cpp-mathmatic-vector/vector.hpp

//
//  vector.hpp
//  vector
//
//  Created by Sam Jaffe on 8/15/16.
//

#pragma once

#include <cassert>
#include <cmath>
#include <cstddef>

#include <array>
#include <initializer_list>
#include <stdexcept>
#include <type_traits>

namespace math { namespace vector {
#define VECTOR_ENABLE_IF_LT_N(index, expr) \
template <bool _ = true> \
typename std::enable_if<std::size_t(index) < N && _, expr>::type
  
#define VECTOR_ENABLE_IF_EQ_N(index, t, n) \
template <bool _ = true> \
typename std::enable_if<std::size_t(index) == N && _, vector<t, n> >::type

#define VECTOR_ENABLE_IF_EQ_T(_type, t, n) \
vector<typename std::enable_if<std::is_same<_type, T>::value,T>::type, N>
  
#define VECTOR_ACCESS_FN(name, i) \
VECTOR_ENABLE_IF_LT_N(i, value_type const &) name() const { return _data[i]; } \
VECTOR_ENABLE_IF_LT_N(i, value_type &) name() { return _data[i]; }
  
#define VECTOR_FOR_EACH(var) for (std::size_t var = 0; var < N; ++var)
  
  struct {} fill;
  using fill_t = decltype(fill);
  
  template <typename T, std::size_t N>
  struct vector {
  public:
    using value_type = T;
  private:
    using mag_t = decltype(std::sqrt(std::declval<T>()));
    template <typename M>
    using mul_t = decltype(std::declval<T>()*std::declval<M>());
    template <typename M>
    using div_t = decltype(std::declval<T>()/std::declval<M>());
  public:
    
    // Constructors
    vector() = default;
    vector(std::initializer_list<T> && init) {
      std::size_t idx = 0;
      for ( auto it = init.begin(), end = init.end(); it != end && idx < N; ++it, ++idx ) {
        _data[idx] = *it;
      }
    }
    vector(std::array<T, N> const & init) {
      for (std::size_t i = 0; i < N && i < init.size(); ++i) {
        _data[i] = init[i];
      }
    }
    vector(vector const & other) {
      *this = other;
    }
    vector(vector && other) {
      *this = std::move(other);
    }
    
    // Conversion
    template <typename T2, std::size_t N2>
    explicit vector(vector<T2, N2> const & other) {
      for (std::size_t i = 0; i < N && i < N2; ++i) {
        _data[i] = static_cast<T>(other[i]);
      }
    }
    vector(T const & v, fill_t) {
      VECTOR_FOR_EACH(i) { _data[i] = v; }
    }
    
    // Assignment
    vector& operator=(vector const & other) {
      VECTOR_FOR_EACH(i) { _data[i] = other[i]; }
      return *this;
    }
    vector& operator=(vector && other) {
      VECTOR_FOR_EACH(i) { _data[i] = std::move(other._data[i]); }
      return *this;
    }
    
    // Named Accessors
    // - Numeric Vector Accessors
    VECTOR_ACCESS_FN(x, 0)
    VECTOR_ACCESS_FN(y, 1)
    VECTOR_ACCESS_FN(z, 2)
    VECTOR_ACCESS_FN(w, 3)
    
    // - Color Vector Accessors
    VECTOR_ACCESS_FN(r, 0)
    VECTOR_ACCESS_FN(g, 1)
    VECTOR_ACCESS_FN(b, 2)
    VECTOR_ACCESS_FN(a, 3)
    
    // Unnamed Accessors
    value_type const & operator[](std::size_t idx) const { return _data[idx]; }
    value_type & operator[](std::size_t idx) { return _data[idx]; }
    
    value_type const & at(std::size_t idx) const {
      if (idx >= N) throw std::out_of_range{"index out of range"};
      assert(idx < N);
      return operator[](idx);
    }
    value_type & at(std::size_t idx) {
      if (idx >= N) throw std::out_of_range{"index out of range"};
      assert(idx < N);
      return operator[](idx);
    }
    
    // Mathematical Operations
    vector& operator+=(vector const & other) {
      VECTOR_FOR_EACH(i) {
        _data[i] += other[i];
      }
      return *this;
    }
    
    vector& operator-=(vector const & other) {
      VECTOR_FOR_EACH(i) {
        _data[i] -= other[i];
      }
      return *this;
    }
    
    template <typename M>
    VECTOR_ENABLE_IF_EQ_T(mul_t<M>, T, N)& operator*=(M c) {
      VECTOR_FOR_EACH(i) {
        _data[i] *= c;
      }
      return *this;
    }
    
    template <typename M>
    VECTOR_ENABLE_IF_EQ_T(div_t<M>, T, N)& operator/=(M c) {
      VECTOR_FOR_EACH(i) {
        _data[i] /= c;
      }
      return *this;
    }
    
    template <typename M>
    VECTOR_ENABLE_IF_EQ_T(mul_t<M>, T, N)& operator*=(vector<M, N> c) {
      VECTOR_FOR_EACH(i) {
        _data[i] *= c[i];
      }
      return *this;
    }
    
    template <typename M>
    VECTOR_ENABLE_IF_EQ_T(div_t<M>, T, N)& operator/=(vector<M, N> c) {
      VECTOR_FOR_EACH(i) {
        _data[i] /= c[i];
      }
      return *this;
    }
      
    vector operator+(vector const & other) const {
      return vector{*this} += other;
    }
    
    vector operator-(vector const & other) const {
      return vector{*this} -= other;
    }
    
    template <typename M>
    vector<mul_t<M>, N> scaled(vector<M, N> const & other) const {
      return vector<mul_t<M>, N>{*this} *= other;
    }
    
    template <typename M>
    vector<mul_t<M>, N> operator*(M c) const {
      return vector<mul_t<M>, N>{*this} *= c;
    }
    
    template <typename M>
    friend vector<mul_t<M>, N> operator*(M c, vector<T, N> const & v) {
      return v * c;
    }
    
    template <typename M>
    vector<div_t<M>, N> invscaled(vector<M, N> const & other) const {
      return vector<div_t<M>, N>{*this} /= other;
    }
    
    template <typename M>
    vector<div_t<M>, N> operator/(M c) const {
      return vector<div_t<M>, N>{*this} /= c;
    }
    
    vector operator-() const {
      return vector{} -= *this;
    }
    
    // Vector Operations
    value_type dot(vector const & other) const {
      value_type accum{};
      VECTOR_FOR_EACH(i) {
        accum += at(i) * other.at(i);
      }
      return accum;
    }
    
    mag_t magnitude() const {
      return std::sqrt(dot(*this));
    }
    
    vector<mag_t, N> unit() const {
      return *this / magnitude();
    }
    
    friend vector abs(vector const & self) {
      vector tmp(self);
      using std::abs;
      for (std::size_t i = 0; i < N; ++i) {
        tmp._data[i] = abs(tmp._data[i]);
      }
      return tmp;
    }
    
    friend void swap(vector & lhs, vector & rhs) {
      vector tmp(lhs);
      lhs = rhs;
      rhs = tmp;
    }
    
    VECTOR_ENABLE_IF_EQ_N(3, T, N) cross(vector const & other) const {
      return {
        y()*other.z() - z()*other.y(),
        z()*other.x() - x()*other.z(),
        x()*other.y() - y()*other.x()
      };
    }
    VECTOR_ENABLE_IF_EQ_N(2, T, 3) cross(vector const & other) const {
      return { 0, 0, x()*other.y() - y()*other.x() };
    }
    
    vector<mag_t, N> projection(vector const & other) const {
      vector<mag_t, N> b_p = other.unit();
      return b_p * vector<mag_t, N>{*this}.dot(b_p);
    }
    
    friend bool operator==(vector const & lhs, vector const & rhs) { return lhs.compare(rhs) == 0; }
    friend bool operator!=(vector const & lhs, vector const & rhs) { return lhs.compare(rhs) != 0; }
    friend bool operator< (vector const & lhs, vector const & rhs) { return lhs.compare(rhs) <  0; }
    friend bool operator<=(vector const & lhs, vector const & rhs) { return lhs.compare(rhs) <= 0; }
    friend bool operator> (vector const & lhs, vector const & rhs) { return lhs.compare(rhs) >  0; }
    friend bool operator>=(vector const & lhs, vector const & rhs) { return lhs.compare(rhs) >= 0; }
    
  private:
    int compare(vector const & other) const {
      int rv = 0;
      for (std::size_t i = 0; i < N && rv == 0; ++i) {
        if (_data[i] < other[i]) rv = -1;
        else if (_data[i] > other[i]) rv = 1;
      }
      return rv;
    }
    
    value_type _data[N] = {value_type()};
  };
} }