// adapted from
// https://github.com/datenwolf/linmath.h

#ifndef LINMATH_H
#define LINMATH_H

#include <math.h>
#include <string.h>

#ifdef LINMATH_NO_INLINE
#define LINMATH_H_FUNC static
#else
#define LINMATH_H_FUNC static inline
#endif

#define LINMATH_H_DEFINE_VEC(n)                                                \
  typedef float vec##n[n];                                                     \
  LINMATH_H_FUNC void vec##n##_add(vec##n r, vec##n const a, vec##n const b) { \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = a[i] + b[i];                                                      \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) { \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = a[i] - b[i];                                                      \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_scale(vec##n r, vec##n const v,                 \
                                     float const s) {                          \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = v[i] * s;                                                         \
  }                                                                            \
  LINMATH_H_FUNC float vec##n##_mul_inner(vec##n const a, vec##n const b) {    \
    float p = 0.f;                                                             \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      p += b[i] * a[i];                                                        \
    return p;                                                                  \
  }                                                                            \
  LINMATH_H_FUNC float vec##n##_len(vec##n const v) {                          \
    return sqrtf(vec##n##_mul_inner(v, v));                                    \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_norm(vec##n r, vec##n const v) {                \
    float l = vec##n##_len(v);                                                 \
    float k = 1.f / (l == 0.0 ? 1.0 : l);                                      \
    vec##n##_scale(r, v, k);                                                   \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_min(vec##n r, vec##n const a, vec##n const b) { \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = a[i] < b[i] ? a[i] : b[i];                                        \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_max(vec##n r, vec##n const a, vec##n const b) { \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = a[i] > b[i] ? a[i] : b[i];                                        \
  }                                                                            \
  LINMATH_H_FUNC void vec##n##_dup(vec##n r, vec##n const src) {               \
    int i;                                                                     \
    for (i = 0; i < n; ++i)                                                    \
      r[i] = src[i];                                                           \
  }

LINMATH_H_DEFINE_VEC(2)
LINMATH_H_DEFINE_VEC(3)
LINMATH_H_DEFINE_VEC(4)

LINMATH_H_FUNC void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) {
  r[0] = a[1] * b[2] - a[2] * b[1];
  r[1] = a[2] * b[0] - a[0] * b[2];
  r[2] = a[0] * b[1] - a[1] * b[0];
}

LINMATH_H_FUNC void vec3_reflect(vec3 r, vec3 const v, vec3 const n) {
  float p = 2.f * vec3_mul_inner(v, n);
  int i;
  for (i = 0; i < 3; ++i)
    r[i] = v[i] - p * n[i];
}

LINMATH_H_FUNC void vec4_mul_cross(vec4 r, vec4 const a, vec4 const b) {
  r[0] = a[1] * b[2] - a[2] * b[1];
  r[1] = a[2] * b[0] - a[0] * b[2];
  r[2] = a[0] * b[1] - a[1] * b[0];
  r[3] = 1.f;
}

LINMATH_H_FUNC void vec4_reflect(vec4 r, vec4 const v, vec4 const n) {
  float p = 2.f * vec4_mul_inner(v, n);
  int i;
  for (i = 0; i < 4; ++i)
    r[i] = v[i] - p * n[i];
}

typedef vec4 mat4x4[4];
LINMATH_H_FUNC void mat4x4_identity(mat4x4 M) {
  int i, j;
  for (i = 0; i < 4; ++i)
    for (j = 0; j < 4; ++j)
      M[i][j] = i == j ? 1.f : 0.f;
}
LINMATH_H_FUNC void mat4x4_dup(mat4x4 M, mat4x4 const N) {
  int i;
  for (i = 0; i < 4; ++i)
    vec4_dup(M[i], N[i]);
}
LINMATH_H_FUNC void mat4x4_row(vec4 r, mat4x4 const M, int i) {
  int k;
  for (k = 0; k < 4; ++k)
    r[k] = M[k][i];
}
LINMATH_H_FUNC void mat4x4_col(vec4 r, mat4x4 const M, int i) {
  int k;
  for (k = 0; k < 4; ++k)
    r[k] = M[i][k];
}
LINMATH_H_FUNC void mat4x4_transpose(mat4x4 M, mat4x4 const N) {
  // Note: if M and N are the same, the user has to
  // explicitly make a copy of M and set it to N.
  int i, j;
  for (j = 0; j < 4; ++j)
    for (i = 0; i < 4; ++i)
      M[i][j] = N[j][i];
}
LINMATH_H_FUNC void mat4x4_add(mat4x4 M, mat4x4 const a, mat4x4 const b) {
  int i;
  for (i = 0; i < 4; ++i)
    vec4_add(M[i], a[i], b[i]);
}
LINMATH_H_FUNC void mat4x4_sub(mat4x4 M, mat4x4 const a, mat4x4 const b) {
  int i;
  for (i = 0; i < 4; ++i)
    vec4_sub(M[i], a[i], b[i]);
}
LINMATH_H_FUNC void mat4x4_scale(mat4x4 M, mat4x4 const a, float k) {
  int i;
  for (i = 0; i < 4; ++i)
    vec4_scale(M[i], a[i], k);
}
LINMATH_H_FUNC void mat4x4_scale_aniso(mat4x4 M, mat4x4 const a, float x,
                                       float y, float z) {
  vec4_scale(M[0], a[0], x);
  vec4_scale(M[1], a[1], y);
  vec4_scale(M[2], a[2], z);
  vec4_dup(M[3], a[3]);
}
LINMATH_H_FUNC void mat4x4_mul(mat4x4 M, mat4x4 const a, mat4x4 const b) {
  mat4x4 temp;
  int k, r, c;
  for (c = 0; c < 4; ++c)
    for (r = 0; r < 4; ++r) {
      temp[c][r] = 0.f;
      for (k = 0; k < 4; ++k)
        temp[c][r] += a[k][r] * b[c][k];
    }
  mat4x4_dup(M, temp);
}
LINMATH_H_FUNC void mat4x4_mul_vec4(vec4 r, mat4x4 const M, vec4 const v) {
  int i, j;
  for (j = 0; j < 4; ++j) {
    r[j] = 0.f;
    for (i = 0; i < 4; ++i)
      r[j] += M[i][j] * v[i];
  }
}
LINMATH_H_FUNC void mat4x4_translate(mat4x4 T, float x, float y, float z) {
  mat4x4_identity(T);
  T[3][0] = x;
  T[3][1] = y;
  T[3][2] = z;
}
LINMATH_H_FUNC void mat4x4_translate_in_place(mat4x4 M, float x, float y,
                                              float z) {
  vec4 t = {x, y, z, 0};
  vec4 r;
  int i;
  for (i = 0; i < 4; ++i) {
    mat4x4_row(r, M, i);
    M[3][i] += vec4_mul_inner(r, t);
  }
}
LINMATH_H_FUNC void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 const a,
                                               vec3 const b) {
  int i, j;
  for (i = 0; i < 4; ++i)
    for (j = 0; j < 4; ++j)
      M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.f;
}
LINMATH_H_FUNC void mat4x4_rotate(mat4x4 R, mat4x4 const M, float x, float y,
                                  float z, float angle) {
  float s = sinf(angle);
  float c = cosf(angle);
  vec3 u = {x, y, z};

  if (vec3_len(u) > 1e-4) {
    vec3_norm(u, u);
    mat4x4 T;
    mat4x4_from_vec3_mul_outer(T, u, u);

    mat4x4 S = {{0, u[2], -u[1], 0},
                {-u[2], 0, u[0], 0},
                {u[1], -u[0], 0, 0},
                {0, 0, 0, 0}};
    mat4x4_scale(S, S, s);

    mat4x4 C;
    mat4x4_identity(C);
    mat4x4_sub(C, C, T);

    mat4x4_scale(C, C, c);

    mat4x4_add(T, T, C);
    mat4x4_add(T, T, S);

    T[3][3] = 1.f;
    mat4x4_mul(R, M, T);
  } else {
    mat4x4_dup(R, M);
  }
}
LINMATH_H_FUNC void mat4x4_rotate_X(mat4x4 Q, mat4x4 const M, float angle) {
  float s = sinf(angle);
  float c = cosf(angle);
  mat4x4 R = {{1.f, 0.f, 0.f, 0.f},
              {0.f, c, s, 0.f},
              {0.f, -s, c, 0.f},
              {0.f, 0.f, 0.f, 1.f}};
  mat4x4_mul(Q, M, R);
}
LINMATH_H_FUNC void mat4x4_rotate_Y(mat4x4 Q, mat4x4 const M, float angle) {
  float s = sinf(angle);
  float c = cosf(angle);
  mat4x4 R = {{c, 0.f, -s, 0.f},
              {0.f, 1.f, 0.f, 0.f},
              {s, 0.f, c, 0.f},
              {0.f, 0.f, 0.f, 1.f}};
  mat4x4_mul(Q, M, R);
}
LINMATH_H_FUNC void mat4x4_rotate_Z(mat4x4 Q, mat4x4 const M, float angle) {
  float s = sinf(angle);
  float c = cosf(angle);
  mat4x4 R = {{c, s, 0.f, 0.f},
              {-s, c, 0.f, 0.f},
              {0.f, 0.f, 1.f, 0.f},
              {0.f, 0.f, 0.f, 1.f}};
  mat4x4_mul(Q, M, R);
}
LINMATH_H_FUNC void mat4x4_invert(mat4x4 T, mat4x4 const M) {
  float s[6];
  float c[6];
  s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1];
  s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2];
  s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3];
  s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2];
  s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3];
  s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3];

  c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1];
  c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2];
  c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3];
  c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2];
  c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3];
  c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3];

  /* Assumes it is invertible */
  float idet = 1.0f / (s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] -
                       s[4] * c[1] + s[5] * c[0]);

  T[0][0] = (M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet;
  T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet;
  T[0][2] = (M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet;
  T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet;

  T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet;
  T[1][1] = (M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet;
  T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet;
  T[1][3] = (M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet;

  T[2][0] = (M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet;
  T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet;
  T[2][2] = (M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet;
  T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet;

  T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet;
  T[3][1] = (M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet;
  T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet;
  T[3][3] = (M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet;
}
LINMATH_H_FUNC void mat4x4_orthonormalize(mat4x4 R, mat4x4 const M) {
  mat4x4_dup(R, M);
  float s = 1.f;
  vec3 h;

  vec3_norm(R[2], R[2]);

  s = vec3_mul_inner(R[1], R[2]);
  vec3_scale(h, R[2], s);
  vec3_sub(R[1], R[1], h);
  vec3_norm(R[1], R[1]);

  s = vec3_mul_inner(R[0], R[2]);
  vec3_scale(h, R[2], s);
  vec3_sub(R[0], R[0], h);

  s = vec3_mul_inner(R[0], R[1]);
  vec3_scale(h, R[1], s);
  vec3_sub(R[0], R[0], h);
  vec3_norm(R[0], R[0]);
}

LINMATH_H_FUNC void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t,
                                   float n, float f) {
  M[0][0] = 2.f * n / (r - l);
  M[0][1] = M[0][2] = M[0][3] = 0.f;

  M[1][1] = 2.f * n / (t - b);
  M[1][0] = M[1][2] = M[1][3] = 0.f;

  M[2][0] = (r + l) / (r - l);
  M[2][1] = (t + b) / (t - b);
  M[2][2] = -(f + n) / (f - n);
  M[2][3] = -1.f;

  M[3][2] = -2.f * (f * n) / (f - n);
  M[3][0] = M[3][1] = M[3][3] = 0.f;
}
LINMATH_H_FUNC void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t,
                                 float n, float f) {
  M[0][0] = 2.f / (r - l);
  M[0][1] = M[0][2] = M[0][3] = 0.f;

  M[1][1] = 2.f / (t - b);
  M[1][0] = M[1][2] = M[1][3] = 0.f;

  M[2][2] = -2.f / (f - n);
  M[2][0] = M[2][1] = M[2][3] = 0.f;

  M[3][0] = -(r + l) / (r - l);
  M[3][1] = -(t + b) / (t - b);
  M[3][2] = -(f + n) / (f - n);
  M[3][3] = 1.f;
}
LINMATH_H_FUNC void mat4x4_perspective(mat4x4 m, float y_fov, float aspect,
                                       float n, float f) {
  /* NOTE: Degrees are an unhandy unit to work with.
   * linmath.h uses radians for everything! */
  float const a = 1.f / tanf(y_fov / 2.f);

  m[0][0] = a / aspect;
  m[0][1] = 0.f;
  m[0][2] = 0.f;
  m[0][3] = 0.f;

  m[1][0] = 0.f;
  m[1][1] = a;
  m[1][2] = 0.f;
  m[1][3] = 0.f;

  m[2][0] = 0.f;
  m[2][1] = 0.f;
  m[2][2] = -((f + n) / (f - n));
  m[2][3] = -1.f;

  m[3][0] = 0.f;
  m[3][1] = 0.f;
  m[3][2] = -((2.f * f * n) / (f - n));
  m[3][3] = 0.f;
}
LINMATH_H_FUNC void mat4x4_look_at(mat4x4 m, vec3 const eye, vec3 const center,
                                   vec3 const up) {
  /* Adapted from Android's OpenGL Matrix.java.                        */
  /* See the OpenGL GLUT documentation for gluLookAt for a description */
  /* of the algorithm. We implement it in a straightforward way:       */

  /* TODO: The negation of of can be spared by swapping the order of
   *       operands in the following cross products in the right way. */
  vec3 f;
  vec3_sub(f, center, eye);
  vec3_norm(f, f);

  vec3 s;
  vec3_mul_cross(s, f, up);
  vec3_norm(s, s);

  vec3 t;
  vec3_mul_cross(t, s, f);

  m[0][0] = s[0];
  m[0][1] = t[0];
  m[0][2] = -f[0];
  m[0][3] = 0.f;

  m[1][0] = s[1];
  m[1][1] = t[1];
  m[1][2] = -f[1];
  m[1][3] = 0.f;

  m[2][0] = s[2];
  m[2][1] = t[2];
  m[2][2] = -f[2];
  m[2][3] = 0.f;

  m[3][0] = 0.f;
  m[3][1] = 0.f;
  m[3][2] = 0.f;
  m[3][3] = 1.f;

  mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]);
}

typedef float quat[4];
#define quat_add vec4_add
#define quat_sub vec4_sub
#define quat_norm vec4_norm
#define quat_scale vec4_scale
#define quat_mul_inner vec4_mul_inner

LINMATH_H_FUNC void quat_identity(quat q) {
  q[0] = q[1] = q[2] = 0.f;
  q[3] = 1.f;
}
LINMATH_H_FUNC void quat_mul(quat r, quat const p, quat const q) {
  vec3 w;
  vec3_mul_cross(r, p, q);
  vec3_scale(w, p, q[3]);
  vec3_add(r, r, w);
  vec3_scale(w, q, p[3]);
  vec3_add(r, r, w);
  r[3] = p[3] * q[3] - vec3_mul_inner(p, q);
}
LINMATH_H_FUNC void quat_conj(quat r, quat const q) {
  int i;
  for (i = 0; i < 3; ++i)
    r[i] = -q[i];
  r[3] = q[3];
}
LINMATH_H_FUNC void quat_rotate(quat r, float angle, vec3 const axis) {
  vec3 axis_norm;
  vec3_norm(axis_norm, axis);
  float s = sinf(angle / 2);
  float c = cosf(angle / 2);
  vec3_scale(r, axis_norm, s);
  r[3] = c;
}
LINMATH_H_FUNC void quat_mul_vec3(vec3 r, quat const q, vec3 const v) {
  /*
   * Method by Fabian 'ryg' Giessen (of Farbrausch)
  t = 2 * cross(q.xyz, v)
  v' = v + q.w * t + cross(q.xyz, t)
   */
  vec3 t;
  vec3 q_xyz = {q[0], q[1], q[2]};
  vec3 u = {q[0], q[1], q[2]};

  vec3_mul_cross(t, q_xyz, v);
  vec3_scale(t, t, 2);

  vec3_mul_cross(u, q_xyz, t);
  vec3_scale(t, t, q[3]);

  vec3_add(r, v, t);
  vec3_add(r, r, u);
}
LINMATH_H_FUNC void mat4x4_from_quat(mat4x4 M, quat const q) {
  float a = q[3];
  float b = q[0];
  float c = q[1];
  float d = q[2];
  float a2 = a * a;
  float b2 = b * b;
  float c2 = c * c;
  float d2 = d * d;

  M[0][0] = a2 + b2 - c2 - d2;
  M[0][1] = 2.f * (b * c + a * d);
  M[0][2] = 2.f * (b * d - a * c);
  M[0][3] = 0.f;

  M[1][0] = 2 * (b * c - a * d);
  M[1][1] = a2 - b2 + c2 - d2;
  M[1][2] = 2.f * (c * d + a * b);
  M[1][3] = 0.f;

  M[2][0] = 2.f * (b * d + a * c);
  M[2][1] = 2.f * (c * d - a * b);
  M[2][2] = a2 - b2 - c2 + d2;
  M[2][3] = 0.f;

  M[3][0] = M[3][1] = M[3][2] = 0.f;
  M[3][3] = 1.f;
}

LINMATH_H_FUNC void mat4x4o_mul_quat(mat4x4 R, mat4x4 const M, quat const q) {
  /*  XXX: The way this is written only works for orthogonal matrices. */
  /* TODO: Take care of non-orthogonal case. */
  quat_mul_vec3(R[0], q, M[0]);
  quat_mul_vec3(R[1], q, M[1]);
  quat_mul_vec3(R[2], q, M[2]);

  R[3][0] = R[3][1] = R[3][2] = 0.f;
  R[0][3] = M[0][3];
  R[1][3] = M[1][3];
  R[2][3] = M[2][3];
  R[3][3] = M[3][3]; // typically 1.0, but here we make it general
}
LINMATH_H_FUNC void quat_from_mat4x4(quat q, mat4x4 const M) {
  float r = 0.f;
  int i;

  int perm[] = {0, 1, 2, 0, 1};
  int *p = perm;

  for (i = 0; i < 3; i++) {
    float m = M[i][i];
    if (m < r)
      continue;
    m = r;
    p = &perm[i];
  }

  r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]);

  if (r < 1e-6) {
    q[0] = 1.f;
    q[1] = q[2] = q[3] = 0.f;
    return;
  }

  q[0] = r / 2.f;
  q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]]) / (2.f * r);
  q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]]) / (2.f * r);
  q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]]) / (2.f * r);
}

LINMATH_H_FUNC void mat4x4_arcball(mat4x4 R, mat4x4 const M, vec2 const _a,
                                   vec2 const _b, float s) {
  vec2 a;
  memcpy(a, _a, sizeof(a));
  vec2 b;
  memcpy(b, _b, sizeof(b));

  float z_a = 0.f;
  float z_b = 0.f;

  if (vec2_len(a) < 1.f) {
    z_a = sqrtf(1.f - vec2_mul_inner(a, a));
  } else {
    vec2_norm(a, a);
  }

  if (vec2_len(b) < 1.f) {
    z_b = sqrtf(1.f - vec2_mul_inner(b, b));
  } else {
    vec2_norm(b, b);
  }

  vec3 a_ = {a[0], a[1], z_a};
  vec3 b_ = {b[0], b[1], z_b};

  vec3 c_;
  vec3_mul_cross(c_, a_, b_);

  float const angle = acos(vec3_mul_inner(a_, b_)) * s;
  mat4x4_rotate(R, M, c_[0], c_[1], c_[2], angle);
}
#endif