├── .gitignore ├── LICENSE ├── README.md ├── img └── CSAPP-IEEE-754.png ├── 决策与判断.md ├── 历史的教训.md ├── 李光耀观天下.md ├── 深入理解计算机系统.md ├── 深度工作.md ├── 禅与摩托车维修艺术.md ├── 简单的艺术.md ├── 链接 装载与库.md ├── 非暴力沟通.md └── 高效程序员的45个习惯.md /.gitignore: -------------------------------------------------------------------------------- 1 | plan.md -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. 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Of course, the commands you use may 322 | be called something other than `show w' and `show c'; they could even be 323 | mouse-clicks or menu items--whatever suits your program. 324 | 325 | You should also get your employer (if you work as a programmer) or your 326 | school, if any, to sign a "copyright disclaimer" for the program, if 327 | necessary. Here is a sample; alter the names: 328 | 329 | Yoyodyne, Inc., hereby disclaims all copyright interest in the program 330 | `Gnomovision' (which makes passes at compilers) written by James Hacker. 331 | 332 | {signature of Ty Coon}, 1 April 1989 333 | Ty Coon, President of Vice 334 | 335 | This General Public License does not permit incorporating your program into 336 | proprietary programs. If your program is a subroutine library, you may 337 | consider it more useful to permit linking proprietary applications with the 338 | library. If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Tim的读书笔记 2 | 我是一名游戏程序员，有一个技术博客：[Tim's Blog](http://wuzhiwei.net)。 3 | 4 | 这是我的读书笔记集群，笔记将全部用markdown编写。 5 | 6 | 读书笔记将显著的分为两类：技术和非技术。 7 | 8 | 技术类一般不包括编程语言学习书籍。 9 | 10 | 非技术类不涉及小说类。 11 | 12 | 我的豆瓣读书主页为：[http://book.douban.com/people/timcs/](http://book.douban.com/people/timcs/)。 13 | 14 | ## 目录 15 | * [简单的艺术](https://github.com/iWoz/ReadingNotes/blob/master/%E7%AE%80%E5%8D%95%E7%9A%84%E8%89%BA%E6%9C%AF.md) 16 | * [高效程序员的45个习惯](https://github.com/iWoz/ReadingNotes/blob/master/%E9%AB%98%E6%95%88%E7%A8%8B%E5%BA%8F%E5%91%98%E7%9A%8445%E4%B8%AA%E4%B9%A0%E6%83%AF.md) 17 | * [禅与摩托车维修艺术](https://github.com/iWoz/ReadingNotes/blob/master/%E7%A6%85%E4%B8%8E%E6%91%A9%E6%89%98%E8%BD%A6%E7%BB%B4%E4%BF%AE%E8%89%BA%E6%9C%AF.md) 18 | * [深入理解计算机系统](https://github.com/iWoz/ReadingNotes/blob/master/%E6%B7%B1%E5%85%A5%E7%90%86%E8%A7%A3%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F.md) 19 | * [决策与判断](https://github.com/iWoz/ReadingNotes/blob/master/%E5%86%B3%E7%AD%96%E4%B8%8E%E5%88%A4%E6%96%AD.md) 20 | * [链接 装载与库](https://github.com/iWoz/ReadingNotes/blob/master/%E9%93%BE%E6%8E%A5%20%E8%A3%85%E8%BD%BD%E4%B8%8E%E5%BA%93.md) 21 | * [非暴力沟通](https://github.com/iWoz/ReadingNotes/blob/master/%E9%9D%9E%E6%9A%B4%E5%8A%9B%E6%B2%9F%E9%80%9A.md) 22 | * [深度工作](https://github.com/iWoz/ReadingNotes/blob/master/%E6%B7%B1%E5%BA%A6%E5%B7%A5%E4%BD%9C.md) 23 | * [历史的教训](https://github.com/iWoz/ReadingNotes/blob/master/历史的教训.md) 24 | 25 | 欢迎关注公众号： 26 | ![image](https://user-images.githubusercontent.com/1621110/215088294-fc24b001-23d3-40e4-be2e-1f50a0d6d936.png) 27 | -------------------------------------------------------------------------------- /img/CSAPP-IEEE-754.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/iWoz/ReadingNotes/7d20da3b5ece14c109bd215c2a50bd2ef8c86141/img/CSAPP-IEEE-754.png -------------------------------------------------------------------------------- /决策与判断.md: -------------------------------------------------------------------------------- 1 | #《决策与判断》读书笔记 2 | 3 | ##Chapter 1 - 选择性知觉 4 | * 知觉具有选择性，即容易受自己的**预期**影响 5 | * 知觉也会受到做出的承诺的影响，人们的知觉倾向于与自己的承诺保持一致 6 | * 由于知觉易受影响，所以在做重大决策前，问自己几个关键的问题： 7 | * 我看待事物的方式是否受到某种动机的驱使？ 8 | * 我看待和处理问题是是否夹杂了自身的预期？ 9 | * 我是否与那些与我有不同预期的人交换过意见？ 10 | 11 | ##Chapter 2 - 认知不协调 12 | * 人们往往想要减少或者避免心理上的不一致，不一致会引起不协调，而可能会感到不满或不爽 13 | * 人们会尽一切可能减少认知不协调感，为了降低这种不协调感，人们可能会通过撒谎等方式 14 | * 当人们为一件事情付出越多，他们就认为这件事越有价值，而且越有压力为这件事情持续付出 15 | * 当下注之后，人们会更加相信自己的选择，即使概率是一样的，这就是为了降低决策后的认知不协调感 16 | * 如果你希望一个人形成对某个事物的积极态度，就引导他，使他致力得到这个事物 17 | * 如果你希望一个人对某种错误行为的态度更加温和，则引导他做出这种错误行为；相反，则引导他不去做出这种错误行为 18 | 19 | ##Chapter 3 - 记忆和事后聪明式偏差 20 | * 记忆不是过去存进记忆库的拷贝，而是在提取它的时候建立起来的，简而言之，记忆是根据碎片重建的 21 | * 记忆的重建高度取决于情境因素，所以约会时第一印象，周边环境，共同做的事情是否留下了愉快的心情都很重要 22 | 23 | ##Chapter 4 - 情境依赖性 24 | * 对比效应：在绝对条件下去了解一个人是不可能的，人的品质是对比出来的 25 | * 房地产经纪先带去看破房子或者贵的离谱的房子，然后再去看一般的房子就是利用了对比效应 26 | * 初始效应：第一印象很重要，人们往往会先入为主。当然，第二第三印象也很重要，它们都是初始印象 27 | * 近因效应：人们更加清楚的记得最后出现的信息而非最先出现的信息。这与初始效应产生了对抗 28 | * 在辩论中，如果对方会立即回击，且辩论结束后人们要过一会才会做出判断应该选择最先发言，这时初始效应最大，近因效应随着时间的流逝而威力减少 29 | * 但是如果各自的发言有一定的时间间隔，而且人们要在双方发言结束后立即做出判断，则应该最后发言，这时近因效应最大 30 | * 晕轮效应：好看的人会得到更高的评价，也更聪明，牛校的毕业生就一定都很牛逼，明星拍广告销量会变大等等 31 | * 晕轮效应容易使人们因为一两项的好而做出全部都好的错误判断 32 | 33 | ##Chapter 5 - 可塑性 34 | * 人们的答案会受到问题或者答案选项顺序的影响。如果两个问题都是关于同一主题的，则回答者为了保持一致，后一个答案通常会按照前一个答案的思路来组织 35 | * 答案选项越多，顺序效应则越强烈，往往最后一个选项被选择的频率最高 36 | * 当人们对一个问题知之甚少时，这种顺序效应则更加明显，人们可能会被问题的语境和顺序来诱导出一个答案 37 | * 这种答案往往是「虚假意见」，为了过滤这种「虚假意见」，在提问时，要先问是否听说过这个问题，否则就不要采纳其答案 38 | * 人们宣称的态度和行为相关性很小，永远不要轻信别人的承诺，而要看他的具体行动 39 | 40 | ##Chapter 6 - 问题的措辞和框架的影响 41 | * 在问题的答案中引入一个中间选项可能会鼓励人们选择中立，去除中间选项，常常能有效检测出人们的一般倾向 42 | * 另外，问题的度量单位会影响调查答案的大小，比如多长时间和多短时间，往往前者的回答的时间会更长；同理多高和多矮 43 | * 当面临获利时，人们往往倾向规避风险，「二鸟在林」不如「一鸟在手」；然而当面临损失时，人们往往喜欢赌一赌运气 44 | * 心理分账：人们会以不同的态度对等值的钱，并做出不同的决策行为。对工资的钱，我们往往会精打细算，然而对于彩票中奖的钱，就划分到另外一个账户里去了，可能会胡乱花费 45 | * 消费者对绝对值（优惠XX元）和相对值（打X.X折）优惠的体验存在较大差异，而且呈现这样一种规律：当购买额度较小时，消费者对相对值优惠更敏感，即在商家相同让利水平的情况下，相对值比绝对值能让消费者体验到更多的优惠。相反在购买额度较大时，消费者对绝对者优惠更敏感。 46 | 47 | ##Chapter 7 - 期望效用理论 48 | * 金钱的价值（效用）随着获取金额的增多而递减 -------------------------------------------------------------------------------- /历史的教训.md: -------------------------------------------------------------------------------- 1 | @(读书笔记) 2 | # 历史的教训 3 | 4 | * 历史的第一个教训就是要**学会谦逊**，人类历史只是宇宙的一瞬，一颗小行星的撞击就可能让人类全体灭绝。 5 | * 飞机的发展会让地理上的限制变小，制空权在新形势下要比制海权更为重要。 6 | * 弱肉强食，适者生存，生命即是竞争，竞争养分，粮食，阳光，土地和配偶，乃至上升到国与国的层次。**不平等是与生俱来的**，人人生而平等是指人权上的平等，但是出身，家境，智力，体格等等各方面人们都存在差异和不平等。 7 | * **平等和自由互相对立**，往往是弱者要求平等，而强者追求自由。 8 | * 生命需要繁衍，自然喜欢数量，量变产生质变。当一个族群的人口越来越多时，它在经济和政治上的权力也会随之增大。子宫战争，**出生率就像战争**一样，决定着族群的命运。 9 | * 历史大体是由少数求新的人（伟人）之前的冲突造成的，大多数人只为胜利者鼓掌，充当社会实验的人类原材料。 10 | * 保守派和激进派都互相有他们的价值，激进派可以拓展人类的边界，创造出新事物；而保守派则会对新事物进行反复研磨，以确保安全。两者对立共存，能确保人类的良性发展。对于生存来说，保守派可能更有价值，因为根须深厚比枝繁叶茂更加重要。 11 | * 道德规范会随着经济史的阶段而发生改变。譬如，在原始狩猎时代，人必须要残暴，贪婪才能确保自己能生存下来，好色才能确保自己的基因得以繁衍。这些品质到了农业时代和工业时代便成为了坏品质。随着信息化时代的到来，道德规范或许会进一步进行调整。 12 | * **宗教会死而不僵**，是人们的一种心灵寄托，也能帮助维护社会道德秩序。只要有贫穷和压迫，就会有宗教的市场。共产主义的国家基本都脱离了宗教，也许是因为人们把共产主义当做了自己的信仰吧。 13 | * 财富集中（两极分化）是一种不可避免的自然现象，通过暴力（战争，革命）或和平手段（改革）来进行再分配，从而得到**周期性**的缓解。 14 | * 这种周期性的过程往往是因为人性导致的，**人性不变，所以历史总是惊人的相似**。唯一真正的革命，是对心灵的启蒙和对能力的提升，只有这样，人类才能不断进步。只有**教育**，才能带来民主。 15 | * 社会主义和资本主义会彼此吸取对方的优点而逐渐产生融合，随着全球化时代的到来，意识形态上的隔阂将会被逐渐消除。 16 | * 战争和对立是常态，而和平是短暂的，**要居安思危**。没有永远的朋友，只有不变的利益，当人类面临外星生物的入侵时，全球或许才能统一起来一致对外。 17 | * 文明终究会面临死亡，人也会面临死亡。然而思想和文化遗产会一代一代的流传下去，生生不息。 18 | 19 | 于己，修身齐家治国安天下，先修身养性，传播先进正确的思想给其他人，力争握住历史浪潮，顺势而为！ -------------------------------------------------------------------------------- /李光耀观天下.md: -------------------------------------------------------------------------------- 1 | @(读书笔记) 2 | #「李光耀观天下」书评 3 | 4 | 我很欣赏务实主义者，或者说问题解决者，也许因为我自己就是一个比较注重务实和喜欢解决问题的人。李光耀显然就是这么一个人，李最欣赏的领导人邓小平也是这种人。 5 | 6 | 在本书中，李光耀散发出自信和理性的光芒，对世界政治和经济做了分析，读之感觉受益匪浅。 7 | 8 | ##领导者 9 | 10 | 改革开放四十年来，我国取得举世瞩目的进步，正在朝着世界第一强国迈进。这一切取决于邓小平及那一代改革派领导人的决定。 11 | 12 | 邓之所以能将中国从文革泥潭中拉出来并成功推行改革开放，主要是因为： 13 | 1. 邓参加过红军，是老一辈革命家，在军队中享有威望。 14 | 2. 邓在75年主持政府工作时，积累了大量的信任，让大家看到了邓的能力。 15 | 3. 邓是一个实干主义者，不管白猫黑猫，只要抓到老鼠就是好猫。所以邓不怕扣上走资派的帽子。 16 | 17 | 李光耀在书中对邓大为赞扬，称之为「最伟大的领袖」，除了邓的能力和手腕外，还有邓的胸怀和自律。李在一次晚宴中向中国在东南亚输出革命表达不满，以为邓会大为光火，没想到邓主动接纳，海纳百川，有容乃大。邓喜欢抽烟，李已经戒烟，所以邓在和李会谈时一根烟未抽，显示出强大的自制力。 18 | 19 | 李在书中对习大大也是颇有好评，认为习心胸宽广，不摆架子又具有使命感。 20 | 21 | 李说到自己在近90岁时还能端坐，不需要轮椅和拐杖，主要是因为生活规律，戒烟，又保持运动习惯，归结为一点，即自律。 22 | 23 | 由此可见，成为一个卓越的领导者，需要具备以下几点素质： 24 | 1. 言必行，行必果，言行一致 25 | 2. 能力出色，可以令人信服 26 | 3. 心胸宽广，可以吸取不同意见 27 | 4. 自律 28 | 29 | ##中国崛起 30 | 31 | 中国需要一个强大的中央政府，即中央集权，才能兴旺发达，国泰民安。现如今中央更为强大，权力也更加集中，这也许对现在的中国是一件好事。 32 | 33 | 随着沿海城市的人口爆满，书中提到中国计划在中部建立6个城市群，以容纳近3亿的农村人口流入城市。 34 | 35 | 中国正处在一个高速发展期，已经对美国的霸主地位产生威胁，未来势必将取代美国成为世界第一强国。 36 | 37 | 与此同时，中国也面临着诸多问题： 38 | 1. 法制不够完善，更多的时候还是人治。 39 | 2. 对知识产权和专利保护较弱，缺乏创新土壤。 40 | 3. 国企效率低下。 41 | 4. 环境污染日益加剧。 42 | 5. 国人储蓄观念（穷怕了）很重，国内消费仍未完全打开。 43 | 44 | 我相信，随着全面深化改革的进一步推进，中国会朝着更好的方向发展。 45 | 46 | ##国际环境 47 | 48 | 美国由于其强大的经济实力和优秀的人才储备，未来仍将是世界强国。未来最重要的双边关系就是中美关系。然而随着中国的全面崛起，美国在亚洲的影响力将下降，在台湾问题上美国或许将不得不向中国妥协。随着中国的日益强大，中国统一是必然趋势。 49 | 50 | 日本由于其低生育率和排斥移民的风俗，导致其在未来将走向平庸。 51 | 52 | 朝韩或许很难统一，因为这并不符合中国的利益。 53 | 54 | 印度受限于种姓制导致其优秀基因流动受限，又因为没有一个全国统一的语言，使得很难让所有国民在思想上统一起来，而导致其发展受限。 55 | 56 | 李很推崇一门统一的，有优势的语言。譬如新加坡选择英语作为第一语言，使得其更能与世界接轨。 57 | 58 | 欧洲则是陷入各种危机，比如长时间的福利社会导致人们工作热情衰减，从而发展缓慢。欧洲若不能统一行动，则将实力大减。 59 | 60 | 中东则是李预言最先可能爆发核战的地方，伊朗一旦研制出核武器，势必会对中东乃至世界局势造成深远影响。 61 | 62 | 全球化早已到来，世界已经变成一个地球村。只有积极建设自己，准备充足，以开放的姿态面对世界，才有可能取得成功。 63 | 64 | ##最后 65 | 66 | 修身，齐家，治国，安天下。 67 | 68 | 多读书，多思考，多总结。 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | -------------------------------------------------------------------------------- /深入理解计算机系统.md: -------------------------------------------------------------------------------- 1 | #《深入理解计算机系统》 读书笔记 2 | 3 | ##Chapter 1 - 计算机系统漫游 4 | * 只由ASCII字符构成的文件成为*文本文件*，其他的所有文件成为*二进制文件* 5 | * 编译系统的四个阶段： 6 | * 预处理阶段 7 | * 编译阶段 8 | * 汇编阶段 9 | * 链接阶段 10 | * 系统的硬件组成 11 | * 总线 ：贯穿整个系统的电子管道，通常被设计为传送定长的字节块，也就是字（word）。字的字节数是一个基本的系统参数，称为字长。 12 | * I/O设备：负责系统和外界的联系通道。例如显示器，键鼠，磁盘等等。 13 | * 主存：有一组DRAM芯片组成，是一个临时存储设备，用于存放处理器所需的程序和数据。 14 | * 处理器：解释储存在主存中指令的引擎。处理器的核心为*程序计数器*（PC）的字长大小的寄存器。在任意时间点，PC都指向主存中的某条机器语言指令（地址）。 15 | * 高速缓存 16 | * 由于主存与处理器寄存器的读取速度差距过大，需要在主存和寄存器中间加入高速缓存，用于存放处理器在不久的将来可能会用到的信息。 17 | * 高速缓存可以使存储设备分层。速度越快的设备容量越小；而容量越大的设备速度则越慢。针对不同的需求进行满足，同时节约成本。 18 | * 操作系统 19 | * 操作系统是硬件和应用程序中间的一层软件 20 | * 可以防止硬件被失控的应用程序滥用 21 | * 和为应用程序提供使用复杂硬件的简单接口 22 | * **进程** 23 | * 进程是操作系统对应用程序的一种抽象。一个系统上可以同时运行多个进程，然而每个进程都好像独占地使用硬件。实际一个进程的指令和另一个进程的指令是交错执行的。操作系统实现这种交错执行的机制称为**上下文切换**（context switching）。 24 | * 上下文（context）为操作系统保持进程运行所需的所有状态信息。任何时刻，只有一个进程在运行，当操作系统决定从当前进程转移到某个新进程时，就会进行上下文切换。 25 | * 上下文切换的过程为：系统保存当前进程的上下文，恢复新进程的上下文，将控制权转移到新进程，新进程从它上次停止的地方开始。 26 | * 线程：一个进程由多个线程组成，每个线程都运行在进程的上下文中，并**共享相同代码和全局数据**。 27 | * 虚拟存储器：是一个抽象概念，为每个进程提供假象，好像每个进程都在独占的使用内存，每个进程看到的存储器都是一样的，称为**虚拟地址空间**。 28 | * 虚拟地址空间由大量定义的区组成，每个区都有专门的功能。 29 | * 代码和数据 30 | * 堆：运行时可以动态分配的地址空间 31 | * 共享库：动态链接 32 | * 栈：函数调用 33 | * 内核虚拟存储器：应用程序不可读写 34 | * 文件：字节序列。**每个I/O设备，包括键鼠，显示器，甚至网络都可以被视为文件**。文件使应用程序可以统一的看待各式的I/O设备，而无需了解I/O设备的不同技术。 35 | * 操作系统内核提供了三个基础的抽象概念： 36 | * 文件：I/O设备的抽象 37 | * 虚拟存储器：主存和磁盘的抽象 38 | * 进程：处理器，主存和I/O设备的抽象 39 | * 网络提供了计算机系统间的通信，网络实际可以视为一种I/O设备。 40 | 41 | ##Chapter 2 - 信息的表示和处理 42 | * 最重要的三个数字编码 43 | * 无符号（unsigned），表示大于或等于0的数字 44 | * 二进制补码（two's-complement），表示有符号（正负）整数 45 | * 浮点数（floating-point），表示实数的科学记数法 46 | * **值得注意的是，浮点数是不可结合的**，因为精度有限 47 | * 在Lua中，`print(3.14+1e+20-1e+20)`得`0`，而`print(3.14+(1e+20-1e+20))`得`3.14` 48 | * 字节（byte）：8位的块，是大多数计算机的最小可寻址存储器单位 49 | * 字长（word size）：指明整数和指针的标称大小。其决定了虚拟地址空间的最大大小。如32位字长，限制了虚拟地址空间大小为`2^32Byte = 4GB`。 50 | * 寻址：多字节对象被存储为连续的字节序列，对象的地址为字节序列的最小地址。 51 | * 字节顺序： 52 | * 如：`0x01234567`，存在0x100~0x103的字节顺序中，最高的字节为01，最低的字节为67 53 | * 小端法：最低的地址存最低的位 从0x100~0x103分别为 67 45 23 01 54 | * 大端法：最高的地址存最低的位 从0x100~0x103分别为 01 23 45 67 55 | * 使用ascii码在任何系统都将得到相同的结果，与字节顺序和字大小规则无关。因而，文本数据比二进制数据有更强的平台独立性。 56 | * 有关字符编码，可参考博文：[字符编码笔记：ASCII，Unicode和UTF-8](http://www.ruanyifeng.com/blog/2007/10/ascii_unicode_and_utf-8.html)。 57 | * 布尔代数的特性： 58 | * a | ~a = 1 59 | * a & ~a = 0 60 | * a ^ a = 0 61 | * a ^ ~a = 1 62 | * a ^ 0 = a 63 | * a ^ 1 = ~a 64 | * DeMorgan's law: 65 | * ~(a&b) = ~a | ~b 66 | * ~(a|b) = ~a & ~b 67 | * 利用亦或操作的特性构造的原地换位代码： 68 | ```C 69 | void inplace_swap(int *x, int *y) 70 | { 71 | *x = *x ^ *y; 72 | *y = *x ^ *y; 73 | *x = *x ^ *y; 74 | } 75 | ``` 76 | 77 | * 位向量的应用： 78 | * 有限集合，若位为1，则表示集合中包含了该位下标的值的数字；若位为0，则相反。 79 | 80 | 例如一个位向量为a=[01101001]表示集合A={0,3,5,6}；位向量b=[01010101]表示集合B={0,2,4,6}。则 a|b = A并B ; a&b = A交B，而~a = A的补集。 81 | 82 | * 掩码（masking）运算： 83 | 84 | 掩码0xFF = 000...00011111111 则x&0xFF = 由x最低有效字节组成的值，其他字节都被置为0。 85 | 86 | ~0将生成一个全1的掩码，不管机器的字长是多少，具有很强的移植性。 87 | 88 | C中逻辑运算和位运算是完全不同的。而且逻辑运算具有断路的特性：若对第一个参数求值能确定表达式的值，那么逻辑运算符将不会对第二个参数进行求值。 89 | 90 | * 移位运算： 91 | * 左移 <<：丢弃k个最高位，最低位补k个0 92 | * 逻辑右移 >>：丢弃k个最低位，最高位补k个0 93 | * **算术右移** >>：丢弃k个最低位，最高位**补k个最高位的拷贝** 94 | * 无符号数（unsigned）的右移必须是逻辑右移，补0 95 | * 有符号数的右移大多数使用算术右移，补最高位的拷贝 96 | 97 | * **二进制补码**（two's-complement）的表示：将字的最高有效位解释为负权。 98 | * 二进制补码的值可用如下公式求出：$B2T_{w}(\vec x) \equiv -x_{w-1}2^{w-1} + \sum_{i=0}^{w-2}x_{i}2^{i} $ 99 | 100 | * 最高有效位（$x_{w-1}$）被称为符号位（sign bit），设为1时，表示值为负数；设为0时，表示非负。 101 | * 二进制补码的范围是不对称的： 102 | * $ |TMin_{w} = TMax_{w} + 1| $ 即，**$TMin_{w}$没有与之对应的正数** 103 | * 最大的无符号值比最大的补码值的两倍大一：$UMax_{w} = 2TMax_{w} + 1$ 104 | * 补码中的-1与$UMax_{w}$是同样的位序列 105 | * 强制类型转换：没有改变参数的位表示，即位序列不变，但是改变了这些位的解释 106 | * **二进制补码与无符号数的映射关系**如下： 107 | $$T2U_{w}(x) = \begin{cases} 108 | x+2^{w},& x<0\\ 109 | x,& x\geq0 110 | \end{cases}$$ 111 | 可见-1在补码中被转换成了最大的无符号数 112 | * **无符号数与二进制补码的映射关系**如下： 113 | $$U2T_{w}(x) = \begin{cases} 114 | x,& x<2^{w-1}\\ 115 | x-2^{w},& x\geq2^{w-1} 116 | \end{cases}$$ 117 | * 一个方便记忆的记法是：对于$0 \leq x < 2^{w-1}$的值，二进制补码与无符号的表示是一样的，值都是x；对于之外的值只需加上或减去$2^{w-1}$即可 118 | * 在C语言中的`printf`函数中，%d表示有符号十进制，%u表示无符号十进制 119 | * 在C语言中，如果表达式两端分别为有符号和无符号，则会**隐含地将有符号强制转换为无符号然后进行运算**，这常常导致bug出现 120 | * 无符号整数扩展：在开头添加k个0，称之为零扩展 121 | * 二进制补码扩展：在开头添加k个最高有效位的值，被称为**符号扩展** 122 | * 由于有符号与无符号的强制转换经常导致困扰，因此建议**不使用无符号整数类型**。 123 | * 整数运算 124 | * 无符号加法：对于精度有限的无符号整数的加法，可能会产生溢出（丢弃最高位）。 125 | 对于$0\leq x,y \leq2^{w}-1$: 126 | $$x+y = \begin{cases} 127 | x+y,& x+y<2^{w}\\ 128 | x+y-2^{w}& 2^{w}\leq x+y<2^{w+1} 129 | \end{cases}$$ 130 | 判断溢出的一个方法是对于$s=x+y$，如果$s < x$或 $s < y$则表示溢出。 131 | * 二进制补码加法：先将加号两端二进制补码转为无符号，然后执行无符号加法，然后再转为二进制补码形式 132 | 对于$-2^{w-1}\leq x,y \leq2^{w}-1$: 133 | $$x+y = \begin{cases} 134 | x+y-2^{w},& 2^{w-1}\leq x+y & 正溢出（更小）\\ 135 | x+y,& -2^{w-1}\leq x+y<2^{w-1} & 正常\\ 136 | x+y+2^{w}& x+y<-2^{w+1} & 负溢出（更大） 137 | \end{cases}$$ 138 | * 二进制补码的负运算（非） 139 | 对于$-2^{w-1}\leq x < 2^{w-1}$: 140 | $$-x = \begin{cases} 141 | -2^{w-1},& x=-2^{w-1}\\ 142 | -x& x > -2^{w-1} 143 | \end{cases}$$ 144 | 一种有名的位运算技术：$-x = \tilde x + 1$ 145 | 即对x的每位取反然后再+1。 146 | * 整数乘法： 147 | 对于$-2^{w-1}\leq x,y \leq2^{w-1}-1$: 148 | $$x * y = (x * y)\ mod\ 2^{w} $$ 149 | * 整数除法 $x/y$ 150 | * 永远得到整数 151 | * 若得到小数，则： 152 | * **若x与y同号，说明得到正数，则对结果向下取整**，如$5/2 = \lfloor2.5\rfloor = 2$ 153 | * **若x与y不同号，说明得到负数，则对结果向上取整**，如$-5/2 = \lceil-2.5\rceil = -2$ 154 | * IEEE 754 **浮点数表示** 155 | * 浮点数的表示：$V = (-1)^{s} \times M \times 2^{E} $ 156 | * s表示sign，符号位，负数为1，正数为0 157 | * M表示有效位，为一个二进制小数 158 | * E表示2的幂 159 | * 域（二进制位序列）的划分： 160 | * 单独的符号位s 161 | * k位的指数域$e_{k-1}...e_{1}e_{0}$ 编码E 162 | * n位的小数域$f_{n-1}...f_{1}f_{0}$ 编码M 163 | * 其中指数域的有三种不同表达： 164 | * 规格化值：指数域不全是0，也不全是1 165 | $$E = e_{k-1}...e_{1}e_{0} - (2^{k-1} - 1)$$ 166 | $$M = 1 + \frac {f_{n-1}...f_{1}f_{0}} {2^n} $$ 167 | 168 | * 非规格化值：指数域全是0 169 | $$E = 1 - (2^{k-1} - 1)$$ 170 | $$M = \frac {f_{n-1}...f_{1}f_{0}} {2^n} $$ 171 | * 特殊数值：指数域全为1，若小数域全部为0，则表示无穷大；否则，表达NaN（Not a Number） 172 | ![Alt text](./img/CSAPP-IEEE-754.png) 173 | 174 | * 舍入：由于浮点数的表示精度有限，所以会需要进行舍入。 175 | * 最常用的舍入方式为偶数舍入，即先向最近的值进行舍入，如果为中间数值，则向偶数进行舍入。 176 | * 向偶数舍入可以避免统计偏差，即向上舍入或者向下舍入都容易使平均值的结果偏高或者偏低。 177 | * 浮点数运算：因为舍入会带来精度丢失，而且浮点数加法不具备结合性（即：只要运算符的位置不改变，则运算顺序的改变不会带来结果的影响），所以会有不一致的情况出现。 178 | * 如：`(3.14+1e10) - 1e10`因为舍入会得到0.0；而`3.14+(1e10-1e10)`则会得到3.14。**这是在日常编码中需要注意到的地方。** 179 | * **奇技淫巧** 180 | * 使用二进制补码，可以利用位运算求负`~x+1 = -x` 181 | * 可以利用移位运算轻松制造掩码。比如制造0xFF，可以用`(1<<8)-1`获得。更一般的，制造最低位为连续k个1时，可用`(1<