| /* |

| * Copyright 2023 Google LLC |

| * |

| * Use of this source code is governed by a BSD-style license that can be |

| * found in the LICENSE file. |

| */ |

| |

| #ifndef SkQuads_DEFINED |

| #define SkQuads_DEFINED |

| |

| /** |

| * Utilities for dealing with quadratic formulas with one variable: |

| * f(t) = A*t^2 + B*t + C |

| */ |

| class SkQuads { |

| public: |

| /** |

| * Calculate a very accurate discriminant. |

| * Given |

| * A*t^2 -2*B*t + C = 0, |

| * calculate |

| * B^2 - AC |

| * accurate to 2 bits. |

| * Note the form of the quadratic is slightly different from the normal formulation. |

| * |

| * The method used to calculate the discriminant is from |

| * "On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic" |

| * by W. Kahan. |

| */ |

| static double Discriminant(double A, double B, double C); |

| |

| struct RootResult { |

| double discriminant; |

| double root0; |

| double root1; |

| }; |

| |

| /** |

| * Calculate the roots of a quadratic. |

| * Given |

| * A*t^2 -2*B*t + C = 0, |

| * calculate the roots. |

| * |

| * This does not try to detect a linear configuration of the equation, or detect if the two |

| * roots are the same. It returns the discriminant and the two roots. |

| * |

| * Not this uses a different form the quadratic equation to reduce rounding error. Give |

| * standard A, B, C. You can call this root finder with: |

| * Roots(A, -0.5*B, C) |

| * to find the roots of A*x^2 + B*x + C. |

| * |

| * The method used to calculate the roots is from |

| * "On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic" |

| * by W. Kahan. |

| * |

| * If the roots are imaginary then nan is returned. |

| * If the roots can't be represented as double then inf is returned. |

| */ |

| static RootResult Roots(double A, double B, double C); |

| |

| /** |

| * Puts up to 2 real solutions to the equation |

| * A*t^2 + B*t + C = 0 |

| * in the provided array. |

| */ |

| static int RootsReal(double A, double B, double C, double solution[2]); |

| |

| /** |

| * Evaluates the quadratic function with the 3 provided coefficients and the |

| * provided variable. |

| */ |

| static double EvalAt(double A, double B, double C, double t); |

| }; |

| |

| #endif |