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/* Copyright (c) 2014-2016, Stanislaw Halik <sthalik@misaki.pl>
* Permission to use, copy, modify, and/or distribute this
* software for any purpose with or without fee is hereby granted,
* provided that the above copyright notice and this permission
* notice appear in all copies.
*/
#pragma once
#include <type_traits>
#include <utility>
#include <cmath>
namespace simple_mat {
// last param to fool SFINAE into overloading
template<int i, int j, int>
struct equals
{
enum { value = i == j };
};
template<int i, int j, int min, int max>
struct maybe_add_swizzle
{
enum { value = (i == 1 || j == 1) && (i >= min || j >= min) && (i <= max || j <= max) };
};
template<int j, int i>
struct is_vector
{
enum { value = j == 1 || i == 1 };
};
template<int i1, int j1, int i2, int j2>
struct is_vector_pair
{
enum { value = (i1 == i2 && j1 == 1 && j2 == 1) || (j1 == j2 && i1 == 1 && i2 == 1) };
};
template<int i, int j>
struct vector_len
{
enum { value = i > j ? i : j };
};
template<int a, int b, int c, int d>
struct is_dim3
{
enum { value = (a == 1 && c == 1 && b == 3 && d == 3) || (a == 3 && c == 3 && b == 1 && d == 1) };
enum { P = a == 1 ? 1 : 3 };
enum { Q = a == 1 ? 3 : 1 };
};
template<typename, int h, int w, typename...ts>
struct is_arglist_correct
{
enum { value = h * w == sizeof...(ts) };
};
template<typename num, int H, int W>
class Mat
{
static_assert(H > 0 && W > 0, "must have positive mat dimensions");
num data[H][W];
public:
// parameters W and H are rebound so that SFINAE occurs
// removing them causes a compile-time error -sh 20150811
template<typename t, int Q = W> std::enable_if_t<equals<Q, 1, 0>::value, num>
constexpr inline operator()(t i) const& { return data[(unsigned)i][0]; }
template<typename t, int P = H> std::enable_if_t<equals<P, 1, 1>::value, num>
constexpr inline operator()(t i) const& { return data[0][(unsigned)i]; }
template<typename t, int Q = W> std::enable_if_t<equals<Q, 1, 2>::value, num&>
constexpr inline operator()(t i) & { return data[(unsigned)i][0]; }
template<typename t, int P = H> std::enable_if_t<equals<P, 1, 3>::value, num&>
constexpr inline operator()(t i) & { return data[0][(unsigned)i]; }
#define OTR_MAT_ASSERT_SWIZZLE static_assert(P == H && Q == W)
// const variants
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 1, 4>::value, num>
constexpr inline x() const& { OTR_MAT_ASSERT_SWIZZLE; return operator()(0); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 2, 4>::value, num>
constexpr inline y() const& { OTR_MAT_ASSERT_SWIZZLE; return operator()(1); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 3, 4>::value, num>
constexpr inline z() const& { OTR_MAT_ASSERT_SWIZZLE; return operator()(2); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 4, 4>::value, num>
constexpr inline w() const& { OTR_MAT_ASSERT_SWIZZLE; return operator()(3); }
// mutable variants
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 1, 4>::value, num&>
constexpr inline x() & { OTR_MAT_ASSERT_SWIZZLE; return operator()(0); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 2, 4>::value, num&>
constexpr inline y() & { OTR_MAT_ASSERT_SWIZZLE; return operator()(1); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 3, 4>::value, num&>
constexpr inline z() & { OTR_MAT_ASSERT_SWIZZLE; return operator()(2); }
template<int P = H, int Q = W> std::enable_if_t<maybe_add_swizzle<P, Q, 4, 4>::value, num&>
constexpr inline w() & { OTR_MAT_ASSERT_SWIZZLE; return operator()(3); }
template<int P = H, int Q = W>
constexpr auto norm_squared() const -> std::enable_if_t<is_vector<P, Q>::value, num>
{
static_assert(P == H && Q == W);
const num val = dot(*this);
constexpr num eps = num(1e-4);
if (val < eps)
return num(0);
else
return val;
}
inline auto norm() const { return num(std::sqrt(norm_squared())); }
template<int R, int S, int P = H, int Q = W>
std::enable_if_t<is_vector_pair<R, S, P, Q>::value, num>
constexpr dot(const Mat<num, R, S>& p2) const
{
static_assert(P == H && Q == W);
num ret = 0;
constexpr int len = vector_len<R, S>::value;
for (int i = 0; i < len; i++)
ret += operator()(i) * p2(i);
return ret;
}
template<int R, int S, int P = H, int Q = W>
std::enable_if_t<is_dim3<P, Q, R, S>::value, Mat<num, is_dim3<P, Q, R, S>::P, is_dim3<P, Q, R, S>::Q>>
constexpr cross(const Mat<num, R, S>& b) const
{
static_assert(P == H && Q == W);
const auto& a = *this;
return Mat<num, R, S>(a.y()*b.z() - a.z()*b.y(),
a.z()*b.x() - a.x()*b.z(),
a.x()*b.y() - a.y()*b.x());
}
constexpr Mat<num, H, W> operator+(const Mat<num, H, W>& other) const
{
Mat<num, H, W> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(j, i) = data[j][i] + other.data[j][i];
return ret;
}
constexpr Mat<num, H, W> operator-(const Mat<num, H, W>& other) const
{
Mat<num, H, W> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(j, i) = data[j][i] - other.data[j][i];
return ret;
}
constexpr Mat<num, H, W> operator+(const num other) const
{
Mat<num, H, W> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(j, i) = data[j][i] + other;
return ret;
}
constexpr Mat<num, H, W> operator-(const num other) const
{
Mat<num, H, W> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(j, i) = data[j][i] - other;
return ret;
}
template<int p>
constexpr Mat<num, H, p> operator*(const Mat<num, W, p>& other) const
{
Mat<num, H, p> ret;
for (int k = 0; k < H; k++)
for (int i = 0; i < p; i++)
{
ret(k, i) = 0;
for (int j = 0; j < W; j++)
ret(k, i) += data[k][j] * other(j, i);
}
return ret;
}
constexpr Mat<num, H, W> mult_elementwise(const Mat<num, H, W>& other) const&
{
Mat<num, H, W> ret;
for (unsigned j = 0; j < H; j++)
for (unsigned i = 0; i < W; i++)
ret(j, i) = data[j][i] * other.data[j][i];
return ret;
}
template<typename t, typename u>
constexpr inline num operator()(t j, u i) const& { return data[(unsigned)j][(unsigned)i]; }
template<typename t, typename u>
constexpr inline num& operator()(t j, u i) & { return data[(unsigned)j][(unsigned)i]; }
#ifdef __clang__
# pragma clang diagnostic push
# pragma clang diagnostic ignored "-Wmissing-braces"
#endif
template<typename... ts, int h2 = H, int w2 = W,
typename = std::enable_if_t<is_arglist_correct<num, h2, w2, ts...>::value>>
constexpr Mat(const ts... xs) : data{static_cast<num>(xs)...}
{
static_assert(h2 == H && w2 == W);
}
#ifdef __clang__
# pragma clang diagnostic pop
#endif
constexpr Mat()
{
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
data[j][i] = num(0);
}
constexpr Mat(const num* mem)
{
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
data[j][i] = mem[i*H+j];
}
constexpr operator num*() & { return (num*)data; }
constexpr operator const num*() const& { return (const num*)data; }
// XXX add more operators as needed, third-party dependencies mostly
// not needed merely for matrix algebra -sh 20141030
template<int H_ = H>
static constexpr std::enable_if_t<H == W, Mat<num, H_, H_>> eye()
{
static_assert(H == H_);
Mat<num, H, H> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret.data[j][i] = 0;
for (int i = 0; i < H; i++)
ret.data[i][i] = 1;
return ret;
}
constexpr Mat<num, W, H> t() const
{
Mat<num, W, H> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(i, j) = data[j][i];
return ret;
}
constexpr Mat<num, H, W>& operator=(const Mat<num, H, W>& rhs)
{
for (unsigned j = 0; j < H; j++)
for (unsigned i = 0; i < W; i++)
data[j][i] = rhs(j, i);
return *this;
}
};
} // ns simple_mat
template<typename num, int h, int w>
using Mat = simple_mat::Mat<num, h, w>;
template<typename num, int h, int w>
constexpr Mat<num, h, w> operator*(num scalar, const Mat<num, h, w>& mat)
{
return mat * scalar;
}
template<typename num, int H, int W>
constexpr Mat<num, H, W> operator*(const Mat<num, H, W>& self, num other)
{
Mat<num, H, W> ret;
for (int j = 0; j < H; j++)
for (int i = 0; i < W; i++)
ret(j, i) = self(j, i) * other;
return ret;
}
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