mat4.h

/*
 * Copyright (c), Recep Aslantas.
 *
 * MIT License (MIT), http://opensource.org/licenses/MIT
 * Full license can be found in the LICENSE file
 */

/*!
 * Most of functions in this header are optimized manually with SIMD
 * if available. You dont need to call/incude SIMD headers manually
 */

/*
 Macros:
   GLM_MAT4_IDENTITY_INIT
   GLM_MAT4_ZERO_INIT
   GLM_MAT4_IDENTITY
   GLM_MAT4_ZERO

 Functions:
   CGLM_INLINE void  glm_mat4_ucopy(mat4 mat, mat4 dest);
   CGLM_INLINE void  glm_mat4_copy(mat4 mat, mat4 dest);
   CGLM_INLINE void  glm_mat4_identity(mat4 mat);
   CGLM_INLINE void  glm_mat4_identity_array(mat4 * restrict mat, size_t count);
   CGLM_INLINE void  glm_mat4_zero(mat4 mat);
   CGLM_INLINE void  glm_mat4_pick3(mat4 mat, mat3 dest);
   CGLM_INLINE void  glm_mat4_pick3t(mat4 mat, mat3 dest);
   CGLM_INLINE void  glm_mat4_ins3(mat3 mat, mat4 dest);
   CGLM_INLINE void  glm_mat4_mul(mat4 m1, mat4 m2, mat4 dest);
   CGLM_INLINE void  glm_mat4_mulN(mat4 *matrices[], int len, mat4 dest);
   CGLM_INLINE void  glm_mat4_mulv(mat4 m, vec4 v, vec4 dest);
   CGLM_INLINE void  glm_mat4_mulv3(mat4 m, vec3 v, float last, vec3 dest);
   CGLM_INLINE float glm_mat4_trace(mat4 m);
   CGLM_INLINE float glm_mat4_trace3(mat4 m);
   CGLM_INLINE void  glm_mat4_quat(mat4 m, versor dest) ;
   CGLM_INLINE void  glm_mat4_transpose_to(mat4 m, mat4 dest);
   CGLM_INLINE void  glm_mat4_transpose(mat4 m);
   CGLM_INLINE void  glm_mat4_scale_p(mat4 m, float s);
   CGLM_INLINE void  glm_mat4_scale(mat4 m, float s);
   CGLM_INLINE float glm_mat4_det(mat4 mat);
   CGLM_INLINE void  glm_mat4_inv(mat4 mat, mat4 dest);
   CGLM_INLINE void  glm_mat4_inv_fast(mat4 mat, mat4 dest);
   CGLM_INLINE void  glm_mat4_swap_col(mat4 mat, int col1, int col2);
   CGLM_INLINE void  glm_mat4_swap_row(mat4 mat, int row1, int row2);
   CGLM_INLINE float glm_mat4_rmc(vec4 r, mat4 m, vec4 c);
   CGLM_INLINE void  glm_mat4_make(float * restrict src, mat4 dest);
 */

#ifndef cglm_mat_h
#define cglm_mat_h

#include "common.h"
#include "vec4.h"
#include "vec3.h"

#ifdef CGLM_SSE_FP
#  include "simd/sse2/mat4.h"
#endif

#ifdef CGLM_AVX_FP
#  include "simd/avx/mat4.h"
#endif

#ifdef CGLM_NEON_FP
#  include "simd/neon/mat4.h"
#endif

#ifdef CGLM_SIMD_WASM
#  include "simd/wasm/mat4.h"
#endif

#ifndef NDEBUG
# include <assert.h>
#endif

#define GLM_MAT4_IDENTITY_INIT  {{1.0f, 0.0f, 0.0f, 0.0f},                    \
                                 {0.0f, 1.0f, 0.0f, 0.0f},                    \
                                 {0.0f, 0.0f, 1.0f, 0.0f},                    \
                                 {0.0f, 0.0f, 0.0f, 1.0f}}

#define GLM_MAT4_ZERO_INIT      {{0.0f, 0.0f, 0.0f, 0.0f},                    \
                                 {0.0f, 0.0f, 0.0f, 0.0f},                    \
                                 {0.0f, 0.0f, 0.0f, 0.0f},                    \
                                 {0.0f, 0.0f, 0.0f, 0.0f}}

/* for C only */
#define GLM_MAT4_IDENTITY ((mat4)GLM_MAT4_IDENTITY_INIT)
#define GLM_MAT4_ZERO     ((mat4)GLM_MAT4_ZERO_INIT)

/* DEPRECATED! use _copy, _ucopy versions */
#define glm_mat4_udup(mat, dest) glm_mat4_ucopy(mat, dest)
#define glm_mat4_dup(mat, dest)  glm_mat4_copy(mat, dest)

/* DEPRECATED! default is precise now. */
#define glm_mat4_inv_precise(mat, dest) glm_mat4_inv(mat, dest)

/*!
 * @brief copy all members of [mat] to [dest]
 *
 * matrix may not be aligned, u stands for unaligned, this may be useful when
 * copying a matrix from external source e.g. asset importer...
 *
 * @param[in]  mat  source
 * @param[out] dest destination
 */
CGLM_INLINE
void
glm_mat4_ucopy(mat4 mat, mat4 dest) {
  dest[0][0] = mat[0][0];  dest[1][0] = mat[1][0];
  dest[0][1] = mat[0][1];  dest[1][1] = mat[1][1];
  dest[0][2] = mat[0][2];  dest[1][2] = mat[1][2];
  dest[0][3] = mat[0][3];  dest[1][3] = mat[1][3];

  dest[2][0] = mat[2][0];  dest[3][0] = mat[3][0];
  dest[2][1] = mat[2][1];  dest[3][1] = mat[3][1];
  dest[2][2] = mat[2][2];  dest[3][2] = mat[3][2];
  dest[2][3] = mat[2][3];  dest[3][3] = mat[3][3];
}

/*!
 * @brief copy all members of [mat] to [dest]
 *
 * @param[in]  mat  source
 * @param[out] dest destination
 */
CGLM_INLINE
void
glm_mat4_copy(mat4 mat, mat4 dest) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glmm_store(dest[0], glmm_load(mat[0]));
  glmm_store(dest[1], glmm_load(mat[1]));
  glmm_store(dest[2], glmm_load(mat[2]));
  glmm_store(dest[3], glmm_load(mat[3]));
#elif defined(__AVX__)
  glmm_store256(dest[0], glmm_load256(mat[0]));
  glmm_store256(dest[2], glmm_load256(mat[2]));
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glmm_store(dest[0], glmm_load(mat[0]));
  glmm_store(dest[1], glmm_load(mat[1]));
  glmm_store(dest[2], glmm_load(mat[2]));
  glmm_store(dest[3], glmm_load(mat[3]));
#elif defined(CGLM_NEON_FP)
  vst1q_f32(dest[0], vld1q_f32(mat[0]));
  vst1q_f32(dest[1], vld1q_f32(mat[1]));
  vst1q_f32(dest[2], vld1q_f32(mat[2]));
  vst1q_f32(dest[3], vld1q_f32(mat[3]));
#else
  glm_mat4_ucopy(mat, dest);
#endif
}

/*!
 * @brief make given matrix identity. It is identical with below, 
 *        but it is more easy to do that with this func especially for members
 *        e.g. glm_mat4_identity(aStruct->aMatrix);
 *
 * @code
 * glm_mat4_copy(GLM_MAT4_IDENTITY, mat); // C only
 *
 * // or
 * mat4 mat = GLM_MAT4_IDENTITY_INIT;
 * @endcode
 *
 * @param[in, out]  mat  destination
 */
CGLM_INLINE
void
glm_mat4_identity(mat4 mat) {
  CGLM_ALIGN_MAT mat4 t = GLM_MAT4_IDENTITY_INIT;
  glm_mat4_copy(t, mat);
}

/*!
 * @brief make given matrix array's each element identity matrix
 *
 * @param[in, out]  mat   matrix array (must be aligned (16/32)
 *                        if alignment is not disabled)
 *
 * @param[in]       count count of matrices
 */
CGLM_INLINE
void
glm_mat4_identity_array(mat4 * __restrict mat, size_t count) {
  CGLM_ALIGN_MAT mat4 t = GLM_MAT4_IDENTITY_INIT;
  size_t i;

  for (i = 0; i < count; i++) {
    glm_mat4_copy(t, mat[i]);
  }
}

/*!
 * @brief make given matrix zero.
 *
 * @param[in, out]  mat  matrix
 */
CGLM_INLINE
void
glm_mat4_zero(mat4 mat) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glmm_128 x0;
  x0 = wasm_f32x4_const_splat(0.f);
  glmm_store(mat[0], x0);
  glmm_store(mat[1], x0);
  glmm_store(mat[2], x0);
  glmm_store(mat[3], x0);
#elif defined(__AVX__)
  __m256 y0;
  y0 = _mm256_setzero_ps();
  glmm_store256(mat[0], y0);
  glmm_store256(mat[2], y0);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glmm_128 x0;
  x0 = _mm_setzero_ps();
  glmm_store(mat[0], x0);
  glmm_store(mat[1], x0);
  glmm_store(mat[2], x0);
  glmm_store(mat[3], x0);
#elif defined(CGLM_NEON_FP)
  glmm_128 x0;
  x0 = vdupq_n_f32(0.0f);
  vst1q_f32(mat[0], x0);
  vst1q_f32(mat[1], x0);
  vst1q_f32(mat[2], x0);
  vst1q_f32(mat[3], x0);
#else
  CGLM_ALIGN_MAT mat4 t = GLM_MAT4_ZERO_INIT;
  glm_mat4_copy(t, mat);
#endif
}

/*!
 * @brief copy upper-left of mat4 to mat3
 *
 * @param[in]  mat  source
 * @param[out] dest destination
 */
CGLM_INLINE
void
glm_mat4_pick3(mat4 mat, mat3 dest) {
  dest[0][0] = mat[0][0];
  dest[0][1] = mat[0][1];
  dest[0][2] = mat[0][2];

  dest[1][0] = mat[1][0];
  dest[1][1] = mat[1][1];
  dest[1][2] = mat[1][2];

  dest[2][0] = mat[2][0];
  dest[2][1] = mat[2][1];
  dest[2][2] = mat[2][2];
}

/*!
 * @brief copy upper-left of mat4 to mat3 (transposed)
 *
 * the postfix t stands for transpose
 *
 * @param[in]  mat  source
 * @param[out] dest destination
 */
CGLM_INLINE
void
glm_mat4_pick3t(mat4 mat, mat3 dest) {
  dest[0][0] = mat[0][0];
  dest[0][1] = mat[1][0];
  dest[0][2] = mat[2][0];

  dest[1][0] = mat[0][1];
  dest[1][1] = mat[1][1];
  dest[1][2] = mat[2][1];

  dest[2][0] = mat[0][2];
  dest[2][1] = mat[1][2];
  dest[2][2] = mat[2][2];
}

/*!
 * @brief copy mat3 to mat4's upper-left
 *
 * @param[in]  mat  source
 * @param[out] dest destination
 */
CGLM_INLINE
void
glm_mat4_ins3(mat3 mat, mat4 dest) {
  dest[0][0] = mat[0][0];
  dest[0][1] = mat[0][1];
  dest[0][2] = mat[0][2];

  dest[1][0] = mat[1][0];
  dest[1][1] = mat[1][1];
  dest[1][2] = mat[1][2];

  dest[2][0] = mat[2][0];
  dest[2][1] = mat[2][1];
  dest[2][2] = mat[2][2];
}

/*!
 * @brief multiply m1 and m2 to dest
 *
 * m1, m2 and dest matrices can be same matrix, it is possible to write this:
 *
 * @code
 * mat4 m = GLM_MAT4_IDENTITY_INIT;
 * glm_mat4_mul(m, m, m);
 * @endcode
 *
 * @param[in]  m1   left matrix
 * @param[in]  m2   right matrix
 * @param[out] dest destination matrix
 */
CGLM_INLINE
void
glm_mat4_mul(mat4 m1, mat4 m2, mat4 dest) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_mul_wasm(m1, m2, dest);
#elif defined(__AVX__)
  glm_mat4_mul_avx(m1, m2, dest);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_mul_sse2(m1, m2, dest);
#elif defined(CGLM_NEON_FP)
  glm_mat4_mul_neon(m1, m2, dest);
#else
  float a00 = m1[0][0], a01 = m1[0][1], a02 = m1[0][2], a03 = m1[0][3],
        a10 = m1[1][0], a11 = m1[1][1], a12 = m1[1][2], a13 = m1[1][3],
        a20 = m1[2][0], a21 = m1[2][1], a22 = m1[2][2], a23 = m1[2][3],
        a30 = m1[3][0], a31 = m1[3][1], a32 = m1[3][2], a33 = m1[3][3],

        b00 = m2[0][0], b01 = m2[0][1], b02 = m2[0][2], b03 = m2[0][3],
        b10 = m2[1][0], b11 = m2[1][1], b12 = m2[1][2], b13 = m2[1][3],
        b20 = m2[2][0], b21 = m2[2][1], b22 = m2[2][2], b23 = m2[2][3],
        b30 = m2[3][0], b31 = m2[3][1], b32 = m2[3][2], b33 = m2[3][3];

  dest[0][0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;
  dest[0][1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;
  dest[0][2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;
  dest[0][3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;
  dest[1][0] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;
  dest[1][1] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;
  dest[1][2] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;
  dest[1][3] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;
  dest[2][0] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;
  dest[2][1] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;
  dest[2][2] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;
  dest[2][3] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;
  dest[3][0] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;
  dest[3][1] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;
  dest[3][2] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;
  dest[3][3] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;
#endif
}

/*!
 * @brief mupliply N mat4 matrices and store result in dest
 *
 * this function lets you multiply multiple (more than two or more...) matrices
 * <br><br>multiplication will be done in loop, this may reduce instructions
 * size but if <b>len</b> is too small then compiler may unroll whole loop,
 * usage:
 * @code
 * mat m1, m2, m3, m4, res;
 *
 * glm_mat4_mulN((mat4 *[]){&m1, &m2, &m3, &m4}, 4, res);
 * @endcode
 *
 * @warning matrices parameter is pointer array not mat4 array!
 *
 * @param[in]  matrices mat4 * array
 * @param[in]  len      matrices count
 * @param[out] dest     result
 */
CGLM_INLINE
void
glm_mat4_mulN(mat4 * __restrict matrices[], uint32_t len, mat4 dest) {
  uint32_t i;

#ifndef NDEBUG
  assert(len > 1 && "there must be least 2 matrices to go!");
#endif

  glm_mat4_mul(*matrices[0], *matrices[1], dest);

  for (i = 2; i < len; i++)
    glm_mat4_mul(dest, *matrices[i], dest);
}

/*!
 * @brief multiply mat4 with vec4 (column vector) and store in dest vector
 *
 * @param[in]  m    mat4 (left)
 * @param[in]  v    vec4 (right, column vector)
 * @param[out] dest vec4 (result, column vector)
 */
CGLM_INLINE
void
glm_mat4_mulv(mat4 m, vec4 v, vec4 dest) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_mulv_wasm(m, v, dest);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_mulv_sse2(m, v, dest);
#elif defined(CGLM_NEON_FP)
  glm_mat4_mulv_neon(m, v, dest);
#else
  vec4 res;
  res[0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0] * v[2] + m[3][0] * v[3];
  res[1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1] * v[2] + m[3][1] * v[3];
  res[2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2] * v[2] + m[3][2] * v[3];
  res[3] = m[0][3] * v[0] + m[1][3] * v[1] + m[2][3] * v[2] + m[3][3] * v[3];
  glm_vec4_copy(res, dest);
#endif
}

/*!
 * @brief trace of matrix
 *
 * sum of the elements on the main diagonal from upper left to the lower right
 *
 * @param[in]  m matrix
 */
CGLM_INLINE
float
glm_mat4_trace(mat4 m) {
  return m[0][0] + m[1][1] + m[2][2] + m[3][3];
}

/*!
 * @brief trace of matrix (rotation part)
 *
 * sum of the elements on the main diagonal from upper left to the lower right
 *
 * @param[in]  m matrix
 */
CGLM_INLINE
float
glm_mat4_trace3(mat4 m) {
  return m[0][0] + m[1][1] + m[2][2];
}

/*!
 * @brief convert mat4's rotation part to quaternion
 *
 * @param[in]  m    affine matrix
 * @param[out] dest destination quaternion
 */
CGLM_INLINE
void
glm_mat4_quat(mat4 m, versor dest) {
  float trace, r, rinv;

  /* it seems using like m12 instead of m[1][2] causes extra instructions */

  trace = m[0][0] + m[1][1] + m[2][2];
  if (trace >= 0.0f) {
    r       = sqrtf(1.0f + trace);
    rinv    = 0.5f / r;

    dest[0] = rinv * (m[1][2] - m[2][1]);
    dest[1] = rinv * (m[2][0] - m[0][2]);
    dest[2] = rinv * (m[0][1] - m[1][0]);
    dest[3] = r    * 0.5f;
  } else if (m[0][0] >= m[1][1] && m[0][0] >= m[2][2]) {
    r       = sqrtf(1.0f - m[1][1] - m[2][2] + m[0][0]);
    rinv    = 0.5f / r;

    dest[0] = r    * 0.5f;
    dest[1] = rinv * (m[0][1] + m[1][0]);
    dest[2] = rinv * (m[0][2] + m[2][0]);
    dest[3] = rinv * (m[1][2] - m[2][1]);
  } else if (m[1][1] >= m[2][2]) {
    r       = sqrtf(1.0f - m[0][0] - m[2][2] + m[1][1]);
    rinv    = 0.5f / r;

    dest[0] = rinv * (m[0][1] + m[1][0]);
    dest[1] = r    * 0.5f;
    dest[2] = rinv * (m[1][2] + m[2][1]);
    dest[3] = rinv * (m[2][0] - m[0][2]);
  } else {
    r       = sqrtf(1.0f - m[0][0] - m[1][1] + m[2][2]);
    rinv    = 0.5f / r;

    dest[0] = rinv * (m[0][2] + m[2][0]);
    dest[1] = rinv * (m[1][2] + m[2][1]);
    dest[2] = r    * 0.5f;
    dest[3] = rinv * (m[0][1] - m[1][0]);
  }
}

/*!
 * @brief multiply vector with mat4
 *
 * actually the result is vec4, after multiplication the last component
 * is trimmed. if you need it don't use this func.
 *
 * @param[in]  m    mat4(affine transform)
 * @param[in]  v    vec3
 * @param[in]  last 4th item to make it vec4
 * @param[out] dest result vector (vec3)
 */
CGLM_INLINE
void
glm_mat4_mulv3(mat4 m, vec3 v, float last, vec3 dest) {
  vec4 res;
  glm_vec4(v, last, res);
  glm_mat4_mulv(m, res, res);
  glm_vec3(res, dest);
}

/*!
 * @brief transpose mat4 and store in dest
 *
 * source matrix will not be transposed unless dest is m
 *
 * @param[in]  m    matrix
 * @param[out] dest result
 */
CGLM_INLINE
void
glm_mat4_transpose_to(mat4 m, mat4 dest) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_transp_wasm(m, dest);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_transp_sse2(m, dest);
#elif defined(CGLM_NEON_FP)
  glm_mat4_transp_neon(m, dest);
#else
  dest[0][0] = m[0][0]; dest[1][0] = m[0][1];
  dest[0][1] = m[1][0]; dest[1][1] = m[1][1];
  dest[0][2] = m[2][0]; dest[1][2] = m[2][1];
  dest[0][3] = m[3][0]; dest[1][3] = m[3][1];
  dest[2][0] = m[0][2]; dest[3][0] = m[0][3];
  dest[2][1] = m[1][2]; dest[3][1] = m[1][3];
  dest[2][2] = m[2][2]; dest[3][2] = m[2][3];
  dest[2][3] = m[3][2]; dest[3][3] = m[3][3];
#endif
}

/*!
 * @brief transpose mat4 and store result in same matrix
 *
 * @param[in, out] m source and dest
 */
CGLM_INLINE
void
glm_mat4_transpose(mat4 m) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_transp_wasm(m, m);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_transp_sse2(m, m);
#elif defined(CGLM_NEON_FP)
  glm_mat4_transp_neon(m, m);
#else
  mat4 d;
  glm_mat4_transpose_to(m, d);
  glm_mat4_ucopy(d, m);
#endif
}

/*!
 * @brief scale (multiply with scalar) matrix without simd optimization
 *
 * multiply matrix with scalar
 *
 * @param[in, out] m matrix
 * @param[in]      s scalar
 */
CGLM_INLINE
void
glm_mat4_scale_p(mat4 m, float s) {
  m[0][0] *= s; m[0][1] *= s; m[0][2] *= s; m[0][3] *= s;
  m[1][0] *= s; m[1][1] *= s; m[1][2] *= s; m[1][3] *= s;
  m[2][0] *= s; m[2][1] *= s; m[2][2] *= s; m[2][3] *= s;
  m[3][0] *= s; m[3][1] *= s; m[3][2] *= s; m[3][3] *= s;
}

/*!
 * @brief scale (multiply with scalar) matrix
 *
 * multiply matrix with scalar
 *
 * @param[in, out] m matrix
 * @param[in]      s scalar
 */
CGLM_INLINE
void
glm_mat4_scale(mat4 m, float s) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_scale_wasm(m, s);
#elif defined(__AVX__)
  glm_mat4_scale_avx(m, s);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_scale_sse2(m, s);
#elif defined(CGLM_NEON_FP)
  glm_mat4_scale_neon(m, s);
#else
  glm_mat4_scale_p(m, s);
#endif
}

/*!
 * @brief mat4 determinant
 *
 * @param[in] mat matrix
 *
 * @return determinant
 */
CGLM_INLINE
float
glm_mat4_det(mat4 mat) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  return glm_mat4_det_wasm(mat);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  return glm_mat4_det_sse2(mat);
#elif defined(CGLM_NEON_FP)
  return glm_mat4_det_neon(mat);
#else
  /* [square] det(A) = det(At) */
  float t[6];
  float a = mat[0][0], b = mat[0][1], c = mat[0][2], d = mat[0][3],
        e = mat[1][0], f = mat[1][1], g = mat[1][2], h = mat[1][3],
        i = mat[2][0], j = mat[2][1], k = mat[2][2], l = mat[2][3],
        m = mat[3][0], n = mat[3][1], o = mat[3][2], p = mat[3][3];

  t[0] = k * p - o * l;
  t[1] = j * p - n * l;
  t[2] = j * o - n * k;
  t[3] = i * p - m * l;
  t[4] = i * o - m * k;
  t[5] = i * n - m * j;

  return a * (f * t[0] - g * t[1] + h * t[2])
       - b * (e * t[0] - g * t[3] + h * t[4])
       + c * (e * t[1] - f * t[3] + h * t[5])
       - d * (e * t[2] - f * t[4] + g * t[5]);
#endif
}

/*!
 * @brief inverse mat4 and store in dest
 *
 * @param[in]  mat  matrix
 * @param[out] dest inverse matrix
 */
CGLM_INLINE
void
glm_mat4_inv(mat4 mat, mat4 dest) {
#if defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_inv_sse2(mat, dest);
#elif defined(CGLM_NEON_FP)
  glm_mat4_inv_neon(mat, dest);
#else
  float t[6];
  float det;
  float a = mat[0][0], b = mat[0][1], c = mat[0][2], d = mat[0][3],
        e = mat[1][0], f = mat[1][1], g = mat[1][2], h = mat[1][3],
        i = mat[2][0], j = mat[2][1], k = mat[2][2], l = mat[2][3],
        m = mat[3][0], n = mat[3][1], o = mat[3][2], p = mat[3][3];

  t[0] = k * p - o * l; t[1] = j * p - n * l; t[2] = j * o - n * k;
  t[3] = i * p - m * l; t[4] = i * o - m * k; t[5] = i * n - m * j;

  dest[0][0] =  f * t[0] - g * t[1] + h * t[2];
  dest[1][0] =-(e * t[0] - g * t[3] + h * t[4]);
  dest[2][0] =  e * t[1] - f * t[3] + h * t[5];
  dest[3][0] =-(e * t[2] - f * t[4] + g * t[5]);

  dest[0][1] =-(b * t[0] - c * t[1] + d * t[2]);
  dest[1][1] =  a * t[0] - c * t[3] + d * t[4];
  dest[2][1] =-(a * t[1] - b * t[3] + d * t[5]);
  dest[3][1] =  a * t[2] - b * t[4] + c * t[5];

  t[0] = g * p - o * h; t[1] = f * p - n * h; t[2] = f * o - n * g;
  t[3] = e * p - m * h; t[4] = e * o - m * g; t[5] = e * n - m * f;

  dest[0][2] =  b * t[0] - c * t[1] + d * t[2];
  dest[1][2] =-(a * t[0] - c * t[3] + d * t[4]);
  dest[2][2] =  a * t[1] - b * t[3] + d * t[5];
  dest[3][2] =-(a * t[2] - b * t[4] + c * t[5]);

  t[0] = g * l - k * h; t[1] = f * l - j * h; t[2] = f * k - j * g;
  t[3] = e * l - i * h; t[4] = e * k - i * g; t[5] = e * j - i * f;

  dest[0][3] =-(b * t[0] - c * t[1] + d * t[2]);
  dest[1][3] =  a * t[0] - c * t[3] + d * t[4];
  dest[2][3] =-(a * t[1] - b * t[3] + d * t[5]);
  dest[3][3] =  a * t[2] - b * t[4] + c * t[5];

  det = 1.0f / (a * dest[0][0] + b * dest[1][0]
              + c * dest[2][0] + d * dest[3][0]);

  glm_mat4_scale_p(dest, det);
#endif
}

/*!
 * @brief inverse mat4 and store in dest
 *
 * this func uses reciprocal approximation without extra corrections
 * e.g Newton-Raphson. this should work faster than normal,
 * to get more precise use glm_mat4_inv version.
 *
 * NOTE: You will lose precision, glm_mat4_inv is more accurate
 *
 * @param[in]  mat  matrix
 * @param[out] dest inverse matrix
 */
CGLM_INLINE
void
glm_mat4_inv_fast(mat4 mat, mat4 dest) {
#if defined(__wasm__) && defined(__wasm_simd128__)
  glm_mat4_inv_fast_wasm(mat, dest);
#elif defined( __SSE__ ) || defined( __SSE2__ )
  glm_mat4_inv_fast_sse2(mat, dest);
#else
  glm_mat4_inv(mat, dest);
#endif
}

/*!
 * @brief swap two matrix columns
 *
 * @param[in,out] mat  matrix
 * @param[in]     col1 col1
 * @param[in]     col2 col2
 */
CGLM_INLINE
void
glm_mat4_swap_col(mat4 mat, int col1, int col2) {
  CGLM_ALIGN(16) vec4 tmp;
  glm_vec4_copy(mat[col1], tmp);
  glm_vec4_copy(mat[col2], mat[col1]);
  glm_vec4_copy(tmp, mat[col2]);
}

/*!
 * @brief swap two matrix rows
 *
 * @param[in,out] mat  matrix
 * @param[in]     row1 row1
 * @param[in]     row2 row2
 */
CGLM_INLINE
void
glm_mat4_swap_row(mat4 mat, int row1, int row2) {
  CGLM_ALIGN(16) vec4 tmp;
  tmp[0] = mat[0][row1];
  tmp[1] = mat[1][row1];
  tmp[2] = mat[2][row1];
  tmp[3] = mat[3][row1];

  mat[0][row1] = mat[0][row2];
  mat[1][row1] = mat[1][row2];
  mat[2][row1] = mat[2][row2];
  mat[3][row1] = mat[3][row2];

  mat[0][row2] = tmp[0];
  mat[1][row2] = tmp[1];
  mat[2][row2] = tmp[2];
  mat[3][row2] = tmp[3];
}

/*!
 * @brief helper for  R (row vector) * M (matrix) * C (column vector)
 *
 * rmc stands for Row * Matrix * Column
 *
 * the result is scalar because R * M = Matrix1x4 (row vector),
 * then Matrix1x4 * Vec4 (column vector) = Matrix1x1 (Scalar)
 *
 * @param[in]  r   row vector or matrix1x4
 * @param[in]  m   matrix4x4
 * @param[in]  c   column vector or matrix4x1
 *
 * @return scalar value e.g. B(s)
 */
CGLM_INLINE
float
glm_mat4_rmc(vec4 r, mat4 m, vec4 c) {
  vec4 tmp;
  glm_mat4_mulv(m, c, tmp);
  return glm_vec4_dot(r, tmp);
}

/*!
 * @brief Create mat4 matrix from pointer
 *
 * @param[in]  src  pointer to an array of floats
 * @param[out] dest matrix
 */
CGLM_INLINE
void
glm_mat4_make(const float * __restrict src, mat4 dest) {
  dest[0][0] = src[0];   dest[1][0] = src[4];
  dest[0][1] = src[1];   dest[1][1] = src[5];
  dest[0][2] = src[2];   dest[1][2] = src[6];
  dest[0][3] = src[3];   dest[1][3] = src[7];

  dest[2][0] = src[8];   dest[3][0] = src[12];
  dest[2][1] = src[9];   dest[3][1] = src[13];
  dest[2][2] = src[10];  dest[3][2] = src[14];
  dest[2][3] = src[11];  dest[3][3] = src[15];
}

#endif /* cglm_mat_h */