mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-12-23 21:25:49 +00:00
add sprout/rational.hpp
add sprout/math/common_factor.hpp
This commit is contained in:
parent
dc8cb3d14e
commit
5a9b2e4f7d
8 changed files with 1153 additions and 119 deletions
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@ -1,44 +1,44 @@
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//
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//
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// Sprout C++ Library
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// Sprout C++ Library
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//
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//
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// Copyright (c) 2012
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// Copyright (c) 2012
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// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
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// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
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// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
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// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
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//
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//
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// Readme:
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// Readme:
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// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
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// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
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//
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//
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// License:
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// License:
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// Boost Software License - Version 1.0
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// Boost Software License - Version 1.0
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// <http://www.boost.org/LICENSE_1_0.txt>
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// <http://www.boost.org/LICENSE_1_0.txt>
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//
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//
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#include <sprout/string.hpp>
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#include <sprout/string.hpp>
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//
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//
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// C style string to Sprout.String
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// C style string to Sprout.String
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//
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//
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int
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int
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main(){
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main(){
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constexpr char const* c_str = "homu";
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constexpr char const* c_str = "homu";
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//
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//
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// String length is required
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// String length is required
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//
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//
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constexpr auto length = sprout::char_traits<char>::length(c_str);
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constexpr auto length = sprout::char_traits<char>::length(c_str);
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static_assert(length == 4, "");
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static_assert(length == 4, "");
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//
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//
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// To Sprout.String
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// To Sprout.String
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//
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//
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constexpr auto str = sprout::string_from_c_str<length>( c_str );
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constexpr auto str = sprout::string_from_c_str<length>( c_str );
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static_assert(std::is_same<sprout::string<4> const, decltype(str)>{}, "");
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static_assert(std::is_same<sprout::string<4> const, decltype(str)>{}, "");
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static_assert(str == "homu", "");
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static_assert(str == "homu", "");
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constexpr auto str2 = sprout::string_from_c_str<length>( c_str, 2 );
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constexpr auto str2 = sprout::string_from_c_str<length>( c_str, 2 );
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static_assert(std::is_same<sprout::string<4> const, decltype(str2)>{}, "");
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static_assert(std::is_same<sprout::string<4> const, decltype(str2)>{}, "");
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static_assert(str2 == "ho", "");
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static_assert(str2 == "ho", "");
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return 0;
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return 0;
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}
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}
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@ -1,67 +1,67 @@
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//
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//
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// Sprout C++ Library
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// Sprout C++ Library
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//
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//
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// Copyright (c) 2012
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// Copyright (c) 2012
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// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
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// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
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// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
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// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
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//
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//
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// Readme:
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// Readme:
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// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
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// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
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//
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//
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// License:
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// License:
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// Boost Software License - Version 1.0
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// Boost Software License - Version 1.0
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// <http://www.boost.org/LICENSE_1_0.txt>
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// <http://www.boost.org/LICENSE_1_0.txt>
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//
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//
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#include <sprout/weed.hpp>
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#include <sprout/weed.hpp>
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int
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int
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main(){
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main(){
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namespace w = sprout::weed;
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namespace w = sprout::weed;
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static constexpr auto source = sprout::to_string("homu:mado");
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static constexpr auto source = sprout::to_string("homu:mado");
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// String parser
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// String parser
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static constexpr auto item = *w::lim<4>(w::char_ - ':');
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static constexpr auto item = *w::lim<4>(w::char_ - ':');
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//
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//
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// If you do not want to use the as_tuple
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// If you do not want to use the as_tuple
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//
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//
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{
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{
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static constexpr auto parser = item >> ':' >> item;
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static constexpr auto parser = item >> ':' >> item;
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static constexpr auto result = w::parse(
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static constexpr auto result = w::parse(
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sprout::begin(source), sprout::end(source), parser
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sprout::begin(source), sprout::end(source), parser
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);
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);
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static_assert(result.success(), "");
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static_assert(result.success(), "");
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// !!!!
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// !!!!
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static_assert(result.attr() == "homumado", "");
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static_assert(result.attr() == "homumado", "");
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}
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}
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//
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//
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// You need to use the as_tuple
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// You need to use the as_tuple
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//
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//
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{
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{
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static constexpr auto parser = w::as_tuple[item] >> ':' >> w::as_tuple[item];
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static constexpr auto parser = w::as_tuple[item] >> ':' >> w::as_tuple[item];
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static constexpr auto result = w::parse(
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static constexpr auto result = w::parse(
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sprout::begin(source), sprout::end(source), parser
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sprout::begin(source), sprout::end(source), parser
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);
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);
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static_assert(result.success(), "");
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static_assert(result.success(), "");
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static constexpr auto attr = result.attr();
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static constexpr auto attr = result.attr();
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// OK
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// OK
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static_assert(std::is_same<
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static_assert(std::is_same<
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sprout::tuple<sprout::string<4>, sprout::string<4>> const,
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sprout::tuple<sprout::string<4>, sprout::string<4>> const,
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decltype(attr)
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decltype(attr)
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>::value, "");
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>::value, "");
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static_assert(sprout::get<0>(attr) == "homu", "");
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static_assert(sprout::get<0>(attr) == "homu", "");
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static_assert(sprout::get<1>(attr) == "mado", "");
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static_assert(sprout::get<1>(attr) == "mado", "");
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}
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}
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return 0;
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return 0;
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}
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}
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@ -10,14 +10,6 @@ namespace sprout {
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SPROUT_CONSTEXPR std::intmax_t imaxabs(std::intmax_t j) {
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SPROUT_CONSTEXPR std::intmax_t imaxabs(std::intmax_t j) {
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return j < 0 ? -j : j;
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return j < 0 ? -j : j;
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}
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}
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template<
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typename T,
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typename sprout::enabler_if<std::is_same<T, std::intmax_t>::value>::type = sprout::enabler
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>
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SPROUT_CONSTEXPR T abs(T j) {
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return sprout::imaxabs(j);
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}
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} // namespace sprout
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} // namespace sprout
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#endif // #ifndef SPROUT_CINTTYPES_ABS_HPP
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#endif // #ifndef SPROUT_CINTTYPES_ABS_HPP
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#ifndef SPROUT_CSTDLIB_ABS_HPP
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#ifndef SPROUT_CSTDLIB_ABS_HPP
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#define SPROUT_CSTDLIB_ABS_HPP
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#define SPROUT_CSTDLIB_ABS_HPP
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/config.hpp>
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#include <sprout/utility/enabler_if.hpp>
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namespace sprout {
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namespace sprout {
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// Copyright (C) 2011 RiSK (sscrisk)
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// Copyright (C) 2011 RiSK (sscrisk)
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@ -26,6 +28,25 @@ namespace sprout {
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SPROUT_CONSTEXPR long long abs(long long j) {
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SPROUT_CONSTEXPR long long abs(long long j) {
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return sprout::llabs(j);
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return sprout::llabs(j);
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}
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}
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template<
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typename IntType,
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typename sprout::enabler_if<
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std::is_integral<IntType>::value && std::is_signed<IntType>::value
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>::type = sprout::enabler
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>
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SPROUT_CONSTEXPR IntType abs(IntType j) {
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return j < 0 ? -j : j;
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}
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template<
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typename IntType,
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typename sprout::enabler_if<
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std::is_integral<IntType>::value && std::is_unsigned<IntType>::value
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>::type = sprout::enabler
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>
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SPROUT_CONSTEXPR IntType abs(IntType j) {
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return j;
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}
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} // namespace sprout
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} // namespace sprout
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#endif // #ifndef SPROUT_CSTDLIB_ABS_HPP
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#endif // #ifndef SPROUT_CSTDLIB_ABS_HPP
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7
sprout/math/common_factor.hpp
Normal file
7
sprout/math/common_factor.hpp
Normal file
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#ifndef SPROUT_MATH_COMMON_FACTOR_HPP
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#define SPROUT_MATH_COMMON_FACTOR_HPP
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#include <sprout/math/gcd.hpp>
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#include <sprout/math/lcm.hpp>
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#endif // SPROUT_MATH_COMMON_FACTOR_HPP
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188
sprout/math/gcd.hpp
Normal file
188
sprout/math/gcd.hpp
Normal file
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#ifndef SPROUT_MATH_GCD_HPP
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#define SPROUT_MATH_GCD_HPP
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#include <climits>
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#include <limits>
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#include <sprout/config.hpp>
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#include <sprout/array.hpp>
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#include <sprout/cstdlib/abs.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename RingType>
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inline SPROUT_CONSTEXPR RingType
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gcd_euclidean(RingType a, RingType b) {
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return a == static_cast<RingType>(0) ? b
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: b % a == static_cast<RingType>(0) ? a
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: sprout::math::detail::gcd_euclidean(a % (b % a), b % a)
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;
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}
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template<typename IntType>
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inline SPROUT_CONSTEXPR IntType
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gcd_integer_impl(IntType result) {
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return result < static_cast<IntType>(0) ? -result : result;
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}
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template<typename IntType>
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inline SPROUT_CONSTEXPR IntType
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gcd_integer(IntType const& a, IntType const& b) {
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return sprout::math::detail::gcd_integer_impl(
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sprout::math::detail::gcd_euclidean(a, b)
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);
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return !(r[ which ] & 1u) ? sprout::math::detail::gcd_binary_2_2(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
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,
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which
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)
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: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_1(
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shifts,
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which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which ^ 1u
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)
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: sprout::math::detail::gcd_binary_2_1(
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shifts,
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which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
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: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
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,
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which
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)
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;
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
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return r[which] ? sprout::math::detail::gcd_binary_2_2(shifts, r, which)
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: r[!which] << shifts
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;
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary_1(BuiltInUnsigned u, BuiltInUnsigned v, unsigned shifts = 0) {
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return (!(u & 1u) && !(v & 1u)) ? sprout::math::detail::gcd_binary_1(u >> 1, v >> 1, shifts + 1)
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: sprout::math::detail::gcd_binary_2_2(
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shifts, sprout::array<BuiltInUnsigned, 2>{{u, v}}, static_cast<bool>(u & 1u)
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)
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;
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}
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template<typename BuiltInUnsigned>
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inline SPROUT_CONSTEXPR BuiltInUnsigned
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gcd_binary(BuiltInUnsigned u, BuiltInUnsigned v) {
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return u && v ? sprout::math::detail::gcd_binary_1(u, v)
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: u + v
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;
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}
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template<typename T, bool IsSpecialized, bool IsSigned>
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struct gcd_optimal_evaluator_helper_t {
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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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return sprout::math::detail::gcd_euclidean(a, b);
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}
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};
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template<typename T>
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struct gcd_optimal_evaluator_helper_t<T, true, true> {
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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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return sprout::math::detail::gcd_integer(a, b);
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}
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};
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template<typename T>
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struct gcd_optimal_evaluator {
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public:
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SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
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typedef std::numeric_limits<T> limits_type;
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typedef sprout::math::detail::gcd_optimal_evaluator_helper_t<
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T, limits_type::is_specialized, limits_type::is_signed
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> helper_type;
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return helper_type().operator()(a, b);
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}
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};
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# define SPROUT_PRIVATE_GCD_UF(Ut) \
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template<> \
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struct gcd_optimal_evaluator<Ut> { \
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public: \
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SPROUT_CONSTEXPR Ut operator()(Ut a, Ut b) const { \
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return sprout::math::detail::gcd_binary(a, b); \
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} \
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}
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SPROUT_PRIVATE_GCD_UF(unsigned char);
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SPROUT_PRIVATE_GCD_UF(unsigned short);
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SPROUT_PRIVATE_GCD_UF(unsigned);
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SPROUT_PRIVATE_GCD_UF(unsigned long);
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SPROUT_PRIVATE_GCD_UF(unsigned long long);
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# if CHAR_MIN == 0
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SPROUT_PRIVATE_GCD_UF(char);
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# endif
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#undef SPROUT_PRIVATE_GCD_UF
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# define SPROUT_PRIVATE_GCD_SF(St, Ut) \
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template<> \
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struct gcd_optimal_evaluator<St> { \
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public: \
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SPROUT_CONSTEXPR St operator()(St a, St b) const { \
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using sprout::abs; \
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return static_cast<St>(sprout::math::detail::gcd_optimal_evaluator<Ut>().operator()( \
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static_cast<Ut>(abs(a)), static_cast<Ut>(abs(b)) \
|
||||||
|
)); \
|
||||||
|
} \
|
||||||
|
}
|
||||||
|
SPROUT_PRIVATE_GCD_SF(signed char, unsigned char);
|
||||||
|
SPROUT_PRIVATE_GCD_SF(short, unsigned short);
|
||||||
|
SPROUT_PRIVATE_GCD_SF(int, unsigned);
|
||||||
|
SPROUT_PRIVATE_GCD_SF(long, unsigned long);
|
||||||
|
# if CHAR_MIN < 0
|
||||||
|
SPROUT_PRIVATE_GCD_SF(char, unsigned char);
|
||||||
|
# endif
|
||||||
|
SPROUT_PRIVATE_GCD_SF(long long, unsigned long long);
|
||||||
|
#undef SPROUT_PRIVATE_GCD_SF
|
||||||
|
|
||||||
|
template<typename T>
|
||||||
|
inline SPROUT_CONSTEXPR T
|
||||||
|
gcd_optimal(T const& a, T const& b) {
|
||||||
|
return sprout::math::detail::gcd_optimal_evaluator<T>().operator()(a, b);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
|
||||||
|
//
|
||||||
|
// gcd_evaluator
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
class gcd_evaluator {
|
||||||
|
public:
|
||||||
|
typedef IntType result_type;
|
||||||
|
typedef IntType first_argument_type;
|
||||||
|
typedef IntType second_argument_type;
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR result_type
|
||||||
|
operator()(first_argument_type const& a, second_argument_type const& b) const {
|
||||||
|
return sprout::math::detail::gcd_optimal(a, b);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
//
|
||||||
|
// gcd
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR IntType
|
||||||
|
gcd(IntType const& a, IntType const& b) {
|
||||||
|
return sprout::math::gcd_evaluator<IntType>().operator()(a, b);
|
||||||
|
}
|
||||||
|
} // namespace math
|
||||||
|
} // namespace boost
|
||||||
|
|
||||||
|
#endif // SPROUT_MATH_GCD_HPP
|
101
sprout/math/lcm.hpp
Normal file
101
sprout/math/lcm.hpp
Normal file
|
@ -0,0 +1,101 @@
|
||||||
|
#ifndef SPROUT_MATH_LCM_HPP
|
||||||
|
#define SPROUT_MATH_LCM_HPP
|
||||||
|
|
||||||
|
#include <climits>
|
||||||
|
#include <limits>
|
||||||
|
#include <sprout/config.hpp>
|
||||||
|
#include <sprout/math/gcd.hpp>
|
||||||
|
|
||||||
|
namespace sprout {
|
||||||
|
namespace math {
|
||||||
|
namespace detail {
|
||||||
|
template<typename RingType>
|
||||||
|
inline SPROUT_CONSTEXPR RingType
|
||||||
|
lcm_euclidean_impl(RingType a, RingType b, RingType temp) {
|
||||||
|
return temp != static_cast<RingType>(0) ? (a / temp * b)
|
||||||
|
: static_cast<RingType>(0)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
template<typename RingType>
|
||||||
|
inline SPROUT_CONSTEXPR RingType
|
||||||
|
lcm_euclidean(RingType a, RingType b) {
|
||||||
|
return sprout::math::detail::lcm_euclidean_impl(
|
||||||
|
a, b, sprout::math::detail::gcd_euclidean(a, b)
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR IntType
|
||||||
|
lcm_integer_impl(IntType result) {
|
||||||
|
return result < static_cast<IntType>(0) ? -result : result;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR IntType
|
||||||
|
lcm_integer(IntType const& a, IntType const& b) {
|
||||||
|
return sprout::math::detail::lcm_integer_impl(
|
||||||
|
sprout::math::detail::lcm_euclidean(a, b)
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename T, bool IsSpecialized, bool IsSigned>
|
||||||
|
struct lcm_optimal_evaluator_helper_t {
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
|
||||||
|
return sprout::math::detail::lcm_euclidean(a, b);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
template<typename T>
|
||||||
|
struct lcm_optimal_evaluator_helper_t<T, true, true> {
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
|
||||||
|
return sprout::math::detail::lcm_integer(a, b);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template<typename T>
|
||||||
|
struct lcm_optimal_evaluator {
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
|
||||||
|
typedef std::numeric_limits<T> limits_type;
|
||||||
|
typedef sprout::math::detail::lcm_optimal_evaluator_helper_t<
|
||||||
|
T, limits_type::is_specialized, limits_type::is_signed
|
||||||
|
> helper_type;
|
||||||
|
return helper_type().operator()(a, b);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template<typename T>
|
||||||
|
inline SPROUT_CONSTEXPR T
|
||||||
|
lcm_optimal(T const& a, T const& b) {
|
||||||
|
return sprout::math::detail::lcm_optimal_evaluator<T>().operator()(a, b);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
|
||||||
|
//
|
||||||
|
// lcm_evaluator
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
class lcm_evaluator {
|
||||||
|
public:
|
||||||
|
typedef IntType result_type;
|
||||||
|
typedef IntType first_argument_type;
|
||||||
|
typedef IntType second_argument_type;
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR result_type
|
||||||
|
operator()(first_argument_type const& a, second_argument_type const& b) const {
|
||||||
|
return sprout::math::detail::lcm_optimal(a, b);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
//
|
||||||
|
// lcm
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR IntType
|
||||||
|
lcm(IntType const& a, IntType const& b) {
|
||||||
|
return sprout::math::lcm_evaluator<IntType>().operator()(a, b);
|
||||||
|
}
|
||||||
|
} // namespace math
|
||||||
|
} // namespace boost
|
||||||
|
|
||||||
|
#endif // SPROUT_MATH_LCM_HPP
|
725
sprout/rational.hpp
Normal file
725
sprout/rational.hpp
Normal file
|
@ -0,0 +1,725 @@
|
||||||
|
#ifndef SPROUT_RATIONAL_HPP
|
||||||
|
#define SPROUT_RATIONAL_HPP
|
||||||
|
|
||||||
|
#include <limits>
|
||||||
|
#include <utility>
|
||||||
|
#include <stdexcept>
|
||||||
|
#include <ios>
|
||||||
|
#include <iostream>
|
||||||
|
#include <sprout/config.hpp>
|
||||||
|
#include <sprout/cstdlib/abs.hpp>
|
||||||
|
#include <sprout/math/gcd.hpp>
|
||||||
|
#include <sprout/detail/call_traits.hpp>
|
||||||
|
#include <sprout/detail/io/ios_state.hpp>
|
||||||
|
|
||||||
|
namespace sprout {
|
||||||
|
//
|
||||||
|
// bad_rational
|
||||||
|
//
|
||||||
|
class bad_rational
|
||||||
|
: public std::domain_error
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
explicit bad_rational()
|
||||||
|
: std::domain_error("bad rational: zero denominator")
|
||||||
|
{}
|
||||||
|
};
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
class rational;
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
struct rational_private_constructor_tag {};
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType> make_rational(
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type n,
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type d,
|
||||||
|
sprout::detail::rational_private_constructor_tag
|
||||||
|
);
|
||||||
|
} // namespace detail
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
class rational_impl {
|
||||||
|
protected:
|
||||||
|
typedef IntType int_type;
|
||||||
|
typedef typename sprout::detail::call_traits<IntType>::param_type param_type;
|
||||||
|
protected:
|
||||||
|
IntType num_;
|
||||||
|
IntType den_;
|
||||||
|
protected:
|
||||||
|
SPROUT_CONSTEXPR rational_impl()
|
||||||
|
: num_(0)
|
||||||
|
, den_(1)
|
||||||
|
{}
|
||||||
|
rational_impl(rational_impl const&) = default;
|
||||||
|
SPROUT_CONSTEXPR rational_impl(param_type n)
|
||||||
|
: num_(n)
|
||||||
|
, den_(1)
|
||||||
|
{}
|
||||||
|
SPROUT_CONSTEXPR rational_impl(param_type n, param_type d)
|
||||||
|
: num_(n)
|
||||||
|
, den_(d)
|
||||||
|
{}
|
||||||
|
SPROUT_CONSTEXPR rational_impl(param_type n, param_type d, param_type g)
|
||||||
|
: num_(n / g)
|
||||||
|
, den_(d / g)
|
||||||
|
{}
|
||||||
|
};
|
||||||
|
} // namespace detail
|
||||||
|
|
||||||
|
//
|
||||||
|
// rational
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
class rational
|
||||||
|
: private sprout::detail::rational_impl<IntType>
|
||||||
|
{
|
||||||
|
static_assert(std::numeric_limits<IntType>::is_specialized, "std::numeric_limits<IntType>::is_specialized");
|
||||||
|
public:
|
||||||
|
typedef IntType int_type;
|
||||||
|
typedef typename sprout::detail::call_traits<IntType>::param_type param_type;
|
||||||
|
private:
|
||||||
|
struct private_constructor_tag {};
|
||||||
|
typedef sprout::detail::rational_impl<IntType> base_type;
|
||||||
|
private:
|
||||||
|
static SPROUT_CONSTEXPR IntType normalize_g_1(IntType den, IntType g) {
|
||||||
|
return den / g < 0 ? -g : g;
|
||||||
|
}
|
||||||
|
static SPROUT_CONSTEXPR IntType normalize_g(IntType num, IntType den) {
|
||||||
|
return den == 0 ? throw sprout::bad_rational()
|
||||||
|
: num == 0 ? den
|
||||||
|
: normalize_g_1(den, sprout::math::gcd(num, den))
|
||||||
|
;
|
||||||
|
}
|
||||||
|
private:
|
||||||
|
using base_type::num_;
|
||||||
|
using base_type::den_;
|
||||||
|
private:
|
||||||
|
SPROUT_CONSTEXPR rational(param_type n, param_type d, private_constructor_tag)
|
||||||
|
: base_type(n, d)
|
||||||
|
{}
|
||||||
|
public:
|
||||||
|
SPROUT_CONSTEXPR rational()
|
||||||
|
: base_type()
|
||||||
|
{}
|
||||||
|
rational(rational const&) = default;
|
||||||
|
SPROUT_CONSTEXPR rational(param_type n)
|
||||||
|
: base_type(n)
|
||||||
|
{}
|
||||||
|
SPROUT_CONSTEXPR rational(param_type n, param_type d)
|
||||||
|
: base_type(n, d, normalize_g(n, d))
|
||||||
|
{}
|
||||||
|
|
||||||
|
rational& operator=(rational const&) = default;
|
||||||
|
rational& operator=(param_type n) {
|
||||||
|
return assign(n, 1);
|
||||||
|
}
|
||||||
|
rational& assign(param_type n, param_type d) {
|
||||||
|
using std::swap;
|
||||||
|
rational temp(n, d);
|
||||||
|
swap(temp, *this);
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
|
||||||
|
SPROUT_CONSTEXPR IntType numerator() const {
|
||||||
|
return num_;
|
||||||
|
}
|
||||||
|
SPROUT_CONSTEXPR IntType denominator() const {
|
||||||
|
return den_;
|
||||||
|
}
|
||||||
|
|
||||||
|
rational& operator+=(rational const& rhs) {
|
||||||
|
IntType g = sprout::math::gcd(den_, rhs.den_);
|
||||||
|
den_ /= g;
|
||||||
|
num_ = num_ * (rhs.den_ / g) + rhs.num_ * den_;
|
||||||
|
g = sprout::math::gcd(num_, g);
|
||||||
|
num_ /= g;
|
||||||
|
den_ *= rhs.den_ / g;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational& operator-=(rational const& rhs) {
|
||||||
|
IntType g = sprout::math::gcd(den_, rhs.den_);
|
||||||
|
den_ /= g;
|
||||||
|
num_ = num_ * (rhs.den_ / g) - rhs.num_ * den_;
|
||||||
|
g = sprout::math::gcd(num_, g);
|
||||||
|
num_ /= g;
|
||||||
|
den_ *= rhs.den_ / g;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational& operator*=(rational const& rhs) {
|
||||||
|
IntType gcd1 = sprout::math::gcd(num_, rhs.den_);
|
||||||
|
IntType gcd2 = sprout::math::gcd(rhs.num_, den_);
|
||||||
|
num_ =(num_ / gcd1) * (rhs.num_ / gcd2);
|
||||||
|
den_ =(den_ / gcd2) * (rhs.den_ / gcd1);
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational& operator/=(rational const& rhs) {
|
||||||
|
if (rhs.num_ == IntType(0)) {
|
||||||
|
throw bad_rational();
|
||||||
|
}
|
||||||
|
if (num_ == IntType(0)) {
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
IntType gcd1 = sprout::math::gcd(num_, rhs.num_);
|
||||||
|
IntType gcd2 = sprout::math::gcd(rhs.den_, den_);
|
||||||
|
num_ =(num_ / gcd1) * (rhs.den_ / gcd2);
|
||||||
|
den_ =(den_ / gcd2) * (rhs.num_ / gcd1);
|
||||||
|
if (den_ < IntType(0)) {
|
||||||
|
num_ = -num_;
|
||||||
|
den_ = -den_;
|
||||||
|
}
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational& operator+=(param_type rhs) {
|
||||||
|
return *this += rational(rhs);
|
||||||
|
}
|
||||||
|
rational& operator-=(param_type rhs) {
|
||||||
|
return *this -= rational(rhs);
|
||||||
|
}
|
||||||
|
rational& operator*=(param_type rhs) {
|
||||||
|
return *this *= rational(rhs);
|
||||||
|
}
|
||||||
|
rational& operator/=(param_type rhs) {
|
||||||
|
return *this /= rational(rhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
rational& operator++() {
|
||||||
|
num_ += den_;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational& operator--() {
|
||||||
|
num_ -= den_;
|
||||||
|
return *this;
|
||||||
|
}
|
||||||
|
rational operator++(int) {
|
||||||
|
rational result(*this);
|
||||||
|
++*this;
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
rational operator--(int) {
|
||||||
|
rational result(*this);
|
||||||
|
--*this;
|
||||||
|
return result;
|
||||||
|
}
|
||||||
|
|
||||||
|
SPROUT_CONSTEXPR bool operator!() const {
|
||||||
|
return !num_;
|
||||||
|
}
|
||||||
|
SPROUT_CONSTEXPR operator bool() const {
|
||||||
|
return num_ != 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
public:
|
||||||
|
friend sprout::rational<IntType> sprout::detail::make_rational<IntType>(
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type n,
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type d,
|
||||||
|
sprout::detail::rational_private_constructor_tag
|
||||||
|
);
|
||||||
|
};
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType> make_rational(
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type n,
|
||||||
|
typename sprout::detail::call_traits<IntType>::param_type d,
|
||||||
|
sprout::detail::rational_private_constructor_tag
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return sprout::rational<IntType>(
|
||||||
|
n, d,
|
||||||
|
typename sprout::rational<IntType>::private_constructor_tag()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
|
||||||
|
//
|
||||||
|
// operator+
|
||||||
|
// operator-
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator+(rational<IntType> const& r) {
|
||||||
|
return r;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator-(rational<IntType> const& r) {
|
||||||
|
return sprout::detail::make_rational<IntType>(
|
||||||
|
-r.numerator(), r.denominator(),
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// operator+
|
||||||
|
// operator-
|
||||||
|
// operator*
|
||||||
|
// operator/
|
||||||
|
//
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_add_impl_3(
|
||||||
|
sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den, IntType num
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return sprout::detail::make_rational<IntType>(
|
||||||
|
num / g, den * (rhs.denominator() / g),
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_add_impl_2(
|
||||||
|
sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den, IntType num
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_add_impl_3(
|
||||||
|
rhs,
|
||||||
|
sprout::math::gcd(num, g), den, num
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_add_impl_1(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_add_impl_2(
|
||||||
|
rhs,
|
||||||
|
g, den, lhs.numerator() * (rhs.denominator() / g) + rhs.numerator() * den
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_add_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_add_impl_1(
|
||||||
|
lhs, rhs,
|
||||||
|
g, lhs.denominator() / g
|
||||||
|
);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator+(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::detail::rational_add_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
sprout::math::gcd(lhs.denominator(), rhs.denominator())
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator+(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return lhs + sprout::rational<IntType>(rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator+(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::rational<IntType>(lhs) + rhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_sub_impl_3(
|
||||||
|
sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den, IntType num
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return sprout::detail::make_rational<IntType>(
|
||||||
|
num / g, den * (rhs.denominator() / g),
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_sub_impl_2(
|
||||||
|
sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den, IntType num
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_sub_impl_3(
|
||||||
|
rhs,
|
||||||
|
sprout::math::gcd(num, g), den, num
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_sub_impl_1(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g, IntType den
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_sub_impl_2(
|
||||||
|
rhs,
|
||||||
|
g, den, lhs.numerator() * (rhs.denominator() / g) - rhs.numerator() * den
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_sub_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType g
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return rational_sub_impl_1(
|
||||||
|
lhs, rhs,
|
||||||
|
g, lhs.denominator() / g
|
||||||
|
);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator-(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::detail::rational_sub_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
sprout::math::gcd(lhs.denominator(), rhs.denominator())
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator-(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return lhs - sprout::rational<IntType>(rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator-(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::rational<IntType>(lhs) - rhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_mul_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType gcd1, IntType gcd2
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return sprout::detail::make_rational<IntType>(
|
||||||
|
(lhs.numerator() / gcd1) * (rhs.numerator() / gcd2),
|
||||||
|
(lhs.denominator() / gcd2) * (rhs.denominator() / gcd1),
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator*(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::detail::rational_mul_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
sprout::math::gcd(lhs.numerator(), rhs.denominator()),
|
||||||
|
sprout::math::gcd(rhs.numerator(), lhs.denominator())
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator*(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return lhs * sprout::rational<IntType>(rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator*(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::rational<IntType>(lhs) * rhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_div_impl_1(IntType num, IntType den) {
|
||||||
|
return den < IntType(0) ? sprout::detail::make_rational<IntType>(
|
||||||
|
-num, -den,
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
)
|
||||||
|
: sprout::detail::make_rational<IntType>(
|
||||||
|
num, den,
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
rational_div_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType gcd1, IntType gcd2
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return sprout::detail::rational_div_impl_1(
|
||||||
|
(lhs.numerator() / gcd1) * (rhs.denominator() / gcd2),
|
||||||
|
(lhs.denominator() / gcd2) * (rhs.numerator() / gcd1)
|
||||||
|
);
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator/(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return rhs.numerator() == IntType(0) ? throw sprout::bad_rational()
|
||||||
|
: lhs.numerator() == IntType(0) ? lhs
|
||||||
|
: sprout::detail::rational_div_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
sprout::math::gcd(lhs.numerator(), rhs.numerator()),
|
||||||
|
sprout::math::gcd(rhs.denominator(), lhs.denominator())
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator/(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return lhs / sprout::rational<IntType>(rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
operator/(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::rational<IntType>(lhs) / rhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// operator==
|
||||||
|
// operator!=
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator==(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return lhs.numerator() == rhs.numerator() && lhs.denominator() == rhs.denominator();
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator==(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return lhs.denominator() == IntType(1) && lhs.numerator() == rhs;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator==(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return rhs == lhs;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator!=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(lhs == rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator!=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return !(lhs == rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator!=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(lhs == rhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// operator<
|
||||||
|
// operator>
|
||||||
|
// operator<=
|
||||||
|
// operator>=
|
||||||
|
//
|
||||||
|
namespace detail {
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
rational_less_impl_2(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType d1, IntType q1, IntType r1,
|
||||||
|
IntType d2, IntType q2, IntType r2,
|
||||||
|
unsigned reverse = 0
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return q1 != q2 ? reverse ? q1 > q2 : q1 < q2
|
||||||
|
: r1 == IntType(0) || r2 == IntType(0)
|
||||||
|
? r1 == r2 ? false
|
||||||
|
: (r1 != IntType(0)) != static_cast<bool>(reverse ^ 1)
|
||||||
|
: sprout::detail::rational_less_impl_2(
|
||||||
|
lhs, rhs,
|
||||||
|
r1, d1 / r1, d1 % r1,
|
||||||
|
r2, d2 / r2, d2 % r2,
|
||||||
|
reverse ^ 1
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
rational_less_impl_1(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType d1, IntType q1, IntType r1,
|
||||||
|
IntType d2, IntType q2, IntType r2
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return r2 < IntType(0) ? sprout::detail::rational_less_impl_1(
|
||||||
|
lhs, rhs,
|
||||||
|
d1, q1, r1,
|
||||||
|
d2, q2 - 1, r2 + d2
|
||||||
|
)
|
||||||
|
: sprout::detail::rational_less_impl_2(
|
||||||
|
lhs, rhs,
|
||||||
|
d1, q1, r1,
|
||||||
|
d2, q2, r2
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
rational_less_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
|
||||||
|
IntType d1, IntType q1, IntType r1
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return r1 < IntType(0) ? sprout::detail::rational_less_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
d1, q1 - 1, r1 + d1
|
||||||
|
)
|
||||||
|
: sprout::detail::rational_less_impl_1(
|
||||||
|
lhs, rhs,
|
||||||
|
d1, q1, r1,
|
||||||
|
rhs.denominator(), rhs.numerator() / rhs.denominator(), rhs.numerator() % rhs.denominator()
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
rational_less_impl(
|
||||||
|
sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs,
|
||||||
|
IntType q, IntType r
|
||||||
|
)
|
||||||
|
{
|
||||||
|
return r < IntType(0) ? sprout::detail::rational_less_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
r + lhs.denominator(), q - 1
|
||||||
|
)
|
||||||
|
: q < rhs
|
||||||
|
;
|
||||||
|
}
|
||||||
|
} // namespace detail
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return sprout::detail::rational_less_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
lhs.denominator(), lhs.numerator() / lhs.denominator(), lhs.numerator() % lhs.denominator()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return sprout::detail::rational_less_impl(
|
||||||
|
lhs, rhs,
|
||||||
|
lhs.numerator() / lhs.denominator(), lhs.numerator() % lhs.denominator()
|
||||||
|
);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return lhs != rhs && !(rhs < lhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return rhs < lhs;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return rhs < lhs;
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return rhs < lhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(rhs < lhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return !(rhs < lhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator<=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(rhs < lhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(lhs < rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
|
||||||
|
return !(lhs < rhs);
|
||||||
|
}
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR bool
|
||||||
|
operator>=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return !(lhs < rhs);
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// operator>>
|
||||||
|
// operator<<
|
||||||
|
//
|
||||||
|
template<typename Elem, typename Traits, typename IntType>
|
||||||
|
inline std::basic_istream<Elem, Traits>&
|
||||||
|
operator>>(std::basic_istream<Elem, Traits>& lhs, sprout::rational<IntType>& rhs) {
|
||||||
|
IntType n = IntType(0);
|
||||||
|
IntType d = IntType(1);
|
||||||
|
Elem c = 0;
|
||||||
|
sprout::detail::io::ios_flags_saver saver(lhs);
|
||||||
|
lhs >> n;
|
||||||
|
c = lhs.get();
|
||||||
|
if (c != Elem('/')) {
|
||||||
|
lhs.clear(std::istream::badbit);
|
||||||
|
}
|
||||||
|
lhs >> std::noskipws;
|
||||||
|
lhs >> d;
|
||||||
|
if (lhs) {
|
||||||
|
rhs.assign(n, d);
|
||||||
|
}
|
||||||
|
return lhs;
|
||||||
|
}
|
||||||
|
template<typename Elem, typename Traits, typename IntType>
|
||||||
|
inline std::basic_ostream<Elem, Traits>&
|
||||||
|
operator<<(std::basic_ostream<Elem, Traits>& lhs, sprout::rational<IntType> const& rhs) {
|
||||||
|
return lhs << rhs.numerator() << Elem('/') << rhs.denominator();
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// rational_cast
|
||||||
|
//
|
||||||
|
template<typename T, typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR T
|
||||||
|
rational_cast(sprout::rational<IntType> const& src) {
|
||||||
|
return static_cast<T>(src.numerator()) / static_cast<T>(src.denominator());
|
||||||
|
}
|
||||||
|
|
||||||
|
//
|
||||||
|
// abs
|
||||||
|
//
|
||||||
|
template<typename IntType>
|
||||||
|
inline SPROUT_CONSTEXPR sprout::rational<IntType>
|
||||||
|
abs(sprout::rational<IntType> const& x) {
|
||||||
|
return x.numerator() >= IntType(0) ? x
|
||||||
|
: sprout::detail::make_rational<IntType>(
|
||||||
|
-x.numerator(), x.denominator(),
|
||||||
|
sprout::detail::rational_private_constructor_tag()
|
||||||
|
)
|
||||||
|
;
|
||||||
|
}
|
||||||
|
|
||||||
|
} // namespace sprout
|
||||||
|
|
||||||
|
#endif // SPROUT_RATIONAL_HPP
|
Loading…
Reference in a new issue