BLI: Refactor vector types & functions to use templates

This patch implements the vector types (i.e:`float2`) by making heavy
usage of templating. All vector functions are now outside of the vector
classes (inside the `blender::math` namespace) and are not vector size
dependent for the most part.

In the ongoing effort to make shaders less GL centric, we are aiming
to share more code between GLSL and C++ to avoid code duplication.

####Motivations:
- We are aiming to share UBO and SSBO structures between GLSL and C++.
This means we will use many of the existing vector types and others
we currently don't have (uintX, intX). All these variations were
asking for many more code duplication.
- Deduplicate existing code which is duplicated for each vector size.
- We also want to share small functions. Which means that vector
functions should be static and not in the class namespace.
- Reduce friction to use these types in new projects due to their
incompleteness.
- The current state of the `BLI_(float|double|mpq)(2|3|4).hh` is a
bit of a let down. Most clases are incomplete, out of sync with each
others with different codestyles, and some functions that should be
static are not (i.e: `float3::reflect()`).

####Upsides:
- Still support `.x, .y, .z, .w` for readability.
- Compact, readable and easilly extendable.
- All of the vector functions are available for all the vectors types
and can be restricted to certain types. Also template specialization
let us define exception for special class (like mpq).
- With optimization ON, the compiler unroll the loops and performance
is the same.

####Downsides:
- Might impact debugability. Though I would arge that the bugs are
rarelly caused by the vector class itself (since the operations are
quite trivial) but by the type conversions.
- Might impact compile time. I did not saw a significant impact since
the usage is not really widespread.
- Functions needs to be rewritten to support arbitrary vector length.
For instance, one can't call `len_squared_v3v3` in
`math::length_squared()` and call it a day.
- Type cast does not work with the template version of the `math::`
vector functions. Meaning you need to manually cast `float *` and
`(float *)[3]` to `float3` for the function calls.
i.e: `math::distance_squared(float3(nearest.co), positions[i]);`
- Some parts might loose in readability:
`float3::dot(v1.normalized(), v2.normalized())`
becoming
`math::dot(math::normalize(v1), math::normalize(v2))`
But I propose, when appropriate, to use
`using namespace blender::math;` on function local or file scope to
increase readability.
`dot(normalize(v1), normalize(v2))`

####Consideration:
- Include back `.length()` method. It is quite handy and is more C++
oriented.
- I considered the GLM library as a candidate for replacement. It felt
like too much for what we need and would be difficult to extend / modify
to our needs.
- I used Macros to reduce code in operators declaration and potential
copy paste bugs. This could reduce debugability and could be reverted.
- This touches `delaunay_2d.cc` and the intersection code. I would like
to know @howardt opinion on the matter.
- The `noexcept` on the copy constructor of `mpq(2|3)` is being removed.
But according to @JacquesLucke it is not a real problem for now.

I would like to give a huge thanks to @JacquesLucke who helped during this
and pushed me to reduce the duplication further.

Reviewed By: brecht, sergey, JacquesLucke

Differential Revision: https://developer.blender.org/D13791

1 files changed, 566 insertions, 0 deletions

diff --git a/source/blender/blenlib/BLI_math_vec_types.hh b/source/blender/blenlib/BLI_math_vec_types.hh
new file mode 100644
index 00000000000..52aacd294e4
--- /dev/null
+++ b/source/blender/blenlib/BLI_math_vec_types.hh
@@ -0,0 +1,566 @@
+/*
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * Copyright 2022, Blender Foundation.
+ */
+
+#pragma once
+
+/** \file
+ * \ingroup bli
+ */
+
+#include <array>
+#include <cmath>
+#include <iostream>
+#include <type_traits>
+
+#include "BLI_math_vector.hh"
+#include "BLI_utildefines.h"
+
+namespace blender {
+
+/* clang-format off */
+template<typename T>
+using as_uint_type = std::conditional_t<sizeof(T) == sizeof(uint8_t), uint8_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint16_t), uint16_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint32_t), uint32_t,
+                     std::conditional_t<sizeof(T) == sizeof(uint64_t), uint64_t, void>>>>;
+/* clang-format on */
+
+template<typename T, int Size> struct vec_struct_base {
+  std::array<T, Size> values;
+};
+
+template<typename T> struct vec_struct_base<T, 2> {
+  T x, y;
+};
+
+template<typename T> struct vec_struct_base<T, 3> {
+  T x, y, z;
+};
+
+template<typename T> struct vec_struct_base<T, 4> {
+  T x, y, z, w;
+};
+
+template<typename T, int Size> struct vec_base : public vec_struct_base<T, Size> {
+
+  static constexpr int type_length = Size;
+
+  using base_type = T;
+  using uint_type = vec_base<as_uint_type<T>, Size>;
+
+  vec_base() = default;
+
+  explicit vec_base(uint value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(int value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(float value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+  explicit vec_base(double value)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(value);
+    }
+  }
+
+/* Workaround issue with template BLI_ENABLE_IF((Size == 2)) not working. */
+#define BLI_ENABLE_IF_VEC(_size, _test) int S = _size, BLI_ENABLE_IF((S _test))
+
+  template<BLI_ENABLE_IF_VEC(Size, == 2)> vec_base(T _x, T _y)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+  }
+
+  template<BLI_ENABLE_IF_VEC(Size, == 3)> vec_base(T _x, T _y, T _z)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+    (*this)[2] = _z;
+  }
+
+  template<BLI_ENABLE_IF_VEC(Size, == 4)> vec_base(T _x, T _y, T _z, T _w)
+  {
+    (*this)[0] = _x;
+    (*this)[1] = _y;
+    (*this)[2] = _z;
+    (*this)[3] = _w;
+  }
+
+  /** Mixed scalar-vector constructors. */
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 3)>
+  constexpr vec_base(const vec_base<U, 2> &xy, T z)
+      : vec_base(static_cast<T>(xy.x), static_cast<T>(xy.y), z)
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 3)>
+  constexpr vec_base(T x, const vec_base<U, 2> &yz)
+      : vec_base(x, static_cast<T>(yz.x), static_cast<T>(yz.y))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 3> xyz, T w)
+      : vec_base(
+            static_cast<T>(xyz.x), static_cast<T>(xyz.y), static_cast<T>(xyz.z), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, vec_base<U, 3> yzw)
+      : vec_base(
+            static_cast<T>(x), static_cast<T>(yzw.x), static_cast<T>(yzw.y), static_cast<T>(yzw.z))
+  {
+  }
+
+  template<typename U, typename V, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 2> xy, vec_base<V, 2> zw)
+      : vec_base(
+            static_cast<T>(xy.x), static_cast<T>(xy.y), static_cast<T>(zw.x), static_cast<T>(zw.y))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(vec_base<U, 2> xy, T z, T w)
+      : vec_base(static_cast<T>(xy.x), static_cast<T>(xy.y), static_cast<T>(z), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, vec_base<U, 2> yz, T w)
+      : vec_base(static_cast<T>(x), static_cast<T>(yz.x), static_cast<T>(yz.y), static_cast<T>(w))
+  {
+  }
+
+  template<typename U, BLI_ENABLE_IF_VEC(Size, == 4)>
+  vec_base(T x, T y, vec_base<U, 2> zw)
+      : vec_base(static_cast<T>(x), static_cast<T>(y), static_cast<T>(zw.x), static_cast<T>(zw.y))
+  {
+  }
+
+  /** Masking. */
+
+  template<typename U, int OtherSize, BLI_ENABLE_IF(OtherSize > Size)>
+  explicit vec_base(const vec_base<U, OtherSize> &other)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(other[i]);
+    }
+  }
+
+#undef BLI_ENABLE_IF_VEC
+
+  /** Conversion from pointers (from C-style vectors). */
+
+  vec_base(const T *ptr)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = ptr[i];
+    }
+  }
+
+  vec_base(const T (*ptr)[Size]) : vec_base(static_cast<const T *>(ptr[0]))
+  {
+  }
+
+  /** Conversion from other vector types. */
+
+  template<typename U> explicit vec_base(const vec_base<U, Size> &vec)
+  {
+    for (int i = 0; i < Size; i++) {
+      (*this)[i] = static_cast<T>(vec[i]);
+    }
+  }
+
+  /** C-style pointer dereference. */
+
+  operator const T *() const
+  {
+    return reinterpret_cast<const T *>(this);
+  }
+
+  operator T *()
+  {
+    return reinterpret_cast<T *>(this);
+  }
+
+  /** Array access. */
+
+  const T &operator[](int index) const
+  {
+    BLI_assert(index >= 0);
+    BLI_assert(index < Size);
+    return reinterpret_cast<const T *>(this)[index];
+  }
+
+  T &operator[](int index)
+  {
+    BLI_assert(index >= 0);
+    BLI_assert(index < Size);
+    return reinterpret_cast<T *>(this)[index];
+  }
+
+  /** Internal Operators Macro. */
+
+#define BLI_INT_OP(_T) template<typename U = _T, BLI_ENABLE_IF((std::is_integral_v<U>))>
+
+#define BLI_VEC_OP_IMPL(_result, _i, _op) \
+  vec_base _result; \
+  for (int _i = 0; _i < Size; _i++) { \
+    _op; \
+  } \
+  return _result;
+
+#define BLI_VEC_OP_IMPL_SELF(_i, _op) \
+  for (int _i = 0; _i < Size; _i++) { \
+    _op; \
+  } \
+  return *this;
+
+  /** Arithmetic operators. */
+
+  friend vec_base operator+(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] + b[i]);
+  }
+
+  friend vec_base operator+(const vec_base &a, const T &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] + b);
+  }
+
+  friend vec_base operator+(const T &a, const vec_base &b)
+  {
+    return b + a;
+  }
+
+  vec_base &operator+=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] += b[i]);
+  }
+
+  vec_base &operator+=(const T &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] += b);
+  }
+
+  friend vec_base operator-(const vec_base &a)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = -a[i]);
+  }
+
+  friend vec_base operator-(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] - b[i]);
+  }
+
+  friend vec_base operator-(const vec_base &a, const T &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] - b);
+  }
+
+  friend vec_base operator-(const T &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a - b[i]);
+  }
+
+  vec_base &operator-=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] -= b[i]);
+  }
+
+  vec_base &operator-=(const T &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] -= b);
+  }
+
+  friend vec_base operator*(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] * b[i]);
+  }
+
+  friend vec_base operator*(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] * b);
+  }
+
+  friend vec_base operator*(T a, const vec_base &b)
+  {
+    return b * a;
+  }
+
+  vec_base &operator*=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] *= b);
+  }
+
+  vec_base &operator*=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] *= b[i]);
+  }
+
+  friend vec_base operator/(const vec_base &a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] / b[i]);
+  }
+
+  friend vec_base operator/(const vec_base &a, T b)
+  {
+    BLI_assert(b != T(0));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] / b);
+  }
+
+  friend vec_base operator/(T a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a / b[i]);
+  }
+
+  vec_base &operator/=(T b)
+  {
+    BLI_assert(b != T(0));
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] /= b);
+  }
+
+  vec_base &operator/=(const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] /= b[i]);
+  }
+
+  /** Binary operators. */
+
+  BLI_INT_OP(T) friend vec_base operator&(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] & b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator&(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] & b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator&(T a, const vec_base &b)
+  {
+    return b & a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator&=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] &= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator&=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] &= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] | b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] | b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator|(T a, const vec_base &b)
+  {
+    return b | a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator|=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] |= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator|=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] |= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] ^ b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] ^ b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator^(T a, const vec_base &b)
+  {
+    return b ^ a;
+  }
+
+  BLI_INT_OP(T) vec_base &operator^=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] ^= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator^=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] ^= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator~(const vec_base &a)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = ~a[i]);
+  }
+
+  /** Bit-shift operators. */
+
+  BLI_INT_OP(T) friend vec_base operator<<(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] << b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator<<(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] << b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator<<=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] <<= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator<<=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] <<= b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator>>(const vec_base &a, const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] >> b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator>>(const vec_base &a, T b)
+  {
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] >> b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator>>=(T b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] >>= b);
+  }
+
+  BLI_INT_OP(T) vec_base &operator>>=(const vec_base &b)
+  {
+    BLI_VEC_OP_IMPL_SELF(i, (*this)[i] >>= b[i]);
+  }
+
+  /** Modulo operators. */
+
+  BLI_INT_OP(T) friend vec_base operator%(const vec_base &a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] % b[i]);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator%(const vec_base &a, T b)
+  {
+    BLI_assert(b != 0);
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a[i] % b);
+  }
+
+  BLI_INT_OP(T) friend vec_base operator%(T a, const vec_base &b)
+  {
+    BLI_assert(!math::is_any_zero(b));
+    BLI_VEC_OP_IMPL(ret, i, ret[i] = a % b[i]);
+  }
+
+#undef BLI_INT_OP
+#undef BLI_VEC_OP_IMPL
+#undef BLI_VEC_OP_IMPL_SELF
+
+  /** Compare. */
+
+  friend bool operator==(const vec_base &a, const vec_base &b)
+  {
+    for (int i = 0; i < Size; i++) {
+      if (a[i] != b[i]) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  friend bool operator!=(const vec_base &a, const vec_base &b)
+  {
+    return !(a == b);
+  }
+
+  /** Misc. */
+
+  uint64_t hash() const
+  {
+    return math::vector_hash(*this);
+  }
+
+  friend std::ostream &operator<<(std::ostream &stream, const vec_base &v)
+  {
+    stream << "(";
+    for (int i = 0; i < Size; i++) {
+      stream << v[i];
+      if (i != Size - 1) {
+        stream << ", ";
+      }
+    }
+    stream << ")";
+    return stream;
+  }
+};
+
+using int2 = vec_base<int32_t, 2>;
+using int3 = vec_base<int32_t, 3>;
+using int4 = vec_base<int32_t, 4>;
+
+using uint2 = vec_base<uint32_t, 2>;
+using uint3 = vec_base<uint32_t, 3>;
+using uint4 = vec_base<uint32_t, 4>;
+
+using float2 = vec_base<float, 2>;
+using float3 = vec_base<float, 3>;
+using float4 = vec_base<float, 4>;
+
+using double2 = vec_base<double, 2>;
+using double3 = vec_base<double, 3>;
+using double4 = vec_base<double, 4>;
+
+}  // namespace blender