1. 4FipS.com
  2. Photos
  3. Videos
  4. Code
  5. Forums
  6. pfQuizzz
  7. About
/*
(c) 2004-14 Filip Stoklas, aka FipS, www.4FipS.com
THIS CODE IS FREE - LICENSED UNDER THE MIT LICENSE
*/

#include "fs_math_func.h"
#include "fs_common.h"

#include <cmath>

#if !defined(M_PI)
#   define M_PI 3.14159265358979323846
#endif

namespace fs { namespace math {

float sin(float x) FS_NOEXCEPT
{
    return std::sin(x);
}

float cos(float x) FS_NOEXCEPT
{
    return std::cos(x);
}

std::pair<float, float> sin_cos(float x) FS_NOEXCEPT
{
    return std::make_pair(sin(x), cos(x));
}

float sqrt(float x) FS_NOEXCEPT
{
    return std::sqrt(x);
}

template<typename T> T inv(T x) FS_NOEXCEPT
{
    FS_ASSERT(x != T(0));
    return T(1) / x;
}

#define T float
template T inv(T x);
#undef T

// --- color3 ---

color3 color3_make(uint8_t r, uint8_t g, uint8_t b) FS_NOEXCEPT
{
    return { r, g, b };
}

// --- color4 ---

color4 color4_make(uint8_t r, uint8_t g, uint8_t b, uint8_t a) FS_NOEXCEPT
{
    return { r, g, b, a };
}

// --- vec2 ---

template <typename T>
inline vec2<T> & vec2<T>::operator += (const vec2 &v) FS_NOEXCEPT
{
    x += v.x;
    y += v.y;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator += (T t) FS_NOEXCEPT
{
    x += t;
    y += t;

    return *this;
}
    
template <typename T>
inline vec2<T> & vec2<T>::operator -= (const vec2 &v) FS_NOEXCEPT
{
    x -= v.x;
    y -= v.y;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator -= (T t) FS_NOEXCEPT
{
    x -= t;
    y -= t;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator *= (const vec2 &v) FS_NOEXCEPT
{
    x *= v.x;
    y *= v.y;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator *= (T t) FS_NOEXCEPT
{
    x *= t;
    y *= t;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator /= (const vec2 &v) FS_NOEXCEPT
{
    x /= v.x;
    y /= v.y;

    return *this;
}

template <typename T>
inline vec2<T> & vec2<T>::operator /= (T t) FS_NOEXCEPT
{
    const T it = inv(t);
    x *= it;
    y *= it;

    return *this;
}

template <typename T>
inline const T & vec2<T>::operator [] (int i) const FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 2);
    return (&x)[i];
}

template <typename T>
inline T & vec2<T>::operator [] (int i) FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 2);
    return (&x)[i];
}

template <typename T>
inline vec2<T> vec2_make(T x, T y) FS_NOEXCEPT
{
    return { x, y };
}

template <typename T>
inline bool operator == (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return
     v1.x == v2.x &&
     v1.y == v2.y
    ;
}

template <typename T> 
inline bool operator != (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return !(v1 == v2);
}

template <typename T>
inline vec2<T> operator - (const vec2<T> &v) FS_NOEXCEPT
{
    return vec2_make(-v.x, -v.y);
}

template <typename T> 
inline vec2<T> operator + (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return vec2_make(
     v1.x + v2.x,
     v1.y + v2.y
    );
}

template <typename T>
inline vec2<T> operator + (const vec2<T> &v, T t) FS_NOEXCEPT
{
    return vec2_make(
     v.x + t,
     v.y + t
    );
}

template <typename T>
inline vec2<T> operator + (T t, const vec2<T> &v) FS_NOEXCEPT
{
    return v + t;
}

template <typename T> 
inline vec2<T> operator - (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return vec2_make(
     v1.x - v2.x,
     v1.y - v2.y
    );
}

template <typename T>
inline vec2<T> operator - (const vec2<T> &v, T t) FS_NOEXCEPT
{
    return vec2_make(
     v.x - t,
     v.y - t
    );
}

template <typename T>
inline vec2<T> operator - (T t, const vec2<T> &v) FS_NOEXCEPT
{
    return v - t;
}

template <typename T> 
inline vec2<T> operator * (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return vec2_make(
     v1.x * v2.x,
     v1.y * v2.y
    );
}

template <typename T>
inline vec2<T> operator * (const vec2<T> &v, T t) FS_NOEXCEPT
{
    return vec2_make(
     v.x * t,
     v.y * t
    );
}

template <typename T>
inline vec2<T> operator * (T t, const vec2<T> &v) FS_NOEXCEPT
{
    return v * t;
}

template <typename T>
inline vec2<T> operator / (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT
{
    return vec2_make(
     v1.x / v2.x,
     v1.y / v2.y
    );
}

template <typename T>
inline vec2<T> operator / (const vec2<T> &v, T t) FS_NOEXCEPT
{
    return vec2_make(
     v.x / t,
     v.y / t
    );
}

template <typename T>
inline vec2<T> operator / (T t, const vec2<T> &v) FS_NOEXCEPT
{
    return v / t;
}

#define T float // explicit instantiation <float>
template struct vec2<T>;
template vec2<T> vec2_make(T x, T y) FS_NOEXCEPT;
template bool operator == (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template bool operator != (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template vec2<T> operator - (const vec2<T> &v) FS_NOEXCEPT;
template vec2<T> operator + (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template vec2<T> operator + (const vec2<T> &v, T t) FS_NOEXCEPT;
template vec2<T> operator + (T t, const vec2<T> &v) FS_NOEXCEPT;
template vec2<T> operator - (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template vec2<T> operator - (const vec2<T> &v, T t) FS_NOEXCEPT;
template vec2<T> operator - (T t, const vec2<T> &v) FS_NOEXCEPT;
template vec2<T> operator * (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template vec2<T> operator * (const vec2<T> &v, T t) FS_NOEXCEPT;
template vec2<T> operator * (T t, const vec2<T> &v) FS_NOEXCEPT;
template vec2<T> operator / (const vec2<T> &v1, const vec2<T> &v2) FS_NOEXCEPT;
template vec2<T> operator / (const vec2<T> &v, T t) FS_NOEXCEPT;
template vec2<T> operator / (T t, const vec2<T> &v) FS_NOEXCEPT;
#undef T

// --- vec3 ---

template <typename T>
inline vec3<T> & vec3<T>::operator += (const vec3 &v) FS_NOEXCEPT
{
    x += v.x;
    y += v.y;
    z += v.z;
    
    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator += (T t) FS_NOEXCEPT
{
    x += t;
    y += t;
    z += t;

    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator -= (const vec3 &v) FS_NOEXCEPT
{
    x -= v.x;
    y -= v.y;
    z -= v.z;
    
    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator -= (T t) FS_NOEXCEPT
{
    x -= t;
    y -= t;
    z -= t;

    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator *= (const vec3 &v) FS_NOEXCEPT
{
    x *= v.x;
    y *= v.y;
    z *= v.z;
    
    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator *= (T t) FS_NOEXCEPT
{
    x *= t;
    y *= t;
    z *= t;

    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator /= (const vec3 &v) FS_NOEXCEPT
{
    x /= v.x;
    y /= v.y;
    z /= v.z;
    
    return *this;
}

template <typename T>
inline vec3<T> & vec3<T>::operator /= (T t) FS_NOEXCEPT
{
    const T it = inv(t);
    x *= it;
    y *= it;
    z *= it;

    return *this;
}

template <typename T>
inline const T & vec3<T>::operator [] (int i) const FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 3);
    return (&x)[i];
}

template <typename T>
inline T & vec3<T>::operator [] (int i) FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 3);
    return (&x)[i];
}

template <typename T>
inline vec3<T> vec3_make(T x, T y, T z) FS_NOEXCEPT
{
    return { x, y, z };
}

template <typename T>
inline bool operator == (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{
    return
     v1.x == v2.x &&
     v1.y == v2.y &&
     v1.z == v2.z
    ;
}

template <typename T> 
inline bool operator != (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{
    return !(v1 == v2);
}

template <typename T> vec3<T>
inline operator - (const vec3<T> &v) FS_NOEXCEPT
{
    return vec3_make(-v.x, -v.y, -v.z);
}

template <typename T> 
inline vec3<T> operator + (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{
    return vec3_make(
     v1.x + v2.x,
     v1.y + v2.y,
     v1.z + v2.z
    );
}

template <typename T>
inline vec3<T> operator + (const vec3<T> &v, T t) FS_NOEXCEPT
{
    return vec3_make(
     v.x + t,
     v.y + t,
     v.z + t
    );
}

template <typename T>
inline vec3<T> operator + (T t, const vec3<T> &v) FS_NOEXCEPT
{
    return v + t;
}

template <typename T> 
inline vec3<T> operator - (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{   
    return vec3_make(
     v1.x - v2.x,
     v1.y - v2.y,
     v1.z - v2.z
    );
}

template <typename T>
inline vec3<T> operator - (const vec3<T> &v, T t) FS_NOEXCEPT
{
    return vec3_make(
     v.x - t,
     v.y - t,
     v.z - t
    );
}

template <typename T>
inline vec3<T> operator - (T t, const vec3<T> &v) FS_NOEXCEPT
{
    return v - t;
}

template <typename T> 
inline vec3<T> operator * (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{
    return vec3_make(
     v1.x * v2.x,
     v1.y * v2.y,
     v1.z * v2.z
    );
}

template <typename T>
inline vec3<T> operator * (const vec3<T> &v, T t) FS_NOEXCEPT
{
    return vec3_make(
     v.x * t,
     v.y * t,
     v.z * t
    );
}

template <typename T>
inline vec3<T> operator * (T t, const vec3<T> &v) FS_NOEXCEPT
{
    return v * t;
}

template <typename T>
inline vec3<T> operator / (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT
{
    return vec3_make(
     v1.x / v2.x,
     v1.y / v2.y,
     v1.z / v2.z
    );
}

template <typename T>
inline vec3<T> operator / (const vec3<T> &v, T t) FS_NOEXCEPT
{
    return vec3_make(
     v.x / t,
     v.y / t,
     v.z / t
    );
}

template <typename T>
inline vec3<T> operator / (T t, const vec3<T> &v) FS_NOEXCEPT
{
    return v / t;
}

#define T float // explicit instantiation <float>
template struct vec3<T>;
template vec3<T> vec3_make(T x, T y, T z) FS_NOEXCEPT;
template bool operator == (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template bool operator != (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template vec3<T> operator - (const vec3<T> &v) FS_NOEXCEPT;
template vec3<T> operator + (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template vec3<T> operator + (const vec3<T> &v, T t) FS_NOEXCEPT;
template vec3<T> operator + (T t, const vec3<T> &v) FS_NOEXCEPT;
template vec3<T> operator - (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template vec3<T> operator - (const vec3<T> &v, T t) FS_NOEXCEPT;
template vec3<T> operator - (T t, const vec3<T> &v) FS_NOEXCEPT;
template vec3<T> operator * (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template vec3<T> operator * (const vec3<T> &v, T t) FS_NOEXCEPT;
template vec3<T> operator * (T t, const vec3<T> &v) FS_NOEXCEPT;
template vec3<T> operator / (const vec3<T> &v1, const vec3<T> &v2) FS_NOEXCEPT;
template vec3<T> operator / (const vec3<T> &v, T t) FS_NOEXCEPT;
template vec3<T> operator / (T t, const vec3<T> &v) FS_NOEXCEPT;
#undef T

// --- vec4 ---

template <typename T>
inline vec4<T> & vec4<T>::operator += (const vec4 &v) FS_NOEXCEPT
{
    x += v.x;
    y += v.y;
    z += v.z;
    w += v.w;
    
    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator += (T t) FS_NOEXCEPT
{
    x += t;
    y += t;
    z += t;
    w += t;

    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator -= (const vec4 &v) FS_NOEXCEPT
{
    x -= v.x;
    y -= v.y;
    z -= v.z;
    w -= v.w;
    
    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator -= (T t) FS_NOEXCEPT
{
    x -= t;
    y -= t;
    z -= t;
    w -= t;

    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator *= (const vec4 &v) FS_NOEXCEPT
{
    x *= v.x;
    y *= v.y;
    z *= v.z;
    w *= v.w;
    
    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator *= (T t) FS_NOEXCEPT
{
    x *= t;
    y *= t;
    z *= t;
    w *= t;

    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator /= (const vec4 &v) FS_NOEXCEPT
{
    x /= v.x;
    y /= v.y;
    z /= v.z;
    w /= v.w;
    
    return *this;
}

template <typename T>
inline vec4<T> & vec4<T>::operator /= (T t) FS_NOEXCEPT
{
    const T it = inv(t);
    x *= it;
    y *= it;
    z *= it;
    w *= it;

    return *this;
}

template <typename T>
inline const T & vec4<T>::operator [] (int i) const FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 4);
    return (&x)[i];
}

template <typename T>
inline T & vec4<T>::operator [] (int i) FS_NOEXCEPT
{
    FS_ASSERT(i >= 0 && i < 4);
    return (&x)[i];
}

template <typename T>
inline vec4<T> vec4_make(T x, T y, T z, T w) FS_NOEXCEPT
{
    return { x, y, z, w };
}

template <typename T>
inline bool operator == (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{
    return
     v1.x == v2.x &&
     v1.y == v2.y &&
     v1.z == v2.z &&
     v1.w == v2.w
    ;
}

template <typename T> 
inline bool operator != (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{
    return !(v1 == v2);
}

template <typename T> vec4<T>
inline operator - (const vec4<T> &v) FS_NOEXCEPT
{
    return vec4_make(-v.x, -v.y, -v.z, -v.w);
}

template <typename T> 
inline vec4<T> operator + (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{
    return vec4_make(
     v1.x + v2.x,
     v1.y + v2.y,
     v1.z + v2.z,
     v1.w + v2.w
    );
}

template <typename T>
inline vec4<T> operator + (const vec4<T> &v, T t) FS_NOEXCEPT
{
    return vec4_make(
     v.x + t,
     v.y + t,
     v.z + t,
     v.w + t
    );
}

template <typename T>
inline vec4<T> operator + (T t, const vec4<T> &v) FS_NOEXCEPT
{
    return v + t;
}

template <typename T> 
inline vec4<T> operator - (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{   
    return vec4_make(
     v1.x - v2.x,
     v1.y - v2.y,
     v1.z - v2.z,
     v1.w - v2.w
    );
}

template <typename T>
inline vec4<T> operator - (const vec4<T> &v, T t) FS_NOEXCEPT
{
    return vec4_make(
     v.x - t,
     v.y - t,
     v.z - t,
     v.w - t
    );
}

template <typename T>
inline vec4<T> operator - (T t, const vec4<T> &v) FS_NOEXCEPT
{
    return v - t;
}

template <typename T> 
inline vec4<T> operator * (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{
    return vec4_make(
     v1.x * v2.x,
     v1.y * v2.y,
     v1.z * v2.z,
     v1.w * v2.w
    );
}

template <typename T>
inline vec4<T> operator * (const vec4<T> &v, T t) FS_NOEXCEPT
{
    return vec4_make(
     v.x * t,
     v.y * t,
     v.z * t,
     v.w * t
    );
}

template <typename T>
inline vec4<T> operator * (T t, const vec4<T> &v) FS_NOEXCEPT
{
    return v * t;
}

template <typename T>
inline vec4<T> operator / (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT
{
    return vec4_make(
     v1.x / v2.x,
     v1.y / v2.y,
     v1.z / v2.z,
     v1.w / v2.w
    );
}

template <typename T>
inline vec4<T> operator / (const vec4<T> &v, T t) FS_NOEXCEPT
{
    return vec4_make(
     v.x / t,
     v.y / t,
     v.z / t,
     v.w / t
    );
}

template <typename T>
inline vec4<T> operator / (T t, const vec4<T> &v) FS_NOEXCEPT
{
    return v / t;
}

#define T float // explicit instantiation <float>
template struct vec4<T>;
template vec4<T> vec4_make(T x, T y, T z, T w) FS_NOEXCEPT;
template bool operator == (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template bool operator != (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template vec4<T> operator - (const vec4<T> &v) FS_NOEXCEPT;
template vec4<T> operator + (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template vec4<T> operator + (const vec4<T> &v, T t) FS_NOEXCEPT;
template vec4<T> operator + (T t, const vec4<T> &v) FS_NOEXCEPT;
template vec4<T> operator - (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template vec4<T> operator - (const vec4<T> &v, T t) FS_NOEXCEPT;
template vec4<T> operator - (T t, const vec4<T> &v) FS_NOEXCEPT;
template vec4<T> operator * (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template vec4<T> operator * (const vec4<T> &v, T t) FS_NOEXCEPT;
template vec4<T> operator * (T t, const vec4<T> &v) FS_NOEXCEPT;
template vec4<T> operator / (const vec4<T> &v1, const vec4<T> &v2) FS_NOEXCEPT;
template vec4<T> operator / (const vec4<T> &v, T t) FS_NOEXCEPT;
template vec4<T> operator / (T t, const vec4<T> &v) FS_NOEXCEPT;
#undef T

// --- mat4 ---

template <typename T>
inline mat4<T> mat4_make(
 T e11, T e12, T e13, T e14,
 T e21, T e22, T e23, T e24,
 T e31, T e32, T e33, T e34,
 T e41, T e42, T e43, T e44
) FS_NOEXCEPT
{
    return
    {
        { e11, e21, e31, e41 }, // cx
        { e12, e22, e32, e42 }, // cy
        { e13, e23, e33, e43 }, // cz
        { e14, e24, e34, e44 }  // cw
    };
}

template <typename T>
inline mat4<T> mat4_make(
 const vec4<T> &cx,
 const vec4<T> &cy,
 const vec4<T> &cz,
 const vec4<T> &cw
) FS_NOEXCEPT
{
    return { cx, cy, cz, cw };
}

template <typename T>
inline mat4<T> mat4_make(T e) FS_NOEXCEPT
{
    return mat4_make(
       e,  T(0), T(0), T(0),
     T(0),   e,  T(0), T(0),
     T(0), T(0),   e,  T(0),
     T(0), T(0), T(0),   e
    );
}

template <typename T>
inline bool operator == (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT
{
    return
     m1.cx == m2.cx &&
     m1.cy == m2.cy &&
     m1.cz == m2.cz &&
     m1.cw == m2.cw
    ;
}

template <typename T>
inline bool operator != (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT
{
    return !(m1 == m2);
}

template <typename T>
inline mat4<T> operator * (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT
{
    return mat4_make(
     // 1st row
     m1.cx.x*m2.cx.x + m1.cy.x*m2.cx.y + m1.cz.x*m2.cx.z + m1.cw.x*m2.cx.w, // cx.x
     m1.cx.x*m2.cy.x + m1.cy.x*m2.cy.y + m1.cz.x*m2.cy.z + m1.cw.x*m2.cy.w, // cy.x
     m1.cx.x*m2.cz.x + m1.cy.x*m2.cz.y + m1.cz.x*m2.cz.z + m1.cw.x*m2.cz.w, // cz.x
     m1.cx.x*m2.cw.x + m1.cy.x*m2.cw.y + m1.cz.x*m2.cw.z + m1.cw.x*m2.cw.w, // cw.x
     // 2nd row
     m1.cx.y*m2.cx.x + m1.cy.y*m2.cx.y + m1.cz.y*m2.cx.z + m1.cw.y*m2.cx.w, // cx.y
     m1.cx.y*m2.cy.x + m1.cy.y*m2.cy.y + m1.cz.y*m2.cy.z + m1.cw.y*m2.cy.w, // cy.y
     m1.cx.y*m2.cz.x + m1.cy.y*m2.cz.y + m1.cz.y*m2.cz.z + m1.cw.y*m2.cz.w, // cz.y
     m1.cx.y*m2.cw.x + m1.cy.y*m2.cw.y + m1.cz.y*m2.cw.z + m1.cw.y*m2.cw.w, // cw.y
     // 3rd row
     m1.cx.z*m2.cx.x + m1.cy.z*m2.cx.y + m1.cz.z*m2.cx.z + m1.cw.z*m2.cx.w, // cx.z
     m1.cx.z*m2.cy.x + m1.cy.z*m2.cy.y + m1.cz.z*m2.cy.z + m1.cw.z*m2.cy.w, // cy.z
     m1.cx.z*m2.cz.x + m1.cy.z*m2.cz.y + m1.cz.z*m2.cz.z + m1.cw.z*m2.cz.w, // cz.z
     m1.cx.z*m2.cw.x + m1.cy.z*m2.cw.y + m1.cz.z*m2.cw.z + m1.cw.z*m2.cw.w, // cw.z
     // 4th row
     m1.cx.w*m2.cx.x + m1.cy.w*m2.cx.y + m1.cz.w*m2.cx.z + m1.cw.w*m2.cx.w, // cx.w
     m1.cx.w*m2.cy.x + m1.cy.w*m2.cy.y + m1.cz.w*m2.cy.z + m1.cw.w*m2.cy.w, // cy.w
     m1.cx.w*m2.cz.x + m1.cy.w*m2.cz.y + m1.cz.w*m2.cz.z + m1.cw.w*m2.cz.w, // cz.w
     m1.cx.w*m2.cw.x + m1.cy.w*m2.cw.y + m1.cz.w*m2.cw.z + m1.cw.w*m2.cw.w  // cw.w
    );
}

template <typename T>
inline vec4<T> operator * (const mat4<T> &m, const vec4<T> &v) FS_NOEXCEPT
{
    return vec4_make(
     m.cx.x * v.x + m.cy.x * v.y + m.cz.x * v.z + m.cw.x * v.w,
     m.cx.y * v.x + m.cy.y * v.y + m.cz.y * v.z + m.cw.y * v.w,
     m.cx.z * v.x + m.cy.z * v.y + m.cz.z * v.z + m.cw.z * v.w,
     m.cx.w * v.x + m.cy.w * v.y + m.cz.w * v.z + m.cw.w * v.w
    );
}

template <typename T>
inline mat4<T> mat4_make_xyz(T x, T y, T z) FS_NOEXCEPT
{
    return mat4_make(
     T(1), T(0), T(0),   x,
     T(0), T(1), T(0),   y,
     T(0), T(0), T(1),   z,
     T(0), T(0), T(0), T(1)
    );
}

template <typename T>
inline mat4<T> mat4_make_scale(T sx, T sy, T sz) FS_NOEXCEPT
{
    return mat4_make(
      sx,  T(0), T(0), T(0),
     T(0),  sy,  T(0), T(0),
     T(0), T(0),  sz,  T(0),
     T(0), T(0), T(0), T(1)
    );
}

template <typename T>
inline mat4<T> mat4_make_rot_x(T rad) FS_NOEXCEPT
{
    const auto sx_cx = sin_cos(rad);
    const T sx = sx_cx.first;
    const T cx = sx_cx.second;

    return mat4_make(
     T(1), T(0), T(0), T(0),
     T(0),  cx,  -sx,  T(0),
     T(0),  sx,   cx,  T(0),
     T(0), T(0), T(0), T(1)
    );
}

template <typename T>
inline mat4<T> mat4_make_rot_y(T rad) FS_NOEXCEPT
{
    const auto sy_cy = sin_cos(rad);
    const T sy = sy_cy.first;
    const T cy = sy_cy.second;

    return mat4_make(
      cy,  T(0),  sy,  T(0),
     T(0), T(1), T(0), T(0),
     -sy,  T(0),  cy,  T(0),
     T(0), T(0), T(0), T(1)
    );
}

template <typename T>
inline mat4<T> mat4_make_rot_z(T rad) FS_NOEXCEPT
{
    const auto sz_cz = sin_cos(rad);
    const T sz = sz_cz.first;
    const T cz = sz_cz.second;

    return mat4_make(
      cz,  -sz,  T(0), T(0),
      sz,   cz,  T(0), T(0),
     T(0), T(0), T(1), T(0),
     T(0), T(0), T(0), T(1)
    );
}

template <typename T>
inline mat4<T> mat4_make_ortho(T left, T right, T bottom, T top, T znear, T zfar) FS_NOEXCEPT
{
    // from the OpenGL spec PDF:                             can be rewritten as:
    // / 2/(r-l)     0        0       -(r+l)/(r-l)  \        / 2/(r-l)     0        0      (r+l)/(l-r)  \
    // |   0      2/(t-b)     0       -(t+b)/(t-b)  |   =>   |   0      2/(t-b)     0      (t+b)/(b-t)  |
    // |   0         0     -2/(f-n)   -(f+n)/(f-n)  |        |   0         0     2/(n-f)   (f+n)/(n-f)  |
    // \   0         0        0             1       /        \   0         0        0           1       /
    // invalid for: l=r, b=t, or n=f

    FS_ASSERT(left != right);
    FS_ASSERT(bottom != top);
    FS_ASSERT(znear != zfar);

    const T p_fn = zfar + znear;
    const T m_nf = znear - zfar; // ~ -m_fn

    const T p_rl = right + left;
    const T m_rl = right - left;
    const T p_tb = top + bottom;
    const T m_tb = top - bottom;

    const T m_lr = -m_rl;
    const T m_bt = -m_tb;

    return mat4_make(
     T(2)/m_rl,    T(0),       T(0),     p_rl/m_lr,
       T(0),     T(2)/m_tb,    T(0),     p_tb/m_bt,
       T(0),       T(0),     T(2)/m_nf,  p_fn/m_nf,
       T(0),       T(0),       T(0),       T(1)
    );
}

template <typename T> 
inline mat4<T> mat4_make_frustum(T left, T right, T bottom, T top, T znear, T zfar) FS_NOEXCEPT
{
    // from the OpenGL spec PDF:                                 can be rewritten as:
    // /  2n/(r-l)    0        (r+l)/(r-l)       0      \        /  2n/(r-l)    0        (r+l)/(r-l)       0      \
    // |     0     2n/(t-b)    (t+b)/(t-b)       0      |   =>   |     0     2n/(t-b)    (t+b)/(t-b)       0      |
    // |     0        0       -(f+n)/(f-n)  -2fn/(f-n)  |        |     0        0        (f+n)/(n-f)   2fn/(n-f)  |
    // \     0        0            -1            0      /        \     0        0            -1            0      /
    // invalid for: n<=0, f<=0, l=r, b=t, or n=f

    FS_ASSERT(znear > T(0));
    FS_ASSERT(zfar > T(0));
    FS_ASSERT(left != right);
    FS_ASSERT(bottom != top);
    FS_ASSERT(znear != zfar);

    const T x_2n = znear + znear;
    const T x_2nf = T(2) * znear * zfar;

    const T p_fn = zfar + znear;
    const T m_nf = znear - zfar; // ~ -m_fn

    const T p_rl = right + left;
    const T m_rl = right - left;
    const T p_tb = top + bottom;
    const T m_tb = top - bottom;

    return mat4_make(
     x_2n/m_rl,    T(0),     p_rl/m_rl,    T(0),
       T(0),     x_2n/m_tb,  p_tb/m_tb,    T(0),
       T(0),       T(0),     p_fn/m_nf,  x_2nf/m_nf,
       T(0),       T(0),       T(-1),      T(0)
    );
}

template <typename T> 
inline mat4<T> mat4_make_perspective(T fovy_deg, T aspect, T znear, T zfar) FS_NOEXCEPT
{
    // from the OpenGL spec PDF:                         can be rewritten as:
    // /    c/a    0        0            0       \       /    c/a    0         0           0      \
    // |     0     c        0            0       |  ==>  |     0     c         0           0      |
    // |     0     0   -(f+n)/(f-n)  -2nf/(f+n)  |       |     0     0    (f+n)/(n-f)  2nf/(n-f)  |
    // \     0     0       -1            0       /       \     0     0        -1           0      /

    FS_ASSERT(znear > T(0));
    FS_ASSERT(zfar > T(0));
    FS_ASSERT(aspect != T(0));
    FS_ASSERT(znear != zfar);

    const T half_fovy_rad = T(M_PI) * fovy_deg / T(360);

    const auto si_co = sin_cos(half_fovy_rad);
    const T si = si_co.first;
    const T co = si_co.second;
    FS_ASSERT(si != T(0));

    const T c = co / si; // cotangent
    const T a = aspect;

    const T x_2nf = T(2) * znear * zfar;
    const T p_fn = zfar + znear;
    const T m_nf = znear - zfar;

    return mat4_make(
     c/a,    T(0),     T(0),       T(0),
     T(0),    c,       T(0),       T(0),
     T(0),   T(0),  p_fn/m_nf,  x_2nf/m_nf,
     T(0),   T(0),     T(-1),      T(0)
    );
}

#define T float
template mat4<T> mat4_make(
 T e11, T e12, T e13, T e14,
 T e21, T e22, T e23, T e24,
 T e31, T e32, T e33, T e34,
 T e41, T e42, T e43, T e44
) FS_NOEXCEPT;
template mat4<T> mat4_make(
 const vec4<T> &cx,
 const vec4<T> &cy,
 const vec4<T> &cz,
 const vec4<T> &cw
) FS_NOEXCEPT;
template mat4<T> mat4_make(T e) FS_NOEXCEPT;
template bool operator == (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT;
template bool operator != (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT;
template mat4<T> operator * (const mat4<T> &m1, const mat4<T> &m2) FS_NOEXCEPT;
template vec4<T> operator * (const mat4<T> &m, const vec4<T> &v) FS_NOEXCEPT;
template mat4<T> mat4_make_xyz(T x, T y, T z) FS_NOEXCEPT;
template mat4<T> mat4_make_scale(T x, T y, T z) FS_NOEXCEPT;
template mat4<T> mat4_make_rot_x(T rad) FS_NOEXCEPT;
template mat4<T> mat4_make_rot_y(T rad) FS_NOEXCEPT;
template mat4<T> mat4_make_rot_z(T rad) FS_NOEXCEPT;
template mat4<T> mat4_make_ortho(T left, T right, T bottom, T top, T znear, T zfar) FS_NOEXCEPT;
template mat4<T> mat4_make_frustum(T left, T right, T bottom, T top, T znear, T zfar) FS_NOEXCEPT;
template mat4<T> mat4_make_perspective(T fovy_deg, T aspect, T znear, T zfar) FS_NOEXCEPT;
#undef T

}} // namespace fs::math