XFixedPoint — Fixed-Point Math & Physics Simulation Library

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Introduction

XFixedPoint is a production-grade fixed-point math and physics simulation library targeting [.NET Standard 2.1]. It aims to deliver:

• Determinism
• High Performance
• Feature Completeness
• Ease of Use

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Features

• Core type XFixed — 64.32 fixed-point representation with + − × ÷, comparison, conversion
• Math functions XFixedMath — Newton Sqrt, CORDIC Sin/Cos/Tan/Atan2, Exp/Log, Lerp/Clamp/Min/Max
• Vectors & Matrices — FixedVector2/3/4, FixedQuaternion, FixedMatrix4x4 for transforms & interpolation
• Physics Simulation — FixedRigidbody integration + AABB/Sphere/OBB SAT collision + elastic impulse response
• Networking — Snapshot, InputBuffer, RollbackSystem for deterministic roll-back and input replay
• Utilities — LCG fixed-point RNG, FixedTime manager, FixedDebugger error statistics
• Full Test Coverage — all modules verified with xUnit

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Project Structure

XFixedPoint/                         ← project root
│
├─ Core/                              ← core fixed-point types & algorithms
│   ├─ XFixedConstants.cs             ← SHIFT, ONE, EPS constants
│   ├─ XFixed.cs                      ← `XFixed` struct & conversions
│   ├─ XFixedArithmetic.cs            ← + − × ÷ implementations
│   ├─ XFixedComparison.cs            ← comparison operators & interfaces
│   └─ XFixedMath.cs                  ← Sqrt, Sin/Cos (CORDIC), Exp/Log, helpers
│
├─ Vectors/                           ← fixed-point vector types
│   ├─ XFixedVector2.cs
│   ├─ XFixedVector3.cs
│   └─ XFixedVector4.cs
│
├─ Quaternions/                       ← fixed-point quaternion
│   ├─ XFixedQuaternion.cs
│   └─ XFixedQuaternionOps.cs
│
├─ Matrices/                          ← 4×4 fixed-point matrix
│   └─ XFixedMatrix4x4.cs
│
├─ Physics/                           ← physics simulation
│   ├─ FixedRigidbody.cs
│   ├─ FixedCollider.cs
│   ├─ Collision/
│   │   ├─ AABBCollider.cs
│   │   ├─ SphereCollider.cs
│   │   └─ OBBCollider.cs
│   └─ PhysicsSystem.cs
│
├─ Networking/                        ← snapshot & rollback systems
│   ├─ Snapshot.cs
│   ├─ InputBuffer.cs
│   └─ RollbackSystem.cs
│
├─ Utilities/                         ← helper utilities
│   ├─ XFixedRandom.cs
│   ├─ XFixedTime.cs
│   └─ XFixedDebugger.cs
│
└─ Tests/                             ← xUnit unit tests
    ├─ CoreTests/
    ├─ VectorTests/
    ├─ QuaternionTests/
    ├─ MatrixTests/
    ├─ PhysicsTests/
    ├─ NetworkingTests/
    └─ UtilitiesTests/

Modules Overview

• Core: XFixed + XFixedArithmetic + XFixedComparison + XFixedConstants + XFixedMath
• Vectors: 2D/3D/4D vector operations
• Quaternions: quaternion rotation, SLERP, Euler ↔ Quat, matrix conversion
• Matrices: 4×4 matrix multiplication & point/vector transform
• Physics: rigid-body integration, AABB/Sphere/OBB SAT collision, impulse response
• Networking: deterministic Snapshot, InputBuffer, RollbackSystem
• Utilities: LCG RNG, fixed-point timekeeping, debugging helpers

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Quick Start

using XFixedPoint.Core;
using XFixedPoint.Vectors;
using XFixedPoint.Quaternions;
using XFixedPoint.Physics;

// Core arithmetic
var a = XFixed.FromDouble(1.25);
var b = XFixed.FromDouble(2.5);
var c = a * b;                     // 3.125
Console.WriteLine(c);

// Vector rotation
var v = new XFixedVector3(a, XFixed.Zero, XFixed.One);
var axis = new XFixedVector3(XFixed.Zero, XFixed.Zero, XFixed.One);
var q = XFixedQuaternion.FromAxisAngle(axis, XFixed.FromDouble(Math.PI/2));
var rotated = q.Rotate(v);

// Physics simulation
var physics = new PhysicsSystem { Gravity = FixedVector3.FromFloat(0, -9.81f, 0) };
var body    = new FixedRigidbody { Mass = XFixed.FromDouble(1.0) };
var sphere  = new XFixedPoint.Physics.Collision.SphereCollider(XFixed.FromDouble(0.5));
physics.AddBody(body, sphere);
physics.Step(XFixed.FromDouble(1.0/60.0));

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Sample Projects

See the Samples/ folder (planned) for Unity and console examples.

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We welcome performance improvements, pure-fixed implementations, new collision shapes, documentation enhancements, and more!