
||||
std::vector<int> mults(n-1,3);
|
||||
mults[n-2] = 2;
|
||||
Group g = Group::schlafli(mults);
|
||||
g.setmult({2,n-1,3});
|
||||
return g;
|
||||
}
|
||||
|
||||
Group F4() {
|
||||
return Group::schlafli({3,4,3});
|
||||
}
|
||||
|
||||
Group G2() {
|
||||
return Group::schlafli({6});
|
||||
}
|
||||
|
||||
Group H(const int n) {
|
||||
std::vector<int> mults(n-1,3);
|
||||
mults[0] = 5;
|
||||
return Group::schlafli(mults);
|
||||
}
|
||||
|
||||
Group I2(const int n) {
|
||||
return Group::schlafli({n});
|
||||
}
|
||||
|
||||
Group T(const int n) {
|
||||
return I2(n)^2;
|
||||
}
|
||||
80
include/tc/core.hpp
Normal file
80
include/tc/core.hpp
Normal file
@@ -0,0 +1,80 @@
|
||||
#pragma once
|
||||
|
||||
#include<array>
|
||||
#include<vector>
|
||||
#include<string>
|
||||
|
||||
namespace tc {
|
||||
struct Action {
|
||||
int coset = -1;
|
||||
int gen = -1;
|
||||
int target = -1;
|
||||
|
||||
Action() = default;
|
||||
|
||||
Action(const Action &) = default;
|
||||
|
||||
Action(int coset, int gen, int target);
|
||||
};
|
||||
|
||||
struct Cosets {
|
||||
int ngens;
|
||||
std::vector<int> data;
|
||||
std::vector<Action> path;
|
||||
|
||||
Cosets(const Cosets &) = default;
|
||||
|
||||
explicit Cosets(int ngens);
|
||||
|
||||
void add_row();
|
||||
|
||||
void put(int coset, int gen, int target);
|
||||
|
||||
void put(int idx, int target);
|
||||
|
||||
[[nodiscard]] int get(int coset, int gen) const;
|
||||
|
||||
[[nodiscard]] int get(int idx) const;
|
||||
|
||||
[[nodiscard]] size_t size() const;
|
||||
};
|
||||
|
||||
struct Rel {
|
||||
std::array<int, 2> gens;
|
||||
int mult;
|
||||
|
||||
Rel() = default;
|
||||
|
||||
Rel(const Rel &) = default;
|
||||
|
||||
Rel(int a, int b, int m);
|
||||
|
||||
[[nodiscard]] Rel shift(int off) const;
|
||||
};
|
||||
|
||||
struct Group {
|
||||
const int ngens;
|
||||
std::vector<std::vector<int>> _mults;
|
||||
std::string name;
|
||||
|
||||
Group(const Group &) = default;
|
||||
|
||||
explicit Group(int ngens, const std::vector<Rel> &rels = {}, std::string name = "G");
|
||||
|
||||
void set(const Rel &r);
|
||||
|
||||
[[nodiscard]] int get(int a, int b) const;
|
||||
|
||||
[[nodiscard]] std::vector<Rel> rels() const;
|
||||
|
||||
[[nodiscard]] Group product(const Group &other) const;
|
||||
|
||||
[[nodiscard]] Group power(int p) const;
|
||||
|
||||
[[nodiscard]] Cosets solve(const std::vector<int>& sub_gens = {}) const;
|
||||
};
|
||||
|
||||
Group operator*(const Group &g, const Group &h);
|
||||
|
||||
Group operator^(const Group &g, int p);
|
||||
}
|
||||
70
include/tc/groups.hpp
Normal file
70
include/tc/groups.hpp
Normal file
@@ -0,0 +1,70 @@
|
||||
#pragma once
|
||||
|
||||
#include "core.hpp"
|
||||
|
||||
|
||||
namespace tc {
|
||||
/**
|
||||
* Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
|
||||
* @param mults: The sequence of multiplicites between adjacent generators.
|
||||
*/
|
||||
Group schlafli(const std::vector<int> &mults, const std::string &name);
|
||||
|
||||
/**
|
||||
* Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
|
||||
* @param mults: The sequence of multiplicites between adjacent generators.
|
||||
*/
|
||||
Group schlafli(const std::vector<int> &mults);
|
||||
|
||||
namespace group {
|
||||
/**
|
||||
* Simplex
|
||||
*/
|
||||
Group A(int dim);
|
||||
|
||||
/**
|
||||
* Cube, Orthoplex
|
||||
*/
|
||||
Group B(int dim);
|
||||
|
||||
/**
|
||||
* Demicube, Orthoplex
|
||||
*/
|
||||
Group D(int dim);
|
||||
|
||||
/**
|
||||
* E groups
|
||||
*/
|
||||
Group E(int dim);
|
||||
|
||||
/**
|
||||
* 24 Cell
|
||||
*/
|
||||
Group F4();
|
||||
|
||||
/**
|
||||
* Hexagon
|
||||
*/
|
||||
Group G2();
|
||||
|
||||
/**
|
||||
* Icosahedron
|
||||
*/
|
||||
Group H(int dim);
|
||||
|
||||
/**
|
||||
* Polygonal
|
||||
*/
|
||||
Group I2(int n);
|
||||
|
||||
/**
|
||||
* Toroidal. I2(n) * I2(m)
|
||||
*/
|
||||
Group T(int n, int m);
|
||||
|
||||
/**
|
||||
* Toroidal. T(n, n)
|
||||
*/
|
||||
Group T(int n);
|
||||
}
|
||||
}
|
||||
290
solver.cpp
290
solver.cpp
@@ -1,290 +0,0 @@
|
||||
#include <vector>
|
||||
#include <algorithm>
|
||||
#include <queue>
|
||||
#include <utility>
|
||||
#include <functional>
|
||||
#include <iostream>
|
||||
|
||||
struct Cosets {
|
||||
int ngens;
|
||||
std::vector<int> data;
|
||||
int len;
|
||||
|
||||
Cosets(int ngens, std::vector<int> data): ngens(ngens), data(data) {
|
||||
len = data.size() / ngens;
|
||||
}
|
||||
|
||||
void add_row() {
|
||||
len++;
|
||||
data.resize(data.size()+ngens, -1);
|
||||
}
|
||||
|
||||
void put(int coset, int gen, int target) {
|
||||
data[coset * ngens + gen] = target;
|
||||
data[target * ngens + gen] = coset;
|
||||
}
|
||||
|
||||
void put(int idx, int target) {
|
||||
int coset = idx / ngens;
|
||||
int gen = idx % ngens;
|
||||
data[idx] = target;
|
||||
data[target * ngens + gen] = coset;
|
||||
}
|
||||
|
||||
int get(int coset, int gen) {
|
||||
return data[coset * ngens + gen];
|
||||
}
|
||||
|
||||
int get(int idx) {
|
||||
return data[idx];
|
||||
}
|
||||
};
|
||||
|
||||
struct Mult {
|
||||
int gen0, gen1, mult;
|
||||
};
|
||||
|
||||
struct RelTablesRow {
|
||||
int* gnrs;
|
||||
int** lst_ptrs;
|
||||
RelTablesRow (int N, int* gnrs, int** lst_ptrs): gnrs(gnrs), lst_ptrs(lst_ptrs) {
|
||||
for (int i = 0; i < N; i++) {
|
||||
lst_ptrs[i] = nullptr;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
struct TableInfo {
|
||||
int gens[2];
|
||||
int mult;
|
||||
TableInfo(Mult m) {
|
||||
gens[0] = m.gen0;
|
||||
gens[1] = m.gen1;
|
||||
mult = m.mult;
|
||||
}
|
||||
};
|
||||
|
||||
struct RelTables {
|
||||
static const int ROW_BLOCK_SIZE = 128;
|
||||
std::vector<TableInfo> table_info;
|
||||
std::vector<RelTablesRow*> rows;
|
||||
int start = 0;
|
||||
int num_tables;
|
||||
int buffer_rows = 0;
|
||||
|
||||
RelTables (std::vector<Mult> mults): num_tables(mults.size()) {
|
||||
for (Mult m : mults) {
|
||||
table_info.emplace_back(m);
|
||||
}
|
||||
}
|
||||
|
||||
void add_row() {
|
||||
if (buffer_rows == 0) {
|
||||
int* gnrs_alloc = new int[num_tables*RelTables::ROW_BLOCK_SIZE];
|
||||
int** lst_ptrs_alloc = new int*[num_tables*RelTables::ROW_BLOCK_SIZE];
|
||||
for (int i = 0; i < RelTables::ROW_BLOCK_SIZE; i++) {
|
||||
rows.push_back(new RelTablesRow(num_tables, &gnrs_alloc[i*num_tables], &lst_ptrs_alloc[i*num_tables]));
|
||||
}
|
||||
buffer_rows = RelTables::ROW_BLOCK_SIZE;
|
||||
}
|
||||
|
||||
buffer_rows--;
|
||||
}
|
||||
|
||||
void del_rows_to(int idx) {
|
||||
const int del_to = (idx/RelTables::ROW_BLOCK_SIZE)*RelTables::ROW_BLOCK_SIZE;
|
||||
for (int i = start; i < del_to; i += RelTables::ROW_BLOCK_SIZE) {
|
||||
delete[] rows[i]->gnrs;
|
||||
delete[] rows[i]->lst_ptrs;
|
||||
for (int j = 0; j < RelTables::ROW_BLOCK_SIZE; j++) {
|
||||
delete rows[i+j];
|
||||
}
|
||||
start += RelTables::ROW_BLOCK_SIZE;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
struct Group {
|
||||
int ngens;
|
||||
std::vector<std::vector<int>> _mults;
|
||||
|
||||
Group(int ngens, std::vector<Mult> rels = {}): ngens(ngens) {
|
||||
_mults.resize(ngens);
|
||||
for (int i = 0; i < ngens; i++) {
|
||||
_mults[i].resize(ngens, 2);
|
||||
}
|
||||
|
||||
for (Mult m : rels) {
|
||||
if (m.gen0 < m.gen1)
|
||||
_mults[m.gen0][m.gen1] = m.mult;
|
||||
else
|
||||
_mults[m.gen1][m.gen0] = m.mult;
|
||||
}
|
||||
}
|
||||
|
||||
void setmult(Mult m) {
|
||||
if (m.gen0 < m.gen1)
|
||||
_mults[m.gen0][m.gen1] = m.mult;
|
||||
else
|
||||
_mults[m.gen1][m.gen0] = m.mult;
|
||||
}
|
||||
|
||||
std::vector<Mult> get_mults() const {
|
||||
std::vector<Mult> mults;
|
||||
for (int i = 0; i < ngens - 1; i++) {
|
||||
for (int j = i+1; j < ngens; j++) {
|
||||
mults.push_back({i,j,_mults[i][j]});
|
||||
}
|
||||
}
|
||||
return mults;
|
||||
}
|
||||
|
||||
Group operator*(const Group &other) {
|
||||
int off = ngens;
|
||||
|
||||
Group g(ngens + other.ngens, get_mults());
|
||||
|
||||
for (Mult m : other.get_mults()) {
|
||||
g.setmult({off + m.gen0, off + m.gen1, m.mult});
|
||||
}
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
Group operator^(int p) {
|
||||
Group g(ngens * p);
|
||||
|
||||
for (Mult m : get_mults()) {
|
||||
for (int off = 0; off < g.ngens; off += ngens) {
|
||||
g.setmult({off + m.gen0, off + m.gen1, m.mult});
|
||||
}
|
||||
}
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
static Group schlafli(std::vector<int> mults) {
|
||||
int ngens = mults.size() + 1;
|
||||
Group g(ngens);
|
||||
for (int i = 0; i < mults.size(); i++) {
|
||||
g.setmult({i, i+1, mults[i]});
|
||||
}
|
||||
return g;
|
||||
}
|
||||
|
||||
Cosets solve(std::vector<int> sub_gens = {}) {
|
||||
std::vector<int> init_row(ngens, -1);
|
||||
for (int i : sub_gens) {
|
||||
init_row[i] = 0;
|
||||
}
|
||||
|
||||
Cosets cosets(ngens, init_row);
|
||||
RelTables rel_tables(get_mults());
|
||||
std::vector<std::vector<int>> gen_map(ngens);
|
||||
int rel_idx = 0;
|
||||
for (Mult m : get_mults()) {
|
||||
gen_map[m.gen0].push_back(rel_idx);
|
||||
gen_map[m.gen1].push_back(rel_idx);
|
||||
rel_idx++;
|
||||
}
|
||||
|
||||
int null_lst_ptr;
|
||||
rel_tables.add_row();
|
||||
RelTablesRow &row = *(rel_tables.rows[0]);
|
||||
for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
|
||||
TableInfo &ti = rel_tables.table_info[table_idx];
|
||||
|
||||
if (cosets.get(ti.gens[0]) + cosets.get(ti.gens[1]) == -2) {
|
||||
row.lst_ptrs[table_idx] = new int;
|
||||
row.gnrs[table_idx] = 0;
|
||||
}
|
||||
else {
|
||||
row.lst_ptrs[table_idx] = &null_lst_ptr;
|
||||
row.gnrs[table_idx] = -1;
|
||||
}
|
||||
}
|
||||
|
||||
int idx = 0;
|
||||
int coset, gen, target, fact_idx, lst, gen_;
|
||||
while (true) {
|
||||
while (idx < cosets.data.size() and cosets.get(idx) >= 0)
|
||||
idx++;
|
||||
|
||||
if (idx == cosets.data.size()) {
|
||||
rel_tables.del_rows_to(idx / ngens);
|
||||
break;
|
||||
}
|
||||
|
||||
target = cosets.len;
|
||||
cosets.add_row();
|
||||
rel_tables.add_row();
|
||||
|
||||
std::vector<int> facts;
|
||||
facts.push_back(idx);
|
||||
|
||||
coset = idx / ngens;
|
||||
gen = idx % ngens;
|
||||
|
||||
rel_tables.del_rows_to(coset);
|
||||
|
||||
RelTablesRow &target_row = *(rel_tables.rows[target]);
|
||||
while (!facts.empty()) {
|
||||
fact_idx = facts.back();
|
||||
facts.pop_back();
|
||||
|
||||
if (cosets.get(fact_idx) != -1)
|
||||
continue;
|
||||
|
||||
cosets.put(fact_idx, target);
|
||||
|
||||
coset = fact_idx / ngens;
|
||||
gen = fact_idx % ngens;
|
||||
|
||||
RelTablesRow &coset_row = *(rel_tables.rows[coset]);
|
||||
for (int table_idx : gen_map[gen]) {
|
||||
if ( target_row.lst_ptrs[table_idx] == nullptr ) {
|
||||
TableInfo &ti = rel_tables.table_info[table_idx];
|
||||
target_row.lst_ptrs[table_idx] = coset_row.lst_ptrs[table_idx];
|
||||
target_row.gnrs[table_idx] = coset_row.gnrs[table_idx] + 1;
|
||||
|
||||
if (coset_row.gnrs[table_idx] < 0)
|
||||
target_row.gnrs[table_idx] -= 2;
|
||||
|
||||
if (target_row.gnrs[table_idx] == ti.mult) {
|
||||
lst = *(target_row.lst_ptrs[table_idx]);
|
||||
delete target_row.lst_ptrs[table_idx];
|
||||
gen_ = ti.gens[(int)(ti.gens[0] == gen)];
|
||||
facts.push_back(lst*ngens + gen_);
|
||||
}
|
||||
else if (target_row.gnrs[table_idx] == -ti.mult) {
|
||||
gen_ = ti.gens[ti.gens[0] == gen];
|
||||
facts.push_back(target*ngens + gen_);
|
||||
}
|
||||
else if (target_row.gnrs[table_idx] == ti.mult - 1) {
|
||||
*(target_row.lst_ptrs[table_idx]) = target;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
std::sort(facts.begin(), facts.end(), std::greater<int>());
|
||||
}
|
||||
|
||||
for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
|
||||
TableInfo &ti = rel_tables.table_info[table_idx];
|
||||
if (target_row.lst_ptrs[table_idx] == nullptr) {
|
||||
if ( (cosets.get(target, ti.gens[0]) != target) and
|
||||
(cosets.get(target, ti.gens[1]) != target) ) {
|
||||
target_row.lst_ptrs[table_idx] = new int;
|
||||
target_row.gnrs[table_idx] = 0;
|
||||
}
|
||||
else {
|
||||
target_row.lst_ptrs[table_idx] = &null_lst_ptr;
|
||||
target_row.gnrs[table_idx] = -1;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return cosets;
|
||||
}
|
||||
};
|
||||
118
src/core.cpp
Normal file
118
src/core.cpp
Normal file
@@ -0,0 +1,118 @@
|
||||
#include "tc/core.hpp"
|
||||
|
||||
#include <utility>
|
||||
#include <sstream>
|
||||
|
||||
namespace tc {
|
||||
Action::Action(int coset, int gen, int target)
|
||||
: coset(coset), gen(gen), target(target) {
|
||||
}
|
||||
|
||||
Cosets::Cosets(int ngens)
|
||||
: ngens(ngens) {
|
||||
}
|
||||
|
||||
void Cosets::add_row() {
|
||||
data.resize(data.size() + ngens, -1);
|
||||
path.resize(path.size() + 1);
|
||||
}
|
||||
|
||||
void Cosets::put(int coset, int gen, int target) {
|
||||
data[coset * ngens + gen] = target;
|
||||
data[target * ngens + gen] = coset;
|
||||
|
||||
if (path[target].coset == -1) {
|
||||
path[target] = Action(coset, gen, target);
|
||||
}
|
||||
}
|
||||
|
||||
void Cosets::put(int idx, int target) {
|
||||
int coset = idx / ngens;
|
||||
int gen = idx % ngens;
|
||||
data[idx] = target;
|
||||
data[target * ngens + gen] = coset;
|
||||
|
||||
if (path[target].coset == -1) {
|
||||
path[target] = Action(coset, gen, target);
|
||||
}
|
||||
}
|
||||
|
||||
int Cosets::get(int coset, int gen) const {
|
||||
return data[coset * ngens + gen];
|
||||
}
|
||||
|
||||
int Cosets::get(int idx) const {
|
||||
return data[idx];
|
||||
}
|
||||
|
||||
size_t Cosets::size() const {
|
||||
return path.size();
|
||||
}
|
||||
|
||||
Rel::Rel(int a, int b, int m)
|
||||
: gens({a, b}), mult(m) {
|
||||
}
|
||||
|
||||
Rel Rel::shift(int off) const {
|
||||
return Rel(gens[0] + off, gens[1] + off, mult);
|
||||
}
|
||||
|
||||
Group::Group(int ngens, const std::vector<Rel> &rels, std::string name)
|
||||
: ngens(ngens), name(std::move(name)) {
|
||||
_mults.resize(ngens);
|
||||
|
||||
for (auto &mult : _mults) {
|
||||
mult.resize(ngens, 2);
|
||||
}
|
||||
|
||||
for (const auto &rel : rels) {
|
||||
set(rel);
|
||||
}
|
||||
}
|
||||
|
||||
void Group::set(const Rel &r) {
|
||||
_mults[r.gens[0]][r.gens[1]] = r.mult;
|
||||
_mults[r.gens[1]][r.gens[0]] = r.mult;
|
||||
}
|
||||
|
||||
int Group::get(int a, int b) const {
|
||||
return _mults[a][b];
|
||||
}
|
||||
|
||||
std::vector<Rel> Group::rels() const {
|
||||
std::vector<Rel> res;
|
||||
for (int i = 0; i < ngens - 1; ++i) {
|
||||
for (int j = i + 1; j < ngens; ++j) {
|
||||
res.emplace_back(i, j, get(i, j));
|
||||
}
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
Group Group::product(const Group &other) const {
|
||||
std::stringstream ss;
|
||||
ss << name << "*" << other.name;
|
||||
|
||||
Group g(ngens + other.ngens, rels(), ss.str());
|
||||
|
||||
for (const auto &rel : other.rels()) {
|
||||
g.set(rel.shift(ngens));
|
||||
}
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
Group Group::power(int p) const {
|
||||
std::stringstream ss;
|
||||
ss << name << "^" << p;
|
||||
|
||||
Group g(ngens * p, {}, ss.str());
|
||||
for (const auto &rel : rels()) {
|
||||
for (int off = 0; off < g.ngens; off += ngens) {
|
||||
g.set(rel.shift(off));
|
||||
}
|
||||
}
|
||||
|
||||
return g;
|
||||
}
|
||||
}
|
||||
120
src/groups.cpp
Normal file
120
src/groups.cpp
Normal file
@@ -0,0 +1,120 @@
|
||||
#include "tc/groups.hpp"
|
||||
|
||||
#include <sstream>
|
||||
|
||||
namespace tc {
|
||||
Group schlafli(const std::vector<int> &mults, const std::string &name) {
|
||||
int ngens = (int) mults.size() + 1;
|
||||
|
||||
Group g(ngens, {}, name);
|
||||
|
||||
for (int i = 0; i < (int) mults.size(); i++) {
|
||||
g.set(Rel(i, i + 1, mults[i]));
|
||||
}
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
Group schlafli(const std::vector<int> &mults) {
|
||||
std::stringstream ss;
|
||||
ss << "[";
|
||||
if (!mults.empty()) {
|
||||
for (size_t i = 0; i < mults.size() - 1; ++i) {
|
||||
ss << mults[i] << ",";
|
||||
}
|
||||
ss << mults.back();
|
||||
}
|
||||
ss << "]";
|
||||
|
||||
return schlafli(mults, ss.str());
|
||||
}
|
||||
|
||||
namespace group {
|
||||
Group A(const int dim) {
|
||||
std::stringstream ss;
|
||||
ss << "A(" << dim << ")";
|
||||
|
||||
if (dim == 0)
|
||||
return Group(0, {}, ss.str());
|
||||
|
||||
const std::vector<int> &mults = std::vector<int>(dim - 1, 3);
|
||||
|
||||
return schlafli(mults, ss.str());
|
||||
}
|
||||
|
||||
Group B(const int dim) {
|
||||
std::stringstream ss;
|
||||
ss << "B(" << dim << ")";
|
||||
|
||||
std::vector<int> mults(dim - 1, 3);
|
||||
mults[0] = 4;
|
||||
|
||||
return schlafli(mults, ss.str());
|
||||
}
|
||||
|
||||
Group D(const int dim) {
|
||||
std::stringstream ss;
|
||||
ss << "D(" << dim << ")";
|
||||
|
||||
std::vector<int> mults(dim - 1, 3);
|
||||
mults[dim - 2] = 2;
|
||||
|
||||
Group g = schlafli(mults, ss.str());
|
||||
g.set(Rel(1, dim - 1, 3));
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
Group E(const int dim) {
|
||||
std::stringstream ss;
|
||||
ss << "E(" << dim << ")";
|
||||
|
||||
std::vector<int> mults(dim - 1, 3);
|
||||
mults[dim - 2] = 2;
|
||||
|
||||
Group g = schlafli(mults, ss.str());
|
||||
g.set(Rel(2, dim - 1, 3));
|
||||
|
||||
return g;
|
||||
}
|
||||
|
||||
Group F4() {
|
||||
return schlafli({3, 4, 3}, "F4");
|
||||
}
|
||||
|
||||
Group G2() {
|
||||
return schlafli({6}, "G2");
|
||||
}
|
||||
|
||||
Group H(const int dim) {
|
||||
std::stringstream ss;
|
||||
ss << "H(" << dim << ")";
|
||||
|
||||
std::vector<int> mults(dim - 1, 3);
|
||||
mults[0] = 5;
|
||||
|
||||
return schlafli(mults, ss.str());
|
||||
}
|
||||
|
||||
Group I2(const int n) {
|
||||
std::stringstream ss;
|
||||
ss << "I2(" << n << ")";
|
||||
|
||||
return schlafli({n}, ss.str());
|
||||
}
|
||||
|
||||
Group T(const int n, const int m) {
|
||||
std::stringstream ss;
|
||||
ss << "T(" << n << "," << m << ")";
|
||||
|
||||
return schlafli({n, 2, m}, ss.str());
|
||||
}
|
||||
|
||||
Group T(const int n) {
|
||||
std::stringstream ss;
|
||||
ss << "T(" << n << ")";
|
||||
|
||||
return schlafli({n, 2, n}, ss.str());
|
||||
}
|
||||
}
|
||||
}
|
||||
178
src/solve.cpp
Normal file
178
src/solve.cpp
Normal file
@@ -0,0 +1,178 @@
|
||||
#include "tc/core.hpp"
|
||||
|
||||
#include <algorithm>
|
||||
|
||||
namespace tc {
|
||||
struct RelTablesRow {
|
||||
int *gnrs;
|
||||
int **lst_ptrs;
|
||||
|
||||
RelTablesRow(int N, int *gnrs, int **lst_ptrs) : gnrs(gnrs), lst_ptrs(lst_ptrs) {
|
||||
for (int i = 0; i < N; i++) {
|
||||
lst_ptrs[i] = nullptr;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
struct RelTables {
|
||||
static const int ROW_BLOCK_SIZE = 64;
|
||||
std::vector<Rel> rels;
|
||||
std::vector<RelTablesRow *> rows;
|
||||
int start = 0;
|
||||
int num_tables;
|
||||
int buffer_rows = 0;
|
||||
|
||||
explicit RelTables(const std::vector<Rel> &rels)
|
||||
: num_tables(rels.size()), rels(rels) {
|
||||
}
|
||||
|
||||
void add_row() {
|
||||
if (buffer_rows == 0) {
|
||||
int *gnrs_alloc = new int[num_tables * RelTables::ROW_BLOCK_SIZE];
|
||||
int **lst_ptrs_alloc = new int *[num_tables * RelTables::ROW_BLOCK_SIZE];
|
||||
for (int i = 0; i < RelTables::ROW_BLOCK_SIZE; i++) {
|
||||
rows.push_back(
|
||||
new RelTablesRow(num_tables, &gnrs_alloc[i * num_tables], &lst_ptrs_alloc[i * num_tables]));
|
||||
}
|
||||
buffer_rows = RelTables::ROW_BLOCK_SIZE;
|
||||
}
|
||||
|
||||
buffer_rows--;
|
||||
}
|
||||
|
||||
void del_rows_to(int idx) {
|
||||
const int del_to = (idx / RelTables::ROW_BLOCK_SIZE) * RelTables::ROW_BLOCK_SIZE;
|
||||
for (int i = start; i < del_to; i += RelTables::ROW_BLOCK_SIZE) {
|
||||
delete[] rows[i]->gnrs;
|
||||
delete[] rows[i]->lst_ptrs;
|
||||
for (int j = 0; j < RelTables::ROW_BLOCK_SIZE; j++) {
|
||||
delete rows[i + j];
|
||||
}
|
||||
start += RelTables::ROW_BLOCK_SIZE;
|
||||
}
|
||||
}
|
||||
|
||||
~RelTables() {
|
||||
while (start < rows.size()) {
|
||||
delete[] rows[start]->gnrs;
|
||||
delete[] rows[start]->lst_ptrs;
|
||||
for (int j = 0; j < RelTables::ROW_BLOCK_SIZE; j++) {
|
||||
delete rows[start + j];
|
||||
}
|
||||
start += RelTables::ROW_BLOCK_SIZE;
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
Cosets Group::solve(const std::vector<int> &sub_gens) const {
|
||||
Cosets cosets(ngens);
|
||||
cosets.add_row();
|
||||
for (int g : sub_gens) {
|
||||
cosets.put(g, 0);
|
||||
}
|
||||
|
||||
RelTables rel_tables(rels());
|
||||
std::vector<std::vector<int>> gen_map(ngens);
|
||||
int rel_idx = 0;
|
||||
for (Rel m : rels()) {
|
||||
gen_map[m.gens[0]].push_back(rel_idx);
|
||||
gen_map[m.gens[1]].push_back(rel_idx);
|
||||
rel_idx++;
|
||||
}
|
||||
|
||||
int null_lst_ptr;
|
||||
rel_tables.add_row();
|
||||
RelTablesRow &row = *(rel_tables.rows[0]);
|
||||
for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
|
||||
Rel &ti = rel_tables.rels[table_idx];
|
||||
|
||||
if (cosets.get(ti.gens[0]) + cosets.get(ti.gens[1]) == -2) {
|
||||
row.lst_ptrs[table_idx] = new int;
|
||||
row.gnrs[table_idx] = 0;
|
||||
} else {
|
||||
row.lst_ptrs[table_idx] = &null_lst_ptr;
|
||||
row.gnrs[table_idx] = -1;
|
||||
}
|
||||
}
|
||||
|
||||
int idx = 0;
|
||||
int coset, gen, target, fact_idx, lst, gen_;
|
||||
while (true) {
|
||||
while (idx < cosets.data.size() and cosets.get(idx) >= 0)
|
||||
idx++;
|
||||
|
||||
if (idx == cosets.data.size()) {
|
||||
rel_tables.del_rows_to(idx / ngens);
|
||||
break;
|
||||
}
|
||||
|
||||
target = cosets.size();
|
||||
cosets.add_row();
|
||||
rel_tables.add_row();
|
||||
|
||||
std::vector<int> facts;
|
||||
facts.push_back(idx);
|
||||
|
||||
coset = idx / ngens;
|
||||
gen = idx % ngens;
|
||||
|
||||
rel_tables.del_rows_to(coset);
|
||||
|
||||
RelTablesRow &target_row = *(rel_tables.rows[target]);
|
||||
while (!facts.empty()) {
|
||||
fact_idx = facts.back();
|
||||
facts.pop_back();
|
||||
|
||||
if (cosets.get(fact_idx) != -1)
|
||||
continue;
|
||||
|
||||
cosets.put(fact_idx, target);
|
||||
|
||||
coset = fact_idx / ngens;
|
||||
gen = fact_idx % ngens;
|
||||
|
||||
RelTablesRow &coset_row = *(rel_tables.rows[coset]);
|
||||
for (int table_idx : gen_map[gen]) {
|
||||
if (target_row.lst_ptrs[table_idx] == nullptr) {
|
||||
Rel &ti = rel_tables.rels[table_idx];
|
||||
target_row.lst_ptrs[table_idx] = coset_row.lst_ptrs[table_idx];
|
||||
target_row.gnrs[table_idx] = coset_row.gnrs[table_idx] + 1;
|
||||
|
||||
if (coset_row.gnrs[table_idx] < 0)
|
||||
target_row.gnrs[table_idx] -= 2;
|
||||
|
||||
if (target_row.gnrs[table_idx] == ti.mult) {
|
||||
lst = *(target_row.lst_ptrs[table_idx]);
|
||||
delete target_row.lst_ptrs[table_idx];
|
||||
gen_ = ti.gens[(int) (ti.gens[0] == gen)];
|
||||
facts.push_back(lst * ngens + gen_);
|
||||
} else if (target_row.gnrs[table_idx] == -ti.mult) {
|
||||
gen_ = ti.gens[ti.gens[0] == gen];
|
||||
facts.push_back(target * ngens + gen_);
|
||||
} else if (target_row.gnrs[table_idx] == ti.mult - 1) {
|
||||
*(target_row.lst_ptrs[table_idx]) = target;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
std::sort(facts.begin(), facts.end(), std::greater<>());
|
||||
}
|
||||
|
||||
for (int table_idx = 0; table_idx < rel_tables.num_tables; table_idx++) {
|
||||
Rel &ti = rel_tables.rels[table_idx];
|
||||
if (target_row.lst_ptrs[table_idx] == nullptr) {
|
||||
if ((cosets.get(target, ti.gens[0]) != target) and
|
||||
(cosets.get(target, ti.gens[1]) != target)) {
|
||||
target_row.lst_ptrs[table_idx] = new int;
|
||||
target_row.gnrs[table_idx] = 0;
|
||||
} else {
|
||||
target_row.lst_ptrs[table_idx] = &null_lst_ptr;
|
||||
target_row.gnrs[table_idx] = -1;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return cosets;
|
||||
}
|
||||
}
|
||||
19
test.cpp
19
test.cpp
@@ -1,19 +0,0 @@
|
||||
#include "groups.cpp"
|
||||
#include <chrono>
|
||||
#include <iostream>
|
||||
|
||||
int main() {
|
||||
Group g = B(8);
|
||||
|
||||
auto s = std::chrono::system_clock::now();
|
||||
auto cosets = g.solve();
|
||||
auto e = std::chrono::system_clock::now();
|
||||
|
||||
std::chrono::duration<double> diff = e - s;
|
||||
int order = cosets.len;
|
||||
|
||||
std::cout << order << std::endl;
|
||||
std::cout << diff.count() << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
Reference in New Issue
Block a user