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77 lines
3.7 KiB
C++
77 lines
3.7 KiB
C++
// The MIT License (MIT)
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//
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// Copyright (c) 2018 Mateusz Pusz
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in all
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// copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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// SOFTWARE.
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#include <mp-units/bits/prime.h>
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#include <type_traits>
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#include <utility>
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using namespace mp_units::detail;
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namespace {
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template<std::size_t BasisSize, std::size_t... Is>
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constexpr bool check_primes(std::index_sequence<Is...>)
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{
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return ((Is < 2 || wheel_factorizer<BasisSize>::is_prime(Is) == is_prime_by_trial_division(Is)) && ...);
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}
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static_assert(check_primes<2>(std::make_index_sequence<122>{}));
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// This is the smallest number that can catch the bug where we use only _prime_ numbers in the first wheel, rather than
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// numbers which are _coprime to the basis_.
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//
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// The basis for N = 4 is {2, 3, 5, 7}, so the wheel size is 210. 11 * 11 = 121 is within the first wheel. It is
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// coprime with every element of the basis, but it is _not_ prime. If we keep only prime numbers, then we will neglect
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// using numbers of the form (210 * n + 121) as trial divisors, which is a problem if any are prime. For n = 1, we have
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// a divisor of (210 + 121 = 331), which happens to be prime but will not be used. Thus, (331 * 331 = 109561) is a
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// composite number which could wrongly appear prime if we skip over 331.
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static_assert(wheel_factorizer<4>::is_prime(109'561) == is_prime_by_trial_division(109'561));
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static_assert(wheel_factorizer<1>::coprimes_in_first_wheel.size() == 1);
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static_assert(wheel_factorizer<2>::coprimes_in_first_wheel.size() == 2);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel.size() == 8);
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static_assert(wheel_factorizer<4>::coprimes_in_first_wheel.size() == 48);
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static_assert(wheel_factorizer<5>::coprimes_in_first_wheel.size() == 480);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[0] == 1);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[1] == 7);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[2] == 11);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[3] == 13);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[4] == 17);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[5] == 19);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[6] == 23);
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static_assert(wheel_factorizer<3>::coprimes_in_first_wheel[7] == 29);
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static_assert(!wheel_factorizer<1>::is_prime(0));
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static_assert(!wheel_factorizer<1>::is_prime(1));
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static_assert(wheel_factorizer<1>::is_prime(2));
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static_assert(!wheel_factorizer<2>::is_prime(0));
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static_assert(!wheel_factorizer<2>::is_prime(1));
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static_assert(wheel_factorizer<2>::is_prime(2));
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static_assert(!wheel_factorizer<3>::is_prime(0));
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static_assert(!wheel_factorizer<3>::is_prime(1));
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static_assert(wheel_factorizer<3>::is_prime(2));
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} // namespace
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