cpp-mathmatic-vector/include/math/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>

#include <expect/expect.hpp>

#include "math/vector/forward.h"
#include "math/vector/traits.hpp"

#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)                                     \
  typename std::enable_if<std::is_same<_type, t>::value, vector<t, n>>::type

#define VECTOR_DISABLE_IF_VECTOR(_type, t, n)                                  \
  typename std::enable_if<!is_vector<_type>::value, vector<t, n>>::type

#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_RANGE(var, end)                                        \
  for (std::size_t var = 0; var < end; ++var)
#define VECTOR_FOR_EACH(var) VECTOR_FOR_EACH_RANGE(var, N)

namespace math::vector {

template <typename T, std::size_t N> class 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;

  template <typename... Us> vector(T arg0, Us... args) {
    static_assert(std::is_same_v<std::common_type_t<T, Us...>, T>,
                  "must be type compatible");
    static_assert(sizeof...(Us) + 1 == N, "size mismatch");
    *this = vector(std::array<T, N>{arg0, static_cast<T>(args)...});
  }

  vector(std::array<T, N> const & init) {
    VECTOR_FOR_EACH(i) { _data[i] = init[i]; }
  }

  // Conversion
  template <typename T2, std::size_t N2>
  explicit vector(vector<T2, N2> const & other) {
    VECTOR_FOR_EACH_RANGE(i, std::min(N, N2)) {
      _data[i] = static_cast<T>(other[i]);
    }
  }

  vector(T const & v, fill_t) {
    VECTOR_FOR_EACH(i) { _data[i] = v; }
  }

  // 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
  constexpr value_type const & operator[](std::size_t idx) const {
    return _data[idx];
  }
  constexpr value_type & operator[](std::size_t idx) { return _data[idx]; }

  value_type const & at(std::size_t idx) const {
    expects(idx < N, std::out_of_range, "index out of range");
    return _data[idx];
  }

  value_type & at(std::size_t idx) {
    expects(idx < N, std::out_of_range, "index out of range");
    return _data[idx];
  }

  // Mathematical Operations
  vector & operator+=(vector const & other) {
    VECTOR_FOR_EACH(i) { _data[i] += other[i]; }
    return *this;
  }

  vector & operator+=(T const & other) {
    return operator+=(vector(other, fill));
  }

  vector operator+(vector const & other) const {
    return vector{*this} += other;
  }

  vector operator+(T const & other) const {
    return operator+(vector(other, fill));
  }

  friend vector operator+(T const & lhs, vector const & rhs) {
    return rhs + lhs;
  }

  vector & operator-=(vector const & other) {
    VECTOR_FOR_EACH(i) { _data[i] -= other[i]; }
    return *this;
  }

  vector & operator-=(T const & other) {
    return operator-=(vector(other, fill));
  }

  vector operator-(vector const & other) const {
    return vector{*this} -= other;
  }

  vector operator-(T const & other) const {
    return operator-(vector(other, fill));
  }

  friend vector operator-(T const & lhs, vector const & rhs) {
    return vector(lhs, fill) - rhs;
  }

  vector operator-() const { return vector{} -= *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_DISABLE_IF_VECTOR(M, mul_t<M>, N)
  operator*(M c) const {
    return vector<mul_t<M>, N>{*this} *= c;
  }

  template <typename M>
  friend VECTOR_DISABLE_IF_VECTOR(M, mul_t<M>, N)
  operator*(M c, vector<T, N> const & v) {
    return v * c;
  }

  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<mul_t<M>, N> operator*(vector<M, N> const & other) const {
    return vector<mul_t<M>, N>{*this} *= other;
  }

  template <typename M>
  VECTOR_ENABLE_IF_EQ_T(div_t<M>, T, N) & operator/=(M c) {
    expects(c != 0, std::domain_error, "divide by zero");
    VECTOR_FOR_EACH(i) { _data[i] /= c; }
    return *this;
  }

  template <typename M>
  VECTOR_DISABLE_IF_VECTOR(M, div_t<M>, N)
  operator/(M c) const {
    return vector<div_t<M>, N>{*this} /= c;
  }

  template <typename M>
  VECTOR_ENABLE_IF_EQ_T(div_t<M>, T, N) & operator/=(vector<M, N> c) {
    VECTOR_FOR_EACH(i) {
      expects(c[i] != 0, std::domain_error, "divide by zero");
    }
    VECTOR_FOR_EACH(i) { _data[i] /= c[i]; }
    return *this;
  }

  template <typename M>
  vector<div_t<M>, N> operator/(vector<M, N> const & other) const {
    return vector<div_t<M>, N>{*this} /= other;
  }

  // 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(); }

  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);
  }

private:
  value_type _data[N] = {value_type()};
};

template <typename T, typename... Us>
vector(T, Us...) -> vector<T, sizeof...(Us) + 1>;

template <typename T, std::size_t N>
vector<T, N> abs(vector<T, N> const & self) {
  vector<T, N> tmp(self);
  using std::abs;
  VECTOR_FOR_EACH(i) { tmp[i] = abs(tmp[i]); }
  return tmp;
}

template <typename T, std::size_t N>
int compare(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  VECTOR_FOR_EACH(i) {
    if (lhs[i] < rhs[i])
      return -1;
    else if (lhs[i] > rhs[i])
      return 1;
  }
  return 0;
}

template <typename T, std::size_t N>
bool operator==(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) == 0;
}
template <typename T, std::size_t N>
bool operator!=(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) != 0;
}
template <typename T, std::size_t N>
bool operator<(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) < 0;
}
template <typename T, std::size_t N>
bool operator<=(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) <= 0;
}
template <typename T, std::size_t N>
bool operator>(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) > 0;
}
template <typename T, std::size_t N>
bool operator>=(vector<T, N> const & lhs, vector<T, N> const & rhs) {
  return compare(lhs, rhs) >= 0;
}
}

using math::vector::abs;