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, 31 insertions, 44 deletions

diff --git a/source/blender/nodes/NOD_math_functions.hh b/source/blender/nodes/NOD_math_functions.hh
index a0a2e6f81f8..6ea89beee2e 100644
--- a/source/blender/nodes/NOD_math_functions.hh
+++ b/source/blender/nodes/NOD_math_functions.hh
@@ -18,9 +18,9 @@
 
 #include "DNA_node_types.h"
 
-#include "BLI_float3.hh"
 #include "BLI_math_base_safe.h"
 #include "BLI_math_rotation.h"
+#include "BLI_math_vec_types.hh"
 #include "BLI_string_ref.hh"
 
 namespace blender::nodes {
@@ -240,6 +240,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                    Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -259,40 +261,21 @@ inline bool try_dispatch_float_math_fl3_fl3_to_fl3(const NodeVectorMathOperation
     case NODE_VECTOR_MATH_MULTIPLY:
       return dispatch([](float3 a, float3 b) { return a * b; });
     case NODE_VECTOR_MATH_DIVIDE:
-      return dispatch([](float3 a, float3 b) {
-        return float3(safe_divide(a.x, b.x), safe_divide(a.y, b.y), safe_divide(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return safe_divide(a, b); });
     case NODE_VECTOR_MATH_CROSS_PRODUCT:
-      return dispatch([](float3 a, float3 b) { return float3::cross_high_precision(a, b); });
+      return dispatch([](float3 a, float3 b) { return cross_high_precision(a, b); });
     case NODE_VECTOR_MATH_PROJECT:
-      return dispatch([](float3 a, float3 b) {
-        float length_squared = b.length_squared();
-        return (length_squared != 0.0) ? (float3::dot(a, b) / length_squared) * b : float3(0.0f);
-      });
+      return dispatch([](float3 a, float3 b) { return project(a, b); });
     case NODE_VECTOR_MATH_REFLECT:
-      return dispatch([](float3 a, float3 b) {
-        b.normalize();
-        return a.reflected(b);
-      });
+      return dispatch([](float3 a, float3 b) { return reflect(a, normalize(b)); });
     case NODE_VECTOR_MATH_SNAP:
-      return dispatch([](float3 a, float3 b) {
-        return float3(floor(safe_divide(a.x, b.x)),
-                      floor(safe_divide(a.y, b.y)),
-                      floor(safe_divide(a.z, b.z))) *
-               b;
-      });
+      return dispatch([](float3 a, float3 b) { return floor(safe_divide(a, b)) * b; });
     case NODE_VECTOR_MATH_MODULO:
-      return dispatch([](float3 a, float3 b) {
-        return float3(safe_modf(a.x, b.x), safe_modf(a.y, b.y), safe_modf(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return mod(a, b); });
     case NODE_VECTOR_MATH_MINIMUM:
-      return dispatch([](float3 a, float3 b) {
-        return float3(min_ff(a.x, b.x), min_ff(a.y, b.y), min_ff(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return min(a, b); });
     case NODE_VECTOR_MATH_MAXIMUM:
-      return dispatch([](float3 a, float3 b) {
-        return float3(max_ff(a.x, b.x), max_ff(a.y, b.y), max_ff(a.z, b.z));
-      });
+      return dispatch([](float3 a, float3 b) { return max(a, b); });
     default:
       return false;
   }
@@ -306,6 +289,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_to_fl(const NodeVectorMathOperation operation,
                                                   Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -319,9 +304,9 @@ inline bool try_dispatch_float_math_fl3_fl3_to_fl(const NodeVectorMathOperation
 
   switch (operation) {
     case NODE_VECTOR_MATH_DOT_PRODUCT:
-      return dispatch([](float3 a, float3 b) { return float3::dot(a, b); });
+      return dispatch([](float3 a, float3 b) { return dot(a, b); });
     case NODE_VECTOR_MATH_DISTANCE:
-      return dispatch([](float3 a, float3 b) { return float3::distance(a, b); });
+      return dispatch([](float3 a, float3 b) { return distance(a, b); });
     default:
       return false;
   }
@@ -335,6 +320,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                        Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -354,7 +341,7 @@ inline bool try_dispatch_float_math_fl3_fl3_fl3_to_fl3(const NodeVectorMathOpera
         return float3(wrapf(a.x, b.x, c.x), wrapf(a.y, b.y, c.y), wrapf(a.z, b.z, c.z));
       });
     case NODE_VECTOR_MATH_FACEFORWARD:
-      return dispatch([](float3 a, float3 b, float3 c) { return float3::faceforward(a, b, c); });
+      return dispatch([](float3 a, float3 b, float3 c) { return faceforward(a, b, c); });
     default:
       return false;
   }
@@ -368,6 +355,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_fl3_fl_to_fl3(const NodeVectorMathOperation operation,
                                                       Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -381,8 +370,7 @@ inline bool try_dispatch_float_math_fl3_fl3_fl_to_fl3(const NodeVectorMathOperat
 
   switch (operation) {
     case NODE_VECTOR_MATH_REFRACT:
-      return dispatch(
-          [](float3 a, float3 b, float c) { return float3::refract(a, b.normalized(), c); });
+      return dispatch([](float3 a, float3 b, float c) { return refract(a, normalize(b), c); });
     default:
       return false;
   }
@@ -396,6 +384,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_to_fl(const NodeVectorMathOperation operation,
                                               Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -409,7 +399,7 @@ inline bool try_dispatch_float_math_fl3_to_fl(const NodeVectorMathOperation oper
 
   switch (operation) {
     case NODE_VECTOR_MATH_LENGTH:
-      return dispatch([](float3 in) { return in.length(); });
+      return dispatch([](float3 in) { return length(in); });
     default:
       return false;
   }
@@ -450,6 +440,8 @@ template<typename Callback>
 inline bool try_dispatch_float_math_fl3_to_fl3(const NodeVectorMathOperation operation,
                                                Callback &&callback)
 {
+  using namespace blender::math;
+
   const FloatMathOperationInfo *info = get_float3_math_operation_info(operation);
   if (info == nullptr) {
     return false;
@@ -463,20 +455,15 @@ inline bool try_dispatch_float_math_fl3_to_fl3(const NodeVectorMathOperation ope
 
   switch (operation) {
     case NODE_VECTOR_MATH_NORMALIZE:
-      return dispatch([](float3 in) {
-        float3 out = in;
-        out.normalize();
-        return out;
-      }); /* Should be safe. */
+      return dispatch([](float3 in) { return normalize(in); }); /* Should be safe. */
     case NODE_VECTOR_MATH_FLOOR:
-      return dispatch([](float3 in) { return float3(floor(in.x), floor(in.y), floor(in.z)); });
+      return dispatch([](float3 in) { return floor(in); });
     case NODE_VECTOR_MATH_CEIL:
-      return dispatch([](float3 in) { return float3(ceil(in.x), ceil(in.y), ceil(in.z)); });
+      return dispatch([](float3 in) { return ceil(in); });
     case NODE_VECTOR_MATH_FRACTION:
-      return dispatch(
-          [](float3 in) { return in - float3(floor(in.x), floor(in.y), floor(in.z)); });
+      return dispatch([](float3 in) { return fract(in); });
     case NODE_VECTOR_MATH_ABSOLUTE:
-      return dispatch([](float3 in) { return float3::abs(in); });
+      return dispatch([](float3 in) { return abs(in); });
     case NODE_VECTOR_MATH_SINE:
       return dispatch([](float3 in) { return float3(sinf(in.x), sinf(in.y), sinf(in.z)); });
     case NODE_VECTOR_MATH_COSINE: