BLI: Implement templated math functions for basic types

This is meant to complement the `blender::math` functions recently
added by D13791. It's sometimes desired to template an operation to work
on vector types, but also basic types like `float` and `int`. This patch
adds that ability with a new `BLI_math_base.hh` header. Particularly
useful examples are `midpoint` and `interpolate`, but I'm sure others
will be added in the future.

Implementing the functions separately, rather than as `if constexpr`
branches in the existing header is meant to be more scalable, for
the possibility of even more math types in the future.

5 files changed, 175 insertions, 15 deletions

diff --git a/source/blender/blenlib/BLI_math_base.hh b/source/blender/blenlib/BLI_math_base.hh
new file mode 100644
index 00000000000..9684867afd3
--- /dev/null
+++ b/source/blender/blenlib/BLI_math_base.hh
@@ -0,0 +1,113 @@
+/* SPDX-License-Identifier: GPL-2.0-or-later
+ * Copyright 2022 Blender Foundation. */
+
+#pragma once
+
+/** \file
+ * \ingroup bli
+ */
+
+#include <algorithm>
+#include <cmath>
+#include <type_traits>
+
+#include "BLI_math_base_safe.h"
+#include "BLI_math_vector.h"
+#include "BLI_utildefines.h"
+
+#ifdef WITH_GMP
+#  include "BLI_math_mpq.hh"
+#endif
+
+namespace blender::math {
+
+#ifdef WITH_GMP
+#  define BLI_ENABLE_IF_FLT(T) \
+    BLI_ENABLE_IF((std::is_floating_point_v<T> || std::is_same_v<T, mpq_class>))
+#else
+#  define BLI_ENABLE_IF_FLT(T) BLI_ENABLE_IF((std::is_floating_point_v<T>))
+#endif
+
+#define BLI_ENABLE_IF_INT(T) BLI_ENABLE_IF((std::is_integral_v<T>))
+
+template<typename T> inline bool is_zero(const T &a)
+{
+  return a == T(0);
+}
+
+template<typename T> inline bool is_any_zero(const T &a)
+{
+  return is_zero(a);
+}
+
+template<typename T> inline T abs(const T &a)
+{
+  return std::abs(a);
+}
+
+template<typename T> inline T min(const T &a, const T &b)
+{
+  return std::min(a, b);
+}
+
+template<typename T> inline T max(const T &a, const T &b)
+{
+  return std::max(a, b);
+}
+
+template<typename T> inline T clamp(const T &a, const T &min, const T &max)
+{
+  return std::clamp(a, min, max);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T mod(const T &a, const T &b)
+{
+  return std::fmod(a, b);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T safe_mod(const T &a, const T &b)
+{
+  return (b != 0) ? std::fmod(a, b) : 0;
+}
+
+template<typename T> inline void min_max(const T &vector, T &min_vec, T &max_vec)
+{
+  min_vec = min(vector, min_vec);
+  max_vec = max(vector, max_vec);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T safe_divide(const T &a, const T &b)
+{
+  return (b != 0) ? a / b : T(0.0f);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T floor(const T &a)
+{
+  return std::floor(a);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T ceil(const T &a)
+{
+  return std::ceil(a);
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T fract(const T &a)
+{
+  return a - std::floor(a);
+}
+
+template<typename T, typename FactorT, BLI_ENABLE_IF_FLT(T), BLI_ENABLE_IF_FLT(FactorT)>
+inline T interpolate(const T &a, const T &b, const FactorT &t)
+{
+  return a * (1 - t) + b * t;
+}
+
+template<typename T, BLI_ENABLE_IF_FLT(T)> inline T midpoint(const T &a, const T &b)
+{
+  return (a + b) * 0.5;
+}
+
+#undef BLI_ENABLE_IF_FLT
+#undef BLI_ENABLE_IF_INT
+
+}  // namespace blender::math
diff --git a/source/blender/blenlib/BLI_math_vec_types.hh b/source/blender/blenlib/BLI_math_vec_types.hh
index 140367b6241..81e59b157ee 100644
--- a/source/blender/blenlib/BLI_math_vec_types.hh
+++ b/source/blender/blenlib/BLI_math_vec_types.hh
@@ -579,4 +579,15 @@ using double2 = vec_base<double, 2>;
 using double3 = vec_base<double, 3>;
 using double4 = vec_base<double, 4>;
 
+template<typename T> constexpr bool is_math_vec_type = false;
+template<typename BaseType, int Size>
+constexpr bool is_math_vec_type<vec_base<BaseType, Size>> = true;
+
+static_assert(is_math_vec_type<int2>);
+static_assert(is_math_vec_type<uint4>);
+static_assert(is_math_vec_type<float2>);
+static_assert(is_math_vec_type<vec_base<float, 20>>);
+static_assert(!is_math_vec_type<int>);
+static_assert(!is_math_vec_type<float>);
+
 }  // namespace blender
diff --git a/source/blender/blenlib/BLI_math_vector.hh b/source/blender/blenlib/BLI_math_vector.hh
index 302ab39a0b9..7c39565cedc 100644
--- a/source/blender/blenlib/BLI_math_vector.hh
+++ b/source/blender/blenlib/BLI_math_vector.hh
@@ -35,17 +35,25 @@ namespace blender::math {
 
 #define bT typename T::base_type
 
+template<typename T>
+inline constexpr bool is_float_vector = (std::is_floating_point_v<typename T::base_type>
 #ifdef WITH_GMP
-#  define BLI_ENABLE_IF_FLT_VEC(T) \
-    BLI_ENABLE_IF((std::is_floating_point_v<typename T::base_type> || \
-                   std::is_same_v<typename T::base_type, mpq_class>))
-#else
-#  define BLI_ENABLE_IF_FLT_VEC(T) BLI_ENABLE_IF((std::is_floating_point_v<typename T::base_type>))
+                                         || std::is_same_v<typename T::base_type, mpq_class>
 #endif
+);
+
+template<typename T>
+inline constexpr bool is_integral_vector = std::is_integral_v<typename T::base_type>;
+
+/* In this file, only implement math functions for the vector types. This allows other
+ * files to use overloading to implement the same functions with different types. */
+#define BLI_ENABLE_IF_VEC(T) BLI_ENABLE_IF((is_math_vec_type<T>))
+
+#define BLI_ENABLE_IF_FLT_VEC(T) BLI_ENABLE_IF_VEC(T), BLI_ENABLE_IF((is_float_vector<T>))
 
-#define BLI_ENABLE_IF_INT_VEC(T) BLI_ENABLE_IF((std::is_integral_v<typename T::base_type>))
+#define BLI_ENABLE_IF_INT_VEC(T) BLI_ENABLE_IF_VEC(T), BLI_ENABLE_IF((is_integral_vector<T>))
 
-template<typename T> inline bool is_zero(const T &a)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline bool is_zero(const T &a)
 {
   for (int i = 0; i < T::type_length; i++) {
     if (a[i] != bT(0)) {
@@ -55,7 +63,7 @@ template<typename T> inline bool is_zero(const T &a)
   return true;
 }
 
-template<typename T> inline bool is_any_zero(const T &a)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline bool is_any_zero(const T &a)
 {
   for (int i = 0; i < T::type_length; i++) {
     if (a[i] == bT(0)) {
@@ -65,7 +73,7 @@ template<typename T> inline bool is_any_zero(const T &a)
   return false;
 }
 
-template<typename T> inline T abs(const T &a)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline T abs(const T &a)
 {
   T result;
   for (int i = 0; i < T::type_length; i++) {
@@ -74,7 +82,7 @@ template<typename T> inline T abs(const T &a)
   return result;
 }
 
-template<typename T> inline T min(const T &a, const T &b)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline T min(const T &a, const T &b)
 {
   T result;
   for (int i = 0; i < T::type_length; i++) {
@@ -83,7 +91,7 @@ template<typename T> inline T min(const T &a, const T &b)
   return result;
 }
 
-template<typename T> inline T max(const T &a, const T &b)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline T max(const T &a, const T &b)
 {
   T result;
   for (int i = 0; i < T::type_length; i++) {
@@ -92,7 +100,8 @@ template<typename T> inline T max(const T &a, const T &b)
   return result;
 }
 
-template<typename T> inline T clamp(const T &a, const T &min_v, const T &max_v)
+template<typename T, BLI_ENABLE_IF_VEC(T)>
+inline T clamp(const T &a, const T &min_v, const T &max_v)
 {
   T result = a;
   for (int i = 0; i < T::type_length; i++) {
@@ -101,7 +110,8 @@ template<typename T> inline T clamp(const T &a, const T &min_v, const T &max_v)
   return result;
 }
 
-template<typename T> inline T clamp(const T &a, const bT &min_v, const bT &max_v)
+template<typename T, BLI_ENABLE_IF_VEC(T)>
+inline T clamp(const T &a, const bT &min_v, const bT &max_v)
 {
   T result = a;
   for (int i = 0; i < T::type_length; i++) {
@@ -151,7 +161,8 @@ template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline T safe_mod(const T &a, bT
   return result;
 }
 
-template<typename T> inline void min_max(const T &vector, T &min_vec, T &max_vec)
+template<typename T, BLI_ENABLE_IF_VEC(T)>
+inline void min_max(const T &vector, T &min_vec, T &max_vec)
 {
   min_vec = min(vector, min_vec);
   max_vec = max(vector, max_vec);
@@ -207,7 +218,7 @@ template<typename T, BLI_ENABLE_IF_FLT_VEC(T)> inline bT dot(const T &a, const T
   return result;
 }
 
-template<typename T> inline bT length_manhattan(const T &a)
+template<typename T, BLI_ENABLE_IF_VEC(T)> inline bT length_manhattan(const T &a)
 {
   bT result = std::abs(a[0]);
   for (int i = 1; i < T::type_length; i++) {
@@ -364,6 +375,7 @@ template<typename T> struct isect_result {
 template<typename T, BLI_ENABLE_IF_FLT_VEC(T)>
 isect_result<T> isect_seg_seg(const T &v1, const T &v2, const T &v3, const T &v4);
 
+#undef BLI_ENABLE_IF_VEC
 #undef BLI_ENABLE_IF_FLT_VEC
 #undef BLI_ENABLE_IF_INT_VEC
 #undef bT
diff --git a/source/blender/blenlib/CMakeLists.txt b/source/blender/blenlib/CMakeLists.txt
index 29015084679..e67d673eb73 100644
--- a/source/blender/blenlib/CMakeLists.txt
+++ b/source/blender/blenlib/CMakeLists.txt
@@ -220,6 +220,7 @@ set(SRC
   BLI_map.hh
   BLI_map_slots.hh
   BLI_math.h
+  BLI_math_base.hh
   BLI_math_base.h
   BLI_math_base_safe.h
   BLI_math_bits.h
diff --git a/source/blender/blenlib/tests/BLI_math_base_test.cc b/source/blender/blenlib/tests/BLI_math_base_test.cc
index 33acefeeac2..34da00cb4bf 100644
--- a/source/blender/blenlib/tests/BLI_math_base_test.cc
+++ b/source/blender/blenlib/tests/BLI_math_base_test.cc
@@ -4,6 +4,12 @@
 
 #include "BLI_math.h"
 
+#include "BLI_math_vector.hh"
+
+#include "BLI_math_base.hh"
+
+namespace blender::tests {
+
 /* In tests below, when we are using -1.0f as max_diff value, we actually turn the function into a
  * pure-ULP one. */
 
@@ -131,3 +137,20 @@ TEST(math_base, FloorPowerOf10)
   EXPECT_NEAR(floor_power_of_10(100.1f), 100.0f, 1e-4f);
   EXPECT_NEAR(floor_power_of_10(99.9f), 10.0f, 1e-4f);
 }
+
+TEST(math_base, MinVectorAndFloat)
+{
+  EXPECT_EQ(math::min(1.0f, 2.0f), 1.0f);
+}
+
+TEST(math_base, ClampInt)
+{
+  EXPECT_EQ(math::clamp(111, -50, 101), 101);
+}
+
+TEST(math_base, Midpoint)
+{
+  EXPECT_NEAR(math::midpoint(100.0f, 200.0f), 150.0f, 1e-4f);
+}
+
+}  // namespace blender::tests