464 lines
20 KiB
C++
464 lines
20 KiB
C++
#include <iostream>
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#include <cstdint>
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#include <vector>
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#include <set>
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#include <map>
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#include <cassert>
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#include <fstream>
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#include <string>
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#include "al_function.hpp"
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#include "al_bool_matrix.hpp"
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using namespace std;
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typedef uint16_t Storage;
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const size_t ARGS_COUNT = 4;
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const size_t FUNCTION_LEN = 1ll << ARGS_COUNT;
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const size_t FUNCTIONS_COUNT = 1ll << FUNCTION_LEN;
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const bool ONLY_CREATE_CLASSES = true;
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typedef Function<Storage, FUNCTION_LEN> MyFunction;
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typedef BoolSquareMatrix<Storage, ARGS_COUNT> MyMatrix;
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map<Storage, string> function_formulas;
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void test_function() {
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Function<uint16_t, 8> f_8(16);
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assert(("sizeof(sizeof(Function<uint16_t, 8>)", sizeof(Function<uint16_t, 8>)==2));
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assert(("f_8(16) = 00010000", "00010000" == f_8.string()));
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assert(("f_8(15) = 00001111", "00001111" == Function<uint16_t, 8>(15).string()));
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assert(("converting 01001001", Function<uint16_t, 8>("01001001").string() == "01001001"));
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assert(("converting 00000000", Function<uint16_t, 8>("00000000").string() == "00000000"));
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assert(("converting 11111111", Function<uint16_t, 8>("11111111").string() == "11111111"));
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assert((Function<uint16_t, 16>("0010101111110001").string() == "0010101111110001"));
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Function<uint16_t, 8> a(12);
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Function<uint16_t, 8> b(5);
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assert(("a = 00001100", a.string() == "00001100"));
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assert(("b = 00000101", b.string() == "00000101"));
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assert(("a ^ b = 00001001", (a xor b).string() == "00001001"));
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assert(("a | b = 00001101", (a or b).string() == "00001101"));
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assert(("a & b = 00000100", (a and b).string() == "00000100"));
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// no changed in this objects
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assert(("a = 00001100", a.string() == "00001100"));
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assert(("b = 00000101", b.string() == "00000101"));
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Function<uint16_t, 8> negation(107);
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assert(("f(x_1 + 1 + 1, x_2, x_3) == f", negation == negation.var_negation(1).var_negation(1)));
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assert(("f(x_1, x_2 + 1 + 1, x_3) == f", negation == negation.var_negation(2).var_negation(2)));
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assert(("f(x_1, x_2, x_3 + 1 + 1) == f", negation == negation.var_negation(3).var_negation(3)));
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assert((Function<uint16_t, 16>("0000000100010111").var_negation(1).string() == "0000001000101011"));
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assert((Function<uint16_t, 16>("0000000100010111").var_negation(4).string() == "0001011100000001"));
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/*
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cout << "f(x_1, x_2, x_3) = " << negation.string() << endl;
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cout << "f(x_1 + 1, x_2, x_3) = " << negation.var_negation(1).string() << endl;
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cout << "f(x_1 + 1 + 1, x_2, x_3) = " << negation.var_negation(1).var_negation(1).string() << endl;
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cout << "f(x_1, x_2 + 1, x_3) = " << negation.var_negation(2).string() << endl;
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cout << "f(x_1, x_2 + 1 + 1, x_3) = " << negation.var_negation(2).var_negation(2).string() << endl;
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cout << "f(x_1, x_2, x_3 + 1) = " << negation.var_negation(3).string() << endl;
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*/
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BoolSquareMatrix<uint16_t, 3> ones_matrix((1 << 10) - 1), i_matrix(0b100010001), minus_i_matrix(0b001010100);
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assert(ones_matrix.string("") == "111111111");
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assert(ones_matrix.get_determinant() == 0);
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assert(i_matrix.string("") == "100010001");
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assert(i_matrix.get_determinant() == 1);
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assert(minus_i_matrix.string("") == "001010100");
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assert(minus_i_matrix.get_determinant() != 0); // == uint16_t(-1)
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assert((BoolSquareMatrix<uint16_t, 3>(0b001001010).get_determinant() == 0));
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assert((BoolSquareMatrix<uint16_t, 3>(0b101000010).get_determinant() == 0));
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assert((BoolSquareMatrix<uint16_t, 3>(0b110101110).get_determinant() == 0));
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assert((BoolSquareMatrix<uint16_t, 3>(0b110101011).get_determinant() %2 == 0));
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assert((BoolSquareMatrix<uint16_t, 3>(0b001011111).get_determinant() != 0)); // == uint16_t(-1)
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BoolSquareMatrix<uint16_t, 4> ones_matrix_4(0b1111111111111111),
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i_matrix_4(0b1000010000100001),
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minus_i_matrix_4(0b0001001001001000);
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assert(ones_matrix_4.string("") == "1111111111111111");
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assert(ones_matrix_4.get_determinant() == 0);
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assert(i_matrix_4.string("") == "1000010000100001");
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assert(i_matrix_4.get_determinant() == 1);
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assert(minus_i_matrix_4.string("") == "0001001001001000");
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assert(minus_i_matrix_4.get_determinant() == 1);
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assert((BoolSquareMatrix<uint16_t, 4>(0b0001100000011010).get_determinant() == 0));
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assert((BoolSquareMatrix<uint16_t, 4>(0b0100011110111001).get_determinant() != 0));
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assert((BoolSquareMatrix<uint16_t, 4>(0b0000110100001101).get_determinant() == 0));
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assert((BoolSquareMatrix<uint16_t, 4>(0b0010101111110001).get_determinant() != 0));
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cout << "self-test passed" << endl;
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}
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template<class STORAGE, size_t ARGUMENTS_COUNT, class Callable>
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Function<STORAGE, 1ll << ARGUMENTS_COUNT > get_function_from_callable(Callable INPUT_FUNCTION) {
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const STORAGE values_count = 1ll << ARGUMENTS_COUNT;
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STORAGE function_values(0);
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for (STORAGE cur_vec_value = values_count; cur_vec_value != 0; --cur_vec_value) {
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BoolVector<STORAGE, ARGUMENTS_COUNT> vec(cur_vec_value - 1);
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function_values *= 2;
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function_values += INPUT_FUNCTION(vec);
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}
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return Function<STORAGE, values_count >(function_values);
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}
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vector< MyMatrix > get_good_matrices() {
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vector< MyMatrix > res;
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for (size_t cur_val = 1ll << (ARGS_COUNT * ARGS_COUNT); cur_val != 0; --cur_val) {
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MyMatrix cur_matrix(cur_val);
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Storage det = cur_matrix.get_determinant();
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// if ( det %2 != 0 )
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if ( det == 1 or det == Storage(-1) )
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res.push_back(cur_matrix);
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}
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return res;
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}
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vector<MyFunction> get_function_class(MyFunction f, const vector< MyMatrix >& tranformations, ostream& out) {
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set<MyFunction> cur_res;
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for (Storage i = 0; i < FUNCTION_LEN; ++i) {
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MyFunction cur_f = f;
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for (Storage arg_ind = 0; arg_ind < ARGS_COUNT; ++arg_ind)
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if ( (i >> arg_ind) % 2 == 1 )
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cur_f = cur_f.var_negation(arg_ind + 1);
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cur_res.insert(cur_f);
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}
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set<MyFunction> transformed_res(cur_res.begin(), cur_res.end());
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for (auto cur_f: cur_res) {
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for (auto transformation: tranformations) {
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MyFunction linear_transformed = get_function_from_callable<Storage, ARGS_COUNT>(
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[transformation, cur_f](const BoolVector<Storage, ARGS_COUNT> vec) -> Storage {
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return cur_f.at((transformation * vec).get_value());
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}
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);
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bool is_inserted = transformed_res.insert(linear_transformed).second;
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if ( is_inserted ) {
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if ( function_formulas.find(linear_transformed.value()) == function_formulas.end() ) {
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function_formulas[linear_transformed.value()] = "LT";
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}
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}
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}
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}
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return vector<MyFunction>(transformed_res.begin(), transformed_res.end());
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}
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vector<MyFunction> get_linear_components() {
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vector<MyFunction> res;
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if constexpr ( ARGS_COUNT == 2 ) {
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res.push_back(MyFunction("0000")); // f = 0
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function_formulas[res.back().value()] = "0";
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res.push_back(MyFunction("1111")); // f = 1
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function_formulas[res.back().value()] = "1";
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res.push_back(MyFunction("0011")); // f = x_1
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function_formulas[res.back().value()] = "x_1";
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res.push_back(MyFunction("0101")); // f = x_2
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function_formulas[res.back().value()] = "x_2";
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} else if constexpr ( ARGS_COUNT == 3 ) {
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res.push_back(MyFunction("00000000")); // f = 0
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function_formulas[res.back().value()] = "0";
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res.push_back(MyFunction("11111111")); // f = 1
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function_formulas[res.back().value()] = "1";
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res.push_back(MyFunction("00001111")); // f = x_1
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function_formulas[res.back().value()] = "x_1";
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res.push_back(MyFunction("00110011")); // f = x_2
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function_formulas[res.back().value()] = "x_2";
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res.push_back(MyFunction("01010101")); // f = x_3
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function_formulas[res.back().value()] = "x_3";
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} else if constexpr ( ARGS_COUNT == 4 ) {
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res.push_back(MyFunction("0000000000000000")); // f = 0
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function_formulas[res.back().value()] = "0";
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res.push_back(MyFunction("1111111111111111")); // f = 1
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function_formulas[res.back().value()] = "1";
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res.push_back(MyFunction("0000000011111111")); // f = x_1
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function_formulas[res.back().value()] = "x_1";
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res.push_back(MyFunction("0000111100001111")); // f = x_2
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function_formulas[res.back().value()] = "x_2";
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res.push_back(MyFunction("0011001100110011")); // f = x_3
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function_formulas[res.back().value()] = "x_3";
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res.push_back(MyFunction("0101010101010101")); // f = x_4
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function_formulas[res.back().value()] = "x_4";
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} else if constexpr ( ARGS_COUNT == 5 ) {
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res.push_back(MyFunction("11111111111111111111111111111111")); // f = 1
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res.push_back(MyFunction("00000000000000001111111111111111")); // f = x_1
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res.push_back(MyFunction("00000000111111110000000011111111")); // f = x_2
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res.push_back(MyFunction("00001111000011110000111100001111")); // f = x_3
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res.push_back(MyFunction("00110011001100110011001100110011")); // f = x_4
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res.push_back(MyFunction("01010101010101010101010101010101")); // f = x_5
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} else {
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assert (("bad args_count", false));
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}
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return res;
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}
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vector<MyFunction> get_linear_combinations(const vector<MyFunction> &linear_components) {
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set<MyFunction> res(linear_components.begin(), linear_components.end());
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bool is_added = true;
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while ( is_added ) {
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is_added = false;
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for (auto el_first: res)
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for (auto el_second: res) {
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bool is_added_now = res.insert(el_first xor el_second).second;
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if ( is_added_now ) {
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Storage cur_value = (el_first xor el_second).value();
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function_formulas[cur_value] = function_formulas[el_first.value()] + " + " + function_formulas[el_second.value()];
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}
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is_added = is_added or is_added_now;
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}
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}
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return vector<MyFunction>(res.begin(), res.end());
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}
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string preprocess_factor(string factor) {
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if ( factor.find("+") != string::npos and factor.find("*") == string::npos )
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return "(" + factor + ")";
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return factor;
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}
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vector<MyFunction> get_all_monomials(const vector<MyFunction> &linear_combinations) {
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set<MyFunction> res(linear_combinations.begin(), linear_combinations.end());
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bool is_added = true;
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while ( is_added ) {
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is_added = false;
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for (auto el_first: res)
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for (auto el_second: res) {
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bool is_added_now = res.insert(el_first and el_second).second;
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if ( is_added_now ) {
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Storage cur_value = (el_first and el_second).value();
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function_formulas[cur_value] = preprocess_factor(function_formulas[el_first.value()])
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+ " " + preprocess_factor(function_formulas[el_second.value()]);
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// no symbol for multiplication needed
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}
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is_added = is_added or is_added_now;
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}
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}
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return vector<MyFunction>(res.begin(), res.end());
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}
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string preprocess_monom(string monom) {
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return monom;
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}
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inline bool exists_test0 (const std::string& name) {
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ifstream f(name.c_str());
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return f.good();
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}
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string get_out_file_name(size_t rank_ind) {
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return string("base_" + to_string(ARGS_COUNT) + "_rank_" + to_string(rank_ind) + ".txt");
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}
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size_t recover_ranks(vector< vector<MyFunction> >& ranks, vector<int8_t>& used_map, size_t& functions_remains) {
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for (size_t rank_ind = 2; true; ++rank_ind) {
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ifstream f_in(get_out_file_name(rank_ind).c_str(), std::ios::binary);
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if ( not f_in.good() )
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return rank_ind;
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ranks.push_back(vector<MyFunction>());
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for (Storage bytes_cnt = 0; bytes_cnt < FUNCTIONS_COUNT / 8; ++bytes_cnt) {
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uint8_t buf;
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f_in.read(reinterpret_cast<char*>(&buf), 1);
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for (int8_t bits_cnt = 7; bits_cnt >= 0; --bits_cnt) {
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bool is_exists = buf % 2;
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if ( is_exists ) {
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Storage function_value = bytes_cnt * 8 + bits_cnt;
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MyFunction f(function_value);
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if (used_map.at(f.value()))
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continue;
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used_map.at(f.value()) = rank_ind;
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--functions_remains;
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ranks.back().push_back(f);
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}
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buf /= 2;
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}
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}
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}
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}
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void save_rank(size_t rank_ind, vector<MyFunction>& rank_items) {
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if ( not is_sorted(rank_items.begin(), rank_items.end()) )
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exit(1);
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ofstream f_out(get_out_file_name(rank_ind).c_str(), ios::binary);
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size_t fn_ptr = 0;
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for (Storage bytes_cnt = 0; bytes_cnt < FUNCTIONS_COUNT / 8; ++bytes_cnt) {
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uint8_t buf = 0;
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for (Storage bits_cnt = 0; bits_cnt < 8; ++bits_cnt) {
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buf *= 2;
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if ( fn_ptr >= rank_items.size() or rank_items[fn_ptr].value() != bytes_cnt * 8 + bits_cnt )
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continue;
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++buf;
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++fn_ptr;
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}
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f_out.write(reinterpret_cast<char*>(&buf), 1);
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}
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}
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void clean_trash_ranks(vector< vector<MyFunction> >& ranks) {
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for (size_t rank_ind = 2; rank_ind < ranks.size() - 1; ++rank_ind)
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ranks.at(rank_ind).clear();
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}
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void fill_ranks(vector<MyFunction> monomials) {
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vector<int8_t> used_map(FUNCTIONS_COUNT, 0);
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size_t functions_remains = FUNCTIONS_COUNT;
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vector< vector<MyFunction> > ranks;
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ranks.push_back(vector<MyFunction>()); // empty set
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ranks.push_back(monomials); // empty set
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cout << "rank index = " << 1 << endl;
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for (auto el: monomials) {
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--functions_remains;
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used_map.at(el.value()) = 1;
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}
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size_t total_ranks = recover_ranks(ranks, used_map, functions_remains);
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clean_trash_ranks(ranks);
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cout << "recovered to " << total_ranks << endl;
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cout << "current ranks: " << endl;
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for (auto&& r: ranks)
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cout << r.size() << " ";
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cout << endl;
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for (; functions_remains; ++total_ranks) {
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cout << "rank index = " << total_ranks << " remains: " << functions_remains << endl;
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vector<int8_t> temp_used_map(FUNCTIONS_COUNT, 0);
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for (size_t ind_first = 0; ind_first != ranks[1].size(); ++ind_first) {
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if ( ind_first % 20 == 0 ) {
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for (auto&& r: ranks)
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cout << r.size() << " ";
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cout << endl;
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cout << 100. * ind_first / ranks[1].size() << "% for " << ranks[1].size()
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<< " x " << ranks.back().size() << endl;
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}
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const auto el_first = ranks[1][ind_first];
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for (auto el_second: ranks.back()) {
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MyFunction res_el = el_first xor el_second;
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if constexpr ( not ONLY_CREATE_CLASSES ) {
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if ( used_map[res_el.value()] == 0 ) {
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function_formulas[res_el.value()] =
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preprocess_monom(function_formulas[el_first.value()]) +
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" + " + preprocess_monom(function_formulas[el_second.value()]);
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}
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}
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temp_used_map[res_el.value()] = total_ranks;
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}
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}
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ranks.push_back(vector<MyFunction>());
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clean_trash_ranks(ranks);
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for (size_t func_ind = 0; func_ind < temp_used_map.size(); ++func_ind) {
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if (not temp_used_map[func_ind] or used_map[func_ind] != 0)
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continue;
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--functions_remains;
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auto cur_fn = MyFunction(func_ind);
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auto val = cur_fn.value();
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if (val >= used_map.size()) {
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cout << val << " " << cur_fn.string() << endl;
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continue;
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}
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used_map[val] = total_ranks;
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ranks.back().push_back(cur_fn);
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}
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save_rank(total_ranks, ranks.back());
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cout << "size for rank " << total_ranks << " is " << ranks.at(total_ranks).size() << endl;
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}
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if constexpr ( ONLY_CREATE_CLASSES ) {
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return;
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}
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auto possible_tranformations = get_good_matrices();
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cout << "Total " << possible_tranformations.size() << " linear tranformations" << endl;
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ofstream f_out("out.tex");
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f_out << "\\begin{longtable}{| l| l | l | p{70mm} |}" << endl
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<< "\\hline" << endl
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<< "\\endhead" << endl
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<< "\\hline \\multicolumn{4}{r}{\\textit{Продолжение на следующей странице}} \\\\" << endl
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<< "\\endfoot" << endl
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<< "\\hline" << endl
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<< "\\endlastfoot" << endl
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<< "\\hline" << endl
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<< "Номер класса & Длина & Размер класса & Полином\\\\" << endl
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<< "\\hline" << endl;
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ranks.clear();
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for (auto i = total_ranks - 1; i != 0; --i)
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ranks.push_back(vector<MyFunction>()); // empty set
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size_t total_unique_functions = 0;
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size_t total_functions = 0;
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map<MyFunction, size_t> class_sizes;
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for (size_t fn_value = 0; fn_value < used_map.size(); ++fn_value) {
|
|
auto cur_rank = used_map[fn_value];
|
|
if ( not cur_rank )
|
|
continue;
|
|
++total_unique_functions;
|
|
MyFunction current_fn(fn_value);
|
|
vector<MyFunction> function_class = get_function_class(
|
|
current_fn, possible_tranformations, cout
|
|
);
|
|
cout << "size of function class " << current_fn.string() << " is " << function_class.size() << endl;
|
|
class_sizes[current_fn] = function_class.size();
|
|
for (auto marked_function: function_class) {
|
|
if ( used_map[marked_function.value()] == 0 )
|
|
f_out << "already 0 at " << marked_function.string() << " " << function_formulas[marked_function.value()]
|
|
<< " from class " << current_fn.string() << " " << function_formulas[current_fn.value()] << endl;
|
|
used_map[marked_function.value()] = 0;
|
|
++total_functions;
|
|
}
|
|
ranks.at(cur_rank - 1).push_back(current_fn);
|
|
}
|
|
if ( total_functions != FUNCTIONS_COUNT)
|
|
cout << "total counted functions: " << total_functions
|
|
<< " but must be " << FUNCTIONS_COUNT << endl;
|
|
cout << "total function classes: " << total_unique_functions << endl;
|
|
size_t function_index = 1;
|
|
for (size_t rank_ind = 0; rank_ind < ranks.size(); ++rank_ind) {
|
|
cout << "rank index = " << rank_ind + 1 << endl;
|
|
f_out << "\\hline" << endl;
|
|
for (auto f: ranks.at(rank_ind)) {
|
|
cout << f.string() << " size: " << class_sizes[f] << " "
|
|
<< function_formulas[f.value()] << endl;
|
|
f_out << " " << function_index << " & " << rank_ind + 1 << " & "
|
|
<< class_sizes[f] << " & $" << function_formulas[f.value()] << "$ \\\\" << endl;
|
|
++function_index;
|
|
}
|
|
}
|
|
|
|
f_out << " \\hline" << endl
|
|
<< "\\end{longtable}" << endl
|
|
<< "\\captionof{figure}{Классы псевдополиномов}" << endl
|
|
<< "\\label{fig:polynoms}" << endl
|
|
<< "\\addtocounter{table}{-1}" << endl;
|
|
f_out.close();
|
|
}
|
|
|
|
int main() {
|
|
test_function();
|
|
cout << "using " << sizeof(Storage) << " bytes for storage" << endl;
|
|
cout << FUNCTIONS_COUNT << " functions with " << ARGS_COUNT
|
|
<< " arguments and " << FUNCTION_LEN << " values" << endl;
|
|
|
|
auto linear_components = get_linear_components();
|
|
cout << "Linear components: " << endl;
|
|
for (auto el: linear_components)
|
|
cout << el.string() << endl;
|
|
|
|
auto linear_combinations = get_linear_combinations(linear_components);
|
|
cout << "Linear combinations: " << linear_combinations.size() << endl;
|
|
|
|
auto monomials = get_all_monomials(linear_combinations);
|
|
cout << "Monomials: " << monomials.size() << endl;
|
|
|
|
fill_ranks(monomials);
|
|
return 0;
|
|
}
|