/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8                                :vi│
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright 2020 Justine Alexandra Roberts Tunney                              │
│                                                                              │
│ Permission to use, copy, modify, and/or distribute this software for         │
│ any purpose with or without fee is hereby granted, provided that the         │
│ above copyright notice and this permission notice appear in all copies.      │
│                                                                              │
│ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL                │
│ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED                │
│ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE             │
│ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL         │
│ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR        │
│ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER               │
│ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR             │
│ PERFORMANCE OF THIS SOFTWARE.                                                │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "dsp/core/core.h"

#define LEIBNIZ_FORMULA(a, b, c, d, e, f, g, h, i) \
  (a * e * i + b * f * g + c * d * h - c * e * g - b * d * i - a * f * h)

/**
 * Computes determinant of 3×3 matrix.
 * i.e. how much space is inside the cube
 *
 * @param 𝐀 is input matrix
 * @param 𝑑 is det(𝐀)
 * @return |𝐀| or 0 if degenerate
 */
double det3(const double A[3][3]) {
  return LEIBNIZ_FORMULA(A[0][0], A[0][1], A[0][2], A[1][0], A[1][1], A[1][2],
                         A[2][0], A[2][1], A[2][2]);
}