Numerics Module

Vectors, matrices, quaternions, BigInteger, and color types.

Overview

The System::Numerics namespace provides hardware-agnostic math types used by game engines and 3D graphics. All types are header-only value types.

Status: Done for all vector/matrix types.

Vector Types

Type	Header	Components	Key Operations
`Vector2`	`System/Numerics/Vector2.hpp`	X, Y (float)	+, -, *, /, Dot, Normalize, Lerp, Clamp, Distance, Length, Zero, One, UnitX, UnitY
`Vector3`	`System/Numerics/Vector3.hpp`	X, Y, Z (float)	+, -, *, /, Dot, Cross, Normalize, Lerp, Zero, One, UnitX, UnitY, UnitZ, Forward, Up
`Vector4`	`System/Numerics/Vector4.hpp`	X, Y, Z, W (float)	+, -, *, /, Dot, Normalize, Lerp, Zero, One

using namespace System::Numerics;

Vector2 a(1.0f, 0.0f);
Vector2 b(0.0f, 1.0f);
float dot = Vector2::Dot(a, b);     // 0.0
Vector2 lerp = Vector2::Lerp(a, b, 0.5f);  // (0.5, 0.5)
float len = a.Length();              // 1.0

Matrix Types

Type	Header	Description
`Matrix3x2`	`System/Numerics/Matrix3x2.hpp`	2D transform matrix (3x2 floats)
`Matrix4x4`	`System/Numerics/Matrix4x4.hpp`	4x4 transform matrix; full transforms, Invert, Identity, CreateTranslation, CreateRotation, CreateScale, CreatePerspective, CreateLookAt

using namespace System::Numerics;

Matrix4x4 translate = Matrix4x4::CreateTranslation(1.0f, 2.0f, 3.0f);
Matrix4x4 rotate = Matrix4x4::CreateRotationY(3.14159f / 4.0f);
Matrix4x4 combined = translate * rotate;

Matrix4x4 inv;
bool ok = Matrix4x4::Invert(combined, inv);

Rotation

Type	Header	Key Operations
`Quaternion`	`System/Numerics/Quaternion.hpp`	Slerp, CreateFromAxisAngle, CreateFromYawPitchRoll, CreateFromRotationMatrix, Conjugate, Inverse, Normalize, Dot, Identity
`Plane`	`System/Numerics/Plane.hpp`	CreateFromVertices, Dot, DotCoordinate, DotNormal, Normalize, Transform

BigInteger

include/System/Numerics/BigInteger.hpp | src/System/Numerics/BigInteger.cpp

Status: Done

Arbitrary-precision integer arithmetic:

+, -, *, /, % operators
TryParse(string, BigInteger&)
ToString()
Comparison operators
Uses Knuth Algorithm D for division

Other Numeric Types

Type	Header	Description
`Complex`	`System/Numerics/Complex.hpp`	Complex number (real, imaginary)
`BFloat16`	`System/Numerics/BFloat16.hpp`	Brain floating-point 16-bit
`BitOperations`	`System/Numerics/BitOperations.hpp`	PopCount, LeadingZeroCount, TrailingZeroCount, Log2, etc.
`DivisionRounding`	`System/Numerics/DivisionRounding.hpp`	Integer division rounding modes

Colors (System::Numerics::Colors)

Type	Header	Description
`Argb`	`System/Numerics/Colors/Argb.hpp`	ARGB 32-bit color
`Rgba`	`System/Numerics/Colors/Rgba.hpp`	RGBA 32-bit color
`Colors`	`System/Numerics/Colors/Colors.hpp`	Named color constants

Math Utilities

Type	Header	Description
`System::Math`	`System/Math.hpp`	Abs, Sin, Cos, Sqrt, Pow, Floor, Ceiling, Round, Max, Min, PI, E, etc.
`System::MathF`	`System/MathF.hpp`	Same as Math but for float