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Parallel numerical verification of the σ_odd problem
October 6, 2018
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Parallel numerical verification of the σ_odd problem
October 6, 2018
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Define type and some generic functions. More...
#include "helper__inline.hpp"Go to the source code of this file.
Namespaces | |
| sigmaodd | |
| A lot of functions and stuffs to deal the sigma_odd problem and related stuffs. | |
Typedefs | |
| typedef uint64_t | sigmaodd::nat_type |
| Type for natural number used in all code, on 64 bits. More... | |
| typedef unsigned __int128 | sigmaodd::tmp_uint128_type |
| Type double size for some temporary calculation. More... | |
Functions | |
| nat_type | sigmaodd::ceil_eighth_root (nat_type n) |
| Return the eighth root of n rounded to above. More... | |
| nat_type | sigmaodd::ceilx_fourth_root (nat_type n) |
| Return the fourth root of n rounded to above. More... | |
| nat_type | sigmaodd::ceil_square_root (nat_type n) |
| Return the square root of n rounded to above. More... | |
| nat_type | sigmaodd::floor_eighth_root (nat_type n) |
| Return the eighth root of n rounded to below. More... | |
| nat_type | sigmaodd::floor_fourth_root (nat_type n) |
| Return the fourth root of n rounded to below. More... | |
| nat_type | sigmaodd::floor_square_root (nat_type n) |
| Return the square root of n rounded to below. More... | |
| constexpr bool | sigmaodd::is_even (nat_type n) |
| Return true iff n is even. More... | |
| constexpr bool | sigmaodd::is_odd (nat_type n) |
| Return true iff n is odd. More... | |
| std::vector< nat_type > | sigmaodd::load_bad_table (const std::string &filename, const std::vector< nat_type > &bad_table=std::vector< nat_type >()) |
| Read a file that contains list of bad numbers, add after bad_table, and return the result. More... | |
| std::vector< nat_type > | sigmaodd::load_numbers (const std::string &filename) |
| Read the file and extract each natural number begining a line. Return the list of these numbers. More... | |
| constexpr nat_type | sigmaodd::pow_nat (nat_type n, unsigned int k) |
| Return x^k, x power k. More... | |
| constexpr double | sigmaodd::square (double x) |
| Return x*x. More... | |
| constexpr nat_type | sigmaodd::square (nat_type n) |
| Return n*n. More... | |
| constexpr nat_type | sigmaodd::sum_even (nat_type n) |
| Return 2 + 4 + 6 + 8 + ... + (n or n-1) = k(k + 1) with k = floor(n/2). More... | |
| constexpr nat_type | sigmaodd::sum_geometric_progression (nat_type r, unsigned int k) |
| Return the sum of the (k + 1) terms of the geometric progression of the common ratio r. More... | |
| constexpr nat_type | sigmaodd::sum_geometric_progression_strict (nat_type r, unsigned int k) |
| Return sum_geometric_progression(r, k) but only for r > 1. More... | |
| constexpr nat_type | sigmaodd::sum_natural (nat_type n) |
| Return 1 + 2 + 3 + 4 + ... + n = n(n + 1)/2. More... | |
| constexpr nat_type | sigmaodd::sum_odd (nat_type n) |
| Return 1 + 3 + 5 + 7 + ... + (n or n-1) = k^2 with k floor((n+1)/2). More... | |
Variables | |
| constexpr nat_type | sigmaodd::MAX_POSSIBLE_N = (static_cast<nat_type>(1) << 56) - 1 |
| Lower bound of the bigger number such that it is possible to compute the result of the sigma function. More... | |
Define type and some generic functions.
(January 6, 2018) GPLv3 — Copyright (C) 2017, 2018 Olivier Pirson http://www.opimedia.be/
Definition in file helper.hpp.
1.8.13