4 files changed, 582 insertions, 1 deletions

diff --git a/src/video_core/CMakeLists.txt b/src/video_core/CMakeLists.txt
index e43e6e1bb..2503b9d18 100644
--- a/src/video_core/CMakeLists.txt
+++ b/src/video_core/CMakeLists.txt
@@ -2,8 +2,9 @@ set(SRCS    video_core.cpp
             utils.cpp
             renderer_opengl/renderer_opengl.cpp)
 
-set(HEADERS video_core.h
+set(HEADERS math.h
             utils.h
+            video_core.h
             renderer_base.h
             renderer_opengl/renderer_opengl.h)
 
diff --git a/src/video_core/math.h b/src/video_core/math.h
new file mode 100644
index 000000000..7030f2cfb
--- /dev/null
+++ b/src/video_core/math.h
@@ -0,0 +1,578 @@
+// Licensed under GPLv2
+// Refer to the license.txt file included.
+
+
+// Copyright 2014 Tony Wasserka
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above copyright
+//       notice, this list of conditions and the following disclaimer in the
+//       documentation and/or other materials provided with the distribution.
+//     * Neither the name of the owner nor the names of its contributors may
+//       be used to endorse or promote products derived from this software
+//       without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#pragma once
+
+#include <cmath>
+
+namespace Math {
+
+template<typename T> class Vec2;
+template<typename T> class Vec3;
+template<typename T> class Vec4;
+
+
+template<typename T>
+class Vec2 {
+public:
+    struct {
+        T x,y;
+    };
+
+    T* AsArray() { return &x; }
+
+    Vec2() = default;
+    Vec2(const T a[2]) : x(a[0]), y(a[1]) {}
+    Vec2(const T& _x, const T& _y) : x(_x), y(_y) {}
+
+    template<typename T2>
+    Vec2<T2> Cast() const {
+        return Vec2<T2>((T2)x, (T2)y);
+    }
+
+    static Vec2 AssignToAll(const T& f)
+    {
+        return Vec2<T>(f, f);
+    }
+
+    void Write(T a[2])
+    {
+        a[0] = x; a[1] = y;
+    }
+
+    Vec2 operator +(const Vec2& other) const
+    {
+        return Vec2(x+other.x, y+other.y);
+    }
+    void operator += (const Vec2 &other)
+    {
+        x+=other.x; y+=other.y;
+    }
+    Vec2 operator -(const Vec2& other) const
+    {
+        return Vec2(x-other.x, y-other.y);
+    }
+    void operator -= (const Vec2& other)
+    {
+        x-=other.x; y-=other.y;
+    }
+    Vec2 operator -() const
+    {
+        return Vec2(-x,-y);
+    }
+    Vec2 operator * (const Vec2& other) const
+    {
+        return Vec2(x*other.x, y*other.y);
+    }
+    template<typename V>
+    Vec2 operator * (const V& f) const
+    {
+        return Vec2(x*f,y*f);
+    }
+    template<typename V>
+    void operator *= (const V& f)
+    {
+        x*=f; y*=f;
+    }
+    template<typename V>
+    Vec2 operator / (const V& f) const
+    {
+        return Vec2(x/f,y/f);
+    }
+    template<typename V>
+    void operator /= (const V& f)
+    {
+        *this = *this / f;
+    }
+
+    T Length2() const
+    {
+        return x*x + y*y;
+    }
+
+    // Only implemented for T=float
+    float Length() const;
+    void SetLength(const float l);
+    Vec2 WithLength(const float l) const;
+    float Distance2To(Vec2 &other);
+    Vec2 Normalized() const;
+    float Normalize(); // returns the previous length, which is often useful
+
+    T& operator [] (int i) //allow vector[1] = 3   (vector.y=3)
+    {
+        return *((&x) + i);
+    }
+    T operator [] (const int i) const
+    {
+        return *((&x) + i);
+    }
+
+    void SetZero()
+    {
+        x=0; y=0;
+    }
+
+    // Common aliases: UV (texel coordinates), ST (texture coordinates)
+    T& u() { return x; }
+    T& v() { return y; }
+    T& s() { return x; }
+    T& t() { return y; }
+
+    const T& u() const { return x; }
+    const T& v() const { return y; }
+    const T& s() const { return x; }
+    const T& t() const { return y; }
+
+    // swizzlers - create a subvector of specific components
+    Vec2 yx() const { return Vec2(y, x); }
+    Vec2 vu() const { return Vec2(y, x); }
+    Vec2 ts() const { return Vec2(y, x); }
+
+    // Inserters to add new elements to effectively create larger vectors containing this Vec2
+    Vec3<T> InsertBeforeX(const T& value) {
+        return Vec3<T>(value, x, y);
+    }
+    Vec3<T> InsertBeforeY(const T& value) {
+        return Vec3<T>(x, value, y);
+    }
+    Vec3<T> Append(const T& value) {
+        return Vec3<T>(x, y, value);
+    }
+};
+
+template<typename T, typename V>
+Vec2<T> operator * (const V& f, const Vec2<T>& vec)
+{
+    return Vec2<T>(f*vec.x,f*vec.y);
+}
+
+typedef Vec2<float> Vec2f;
+
+template<typename T>
+class Vec3
+{
+public:
+    struct
+    {
+        T x,y,z;
+    };
+
+    T* AsArray() { return &x; }
+
+    Vec3() = default;
+    Vec3(const T a[3]) : x(a[0]), y(a[1]), z(a[2]) {}
+    Vec3(const T& _x, const T& _y, const T& _z) : x(_x), y(_y), z(_z) {}
+
+    template<typename T2>
+    Vec3<T2> Cast() const {
+        return Vec3<T2>((T2)x, (T2)y, (T2)z);
+    }
+
+    // Only implemented for T=int and T=float
+    static Vec3 FromRGB(unsigned int rgb);
+    unsigned int ToRGB() const; // alpha bits set to zero
+
+    static Vec3 AssignToAll(const T& f)
+    {
+        return Vec3<T>(f, f, f);
+    }
+
+    void Write(T a[3])
+    {
+        a[0] = x; a[1] = y; a[2] = z;
+    }
+
+    Vec3 operator +(const Vec3 &other) const
+    {
+        return Vec3(x+other.x, y+other.y, z+other.z);
+    }
+    void operator += (const Vec3 &other)
+    {
+        x+=other.x; y+=other.y; z+=other.z;
+    }
+    Vec3 operator -(const Vec3 &other) const
+    {
+        return Vec3(x-other.x, y-other.y, z-other.z);
+    }
+    void operator -= (const Vec3 &other)
+    {
+        x-=other.x; y-=other.y; z-=other.z;
+    }
+    Vec3 operator -() const
+    {
+        return Vec3(-x,-y,-z);
+    }
+    Vec3 operator * (const Vec3 &other) const
+    {
+        return Vec3(x*other.x, y*other.y, z*other.z);
+    }
+    template<typename V>
+    Vec3 operator * (const V& f) const
+    {
+        return Vec3(x*f,y*f,z*f);
+    }
+    template<typename V>
+    void operator *= (const V& f)
+    {
+        x*=f; y*=f; z*=f;
+    }
+    template<typename V>
+    Vec3 operator / (const V& f) const
+    {
+        return Vec3(x/f,y/f,z/f);
+    }
+    template<typename V>
+    void operator /= (const V& f)
+    {
+        *this = *this / f;
+    }
+
+    T Length2() const
+    {
+        return x*x + y*y + z*z;
+    }
+
+    // Only implemented for T=float
+    float Length() const;
+    void SetLength(const float l);
+    Vec3 WithLength(const float l) const;
+    float Distance2To(Vec3 &other);
+    Vec3 Normalized() const;
+    float Normalize(); // returns the previous length, which is often useful
+
+    T& operator [] (int i) //allow vector[2] = 3   (vector.z=3)
+    {
+        return *((&x) + i);
+    }
+    T operator [] (const int i) const
+    {
+        return *((&x) + i);
+    }
+
+    void SetZero()
+    {
+        x=0; y=0; z=0;
+    }
+
+    // Common aliases: UVW (texel coordinates), RGB (colors), STQ (texture coordinates)
+    T& u() { return x; }
+    T& v() { return y; }
+    T& w() { return z; }
+
+    T& r() { return x; }
+    T& g() { return y; }
+    T& b() { return z; }
+
+    T& s() { return x; }
+    T& t() { return y; }
+    T& q() { return z; }
+
+    const T& u() const { return x; }
+    const T& v() const { return y; }
+    const T& w() const { return z; }
+
+    const T& r() const { return x; }
+    const T& g() const { return y; }
+    const T& b() const { return z; }
+
+    const T& s() const { return x; }
+    const T& t() const { return y; }
+    const T& q() const { return z; }
+
+    // swizzlers - create a subvector of specific components
+    // e.g. Vec2 uv() { return Vec2(x,y); }
+    // _DEFINE_SWIZZLER2 defines a single such function, DEFINE_SWIZZLER2 defines all of them for all component names (x<->r) and permutations (xy<->yx)
+#define _DEFINE_SWIZZLER2(a, b, name) Vec2<T> name() const { return Vec2<T>(a, b); }
+#define DEFINE_SWIZZLER2(a, b, a2, b2, a3, b3, a4, b4) \
+    _DEFINE_SWIZZLER2(a, b, a##b); \
+    _DEFINE_SWIZZLER2(a, b, a2##b2); \
+    _DEFINE_SWIZZLER2(a, b, a3##b3); \
+    _DEFINE_SWIZZLER2(a, b, a4##b4); \
+    _DEFINE_SWIZZLER2(b, a, b##a); \
+    _DEFINE_SWIZZLER2(b, a, b2##a2); \
+    _DEFINE_SWIZZLER2(b, a, b3##a3); \
+    _DEFINE_SWIZZLER2(b, a, b4##a4);
+
+    DEFINE_SWIZZLER2(x, y, r, g, u, v, s, t);
+    DEFINE_SWIZZLER2(x, z, r, b, u, w, s, q);
+    DEFINE_SWIZZLER2(y, z, g, b, v, w, t, q);
+#undef DEFINE_SWIZZLER2
+#undef _DEFINE_SWIZZLER2
+
+    // Inserters to add new elements to effectively create larger vectors containing this Vec2
+    Vec4<T> InsertBeforeX(const T& value) {
+        return Vec4<T>(value, x, y, z);
+    }
+    Vec4<T> InsertBeforeY(const T& value) {
+        return Vec4<T>(x, value, y, z);
+    }
+    Vec4<T> InsertBeforeZ(const T& value) {
+        return Vec4<T>(x, y, value, z);
+    }
+    Vec4<T> Append(const T& value) {
+        return Vec4<T>(x, y, z, value);
+    }
+};
+
+template<typename T, typename V>
+Vec3<T> operator * (const V& f, const Vec3<T>& vec)
+{
+    return Vec3<T>(f*vec.x,f*vec.y,f*vec.z);
+}
+
+typedef Vec3<float> Vec3f;
+
+template<typename T>
+class Vec4
+{
+public:
+    struct
+    {
+        T x,y,z,w;
+    };
+
+    T* AsArray() { return &x; }
+
+    Vec4() = default;
+    Vec4(const T a[4]) : x(a[0]), y(a[1]), z(a[2]), w(a[3]) {}
+    Vec4(const T& _x, const T& _y, const T& _z, const T& _w) : x(_x), y(_y), z(_z), w(_w) {}
+
+    template<typename T2>
+    Vec4<T2> Cast() const {
+        return Vec4<T2>((T2)x, (T2)y, (T2)z, (T2)w);
+    }
+
+    // Only implemented for T=int and T=float
+    static Vec4 FromRGBA(unsigned int rgba);
+    unsigned int ToRGBA() const;
+
+    static Vec4 AssignToAll(const T& f) {
+        return Vec4<T>(f, f, f, f);
+    }
+
+    void Write(T a[4])
+    {
+        a[0] = x; a[1] = y; a[2] = z; a[3] = w;
+    }
+
+    Vec4 operator +(const Vec4& other) const
+    {
+        return Vec4(x+other.x, y+other.y, z+other.z, w+other.w);
+    }
+    void operator += (const Vec4& other)
+    {
+        x+=other.x; y+=other.y; z+=other.z; w+=other.w;
+    }
+    Vec4 operator -(const Vec4 &other) const
+    {
+        return Vec4(x-other.x, y-other.y, z-other.z, w-other.w);
+    }
+    void operator -= (const Vec4 &other)
+    {
+        x-=other.x; y-=other.y; z-=other.z; w-=other.w;
+    }
+    Vec4 operator -() const
+    {
+        return Vec4(-x,-y,-z,-w);
+    }
+    Vec4 operator * (const Vec4 &other) const
+    {
+        return Vec4(x*other.x, y*other.y, z*other.z, w*other.w);
+    }
+    template<typename V>
+    Vec4 operator * (const V& f) const
+    {
+        return Vec4(x*f,y*f,z*f,w*f);
+    }
+    template<typename V>
+    void operator *= (const V& f)
+    {
+        x*=f; y*=f; z*=f; w*=f;
+    }
+    template<typename V>
+    Vec4 operator / (const V& f) const
+    {
+        return Vec4(x/f,y/f,z/f,w/f);
+    }
+    template<typename V>
+    void operator /= (const V& f)
+    {
+        *this = *this / f;
+    }
+
+    T Length2() const
+    {
+        return x*x + y*y + z*z + w*w;
+    }
+
+    // Only implemented for T=float
+    float Length() const;
+    void SetLength(const float l);
+    Vec4 WithLength(const float l) const;
+    float Distance2To(Vec4 &other);
+    Vec4 Normalized() const;
+    float Normalize(); // returns the previous length, which is often useful
+
+    T& operator [] (int i) //allow vector[2] = 3   (vector.z=3)
+    {
+        return *((&x) + i);
+    }
+    T operator [] (const int i) const
+    {
+        return *((&x) + i);
+    }
+
+    void SetZero()
+    {
+        x=0; y=0; z=0;
+    }
+
+    // Common alias: RGBA (colors)
+    T& r() { return x; }
+    T& g() { return y; }
+    T& b() { return z; }
+    T& a() { return w; }
+
+    const T& r() const { return x; }
+    const T& g() const { return y; }
+    const T& b() const { return z; }
+    const T& a() const { return w; }
+
+    // swizzlers - create a subvector of specific components
+    // e.g. Vec2 uv() { return Vec2(x,y); }
+    // _DEFINE_SWIZZLER2 defines a single such function, DEFINE_SWIZZLER2 defines all of them for all component names (x<->r) and permutations (xy<->yx)
+#define _DEFINE_SWIZZLER2(a, b, name) Vec2<T> name() const { return Vec2<T>(a, b); }
+#define DEFINE_SWIZZLER2(a, b, a2, b2) \
+    _DEFINE_SWIZZLER2(a, b, a##b); \
+    _DEFINE_SWIZZLER2(a, b, a2##b2); \
+    _DEFINE_SWIZZLER2(b, a, b##a); \
+    _DEFINE_SWIZZLER2(b, a, b2##a2);
+
+    DEFINE_SWIZZLER2(x, y, r, g);
+    DEFINE_SWIZZLER2(x, z, r, b);
+    DEFINE_SWIZZLER2(x, w, r, a);
+    DEFINE_SWIZZLER2(y, z, g, b);
+    DEFINE_SWIZZLER2(y, w, g, a);
+    DEFINE_SWIZZLER2(z, w, b, a);
+#undef DEFINE_SWIZZLER2
+#undef _DEFINE_SWIZZLER2
+
+#define _DEFINE_SWIZZLER3(a, b, c, name) Vec3<T> name() const { return Vec3<T>(a, b, c); }
+#define DEFINE_SWIZZLER3(a, b, c, a2, b2, c2) \
+    _DEFINE_SWIZZLER3(a, b, c, a##b##c); \
+    _DEFINE_SWIZZLER3(a, c, b, a##c##b); \
+    _DEFINE_SWIZZLER3(b, a, c, b##a##c); \
+    _DEFINE_SWIZZLER3(b, c, a, b##c##a); \
+    _DEFINE_SWIZZLER3(c, a, b, c##a##b); \
+    _DEFINE_SWIZZLER3(c, b, a, c##b##a); \
+    _DEFINE_SWIZZLER3(a, b, c, a2##b2##c2); \
+    _DEFINE_SWIZZLER3(a, c, b, a2##c2##b2); \
+    _DEFINE_SWIZZLER3(b, a, c, b2##a2##c2); \
+    _DEFINE_SWIZZLER3(b, c, a, b2##c2##a2); \
+    _DEFINE_SWIZZLER3(c, a, b, c2##a2##b2); \
+    _DEFINE_SWIZZLER3(c, b, a, c2##b2##a2);
+
+    DEFINE_SWIZZLER3(x, y, z, r, g, b);
+    DEFINE_SWIZZLER3(x, y, w, r, g, a);
+    DEFINE_SWIZZLER3(x, z, w, r, b, a);
+    DEFINE_SWIZZLER3(y, z, w, g, b, a);
+#undef DEFINE_SWIZZLER3
+#undef _DEFINE_SWIZZLER3
+};
+
+
+template<typename T, typename V>
+Vec4<T> operator * (const V& f, const Vec4<T>& vec)
+{
+    return Vec4<T>(f*vec.x,f*vec.y,f*vec.z,f*vec.w);
+}
+
+typedef Vec4<float> Vec4f;
+
+
+template<typename T>
+static inline T Dot(const Vec2<T>& a, const Vec2<T>& b)
+{
+    return a.x*b.x + a.y*b.y;
+}
+
+template<typename T>
+static inline T Dot(const Vec3<T>& a, const Vec3<T>& b)
+{
+    return a.x*b.x + a.y*b.y + a.z*b.z;
+}
+
+template<typename T>
+static inline T Dot(const Vec4<T>& a, const Vec4<T>& b)
+{
+    return a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
+}
+
+template<typename T>
+static inline Vec3<T> Cross(const Vec3<T>& a, const Vec3<T>& b)
+{
+    return Vec3<T>(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);
+}
+
+// linear interpolation via float: 0.0=begin, 1.0=end
+template<typename X>
+static inline X Lerp(const X& begin, const X& end, const float t)
+{
+    return begin*(1.f-t) + end*t;
+}
+
+// linear interpolation via int: 0=begin, base=end
+template<typename X, int base>
+static inline X LerpInt(const X& begin, const X& end, const int t)
+{
+    return (begin*(base-t) + end*t) / base;
+}
+
+// Utility vector factories
+template<typename T>
+static inline Vec2<T> MakeVec2(const T& x, const T& y)
+{
+    return Vec2<T>{x, y};
+}
+
+template<typename T>
+static inline Vec3<T> MakeVec3(const T& x, const T& y, const T& z)
+{
+    return Vec3<T>{x, y, z};
+}
+
+template<typename T>
+static inline Vec4<T> MakeVec4(const T& x, const T& y, const T& z, const T& w)
+{
+    return Vec4<T>{x, y, z, w};
+}
+
+} // namespace
diff --git a/src/video_core/video_core.vcxproj b/src/video_core/video_core.vcxproj
index d77be2bef..2dbfc68dd 100644
--- a/src/video_core/video_core.vcxproj
+++ b/src/video_core/video_core.vcxproj
@@ -25,6 +25,7 @@
   </ItemGroup>
   <ItemGroup>
     <ClInclude Include="gpu_debugger.h" />
+    <ClInclude Include="math.h" />
     <ClInclude Include="pica.h" />
     <ClInclude Include="renderer_base.h" />
     <ClInclude Include="utils.h" />
diff --git a/src/video_core/video_core.vcxproj.filters b/src/video_core/video_core.vcxproj.filters
index b89ac1ac4..b42823d2a 100644
--- a/src/video_core/video_core.vcxproj.filters
+++ b/src/video_core/video_core.vcxproj.filters
@@ -17,6 +17,7 @@
       <Filter>renderer_opengl</Filter>
     </ClInclude>
     <ClInclude Include="gpu_debugger.h" />
+    <ClInclude Include="math.h" />
     <ClInclude Include="pica.h" />
     <ClInclude Include="renderer_base.h" />
     <ClInclude Include="utils.h" />