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"

namespace math { namespace matrix {
  template <typename, size_t, size_t> class matrix;
}}

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)                                     \
  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)

  struct {
  } fill;
  using fill_t = decltype(fill);

  template <typename T> struct is_vector {
    static const constexpr bool value = false;
  };

  template <typename T, std::size_t N> class vector;
  template <typename T, std::size_t N> struct is_vector<vector<T, N>> {
    static const constexpr bool value = true;
  };
  template <typename T, std::size_t R, std::size_t C>
  struct is_vector<matrix::matrix<T, R, C>> {
    static const constexpr bool value = true;
  };

  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;

    vector(std::array<T, N> const & init) {
      VECTOR_FOR_EACH(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) {
      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; }
    }

    // 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 {
      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, 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;
  }
}}

template <typename... Ts>
auto make_vector(Ts &&... elems)
    -> math::vector::vector<typename std::common_type<Ts...>::type,
                            sizeof...(Ts)> {
  return {{elems...}};
}

using math::vector::abs;