247 lines
6.9 KiB
C++
247 lines
6.9 KiB
C++
//---------------------------------------------------------------------------//
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// ," /\ ", Azur: A game engine for CASIO fx-CG and PC //
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// | _/__\_ | Designed by Lephe' and the Planète Casio community. //
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// "._`\/'_." License: MIT <https://opensource.org/licenses/MIT> //
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//---------------------------------------------------------------------------//
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// num.vec: Vector arithmetic
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//
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// This header provides basic vector arithmetic. It is type-generic and works
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// on any numerical type, including integers, floating-point types, and this
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// library's fixed-point types. Not all operations are available for all types
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// however.
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//
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// We slightly abuse the underlying object representation by expecting the
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// vector type vec<T,N> to be isomorphic to T[N] so we can perform accesses to
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// members with a pointer cast and array access. This access doesn't break
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// strict aliasing rules since the members' type is correct.
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//---
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#pragma once
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#include <num/num.h>
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namespace libnum {
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/* _vec_mixin: CRTP support type with common methods
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This structure type is inherited by all vec<T,N> types. It assumes that the
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vector type is isomorphic to T[N] and implements all the methods that can be
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derived from that. */
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template<typename Vector, typename T, int N> requires(N > 0)
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struct _vec_mixin
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{
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/* Number of components in the vector. */
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inline constexpr int size() const {
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return N;
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}
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/* Access to the i-th component as an lvalue. */
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inline constexpr T &operator[](int i) {
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return ((T *)this)[i];
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}
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inline constexpr T const &operator[](int i) const {
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return ((T *)this)[i];
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}
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/* Dot product with another vector of the same size. */
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constexpr T dot(Vector const &other) const {
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T r(0);
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for(int i = 0; i < N; ++i)
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r += (*this)[i] * other[i];
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return r;
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}
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/* Vector norm, squared. */
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constexpr T norm2() const {
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T r(0);
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for(int i = 0; i < N; ++i)
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r += (*this)[i] * (*this)[i];
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return r;
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}
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/* Vector norm. */
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// TODO: _vec_mixin<T,N>::norm() only works for num (uses .sqrt() method)
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constexpr T norm() const {
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return norm2().sqrt();
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}
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/* Normalized */
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constexpr Vector normalize() const {
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return *static_cast<const Vector *>(this) / norm();
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}
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};
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/* Vector type implementations. The generic type vec<T,N> uses an array and no
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specific facilities. The specialized types vec<T,2> through vec<T,4> provide
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access to members as .x, .y, .z, .w in addition to operator[]. They also
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provide swizzling-style constructors and methods. */
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template<typename T, int N> requires(N > 0)
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struct vec: _vec_mixin<vec<T,N>, T, N>
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{
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T coords[N];
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};
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template<typename T>
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struct vec<T,2>: _vec_mixin<vec<T,2>, T, 2>
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{
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T x, y;
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vec(): x {0}, y {0} {}
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vec(T _x, T _y): x {_x}, y {_y} {}
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};
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using vec2 = vec<num,2>;
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template<typename T>
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struct vec<T,3>: _vec_mixin<vec<T,3>, T, 3>
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{
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T x, y, z;
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vec(): x {0}, y {0}, z {0} {}
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vec(T _x, T _y, T _z): x {_x}, y {_y}, z {_z} {}
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vec(T scalar): x {scalar}, y {scalar}, z {scalar} {}
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vec(vec<T,2> v): x {v.x}, y {v.y}, z {0} {}
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vec(vec<T,2> v, T _z): x {v.x}, y {v.y}, z {_z} {}
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inline constexpr vec<T,2> xy() const {
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return vec<T,2>(x, y);
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}
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inline constexpr vec<T,2> xz() const {
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return vec<T,2>(x, z);
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}
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inline constexpr vec<T,2> yz() const {
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return vec<T,2>(y, z);
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}
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};
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using vec3 = vec<num,3>;
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template<typename T>
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struct vec<T,4>: _vec_mixin<vec<T,4>, T, 4>
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{
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T x, y, z, w;
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vec(): x {0}, y {0}, z {0} {}
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vec(T _x, T _y, T _z, T _w): x {_x}, y {_y}, z {_z}, w {_w} {}
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vec(T scalar): x {scalar}, y {scalar}, z {scalar}, w {scalar} {}
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vec(vec<T,2> v): x {v.x}, y {v.y}, z {0}, w {0} {}
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vec(vec<T,2> v, T _z, T _w): x {v.x}, y {v.y}, z {_z}, w {_w} {}
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vec(vec<T,3> v): x {v.x}, y {v.y}, z {v.z}, w {0} {}
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vec(vec<T,3> v, T _w): x {v.x}, y {v.y}, z {v.z}, w {_w} {}
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inline constexpr vec<T,3> xyz() const {
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return vec<T,3>(x, y, z);
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}
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};
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using vec4 = vec<num,4>;
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/* The following concept identifies vec types */
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template<typename T>
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struct is_vec_trait: std::false_type {};
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template<typename T, int N>
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struct is_vec_trait<vec<T,N>>: std::true_type {};
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template<typename T>
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concept is_vec = is_vec_trait<T>::value;
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/* Arithmetic */
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template<typename T, int N>
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inline constexpr vec<T,N> &operator+=(vec<T,N> &lhs, vec<T,N> const &rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] += rhs[i];
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> &operator-=(vec<T,N> &lhs, vec<T,N> const &rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] -= rhs[i];
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> &operator*=(vec<T,N> &lhs, T const &rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] *= rhs;
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> &operator*=(vec<T,N> &lhs, int rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] *= rhs;
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> &operator/=(vec<T,N> &lhs, T const &rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] /= rhs;
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> &operator/=(vec<T,N> &lhs, int rhs) {
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for(int i = 0; i < N; i++)
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lhs[i] /= rhs;
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator+(vec<T,N> const &lhs) {
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator-(vec<T,N> lhs) {
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for(int i = 0; i < N; i++)
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lhs[i] = -lhs[i];
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return lhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator+(vec<T,N> lhs, vec<T,N> const &rhs) {
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return lhs += rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator-(vec<T,N> lhs, vec<T,N> const &rhs) {
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return lhs -= rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator*(vec<T,N> lhs, T const &rhs) {
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return lhs *= rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator*(T const &lhs, vec<T,N> rhs) {
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for(int i = 0; i < N; i++)
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rhs[i] *= lhs;
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return rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator*(vec<T,N> lhs, int rhs) {
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return lhs *= rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator/(vec<T,N> lhs, T const &rhs) {
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return lhs /= rhs;
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}
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template<typename T, int N>
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inline constexpr vec<T,N> operator/(vec<T,N> lhs, int rhs) {
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return lhs /= rhs;
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}
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/* Comparisons */
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template<typename T, int N>
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inline constexpr bool operator==(vec<T,N> const &lhs, vec<T,N> const &rhs) {
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for(int i = 0; i < N; i++) {
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if(lhs[i] != rhs[i])
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return false;
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}
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return true;
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}
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template<typename T, int N>
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inline constexpr bool operator!=(vec<T,N> const &lhs, vec<T,N> const &rhs) {
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for(int i = 0; i < N; i++) {
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if(lhs[i] != rhs[i])
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return true;
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}
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return false;
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}
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} /* namespace libnum */
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