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This file is a \"Hello, world!\" in C++ language by GCC for wandbox.\n#include \n#include \n\n#include \"QuarticEquation.hpp\"\n\nint main()\n{\n {\n auto [x1, x2, x3, x4] = SolveQuarticEquation(1.0, -12.0, 49.0, -78.0, 40.0);\n std::cout << x1 << \",\"<< x2 << \",\" << x3 << \",\" << x4 << std::endl;\n }\n \n {\n auto [x1, x2, x3, x4] = SolveQuarticEquation(1.0, 4.0, -21.0, 10.0, -1.0);\n std::cout << x1 << \",\"<< x2 << \",\" << x3 << \",\" << x4 << std::endl;\n }\n \n {\n auto [x1, x2, x3, x4] = SolveQuarticEquation(19.0, 4.0, 58.0, 32.0, 7.0);\n std::cout << x1 << \",\"<< x2 << \",\" << x3 << \",\" << x4 << std::endl;\n }\n}\n\n// GCC reference:\n// https://gcc.gnu.org/\n\n// C++ language references:\n// https://msdn.microsoft.com/library/3bstk3k5.aspx\n// http://www.cplusplus.com/\n// https://isocpp.org/\n// http://www.open-std.org/jtc1/sc22/wg21/\n\n// Boost libraries references:\n// http://www.boost.org/doc/\n","codes",[3396],{"_3397":3398,"_3392":3399},"file","QuarticEquation.hpp","#include \n#include \n#include \n\ntemplate\nauto SolveLinearEquation(const T a, const T b) -> std::tuple {\n\t//ax + b = 0\n\t//x = -b / a\n\treturn { -a / b };\n}\n\ntemplate\nauto SolveQuadraticEquation(const T a, const T b, const T c) -> std::tuple, std::complex> {\n\tif (a == T(0.0)) {\n\t\tconstexpr std::tuple> zero{};\n\n\t\tauto x = SolveLinearEquation(b, c);\n\n\t\treturn std::tuple_cat(std::move(x), zero);\n\t}\n\n\t//D = b^2 - 4ac\n\tconst auto D = b * b - T(4.0) * a * c;\n\n\tstd::complex x1{}, x2{};\n\n\tif (std::fabs(D) < 1.0E-12) {\n\t\t//重解\n\t\tx1 = x2 = -b / (a + a);\n\t}\n\telse if (D < 0.0) {\n\t\t//互いに共役な複素数解\n\t\tconst auto a2 = a + a;\n\t\tconst auto real = -b / a2;\n\t\tconst auto imag = std::sqrt(-D) / a2;\n\t\tx1 = { real, imag };\n\t\tx2 = { real, -imag };\n\t}\n\telse {\n\t\t//異なる実数解\n\n\t\t//桁落ち対策\n\t\tif (T(0.0) < b) {\n\t\t\t//-b - √D\n\t\t\tconst auto tmp = -b - std::sqrt(D);\n\t\t\t//2c/(-b - √D)\n\t\t\tx1 = (c + c) / tmp;\n\t\t}\n\t\telse {\n\t\t\t//(-b + √D)\n\t\t\tconst auto tmp = -b + std::sqrt(D);\n\t\t\t//(-b + √D)/2a\n\t\t\tx1 = tmp / (a + a);\n\t\t}\n\n\t\t//解と係数の関係（x1・x2 = c/a）より\n\t\tx2 = (c / a) / x1;\n\t}\n\n\treturn std::make_tuple(x1, x2);\n}\n\ntemplate\nauto SolveQuadraticEquation(const std::complex a, const std::complex b, const std::complex c) -> std::tuple, std::complex> {\n\t//D = b^2 - 4ac\n\tconst auto D = b * b - T(4.0)*a*c;\n\t//√D\n\tconst auto root_D = std::sqrt(D);\n\tconst auto a2 = a + a;\n\n\tconstexpr T zero(0.0);\n\n\t//桁落ち対策\n\tif (zero < b.real() && zero < b.imag()) {\n\t\tif (root_D.real() <= zero && root_D.imag() <= zero) {\n\t\t\t//-b - √D\n\t\t\tconst auto tmp = -b - root_D;\n\t\t\t//2c/(-b - √D)\n\t\t\tauto x1 = (c + c) / tmp;\n\t\t\tauto x2 = (c / a) / x1;\n\t\t\treturn std::make_tuple(std::move(x1), std::move(x2));\n\t\t}\n\t}\n\telse if(b.real() <= zero && b.imag() <= zero) {\n\t\tif (zero < root_D.real() && zero < root_D.imag()) {\n\t\t\tconst auto tmp = -b + root_D;\n\t\t\t//(-b + √D)/2a\n\t\t\tauto x1 = tmp / a2;\n\t\t\tauto x2 = (c / a) / x1;\n\t\t\treturn std::make_tuple(std::move(x1), std::move(x2));\n\t\t}\n\t}\n\n\t//桁落ち対策を諦めた\n\n\t//(-b + √D)/2a\n\tauto x1 = (-b + root_D) / a2;\n\t//(-b - √D)/2a\n\tauto x2 = (-b - root_D) / a2;\n\treturn std::make_tuple(std::move(x1), std::move(x2));\n}\n \n \ntemplate\nauto SolveCubicEquation(const T p, const T q) -> std::tuple, std::complex, std::complex> {\n\t//p/3\n\tconst auto p_d3 = p / T(3.0);\n\t//q/2\n\tconst auto q_half = q / T(2.0);\n\t//D = (q/2)^2 + (p/3)^3\n\tconst auto D = q_half * q_half + p_d3 * p_d3 * p_d3;\n\n\tT x1{};\n\tstd::complex x2{}, x3{};\n\n\tif (std::fabs(D) < 1.0E-8) {\n\t\t// D == 0 重解\n\n\t\tauto tmp = std::cbrt(q_half);\n\t\tx1 = T(-2.0) * tmp;\n\t\tx2 = x3 = tmp;\n\t}\n\telse if (0.0 < D) {\n\t\t// 0 < D １つの実数解と二つの共役な複素数解\n\n\t\t//√D\n\t\tconst auto D_root = std::sqrt(D);\n\t\t//u = v = ∛(-q/2 ± √D)\n\t\tconst auto u = std::cbrt(-q_half + D_root);\n\t\tconst auto v = std::cbrt(-q_half - D_root);\n\n\t\tx1 = u + v;\n\t\t//-(u + v)/2\n\t\tconst auto real = T(-0.5) * x1;\n\t\t//√3\n\t\tconstexpr T root3 = T(1.7320508075688772935274463415059);\n\t\t//√3(u - v)/2\n\t\tconst auto imag = root3 * (u - v) * T(0.5);\n\n\t\tx2 = { real, imag };\n\t\tx3 = { real, -imag };\n\t}\n\telse {\n\t\t// D < 0 異なる３つの実数解\n\n\t\t//2√(-p/3)\n\t\tconst auto sqrt_p_d3 = T(2.0) * std::sqrt(-p_d3);\n\t\t//θ/3\n\t\tconst auto arg = std::arg(std::complex{ -q_half, std::sqrt(-D) }) / T(3.0);\n\t\t//2π/3\n\t\tconstexpr T pi2d3 = T(2.0 * 3.1415926535897932384626433832795 / 3.0);\n\n\t\tx1 = sqrt_p_d3 * std::cos(arg);\n\t\tx2 = sqrt_p_d3 * std::cos(arg + pi2d3);\n\t\tx3 = sqrt_p_d3 * std::cos(arg + pi2d3 + pi2d3);\n\t}\n\n\treturn std::make_tuple(x1, x2, x3);\n}\n\ntemplate\nauto SolveCubicEquation(const T A, const T B, const T C) -> std::tuple, std::complex, std::complex> {\n\t//A/3\n\tauto A_div3 = A / T(3.0);\n\n\tconst T p = B - A_div3 * A;\n\n\t//A^3/27\n\tauto q_t = A_div3 * A_div3 * A_div3;\n\t//2A^3/27\n\tq_t += q_t;\n\n\tconst T q = q_t - A_div3 * B + C;\n\n\tauto [x1, x2, x3] = SolveCubicEquation(p, q);\n\n\t//xn = yn - A/3\n\treturn std::make_tuple(x1 - A_div3, x2 - A_div3, x3 - A_div3);\n}\n\n\ntemplate\nauto SolveCubicEquation(const T a, const T b, const T c, const T d) -> std::tuple, std::complex, std::complex> {\n\tconstexpr std::tuple> zero{};\n\n\tif (a == 0.0) {\n\t\t//bx^2 + cx + d = 0\n\t\t//x = (-b ± √(b^2 - 4ac))/2a\n\t\tauto x = SolveQuadraticEquation(b, c, d);\n\n\t\treturn std::tuple_cat(std::move(x), zero);\n\t}\n\n\treturn SolveCubicEquation(b / a, c / a, d / a);\n}\n\ntemplate\nauto BiquadraticEquation(const T a, const T c, const T e) -> std::tuple, std::complex, std::complex, std::complex> {\n\tauto [x1, x2] = SolveQuadraticEquation(a, c, e);\n\n\tauto sqrt_x1 = std::sqrt(x1);\n\tauto sqrt_x2 = std::sqrt(x2);\n\n\treturn std::make_tuple(sqrt_x1, -sqrt_x1, sqrt_x2, -sqrt_x2);\n}\n\ntemplate\nauto SolveQuarticEquation(const T p, const T q, const T r) -> std::tuple, std::complex, std::complex, std::complex> {\n\tif (q == T(0.0)) {\n\t\t//複二次式\n\t\treturn BiquadraticEquation(T(1.0), p, r);\n\t}\n\telse if (r == T(0.0)) {\n\t\tconstexpr std::tuple> zero{};\n\n\t\tauto x = SolveCubicEquation(p, q);\n\n\t\treturn std::tuple_cat(std::move(x), zero);\n\t}\n\n\t//tの式の各係数を求める\n\t//t^3 -pt^2-4rt+(4pr-q^2) = 0\n\n\tconst auto r4 = T(4.0)*r;\n\tconst auto c =r4*p - q * q;\n\n\tstd::complex t_c{};\n\n\t//tのうち実数のものを選択\n\tstd::tie(t_c, std::ignore, std::ignore) = SolveCubicEquation(-p, -r4, c);\n\t\t\n\tconst auto t = t_c.real();\n\n\t//t-p\n\tconst auto t_p = t - p;\n\n\tif (T(0.0) <= t_p) {\n\t\t//m = √(t-p)\n\t\tconst auto m = std::sqrt(t_p);\n\n\t\t//n = q/2√(t-p)\n\t\tconst auto n = q / (T(2.0)*m);\n\n\t\t//t/2\n\t\tconst auto half_t = T(0.5)*t;\n\n\t\t//2つの二次式を解く！\n\t\tauto&& y_12 = SolveQuadraticEquation(T(1.0), m, half_t - n);\n\t\tauto&& y_34 = SolveQuadraticEquation(T(1.0), -m, half_t + n);\n\n\t\treturn std::tuple_cat(std::move(y_12), std::move(y_34));\n\t}\n\telse {\n\t\t//負の数の平方根を求めなければならない場合\n\n\t\t//m = √(t-p)\n\t\tconst std::complex m = { 0.0, std::sqrt(-t_p) };\n\n\t\t//n = q/2√(t-p)\n\t\tconst auto n = q / (T(2.0)*m);\n\n\t\t//t/2\n\t\tconst auto half_t = T(0.5)*t;\n\n\t\t//複素係数二次方程式\n\t\tauto&& y_12 = SolveQuadraticEquation({ T(1.0) }, m, half_t - n);\n\t\tauto&& y_34 = SolveQuadraticEquation({ T(1.0) }, -m, half_t + n);\n\n\t\treturn std::tuple_cat(std::move(y_12), std::move(y_34));\n\t}\n}\n\ntemplate\nauto SolveQuarticEquation(const T A, const T B, const T C, const T D) -> std::tuple, std::complex, std::complex, std::complex> {\n\t//(A/4)\n\tconst auto A_d4 = A / T(4.0);\n\t//(A/4)^2\n\tconst auto A_d4_sq = A_d4 * A_d4;\n\t//(A/4)^3\n\tconst auto A_d4_cu = A_d4 * A_d4_sq;\n\n\tconst auto p = T(-6.0) * A_d4_sq + B;\n\tconst auto q = T(2.0) * (T(4.0) * A_d4_cu - B * A_d4) + C;\n\tconst auto r = (T(-3.0) * A_d4_cu - C) * A_d4 + B * A_d4_sq + D;\n\n\tauto [y1, y2, y3, y4] = SolveQuarticEquation(p, q, r);\n\n\treturn std::make_tuple(y1 - A_d4, y2 - A_d4, y3 - A_d4, y4 - A_d4);\n}\n\ntemplate\nauto SolveQuarticEquation(const T a, const T b, const T c,const T d, const T e) -> std::tuple, std::complex, std::complex, std::complex> {\n\tif (a == T(0.0)) {\n\t\tconstexpr std::tuple> zero{};\n\n\t\tauto x = SolveCubicEquation(b, c, d, e);\n \treturn std::tuple_cat(std::move(x), zero);\n\t}\n\telse if (b == T(0.0) && d == T(0.0)) {\n\t\t//複二次式\n\t\treturn BiquadraticEquation(a, c, e);\n\t}\n\n\treturn SolveQuarticEquation(b / a, c / a, d / a, e / a);\n}","stdin","compiler","clang-7.0.0","warning,boost-1.69.0-clang-7.0.0,c++2a,cpp-no-pedantic","createdAt",1550403755,"title","description","isPrivate","compilerInfo",{"_11":3402,"_13":3411,"_15":333,"_17":767,"_19":3412,"_22":23,"_24":25,"_26":890,"_28":3413},"7.0.0",[767],[3414,3416,3418,3420,3466,3471,3476,3490],{"_31":32,"_33":3415},{"_11":35,"_36":23,"_37":38,"_17":39},{"_31":32,"_33":3417},{"_11":42,"_36":25,"_37":43,"_17":44},{"_31":32,"_33":3419},{"_11":47,"_36":25,"_37":48,"_17":49},{"_31":51,"_33":3421},{"_11":3422,"_36":3423,"_55":3424},"boost-clang-7.0.0","boost-1.69.0-clang-7.0.0",[3425,3427,3431,3435,3439,3443,3447,3451,3455,3459,3463],{"_11":3426,"_37":59,"_17":330},"boost-nothing-clang-7.0.0",{"_11":3428,"_37":3429,"_17":3430},"boost-1.61.0-clang-7.0.0","-I/opt/wandbox/boost-1.61.0/clang-7.0.0/include","Boost 1.61.0",{"_11":3432,"_37":3433,"_17":3434},"boost-1.62.0-clang-7.0.0","-I/opt/wandbox/boost-1.62.0/clang-7.0.0/include","Boost 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