// poly34.h : solution of cubic and quartic equation // (c) Khashin S.I. http://math.ivanovo.ac.ru/dalgebra/Khashin/index.html // khash2 (at) gmail.com #include "gpu/vectorTypes.hpp" #undef FN_NAME #undef INL_FN_FLOAT #undef INL_FN_FLOAT2 #undef INL_FN_FLOAT3 #undef INL_FN_QUARTIC_SOL #define FN_NAME(fnName) fnName #define INL_FN_FLOAT(fnName) inline double fnName #define INL_FN_FLOAT2(fnName) inline double2 fnName #define INL_FN_FLOAT3(fnName) inline double3 fnName #define INL_FN_QUARTIC_SOL(fnName) inline vsQuarticSolution fnName namespace VideoStitch { namespace Core { // solve equation a*x^4 + b*x^3 + c*x^2 + d*x + e = 0 , where a, b, c, d, e could be 0 // details of the output parameters are described in the solveP3 and solveP4 INL_FN_QUARTIC_SOL(solveQuartic)(const double a, const double b, const double c, const double d, const double e); INL_FN_QUARTIC_SOL(solveP1)(const double a); // solve linear equation x + a = 0 INL_FN_QUARTIC_SOL(solveP2)(const double a, const double b); // solve quadratic equation x^2 + a*x + b = 0 INL_FN_QUARTIC_SOL(solveP3) (const double a, const double b, const double c); // solve cubic equation x^3 + a*x^2 + b*x + c = 0 INL_FN_QUARTIC_SOL(solveP4) (const double a, const double b, const double c, const double d); // solve equation x^4 + a*x^3 + b*x^2 + c*x + d = 0 by Dekart-Euler method // x - array of size 4 // return 4: 4 real roots x[0], x[1], x[2], x[3], possible multiple roots // return 2: 2 real roots x[0], x[1] and complex x[2]±i*x[3], // return 0: two pair of complex roots: x[0]±i*x[1], x[2]±i*x[3], INL_FN_QUARTIC_SOL(solveP4Bi)(const double b, const double d); // solve equation x^4 + b*x^2 + d = 0 INL_FN_QUARTIC_SOL(solveP4De) (const double b, const double c, const double d); // solve equation x^4 + b*x^2 + c*x + d = 0 INL_FN_FLOAT2(cSqrt)(const double x, const double y); // returns as a+i*s, sqrt(x+i*y) INL_FN_FLOAT(n4Step) (const double x, const double a, const double b, const double c, const double d); // one Newton step for x^4 + a*x^3 + b*x^2 + c*x + d INL_FN_QUARTIC_SOL(setQuarticSolution)(const int solutionCount, const double x[4]); } // namespace Core } // namespace VideoStitch