向量游戏数学处理器技术解析

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"VECTOR GAME MATH PROCESSORS" 是一本由 James Leiterman 撰写的书籍，由 Wordware Publishing, Inc. 出版。这本书主要探讨了向量游戏数学处理器在计算机科学，尤其是游戏编程中的应用。书中包含了对向量处理、计算机游戏编程、超级计算机编程、计算机科学与数学的交叉领域以及算法的详细讨论。书号为 ISBN 1-55622-921-6，并有相关的参考文献和索引。正文: 向量游戏数学处理器（Vector Game Math Processors）是计算机科学中一个专门用于提高游戏性能的技术，特别是在处理大量数学计算时。这些处理器通过使用向量运算，能够同时处理多个数据元素，显著提升了图形渲染、物理模拟和其他计算密集型任务的效率。向量处理是计算机科学中的一个关键概念，它允许处理器同时处理多个数据项，如浮点数或整数。这种并行处理能力在游戏开发中尤其重要，因为游戏通常需要实时计算复杂的图形和物理效果。例如，向量处理器可以一次计算一组顶点的位置、速度和加速度，极大地加快了图形渲染的速度。在游戏编程中，向量数学处理器的运用使得开发者能够创建更为真实、动态的游戏环境。例如，通过向量运算，可以快速计算出角色的运动轨迹、碰撞检测和光照效果，从而提供更流畅的游戏体验。此外，这些处理器在处理高级物理引擎，如流体动力学和刚体动力学时，也发挥了关键作用。超级计算机编程的引入则进一步强调了向量处理器在高性能计算中的价值。游戏行业的许多技术，如实时全局光照、高分辨率纹理和大规模多玩家在线环境，都受益于这种处理能力的提升。超级计算机的编程方法可以被借鉴，优化游戏中的并行处理，使得即使是家用游戏机也能实现接近专业级的计算效果。计算机科学与数学的交叉部分在本书中也是一个重要的讨论点。数学在游戏开发中扮演着基础性角色，如线性代数、几何和概率统计。向量数学处理器利用了这些数学原理，将抽象的数学模型转化为实际的计算操作。算法是实现高效计算的关键，特别是在游戏开发中。书中的内容可能涵盖了各种优化算法，如快速傅里叶变换（FFT）用于音频处理，以及各种空间细分和搜索算法，如kd-trees和Octrees，以加速图形渲染和碰撞检测。《Vector Game Math Processors》这本书为读者提供了深入理解向量处理器在游戏开发中应用的宝贵资源。它不仅讲解了基本理论，还可能包括实践案例和编程技巧，帮助读者掌握如何利用向量处理技术提升游戏的性能和质量。无论是初学者还是经验丰富的开发者，都能从中获得有价值的洞见。

And most of all, I would like to thank my wife for not balking too

much when I bought that new laptop, G4 Macintosh, top-of-the-line

video card, and other computer peripherals. Although I should note that

every time she discovered a new piece of equipment, her rhetorical

question was, “That is the last one, right?”

I finally wish to thank Jim Hill from Wordware Publishing, Inc. for

seeing the niche that this book would fill, Wes Beckwith for not asking

the question I frequently hear from my children, “Is it done yet? Is it

done yet?”, and Paula Price for making sure those checks arrived just in

time when I needed them.

So get up from the floor or chair in the bookstore in which you are

currently reading this book, as you know you will need this book for

work. Besides, I filled it with so much stuff you might as well stop

copying it into that little notebook, grab a second copy for use at home,

walk over to that check stand, and buy them both. Tell your friends how

great the book is so they will buy a copy, too! Insist to your employer

that the technical book library needs a few copies as well. This book is

an instruction manual and a math source library, all rolled into one.

My eight children and outnumbered domestic engineering wife

will be thankful that we will be able to afford school clothes as well as

Christmas presents this year! Unlike the title of that old movie’s impli-

cation that kids are Cheaper by the Dozen, they are not! They eat us out

of house and home!

Keep an eye out for any other book by me because since this one is

finished, my focus has been on their completion.

For any updates or code supplements to any of my books, check my

web site: http://www.leiterman.com/books.html.

Send any questions or comments to books@leiterman.com.

My brother Ranger Robert Leiterman is the writer of mystery-related

nature books that cover diverse topics as natural resources, as well as

his Bigfoot mystery series. Buy his books too, especially if you are a

game designer and interested in crypto zoology or natural resources. If

it was not for him sending me his books to help proofread, I probably

would not have started writing my own books (so blame him!).

Preface xv

Chapter 1

Introduction

Vector math processors have, up until recently, been in the domain of

the supercomputer, such as the Cray computers. Computers that have

recently joined this realm are the Apple Velocity Engine (AltiVec)

coprocessor of the PowerPC G4 in Macintosh and UNIX computers, as

well as IBM’s Power PC-based Gekko used in the GameCube and Digi

tal Signal Processing Systems (DSP). MIPS processors, such as the

Toshiba TX-79, and the Emotion Engine (EE) and Vector Units (VUs)

used in the Sony PlayStation 2 are also in this group. The X86 proces-

sors, such as Intel’s Pentium III used in the Xbox, and all other X86s

including the Pentium IV and AMD’s 3DNow! extension instructions

used in PCs are other recent additions. Both fixed-point as well as float-

ing-point math is being used by the computer, video gaming, and

embedded worlds in vector-based operations.

3D graphic rendering hardware has been going through major

increases in the numbers of polygons that can be handled by using

geometry engines as part of their rendering hardware to accelerate the

speed of mathematical calculations. There is also the recent introduc

tion of the programmable vertex and pixel shaders built into newer

video cards that use this same vector functionality. These work well for

rendering polygons with textures, depth ordering z-buffers or w-buff

ers, and translucency-controlled alpha channels with lighting, perspec

tive correction, etc. at relatively high rates of speed. The problem is that

the burden of all the other 3D processing, culling, transformations, rota

tions, etc. are put on the computer’s central processing unit (CPU),

which is needed for artificial intelligence (AI), terrain following, land

scape management, property management, sound, etc. Well, you get the

idea. For those of you looking for work, keep in mind that this new tech

nology has created a surplus of processor power that is being filled with

the new high-growth occupation of AI and physics programmers.

Recent microprocessor architectures have been updated to include

vector math functionality, but the processor was limited to small

sequences of a vector math calculation; such implementations include

Multimedia Extensions (MMX), AMD’s 3DNow! Professional, or the

Gekko chip, where only half vectors are dealt with at any one time.

These advances, however, have been a boon for engineers on a budget

as their vector-based math used in scientific applications can run faster

on these newer computers when properly coded due to their vector math

ability. The “catch” here is that vector processors have special memory

requirements and must use math libraries designed to use that special

vector functionality of the processor, not that of the slower standard

floating-point unit (FPU), which is still present on the chip. Third-party

libraries tend to be biased toward a favorite processor or are just written

with generic code and thus will not run efficiently on some processors

and/or take advantage of some instruction-based shortcuts.

A full vector processor can be given sequences and arrays of calcu

lations to perform. They typically have their own instruction set

devoted to the movement of mathematical values to and from memory,

as well as the arithmetic instructions to perform the needed transforma-

tions on those values. This allows them to be assigned a mathematical

task and thus free the computer system’s processor(s) to handle the

other running tasks of the application.

The cost of a personal supercomputer was out of range for most

consumers until the end of 2000 with the release of the PlayStation 2

console (PS2) by Sony. Rumor has it that if you interconnect multiple

PS2 consoles as a cluster, you will have a poor man’s supercomputer. In

fact, Sony announced that they would be planning to manufacture the

“GSCube,” a product based upon interconnecting 16 emotion engines

and graphic synthesizers.

Actually, if you think about it, it is a pretty cool idea. A low-budget

version would mean that each console on a rack boots their cluster

CD/DVD with their TCP/IP network connection and optional hard disk,

and their network link becomes a cheap mathematical number-

crunching supercomputer cluster slave.

The vector processor is the next logical step for the micro-

computer used in the home and office, so in this book, we will discuss

the instruction sets that they have as well as how to use them. This book

is targeted at programmers who are less likely to have access to the

expensive supercomputers, but instead have access to licensed console

development boxes, console Linux Dev Kits, cheap unauthorized (and

possibly illegal) hacker setups, or the new inexpensive embedded DSP

vector coprocessors coming out in the market as you read this.

2 Chapter 1: Introduction

I cannot come out and blab what I know about a proprietary proces

sor used in a particular console as much as I would like to. Although it

would definitely increase the sales of this book, it could possibly mess

up my developer license. I do discuss some tidbits here and there, utiliz

ing the public domain GNU C Compiler (GCC) and related access to

inline assembly. Certain console manufacturers are afraid of hackers

developing for their systems and have closed public informational

sources, except for some product overviews. But you are in luck! Some

engineers love to promote their achievements. For example, technical

details related to Sony’s PS2 processing power and overview were

made public at a 1999 Institute of Electrical and Electronics Engineers

(IEEE) International Solid-State Circuits Conference by Sony and

Toshiba engineers (TP 15.1 and 2) with slides. In 2001, Sony released to

the general public their Japanese Linux Development Kit; the LDK will

be released in 2002 for some other countries, of which the EE and VU

will be especially useful to you potential PS2 developers. Manuals are

listed in the references section at the back of this book.

In addition, game developers often release debug code in their

games containing development references, typically due to the haste of

last-minute changes prior to shipping. I also lurk on hacker web sites

and monitor any hacking breakthrough that may come about. All that

information is in a public domain and thus can be selectively discussed

in this forum. You will find some references and Internet links at the

back of this book.

I have pushed the information written in this book (pretty close) to

the edge of that line etched in the sand by those manufacturers. What

this book does is pool processor informational resources together from

publicly available information, especially when related to consoles.

Hint: AltiVec and 3DNow! are two of the publicly documented

instruction sets that have similarities to other unpublished processors.

One thing to keep in mind is that some of the processor manufacturers

typically have published technical information for processors that have

behaviors and instruction sets similar to those that are proprietary. One

of these is Motorola with their AltiVec Velocity Engine, which makes

its information freely available. This is a superset of almost all function

ality of current consumer-based vector processors.

This is not an AltiVec programming manual, but understanding that

particular processor and noting the differences between the other public

processors with their vector functionality embedded in their

Chapter 1: Introduction 3

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