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/* MIT License
*
* Copyright (c) 2016--2017 Felix Lenders
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*/
#include "trlib.h"
#include "trlib_private.h"
#include "_c99compat.h"
trlib_int_t trlib_quadratic_zero(trlib_flt_t c_abs, trlib_flt_t c_lin, trlib_flt_t tol,
trlib_int_t verbose, trlib_int_t unicode, char *prefix, FILE *fout,
trlib_flt_t *t1, trlib_flt_t *t2) {
trlib_int_t n = 0; // number of roots
trlib_flt_t q = 0.0;
trlib_flt_t dq = 0.0;
trlib_flt_t lin_sq = c_lin*c_lin;
*t1 = 0.0; // first root
*t2 = 0.0; // second root
if (fabs(c_abs) > tol*lin_sq) {
// well behaved non-degenerate quadratic
// compute discriminant
q = lin_sq - 4.0 * c_abs;
if ( fabs(q) <= (TRLIB_EPS*c_lin)*(TRLIB_EPS*c_lin) ) {
// two distinct zeros, but discrimant tiny --> numeric double zero
// initialize on same root obtained by standard formula with zero discrement, let newton refinement do the rest
n = 2;
*t1 = -.5*c_lin; *t2 = *t1;
}
else if ( q < 0.0 ) {
n = 2;
*t1 = 0.0; *t2 = 0.0;
return n;
}
else {
// discriminant large enough, two distinc zeros
n = 2;
// start with root according to plus sign to avoid cancellation
*t1 = -.5 * ( c_lin + copysign( sqrt(q), c_lin ) );
*t2 = c_abs/(*t1);
if (*t2 < *t1) { q = *t2; *t2 = *t1; *t1 = q; }
}
}
else {
n = 2;
if (c_lin < 0.0) { *t1 = 0.0; *t2 = - c_lin; }
else { *t1 = - c_lin; *t2 = 0.0; }
}
// newton correction
q = (*t1+c_lin)*(*t1)+c_abs; dq = 2.0*(*t1)+c_lin;
if (dq != 0.0) { *t1 = *t1 - q/dq; }
q = (*t2+c_lin)*(*t2)+c_abs; dq = 2.0*(*t2)+c_lin;
if (dq != 0.0) { *t2 = *t2 - q/dq; }
return n;
}
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