math backend setup

setup libraries for different simd isa's
add float4 functions for c sse2 and avx2 (placeholder file for neon to be implemented on mac)

Engine/source/math/impl/float4_c.cpp

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+#include "math/public/float4_dispatch.h"
+#include "math/mConstants.h"
+#include <math.h>
+
+namespace math_backend::float4::dispatch
+{
+   void install_scalar()
+   {
+      gFloat4.add = [](const float* a, const float* b, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] + b[i];
+      };
+
+      gFloat4.sub = [](const float* a, const float* b, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] - b[i];
+      };
+
+      gFloat4.mul = [](const float* a, const float* b, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] * b[i];
+      };
+
+      gFloat4.mul_scalar = [](const float* a, float s, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] * s;
+      };
+
+      gFloat4.div = [](const float* a, const float* b, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] / b[i];
+      };
+
+      gFloat4.div_scalar = [](const float* a, float s, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = a[i] / s;
+      };
+
+      gFloat4.dot = [](const float* a, const float* b) {
+         float sum = 0.f;
+         for (int i = 0; i < 4; i++) sum += a[i] * b[i];
+         return sum;
+      };
+
+      gFloat4.length = [](const float* a) {
+         float sum = 0.f;
+         for (int i = 0; i < 4; i++) sum += a[i] * a[i];
+         return sqrtf(sum);
+      };
+
+      gFloat4.lengthSquared = [](const float* a) {
+         float sum = 0.f;
+         for (int i = 0; i < 4; i++) sum += a[i] * a[i];
+         return (sum);
+      };
+
+      gFloat4.normalize = [](float* a) {
+         float len = gFloat4.length(a);
+         if (len > POINT_EPSILON) for (int i = 0; i < 4; i++) a[i] /= len;
+      };
+
+      gFloat4.lerp = [](const float* from, const float* to, float f, float* r) {
+         for (int i = 0; i < 4; i++) r[i] = from[i] + (to[i] - from[i]) * f;
+      };
+   }
+}

Engine/source/math/impl/float4_impl.inl

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+#pragma once
+#include <cmath>   // for sqrtf, etc.
+
+namespace math_backend::float4
+{
+
+   //----------------------------------------------------------
+   // Add two float4 vectors: r = a + b
+   inline void float4_add_impl(const float* a, const float* b, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vb = v_load(b);
+      f32x4 vr = v_add(va, vb);
+      v_store(r, vr);
+   }
+
+   // Subtract: r = a - b
+   inline void float4_sub_impl(const float* a, const float* b, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vb = v_load(b);
+      f32x4 vr = v_sub(va, vb);
+      v_store(r, vr);
+   }
+
+   // Multiply element-wise: r = a * b
+   inline void float4_mul_impl(const float* a, const float* b, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vb = v_load(b);
+      f32x4 vr = v_mul(va, vb);
+      v_store(r, vr);
+   }
+
+   // Multiply by scalar: r = a * s
+   inline void float4_mul_scalar_impl(const float* a, float s, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vs = v_set1(s);
+      f32x4 vr = v_mul(va, vs);
+      v_store(r, vr);
+   }
+
+   // Divide element-wise: r = a / b
+   inline void float4_div_impl(const float* a, const float* b, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vb = v_load(b);
+      f32x4 vr = _mm_div_ps(va, vb);
+      v_store(r, vr);
+   }
+
+   // Divide by scalar: r = a / s
+   inline void float4_div_scalar_impl(const float* a, float s, float* r)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vs = v_set1(s);
+      f32x4 vr = v_div(va, vs);
+      v_store(r, vr);
+   }
+
+   // Dot product: returns scalar
+   inline float float4_dot_impl(const float* a, const float* b)
+   {
+      f32x4 va = v_load(a);
+      f32x4 vb = v_load(b);
+      f32x4 vmul = v_mul(va, vb);
+      return v_hadd4(vmul);
+   }
+
+   // Length squared
+   inline float float4_length_squared_impl(const float* a)
+   {
+      return float4_dot_impl(a, a);
+   }
+
+   // Length
+   inline float float4_length_impl(const float* a)
+   {
+      return std::sqrt(float4_length_squared_impl(a));
+   }
+
+   // Normalize in-place
+   inline void float4_normalize_impl(float* a)
+   {
+      float len = float4_length_impl(a);
+      if (len > 1e-6f) // safe threshold
+      {
+         float4_mul_scalar_impl(a, 1.0f / len, a);
+      }
+   }
+
+   // Normalize with magnitude: r = normalize(a) * r
+   inline void float4_normalize_mag_impl(float* a, float r)
+   {
+      float len = float4_length_impl(a);
+      if (len > 1e-6f)
+      {
+         float4_mul_scalar_impl(a, r / len, a);
+      }
+   }
+
+   // Linear interpolation: r = from + (to - from) * f
+   inline void float4_lerp_impl(const float* from, const float* to, float f, float* r)
+   {
+      f32x4 vfrom = v_load(from);
+      f32x4 vto = v_load(to);
+      f32x4 vf = v_set1(f);
+      f32x4 vr = v_add(vfrom, v_mul(vf, v_sub(vto, vfrom)));
+      v_store(r, vr);
+   }
+
+} // namespace math_backend::float4