Vector3.cpp
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#include "Vector3.h"
#include "Math.h"
#include <iostream>
//#define _EULE_NO_INTRINSICS_
#ifndef _EULE_NO_INTRINSICS_
#include <immintrin.h>
#endif
using namespace Eule;
/*
NOTE:
Here you will find bad, unoptimized methods for T=int.
This is because the compiler needs a method for each type in each instantiation of the template!
I can't generalize the methods when heavily optimizing for doubles.
These functions will get called VERY rarely, if ever at all, for T=int, so it's ok.
The T=int instantiation only exists to store a value-pair of two ints. Not so-much as a vector in terms of vector calculus.
*/
// Good, optimized chad version for doubles
double Vector3<double>::DotProduct(const Vector3<double>& other) const
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components into registers
__m256 __vector_self = _mm256_set_ps(0,0,0,0,0, (float)z, (float)y, (float)x);
__m256 __vector_other = _mm256_set_ps(0,0,0,0,0, (float)other.z, (float)other.y, (float)other.x);
// Define bitmask, and execute computation
const int mask = 0x71; // -> 0111 1000 -> use positions 0111 (last 3) of the vectors supplied, and place them in 1000 (first only) element of __dot
__m256 __dot = _mm256_dp_ps(__vector_self, __vector_other, mask);
// Retrieve result, and return it
float result[8];
_mm256_storeu_ps(result, __dot);
return result[0];
#else
return (x * other.x) +
(y * other.y) +
(z * other.z);
#endif
}
// Slow, lame version for intcels
double Vector3<int>::DotProduct(const Vector3<int>& other) const
{
int iDot = (x * other.x) + (y * other.y) + (z * other.z);
return (double)iDot;
}
// Good, optimized chad version for doubles
Vector3<double> Vector3<double>::CrossProduct(const Vector3<double>& other) const
{
Vector3<double> cp;
cp.x = (y * other.z) - (z * other.y);
cp.y = (z * other.x) - (x * other.z);
cp.z = (x * other.y) - (y * other.x);
return cp;
}
// Slow, lame version for intcels
Vector3<double> Vector3<int>::CrossProduct(const Vector3<int>& other) const
{
Vector3<double> cp;
cp.x = ((double)y * (double)other.z) - ((double)z * (double)other.y);
cp.y = ((double)z * (double)other.x) - ((double)x * (double)other.z);
cp.z = ((double)x * (double)other.y) - ((double)y * (double)other.x);
return cp;
}
// Good, optimized chad version for doubles
double Vector3<double>::SqrMagnitude() const
{
// x.DotProduct(x) == x.SqrMagnitude()
return DotProduct(*this);
}
// Slow, lame version for intcels
double Vector3<int>::SqrMagnitude() const
{
int iSqrMag = x*x + y*y + z*z;
return (double)iSqrMag;
}
template <typename T>
double Vector3<T>::Magnitude() const
{
return sqrt(SqrMagnitude());
}
Vector3<double> Vector3<double>::VectorScale(const Vector3<double>& scalar) const
{
#ifndef _EULE_NO_INTRINSICS_
// Load vectors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_scalar = _mm256_set_pd(0, scalar.z, scalar.y, scalar.x);
// Multiply them
__m256d __product = _mm256_mul_pd(__vector_self, __vector_scalar);
// Retrieve result
double result[4];
_mm256_storeu_pd(result, __product);
// Return value
return Vector3<double>(
result[0],
result[1],
result[2]
);
#else
return Vector3<double>(
x * scalar.x,
y * scalar.y,
z * scalar.z
);
#endif
}
Vector3<int> Vector3<int>::VectorScale(const Vector3<int>& scalar) const
{
return Vector3<int>(
x * scalar.x,
y * scalar.y,
z * scalar.z
);
}
template<typename T>
Vector3<double> Vector3<T>::Normalize() const
{
Vector3<double> norm(x, y, z);
norm.NormalizeSelf();
return norm;
}
// Method to normalize a Vector3d
void Vector3<double>::NormalizeSelf()
{
const double length = Magnitude();
// Prevent division by 0
if (length == 0)
{
x = 0;
y = 0;
z = 0;
}
else
{
#ifndef _EULE_NO_INTRINSICS_
// Load vector and length into registers
__m256d __vec = _mm256_set_pd(0, z, y, x);
__m256d __len = _mm256_set1_pd(length);
// Divide
__m256d __prod = _mm256_div_pd(__vec, __len);
// Extract and set values
double prod[4];
_mm256_storeu_pd(prod, __prod);
x = prod[0];
y = prod[1];
z = prod[2];
#else
x /= length;
y /= length;
z /= length;
#endif
}
return;
}
// You can't normalize an int vector, ffs!
// But we need an implementation for T=int
void Vector3<int>::NormalizeSelf()
{
std::cerr << "Stop normalizing int-vectors!!" << std::endl;
x = 0;
y = 0;
z = 0;
return;
}
template<typename T>
bool Vector3<T>::Similar(const Vector3<T>& other, double epsilon) const
{
return
(::Math::Similar(x, other.x, epsilon)) &&
(::Math::Similar(y, other.y, epsilon)) &&
(::Math::Similar(z, other.z, epsilon))
;
}
template<typename T>
Vector3<int> Vector3<T>::ToInt() const
{
return Vector3<int>((int)x, (int)y, (int)z);
}
template<typename T>
Vector3<double> Vector3<T>::ToDouble() const
{
return Vector3<double>((double)x, (double)y, (double)z);
}
template<typename T>
T& Vector3<T>::operator[](std::size_t idx)
{
switch (idx)
{
case 0:
return x;
case 1:
return y;
case 2:
return z;
default:
throw std::out_of_range("Array descriptor on Vector3<T> out of range!");
}
}
template<typename T>
const T& Vector3<T>::operator[](std::size_t idx) const
{
switch (idx)
{
case 0:
return x;
case 1:
return y;
case 2:
return z;
default:
throw std::out_of_range("Array descriptor on Vector3<T> out of range!");
}
}
// Good, optimized chad version for doubles
void Vector3<double>::LerpSelf(const Vector3<double>& other, double t)
{
const double it = 1.0 - t; // Inverse t
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_other = _mm256_set_pd(0, other.z, other.y, other.x);
__m256d __t = _mm256_set1_pd(t);
__m256d __it = _mm256_set1_pd(it); // Inverse t
// Procedure:
// (__vector_self * __it) + (__vector_other * __t)
__m256d __sum = _mm256_set1_pd(0); // this will hold the sum of the two multiplications
__sum = _mm256_fmadd_pd(__vector_self, __it, __sum);
__sum = _mm256_fmadd_pd(__vector_other, __t, __sum);
// Retrieve result, and apply it
double sum[4];
_mm256_storeu_pd(sum, __sum);
x = sum[0];
y = sum[1];
z = sum[2];
#else
x = it*x + t*other.x;
y = it*y + t*other.y;
z = it*z + t*other.z;
#endif
return;
}
// Slow, lame version for intcels
void Vector3<int>::LerpSelf(const Vector3<int>& other, double t)
{
const double it = 1.0 - t; // Inverse t
x = (int)(it * (double)x + t * (double)other.x);
y = (int)(it * (double)y + t * (double)other.y);
z = (int)(it * (double)z + t * (double)other.z);
return;
}
Vector3<double> Vector3<double>::Lerp(const Vector3<double>& other, double t) const
{
Vector3d copy(*this);
copy.LerpSelf(other, t);
return copy;
}
Vector3<double> Vector3<int>::Lerp(const Vector3<int>& other, double t) const
{
Vector3d copy(this->ToDouble());
copy.LerpSelf(other.ToDouble(), t);
return copy;
}
Vector3<double> Vector3<double>::operator+(const Vector3<double>& other) const
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_other = _mm256_set_pd(0, other.z, other.y, other.x);
// Add the components
__m256d __sum = _mm256_add_pd(__vector_self, __vector_other);
// Retrieve and return these values
double sum[4];
_mm256_storeu_pd(sum, __sum);
return Vector3<double>(
sum[0],
sum[1],
sum[2]
);
#else
return Vector3<double>(
x + other.x,
y + other.y,
z + other.z
);
#endif
}
template<typename T>
Vector3<T> Vector3<T>::operator+(const Vector3<T>& other) const
{
return Vector3<T>(
x + other.x,
y + other.y,
z + other.z
);
}
void Vector3<double>::operator+=(const Vector3<double>& other)
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_other = _mm256_set_pd(0, other.z, other.y, other.x);
// Add the components
__m256d __sum = _mm256_add_pd(__vector_self, __vector_other);
// Retrieve and apply these values
double sum[4];
_mm256_storeu_pd(sum, __sum);
x = sum[0];
y = sum[1];
z = sum[2];
#else
x += other.x;
y += other.y;
z += other.z;
#endif
return;
}
template<typename T>
void Vector3<T>::operator+=(const Vector3<T>& other)
{
x += other.x;
y += other.y;
z += other.z;
return;
}
Vector3<double> Vector3<double>::operator-(const Vector3<double>& other) const
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_other = _mm256_set_pd(0, other.z, other.y, other.x);
// Subtract the components
__m256d __diff = _mm256_sub_pd(__vector_self, __vector_other);
// Retrieve and return these values
double diff[4];
_mm256_storeu_pd(diff, __diff);
return Vector3<double>(
diff[0],
diff[1],
diff[2]
);
#else
return Vector3<double>(
x - other.x,
y - other.y,
z - other.z
);
#endif
}
template<typename T>
Vector3<T> Vector3<T>::operator-(const Vector3<T>& other) const
{
return Vector3<T>(
x - other.x,
y - other.y,
z - other.z
);
}
void Vector3<double>::operator-=(const Vector3<double>& other)
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __vector_other = _mm256_set_pd(0, other.z, other.y, other.x);
// Subtract the components
__m256d __diff = _mm256_sub_pd(__vector_self, __vector_other);
// Retrieve and apply these values
double diff[4];
_mm256_storeu_pd(diff, __diff);
x = diff[0];
y = diff[1];
z = diff[2];
#else
x -= other.x;
y -= other.y;
z -= other.z;
#endif
return;
}
template<typename T>
void Vector3<T>::operator-=(const Vector3<T>& other)
{
x -= other.x;
y -= other.y;
z -= other.z;
return;
}
Vector3<double> Vector3<double>::operator*(const double scale) const
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __scalar = _mm256_set1_pd(scale);
// Multiply the components
__m256d __prod = _mm256_mul_pd(__vector_self, __scalar);
// Retrieve and return these values
double prod[4];
_mm256_storeu_pd(prod, __prod);
return Vector3<double>(
prod[0],
prod[1],
prod[2]
);
#else
return Vector3<double>(
x * scale,
y * scale,
z * scale
);
#endif
}
template<typename T>
Vector3<T> Vector3<T>::operator*(const T scale) const
{
return Vector3<T>(
x * scale,
y * scale,
z * scale
);
}
void Vector3<double>::operator*=(const double scale)
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __scalar = _mm256_set1_pd(scale);
// Multiply the components
__m256d __prod = _mm256_mul_pd(__vector_self, __scalar);
// Retrieve and apply these values
double prod[4];
_mm256_storeu_pd(prod, __prod);
x = prod[0];
y = prod[1];
z = prod[2];
#else
x *= scale;
y *= scale;
z *= scale;
#endif
return;
}
template<typename T>
void Vector3<T>::operator*=(const T scale)
{
x *= scale;
y *= scale;
z *= scale;
return;
}
Vector3<double> Vector3<double>::operator/(const double scale) const
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __scalar = _mm256_set1_pd(scale);
// Divide the components
__m256d __prod = _mm256_div_pd(__vector_self, __scalar);
// Retrieve and return these values
double prod[4];
_mm256_storeu_pd(prod, __prod);
return Vector3<double>(
prod[0],
prod[1],
prod[2]
);
#else
return Vector3<double>(
x / scale,
y / scale,
z / scale
);
#endif
}
template<typename T>
Vector3<T> Vector3<T>::operator/(const T scale) const
{
return Vector3<T>(
x / scale,
y / scale,
z / scale
);
}
void Vector3<double>::operator/=(const double scale)
{
#ifndef _EULE_NO_INTRINSICS_
// Move vector components and factors into registers
__m256d __vector_self = _mm256_set_pd(0, z, y, x);
__m256d __scalar = _mm256_set1_pd(scale);
// Divide the components
__m256d __prod = _mm256_div_pd(__vector_self, __scalar);
// Retrieve and apply these values
double prod[4];
_mm256_storeu_pd(prod, __prod);
x = prod[0];
y = prod[1];
z = prod[2];
#else
x /= scale;
y /= scale;
z /= scale;
#endif
return;
}
template<typename T>
void Vector3<T>::operator/=(const T scale)
{
x /= scale;
y /= scale;
z /= scale;
return;
}
// Good, optimized chad version for doubles
Vector3<double> Vector3<double>::operator*(const Matrix4x4& mat) const
{
Vector3<double> newVec;
#ifndef _EULE_NO_INTRINSICS_
// Store x, y, and z values
__m256d __vecx = _mm256_set1_pd(x);
__m256d __vecy = _mm256_set1_pd(y);
__m256d __vecz = _mm256_set1_pd(z);
// Store matrix values
__m256d __mat_row0 = _mm256_set_pd(mat[0][0], mat[1][0], mat[2][0], 0);
__m256d __mat_row1 = _mm256_set_pd(mat[0][1], mat[1][1], mat[2][1], 0);
__m256d __mat_row2 = _mm256_set_pd(mat[0][2], mat[1][2], mat[2][2], 0);
// Multiply x, y, z and matrix values
__m256d __mul_vecx_row0 = _mm256_mul_pd(__vecx, __mat_row0);
__m256d __mul_vecy_row1 = _mm256_mul_pd(__vecy, __mat_row1);
__m256d __mul_vecz_row2 = _mm256_mul_pd(__vecz, __mat_row2);
// Sum up the products
__m256d __sum = _mm256_add_pd(__mul_vecx_row0, _mm256_add_pd(__mul_vecy_row1, __mul_vecz_row2));
// Store translation values
__m256d __translation = _mm256_set_pd(mat[0][3], mat[1][3], mat[2][3], 0);
// Add the translation values
__m256d __final = _mm256_add_pd(__sum, __translation);
double dfinal[4];
_mm256_storeu_pd(dfinal, __final);
newVec.x = dfinal[3];
newVec.y = dfinal[2];
newVec.z = dfinal[1];
#else
// Rotation, Scaling
newVec.x = (mat[0][0] * x) + (mat[1][0] * y) + (mat[2][0] * z);
newVec.y = (mat[0][1] * x) + (mat[1][1] * y) + (mat[2][1] * z);
newVec.z = (mat[0][2] * x) + (mat[1][2] * y) + (mat[2][2] * z);
// Translation
newVec.x += mat[0][3];
newVec.y += mat[1][3];
newVec.z += mat[2][3];
#endif
return newVec;
}
// Slow, lame version for intcels
Vector3<int> Vector3<int>::operator*(const Matrix4x4& mat) const
{
Vector3<double> newVec;
// Rotation, Scaling
newVec.x = ((mat[0][0] * x) + (mat[1][0] * y) + (mat[2][0] * z));
newVec.y = ((mat[0][1] * x) + (mat[1][1] * y) + (mat[2][1] * z));
newVec.z = ((mat[0][2] * x) + (mat[1][2] * y) + (mat[2][2] * z));
// Translation
newVec.x += mat[0][3];
newVec.y += mat[1][3];
newVec.z += mat[2][3];
return Vector3<int>(
(int)newVec.x,
(int)newVec.y,
(int)newVec.z
);
}
// Good, optimized chad version for doubles
void Vector3<double>::operator*=(const Matrix4x4& mat)
{
#ifndef _EULE_NO_INTRINSICS_
// Store x, y, and z values
__m256d __vecx = _mm256_set1_pd(x);
__m256d __vecy = _mm256_set1_pd(y);
__m256d __vecz = _mm256_set1_pd(z);
// Store matrix values
__m256d __mat_row0 = _mm256_set_pd(mat[0][0], mat[1][0], mat[2][0], 0);
__m256d __mat_row1 = _mm256_set_pd(mat[0][1], mat[1][1], mat[2][1], 0);
__m256d __mat_row2 = _mm256_set_pd(mat[0][2], mat[1][2], mat[2][2], 0);
// Multiply x, y, z and matrix values
__m256d __mul_vecx_row0 = _mm256_mul_pd(__vecx, __mat_row0);
__m256d __mul_vecy_row1 = _mm256_mul_pd(__vecy, __mat_row1);
__m256d __mul_vecz_row2 = _mm256_mul_pd(__vecz, __mat_row2);
// Sum up the products
__m256d __sum = _mm256_add_pd(__mul_vecx_row0, _mm256_add_pd(__mul_vecy_row1, __mul_vecz_row2));
// Store translation values
__m256d __translation = _mm256_set_pd(mat[0][3], mat[1][3], mat[2][3], 0);
// Add the translation values
__m256d __final = _mm256_add_pd(__sum, __translation);
double dfinal[4];
_mm256_storeu_pd(dfinal, __final);
x = dfinal[3];
y = dfinal[2];
z = dfinal[1];
#else
Vector3<double> buffer = *this;
x = (mat[0][0] * buffer.x) + (mat[0][1] * buffer.y) + (mat[0][2] * buffer.z);
y = (mat[1][0] * buffer.x) + (mat[1][1] * buffer.y) + (mat[1][2] * buffer.z);
z = (mat[2][0] * buffer.x) + (mat[2][1] * buffer.y) + (mat[2][2] * buffer.z);
// Translation
x += mat[0][3];
y += mat[1][3];
z += mat[2][3];
#endif
return;
}
template<typename T>
Vector3<T> Vector3<T>::operator-() const
{
return Vector3<T>(
-x,
-y,
-z
);
}
template<typename T>
void Vector3<T>::operator=(const Vector3<T>& other)
{
x = other.x;
y = other.y;
z = other.z;
return;
}
template<typename T>
void Vector3<T>::operator=(Vector3<T>&& other) noexcept
{
x = std::move(other.x);
y = std::move(other.y);
z = std::move(other.z);
return;
}
// Slow, lame version for intcels
void Vector3<int>::operator*=(const Matrix4x4& mat)
{
Vector3<double> buffer(x, y, z);
x = (int)((mat[0][0] * buffer.x) + (mat[0][1] * buffer.y) + (mat[0][2] * buffer.z));
y = (int)((mat[1][0] * buffer.x) + (mat[1][1] * buffer.y) + (mat[1][2] * buffer.z));
z = (int)((mat[2][0] * buffer.x) + (mat[2][1] * buffer.y) + (mat[2][2] * buffer.z));
// Translation
x += (int)mat[0][3];
y += (int)mat[1][3];
z += (int)mat[2][3];
return;
}
template<typename T>
bool Vector3<T>::operator==(const Vector3<T>& other) const
{
return
(x == other.x) &&
(y == other.y) &&
(z == other.z);
}
template<typename T>
bool Vector3<T>::operator!=(const Vector3<T>& other) const
{
return !operator==(other);
}
#include "Vector2.h"
#include "Vector4.h"
template<typename T>
Vector3<T>::operator Vector2<T>() const
{
return Vector2<T>(x, y);
}
template<typename T>
Vector3<T>::operator Vector4<T>() const
{
return Vector4<T>(x, y, z, 0);
}
template class Vector3<int>;
template class Vector3<double>;
// Some handy predefines
template <typename T>
const Vector3<double> Vector3<T>::up(0, 1, 0);
template <typename T>
const Vector3<double> Vector3<T>::down(0, -1, 0);
template <typename T>
const Vector3<double> Vector3<T>::right(1, 0, 0);
template <typename T>
const Vector3<double> Vector3<T>::left(-1, 0, 0);
template <typename T>
const Vector3<double> Vector3<T>::forward(0, 0, 1);
template <typename T>
const Vector3<double> Vector3<T>::backward(0, 0, -1);
template <typename T>
const Vector3<double> Vector3<T>::one(1, 1, 1);
template <typename T>
const Vector3<double> Vector3<T>::zero(0, 0, 0);
Eule::Vector3::LerpSelf
void LerpSelf(const Vector3< T > &other, double t)
Will lerp itself towards other by t.
Definition: Vector3.cpp:311
Eule::Vector3< double >
Eule::Vector3::ToDouble
Vector3< double > ToDouble() const
Will convert this vector to a Vector3d.
Definition: Vector3.cpp:229
Math.h
Vector2.h
Eule::Vector3::z
T z
Definition: Vector3.h:96
Eule::Matrix4x4
A matrix 4x4 class representing a 3d transformation.
Definition: Matrix4x4.h:36
Eule::Vector3::x
T x
Definition: Vector3.h:94
Vector4.h
Eule::Vector2
Representation of a 2d vector.
Definition: Vector2.h:14
Eule::Vector3::DotProduct
double DotProduct(const Vector3< T > &other) const
Will compute the dot product to another Vector3.
Definition: Vector3.cpp:48
Vector3.h
Eule::Vector3::NormalizeSelf
void NormalizeSelf()
Will normalize this vector.
Definition: Vector3.cpp:200
Eule
Definition: Collider.h:4
Eule::Vector3::y
T y
Definition: Vector3.h:95
Eule::Vector4
Representation of a 4d vector.
Definition: Vector2.h:8