quadratic.h

Go to the documentation of this file.

// Copyright 2019, Philipp Zabel
// Copyright 2026, Beyley Cardellio
// SPDX-License-Identifier: BSL-1.0
/*!
 * @file
 * @brief  Quadratic root finder, specialized for P3P solving.
 * @author Philipp Zabel <philipp.zabel@gmail.com>
 * @author Beyley Cardellio <ep1cm1n10n123@gmail.com>
 * @ingroup xrt_iface
 */
 
#pragma once
 
#include <math.h>
#include <stdbool.h>
 
 
/*
 * Store the real roots of the reduced quadratic equation x² + bx + c = 0 in
 * r1, r2. Returns true if roots are found, false otherwise.
 */
static inline bool
reduced_quadratic_real_roots(double b, double c, double *r1, double *r2)
{
        const double half_b = 0.5 * b;
        const double quarter_v = half_b * half_b - c;
 
        if (quarter_v < 0) {
                return false;
        }
 
        const double half_y = sqrt(quarter_v);
 
        *r1 = -half_b + half_y;
        *r2 = -half_b - half_y;
 
        return true;
}
 
/*
 * Store the real roots of the quadratic equation ax² + bx + c = 0 in
 * r1, r2. Returns true if roots are found, false otherwise.
 */
static inline bool
quadratic_real_roots(double a, double b, double c, double *r1, double *r2)
{
        const double a_inv = 1.0 / a;
 
        return reduced_quadratic_real_roots(b * a_inv, c * a_inv, r1, r2);
}