Add Math to Core.

.gitignore

@@ -6,4 +6,8 @@ packages
 
 .idea/
 .cache/
-cmake-build-debug-visual-studio/
+cmake-build-debug-visual-studio/
+
+# macOS AppleDouble metadata sidecar files (created on non-HFS volumes)
+._*
+.DS_Store

CMakeLists.txt

@@ -35,12 +35,34 @@ target_compile_definitions(core-options INTERFACE
     $<$<PLATFORM_ID:Darwin>:PLATFORM_MACOS=1>
 )
 target_compile_options(core-options INTERFACE
-    $<$<OR:$<CXX_COMPILER_ID:Clang>,$<CXX_COMPILER_ID:AppleClang>>: -Werror -Wall -Wno-c++2b-extensions -Wno-enum-constexpr-conversion -Wno-c++11-narrowing -Wno-deprecated-declarations -Wno-invalid-offsetof>
+    $<$<OR:$<CXX_COMPILER_ID:Clang>,$<CXX_COMPILER_ID:AppleClang>>: -Werror -Wall -Wno-c++2b-extensions -Wno-c++11-narrowing -Wno-deprecated-declarations -Wno-invalid-offsetof -Wno-missing-braces>
     $<$<CXX_COMPILER_ID:GNU>: -Werror -Wall -Wextra -std=c++2b -Wno-invalid-offsetof -Wno-missing-field-initializers>
-    $<$<CXX_COMPILER_ID:MSVC>: -WX -W4 -Zc:preprocessor>
+    $<$<CXX_COMPILER_ID:MSVC>: -WX -W4 -Zc:preprocessor -wd4201>
 )
 target_include_directories(core-options INTERFACE ${CMAKE_CURRENT_SOURCE_DIR}/)
 
+# SIMD arch gates — compile-time selection per target architecture.
+# ARM64 (Apple Silicon, Linux/Windows ARM): NEON, always available on the ISA.
+# x86_64 (Windows/Linux): AVX, Sandy Bridge (2011+) required. Anything beyond AVX
+# (AVX2, AVX-512) is not guaranteed and stays out of scope.
+#
+# `CORE_SIMD_FORCE_SCALAR` overrides arch detection for parity testing — the
+# arch flags are not emitted when it's on, so every math op falls through to its
+# scalar branch.
+option(CORE_SIMD_FORCE_SCALAR "Force scalar SIMD fallback for parity testing." OFF)
+if(CORE_SIMD_FORCE_SCALAR)
+    target_compile_definitions(core-options INTERFACE SIMD_FORCE_SCALAR=1)
+elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "^(arm64|aarch64)$")
+    target_compile_definitions(core-options INTERFACE SIMD_NEON=1)
+elseif(CMAKE_SYSTEM_PROCESSOR MATCHES "^(x86_64|AMD64|x64)$")
+    target_compile_definitions(core-options INTERFACE SIMD_AVX=1)
+    if(MSVC)
+        target_compile_options(core-options INTERFACE /arch:AVX)
+    else()
+        target_compile_options(core-options INTERFACE -mavx)
+    endif()
+endif()
+
 add_subdirectory(core)
 add_subdirectory(test)
 

README.md

@@ -23,17 +23,20 @@
 
 | Module | Description |
 |---|---|
-| `core/memory/` | Allocator interface, heap, arena, pool, and temp allocators |
+| `core/defines.h` | Primitive aliases (`I8`..`I64`, `U8`..`U64`, `F32`, `F64`) and macro utilities |
+| `core/memory/` | Allocator interface, heap, arena, pool, and temp allocators (with alignment) |
 | `core/containers/array.h` | Dynamic array (`Array<T>`) |
 | `core/containers/stack_array.h` | Fixed-capacity stack array (`Stack_Array<T, N>`) |
 | `core/containers/span.h` | Non-owning view (`Span<T>`) |
 | `core/containers/string.h` | Heap-allocated string (`String`) |
 | `core/containers/hash_table.h` | Open-addressing hash table (`Hash_Table<K, V>`) |
 | `core/containers/hash_set.h` | Hash set (`Hash_Set<K>`) |
 | `core/containers/string_interner.h` | String deduplication (`String_Interner`) |
-| `core/formatter.h` | Type-safe string formatting (`format()`) |
+| `core/math/` | Vectors, matrices, quaternion, scalar helpers, random — NEON / AVX / scalar |
+| `core/formatter.h` | Type-safe string formatting (`format()`) — math types format natively |
 | `core/print.h` / `core/log.h` | Colored output and log levels |
 | `core/defer.h` | Scope-exit macro (`DEFER`) |
+| `core/tester.h` | Minimal unit-test framework (`TESTER_TEST`, `TESTER_CHECK`) |
 | `core/validate.h` | Runtime assertions with source location |
 | `core/result.h` | Error-returning pattern (`Error`, `Result<T>`) |
 | `core/hash.h` | FNV-32 and type-generic `hash()` |
@@ -50,22 +53,25 @@
 
 ```cpp
 #include <core/containers/array.h>
+#include <core/math/f32x3.h>
+#include <core/math/f32x4x4.h>
 #include <core/defer.h>
 #include <core/log.h>
 
 struct Vertex
 {
-    float x, y, z;
-    float nx, ny, nz;
+    F32x3 position;
+    F32x3 normal;
 };
 
 auto vertices = array_init<Vertex>();
 DEFER(array_deinit(vertices));
 
-array_push(vertices, Vertex{1.0f, 2.0f, 3.0f, 0.0f, 0.0f, 1.0f});
-array_push(vertices, Vertex{4.0f, 5.0f, 6.0f, 0.0f, 1.0f, 0.0f});
+array_push(vertices, Vertex{F32x3{1.0f, 2.0f, 3.0f}, F32X3_UP});
+array_push(vertices, Vertex{F32x3{4.0f, 5.0f, 6.0f}, F32X3_FORWARD});
 
-log_info("loaded {} vertices", vertices.count);
+F32x4x4 view = f32x4x4_look_at(F32x3{0, 0, 5}, F32X3_ZERO, F32X3_UP);
+log_info("loaded {} vertices, view matrix:\n{}", vertices.count, view);
 ```
 
 ---

core/CMakeLists.txt

@@ -21,6 +21,32 @@ set(HEADER_FILES
     containers/stack_array.h
     containers/string_interner.h
     containers/string.h
+    math/f32.h
+    math/f64.h
+    math/i32.h
+    math/i64.h
+    math/u32.h
+    math/u64.h
+    math/f32x2.h
+    math/f32x3.h
+    math/f32x4.h
+    math/f64x2.h
+    math/f64x3.h
+    math/f64x4.h
+    math/i32x2.h
+    math/i32x3.h
+    math/i32x4.h
+    math/u32x2.h
+    math/u32x3.h
+    math/u32x4.h
+    math/f32x2x2.h
+    math/f32x3x3.h
+    math/f32x4x4.h
+    math/f64x2x2.h
+    math/f64x3x3.h
+    math/f64x4x4.h
+    math/quaternion.h
+    math/random.h
     memory/memory.h
     memory/heap_allocator.h
     memory/arena_allocator.h

core/base64.cpp

@@ -3,25 +3,25 @@
 inline static constexpr const char *BASE64_CHARACTERS = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
 
 String
-base64_encode(const u8 *data, u64 size, memory::Allocator *allocator)
+base64_encode(const U8 *data, U64 size, memory::Allocator *allocator)
 {
 	String out = string_init(allocator);
 
-	for (u64 i = 0; i < size; i += 3)
+	for (U64 i = 0; i < size; i += 3)
 	{
-		i32 value = (data[i] << 16) + (data[i + 1] << 8) + (data[i + 2]);
+		I32 value = (data[i] << 16) + (data[i + 1] << 8) + (data[i + 2]);
 
-		for (u64 j = 0; j < 4; ++j)
+		for (U64 j = 0; j < 4; ++j)
 		{
-			i32 x = (value >> ((3 - j) * 6)) & 0x3F;
+			I32 x = (value >> ((3 - j) * 6)) & 0x3F;
 			string_append(out, BASE64_CHARACTERS[x]);
 		}
 	}
 
-	i32 padding = size % 3;
+	I32 padding = size % 3;
 	if (padding > 0)
 	{
-		for (i32 i = 0; i < (3 - padding); ++i)
+		for (I32 i = 0; i < (3 - padding); ++i)
 		{
 			out[out.count - i - 1] = '=';
 		}
@@ -33,8 +33,8 @@ base64_encode(const u8 *data, u64 size, memory::Allocator *allocator)
 String
 base64_decode(const String &data, memory::Allocator *allocator)
 {
-	constexpr auto index = [](const String &data, char c) -> u8 {
-		for (u8 i = 0; i < data.count; ++i)
+	constexpr auto index = [](const String &data, char c) -> U8 {
+		for (U8 i = 0; i < data.count; ++i)
 		{
 			if (data[i] == c)
 			{
@@ -47,26 +47,26 @@ base64_decode(const String &data, memory::Allocator *allocator)
 
 	String out = string_init(allocator);
 
-	for (u64 i = 0; i < data.count; i += 4)
+	for (U64 i = 0; i < data.count; i += 4)
 	{
-		i32 a = index(string_literal(BASE64_CHARACTERS), data[i + 0]);
-		i32 b = index(string_literal(BASE64_CHARACTERS), data[i + 1]);
-		i32 c = index(string_literal(BASE64_CHARACTERS), data[i + 2]);
-		i32 d = index(string_literal(BASE64_CHARACTERS), data[i + 3]);
+		I32 a = index(string_literal(BASE64_CHARACTERS), data[i + 0]);
+		I32 b = index(string_literal(BASE64_CHARACTERS), data[i + 1]);
+		I32 c = index(string_literal(BASE64_CHARACTERS), data[i + 2]);
+		I32 d = index(string_literal(BASE64_CHARACTERS), data[i + 3]);
 
-		u32 value = (a << 18) |
+		U32 value = (a << 18) |
 					(b << 12) |
 					(c <<  6) |
 					(d);
 
-		for (u64 j = 0; j < 3; ++j)
+		for (U64 j = 0; j < 3; ++j)
 		{
 			char byte = (value >> ((2 - j) * 8)) & 0xFF;
 			string_append(out, byte);
 		}
 	}
 
-	u64 padding = 0;
+	U64 padding = 0;
 	for (char c : data)
 	{
 		if (c == '=')
@@ -75,7 +75,7 @@ base64_decode(const String &data, memory::Allocator *allocator)
 		}
 	}
 
-	for (u64 i = 0; i < padding; ++i)
+	for (U64 i = 0; i < padding; ++i)
 	{
 		string_remove_last(out);
 	}

core/base64.h

@@ -7,29 +7,29 @@
 
 /*
 	TODO:
-	- [ ] Should decode return a String or an Array<u8>?
+	- [ ] Should decode return a String or an Array<U8>?
 	- [ ] Should use Result<T>?
 */
 
 CORE_API String
-base64_encode(const u8 *data, u64 size, memory::Allocator *allocator = memory::heap_allocator());
+base64_encode(const U8 *data, U64 size, memory::Allocator *allocator = memory::heap_allocator());
 
 inline static String
 base64_encode(const Block &data, memory::Allocator *allocator = memory::heap_allocator())
 {
-	return base64_encode((const u8 *)data.data, data.size, allocator);
+	return base64_encode((const U8 *)data.data, data.size, allocator);
 }
 
 inline static String
-base64_encode(const Array<u8> &data, memory::Allocator *allocator = memory::heap_allocator())
+base64_encode(const Array<U8> &data, memory::Allocator *allocator = memory::heap_allocator())
 {
 	return base64_encode(data.data, data.count, allocator);
 }
 
 inline static String
 base64_encode(const String &data, memory::Allocator *allocator = memory::heap_allocator())
 {
-	return base64_encode((const u8 *)data.data, data.count, allocator);
+	return base64_encode((const U8 *)data.data, data.count, allocator);
 }
 
 inline static String