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deterministic_float

Cross-platform deterministic float point, fast soft float point.
Fast soft float point for deterministic computing, That you can make deterministic plugin by use GFloat to replace float-point. like：
- Physics Engine (Bullet、PhysX)
- AI Path Finding (Recast Navigation)
- AI Engine
Compare the overall performance of hard float IEEE-754 and GFloat numbers, They differ by no more than 500%, Refer to the multiply-add instructions for measuring the computing power of the graphics card. compare multiply and add function:
跨平台的确定性浮点数，高性能的软件浮点数
你可以使用GFloat替代各种中间件的浮点数，从而实现带确定性的计算，实现帧同步游戏逻辑，也可以实现加密货币计算逻辑，例如：
- 物理引擎（Bullet、PhysX）
- AI 寻路（Recast Navigation）
- AI 引擎
整体上GFloat与IEEE754的硬件浮点数float，性能差距在500%以内。参考显卡衡量计算能力的乘加指令，主要比较乘法和加法函数的性能：

IEEE-754 float
<table > <tr> <th align="center" >sign</th> <th align="center" colspan = "5" width="400">exponents（8 bits）</th> <th align="center" colspan = "5" width="400">fractions（23 bits）</th> </tr> <tr> <td >31</td> <td >30</td><td>29</td><td>...</td><td>24</td><td>23</td> <td >22</td><td>21</td><td>...</td><td>1</td><td>0</td> </tr> </table>
- $\mathbf{X}_{IEEE754} = (-1)^\mathbf{sign} \times (1.\mathbf{fraction}) \times 2 ^{\mathbf{exponent} - 127}$
GFloat
<table > <tr> <th align="center" >sign</th> <th align="center" colspan = "5" width="400">fractions（23 bits）</th> <th align="center" colspan = "5" width="400">exponents（8 bits）</th> </tr> <tr> <td >31</td> <td >30</td><td>29</td><td>...</td><td>9</td><td>8</td> <td >7</td><td>6</td><td>...</td><td>1</td><td>0</td> </tr> </table>
- $\mathbf{X}_{GFloat} = (-1)^\mathbf{sign} \times (\mathbf{fraction}) \times 2 ^{\mathbf{exponent} - 127}$

Several important functions compare, for more information to view TestAndBenchMark
Call every function 1000000 Times, get the float vs GFloat time

Platform	Win64	Win64	iOS	OSX	Android
CPU	Ryzen-5950X	i9-12900H	Apple A15	Apple M1Pro	HiSilicon-KIRIN-990
	float vs GFloat	float vs GFloat	float vs GFloat	float vs GFloat	float vs GFloat
Add	0.63 vs 2.63 ms	0.44 vs 1.48ms	0.43 vs 1.85 ms	0.34 vs 2.24 ms	0.89 vs 8.76 ms
Mul	0.70 vs 1.14 ms	0.52 vs 0.79 ms	0.42 vs 0.78 ms	0.34 vs 0.93 ms	0.62 vs 2.10 ms
Sin	10.20 vs 8.39 ms	8.6 vs 3.15 ms	3.6 vs 4.9 ms	2.29 vs 5.28 ms	11.58 vs 15.75 ms
Sqrt	1.08 vs 9.29 ms	0.7 vs 6.2 ms	0.83 vs 5.64 ms	0.64 vs 6.06 ms	0.65 vs 15.77 ms
Exp	2.06 vs 10.83ms	2.15 vs 24.52ms	5.52 vs 7.03 ms	5.75 vs 6.52 ms	6.06 vs 20.90 ms

Target Platform	Compiler	Project
Win	Visual Studio 2022	deterministic/deterministic_float.sln
MacOS	XCode 13.4	deterministic/deterministic_float.xcodeproj
iOS	XCode 13.4	deterministic/deterministic_float_ios.xcodeproj
Android	Android studio 4.0	deterministic/deterministic_float_android

Operation System	Win64	MacOS	iOS	Android
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